Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding...

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Puneet Dokania 1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug, 2018 Jointly with Arslan Chaudhry, Thalaiyasingam Ajanthan, Philip H. S. Torr

Transcript of Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding...

Page 1: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !1

Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence

(ECCV18)

Puneet K. Dokania(University of Oxford)

7th Aug, 2018

Jointly with

Arslan Chaudhry, Thalaiyasingam Ajanthan, Philip H. S. Torr

Page 2: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !2

Why Incremental Learning?

Page 3: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania

• Standard Learning (Classification): Givenlearn mapping

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min✓

Ex,y⇠DL(f✓(x),y)<latexit sha1_base64="+KRzUW1HFN/zif4jSakJhT2U3Bo=">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</latexit><latexit sha1_base64="+KRzUW1HFN/zif4jSakJhT2U3Bo=">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</latexit><latexit sha1_base64="+KRzUW1HFN/zif4jSakJhT2U3Bo=">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</latexit><latexit sha1_base64="+KRzUW1HFN/zif4jSakJhT2U3Bo=">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</latexit>

!2

Why Incremental Learning?

Page 4: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania

• Standard Learning (Classification): Givenlearn mapping

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!2

Why Incremental Learning?

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• Given new dataset (may contain samples for previous labels or new ones)

• Not scalable• Privacy• Redundancy

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Incremental Learning Training Objectives

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Puneet Dokania

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!3

Incremental Learning Training Objectives

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✓1

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!3

Incremental Learning Training Objectives

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• Define Knowledge • Input-Output Behaviour (knowledge distillation type) • Parameters

!3

Incremental Learning Training Objectives

(Previous knowledge)

min✓

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Page 11: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania

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• Define Knowledge • Input-Output Behaviour (knowledge distillation type) • Parameters

• Preserve Knowledge? Avoid Forgetting

!3

Incremental Learning Training Objectives

(Previous knowledge)

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Puneet Dokania

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• Define Knowledge • Input-Output Behaviour (knowledge distillation type) • Parameters

• Preserve Knowledge? Avoid Forgetting• Update Knowledge? Avoid Intransigence (inability to learn new

tasks)!3

Incremental Learning Training Objectives

(Previous knowledge)

min✓

E[ki=1Di

L(f✓(x),y)⌘min✓

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Puneet Dokania !4

Incremental Learning Evaluation Set-up(Multi/Single-head)

Page 14: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !4

Incremental Learning Evaluation Set-up(Multi/Single-head)

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oT1

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Puneet Dokania !4

Incremental Learning Evaluation Set-up(Multi/Single-head)

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oT1

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oT2

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Page 16: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !4

Incremental Learning Evaluation Set-up(Multi/Single-head)

• Multi-head • task id is known (for k-th task, the test label set is )• violates the objective behind incremental learning• if k-th task contains only one label, this evaluation implies

knowing the ground-truth label itself at the test time

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Page 17: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !4

Incremental Learning Evaluation Set-up(Multi/Single-head)

• Single-head • task id is unknown (test set contains all the labels seen )• much more challenging

[ki=1Yi

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• Multi-head • task id is known (for k-th task, the test label set is )• violates the objective behind incremental learning• if k-th task contains only one label, this evaluation implies

knowing the ground-truth label itself at the test time

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Page 18: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !5

RWalk Objective Function and Intuitions✓0

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Importance/Sensitivity

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Puneet Dokania !5

RWalk Objective Function and Intuitions✓0

✓1

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Fisher importance

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Importance/Sensitivity

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Puneet Dokania !5

RWalk Objective Function and Intuitions✓0

✓1

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Fisher importance Optimization pathbased importance

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Importance/Sensitivity

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Puneet Dokania !5

RWalk Objective Function and Intuitions✓0

✓1

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Fisher importance Optimization pathbased importance

Let us now look into these parameter importances individually

L̃k(✓) = Lk(✓) + �X

i

(F✓k�1i

+ stk�1

t0 )(✓i � ✓k�1i )2

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Importance/Sensitivity

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Puneet Dokania !6

Fisher based parameter importance (1/2)(approximate KL and Fisher)

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Puneet Dokania !6

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Fisher based parameter importance (1/2)(approximate KL and Fisher)

Page 24: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !6

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Fisher based parameter importance (1/2)(approximate KL and Fisher)

Page 25: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

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Fisher Information Matrix

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Fisher based parameter importance (1/2)(approximate KL and Fisher)

Page 26: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !6

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Fisher Information Matrix

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Fisher based parameter importance (1/2)(approximate KL and Fisher)

Page 27: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !6

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Fisher Information Matrix

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• Cross Entropy Loss =• By construction PSD (outer-product)• Computationally expensive • Huge matrix

� log p✓(y|x)<latexit sha1_base64="7x38PHCNNTIlA1hpptI1s+a37g8=">AAACInicbZDLSsNAFIYnXmu8VV26GaxCXVgSEXRZdOOygr1AE8pkOmmHTi7MnEhLzAv4HD6AW30Ed+JKcO9rOG2zsK0/DHz85xzOmd+LBVdgWV/G0vLK6tp6YcPc3Nre2S3u7TdUlEjK6jQSkWx5RDHBQ1YHDoK1YslI4AnW9AY343rzgUnFo/AeRjFzA9ILuc8pAW11isdn2BFRD8ed1IE+A5KVU8fz8SjDj3hCw+y0UyxZFWsivAh2DiWUq9Yp/jjdiCYBC4EKolTbtmJwUyKBU8Ey00kUiwkdkB5rawxJwJSbTn6T4RPtdLEfSf1CwBP370RKAqVGgac7AwJ9NV8bm//V2gn4V27KwzgBFtLpIj8RGCI8jgZ3uWQUxEgDoZLrWzHtE0ko6ABntgynp5qmTsaez2ERGucV26rYdxel6nWeUQEdoiNURja6RFV0i2qojih6Qi/oFb0Zz8a78WF8TluXjHzmAM3I+P4FnDmjYw==</latexit><latexit sha1_base64="7x38PHCNNTIlA1hpptI1s+a37g8=">AAACInicbZDLSsNAFIYnXmu8VV26GaxCXVgSEXRZdOOygr1AE8pkOmmHTi7MnEhLzAv4HD6AW30Ed+JKcO9rOG2zsK0/DHz85xzOmd+LBVdgWV/G0vLK6tp6YcPc3Nre2S3u7TdUlEjK6jQSkWx5RDHBQ1YHDoK1YslI4AnW9AY343rzgUnFo/AeRjFzA9ILuc8pAW11isdn2BFRD8ed1IE+A5KVU8fz8SjDj3hCw+y0UyxZFWsivAh2DiWUq9Yp/jjdiCYBC4EKolTbtmJwUyKBU8Ey00kUiwkdkB5rawxJwJSbTn6T4RPtdLEfSf1CwBP370RKAqVGgac7AwJ9NV8bm//V2gn4V27KwzgBFtLpIj8RGCI8jgZ3uWQUxEgDoZLrWzHtE0ko6ABntgynp5qmTsaez2ERGucV26rYdxel6nWeUQEdoiNURja6RFV0i2qojih6Qi/oFb0Zz8a78WF8TluXjHzmAM3I+P4FnDmjYw==</latexit><latexit sha1_base64="7x38PHCNNTIlA1hpptI1s+a37g8=">AAACInicbZDLSsNAFIYnXmu8VV26GaxCXVgSEXRZdOOygr1AE8pkOmmHTi7MnEhLzAv4HD6AW30Ed+JKcO9rOG2zsK0/DHz85xzOmd+LBVdgWV/G0vLK6tp6YcPc3Nre2S3u7TdUlEjK6jQSkWx5RDHBQ1YHDoK1YslI4AnW9AY343rzgUnFo/AeRjFzA9ILuc8pAW11isdn2BFRD8ed1IE+A5KVU8fz8SjDj3hCw+y0UyxZFWsivAh2DiWUq9Yp/jjdiCYBC4EKolTbtmJwUyKBU8Ey00kUiwkdkB5rawxJwJSbTn6T4RPtdLEfSf1CwBP370RKAqVGgac7AwJ9NV8bm//V2gn4V27KwzgBFtLpIj8RGCI8jgZ3uWQUxEgDoZLrWzHtE0ko6ABntgynp5qmTsaez2ERGucV26rYdxel6nWeUQEdoiNURja6RFV0i2qojih6Qi/oFb0Zz8a78WF8TluXjHzmAM3I+P4FnDmjYw==</latexit><latexit sha1_base64="7x38PHCNNTIlA1hpptI1s+a37g8=">AAACInicbZDLSsNAFIYnXmu8VV26GaxCXVgSEXRZdOOygr1AE8pkOmmHTi7MnEhLzAv4HD6AW30Ed+JKcO9rOG2zsK0/DHz85xzOmd+LBVdgWV/G0vLK6tp6YcPc3Nre2S3u7TdUlEjK6jQSkWx5RDHBQ1YHDoK1YslI4AnW9AY343rzgUnFo/AeRjFzA9ILuc8pAW11isdn2BFRD8ed1IE+A5KVU8fz8SjDj3hCw+y0UyxZFWsivAh2DiWUq9Yp/jjdiCYBC4EKolTbtmJwUyKBU8Ey00kUiwkdkB5rawxJwJSbTn6T4RPtdLEfSf1CwBP370RKAqVGgac7AwJ9NV8bm//V2gn4V27KwzgBFtLpIj8RGCI8jgZ3uWQUxEgDoZLrWzHtE0ko6ABntgynp5qmTsaez2ERGucV26rYdxel6nWeUQEdoiNURja6RFV0i2qojih6Qi/oFb0Zz8a78WF8TluXjHzmAM3I+P4FnDmjYw==</latexit>

Fisher based parameter importance (1/2)(approximate KL and Fisher)

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Puneet Dokania !7

Fisher based parameter importance (2/2)

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Puneet Dokania !7

Fisher based parameter importance (2/2)

log-likelihood (CE) gradient

F✓ = Ey⇠p✓(y|x)x⇠D

gg>

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multi backwardpasses

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Puneet Dokania !7

Fisher based parameter importance (2/2)

empirical Fisher (one fwd-bwd)

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log-likelihood (CE) gradient

F✓ = Ey⇠p✓(y|x)x⇠D

gg>

<latexit sha1_base64="gqH+NHi+Uk87yzkv/ze9fqTZAFQ=">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</latexit><latexit sha1_base64="gqH+NHi+Uk87yzkv/ze9fqTZAFQ=">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</latexit><latexit sha1_base64="gqH+NHi+Uk87yzkv/ze9fqTZAFQ=">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</latexit><latexit sha1_base64="gqH+NHi+Uk87yzkv/ze9fqTZAFQ=">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</latexit>

multi backwardpasses

Page 31: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !7

Fisher based parameter importance (2/2)

empirical Fisher (one fwd-bwd)

⇡ E(x,y)⇠D gg><latexit sha1_base64="Uv9yl1OqNyfhij2qc4CYBswpm90=">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</latexit><latexit sha1_base64="Cr/PV6Xo8PEISqgo6NqOwWgypBE=">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</latexit><latexit sha1_base64="Cr/PV6Xo8PEISqgo6NqOwWgypBE=">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</latexit><latexit sha1_base64="1FH2067uj1prhm/9fuv6h6LjsuU=">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</latexit>

2nd order approx

DKL(p✓kp✓+�✓) ⇡1

2�✓>F✓�✓

<latexit sha1_base64="LxTUJxyTfV0GFk/9tWvrd7b4b1o=">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</latexit><latexit sha1_base64="LxTUJxyTfV0GFk/9tWvrd7b4b1o=">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</latexit><latexit sha1_base64="LxTUJxyTfV0GFk/9tWvrd7b4b1o=">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</latexit><latexit sha1_base64="LxTUJxyTfV0GFk/9tWvrd7b4b1o=">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</latexit>

log-likelihood (CE) gradient

F✓ = Ey⇠p✓(y|x)x⇠D

gg>

<latexit sha1_base64="gqH+NHi+Uk87yzkv/ze9fqTZAFQ=">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</latexit><latexit sha1_base64="gqH+NHi+Uk87yzkv/ze9fqTZAFQ=">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</latexit><latexit sha1_base64="gqH+NHi+Uk87yzkv/ze9fqTZAFQ=">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</latexit><latexit sha1_base64="gqH+NHi+Uk87yzkv/ze9fqTZAFQ=">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</latexit>

multi backwardpasses

Page 32: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !7

Fisher based parameter importance (2/2)

empirical Fisher (one fwd-bwd)

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2nd order approx

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• empirical• independence

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log-likelihood (CE) gradient

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multi backwardpasses

Page 33: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !7

Fisher based parameter importance (2/2)

empirical Fisher (one fwd-bwd)

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2nd order approx

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• empirical• independence

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• over batches• moving-average• storage: one set of

Fisher (diagonal)

log-likelihood (CE) gradient

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multi backwardpasses

Page 34: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !7

• Fisher approximates the local curvature of the KL-divergence surface• Higher Fisher, higher curvature, more sensitive, move less in that

direction

Fisher based parameter importance (2/2)

empirical Fisher (one fwd-bwd)

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• over batches• moving-average• storage: one set of

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multi backwardpasses

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Puneet Dokania !8

Optimization path based parameter importance

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Puneet Dokania !8

Optimization path based parameter importance

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Puneet Dokania !8

Optimization path based parameter importance

si =�Lt+�t

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�DKL(✓i)<latexit sha1_base64="bh6cL/8Uvv7RF39zvHXXKB4YhvE=">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</latexit><latexit sha1_base64="bh6cL/8Uvv7RF39zvHXXKB4YhvE=">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</latexit><latexit sha1_base64="bh6cL/8Uvv7RF39zvHXXKB4YhvE=">AAACSHicbVDLSgNBEJyN7/iKevQyGARFCLsi6EUQ9SCaQwSjQjYus5NeMzj7YKZXDMv+k9/hBwie9ObVm3hzkqzgq2Cguqqb7ik/kUKjbT9ZpZHRsfGJyany9Mzs3HxlYfFcx6ni0OSxjNWlzzRIEUETBUq4TBSw0Jdw4d8c9P2LW1BaxNEZ9hJoh+w6EoHgDI3kVY61J+gudQPFeOYegkRG6x5eZUg3aFFjvuZiF5B5Yj3/ajr0spN6Tr85XqVq1+wB6F/iFKRKCjS8yqvbiXkaQoRcMq1bjp1gO2MKBZeQl91UQ8L4DbuGlqERC0G3s8Gfc7pqlA4NYmVehHSgfp/IWKh1L/RNZ8iwq397ffE/r5VisNPORJSkCBEfLgpSSTGm/QBpRyjgKHuGMK6EuZXyLjPxoYn5x5a74anlsknG+Z3DX3K+WXPsmnO6Vd3bLzKaJMtkhawRh2yTPXJEGqRJOLknj+SZvFgP1pv1bn0MW0tWMbNEfqBU+gQzv7Eo</latexit><latexit sha1_base64="bh6cL/8Uvv7RF39zvHXXKB4YhvE=">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</latexit>

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Puneet Dokania !8

Optimization path based parameter importance

si =�Lt+�t

t (✓i)

�DKL(✓i)<latexit sha1_base64="bh6cL/8Uvv7RF39zvHXXKB4YhvE=">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</latexit><latexit sha1_base64="bh6cL/8Uvv7RF39zvHXXKB4YhvE=">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</latexit><latexit sha1_base64="bh6cL/8Uvv7RF39zvHXXKB4YhvE=">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</latexit><latexit sha1_base64="bh6cL/8Uvv7RF39zvHXXKB4YhvE=">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</latexit>

Change in the loss per unit movement in the Riemannian manifold defined by the Fisher (approx. KL-div)

Page 39: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !9

Final Objective Again (RWalk)(combining Fisher and Optimization path )

Page 40: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !9

Final Objective Again (RWalk)(combining Fisher and Optimization path )

L̃k(✓) = Lk(✓) + �X

i

(F✓k�1i

+ stk�1

t0 )(✓i � ✓k�1i )2

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✓0

✓1

✓k�1<latexit sha1_base64="r7M0B23doF+D22FvoYEeiwjhYGk=">AAACCHicbVBLSgNBFHwTf3H8RV26aQyCG8OMCLoMunEZwSRCZgg9nZ6kSc+H7jdiGHIBD+BWj+BO3HoLT+A17CSzMIkFD4qq93hFBakUGh3n2yqtrK6tb5Q37a3tnd29yv5BSyeZYrzJEpmoh4BqLkXMmyhQ8odUcRoFkreD4c3Ebz9ypUUS3+Mo5X5E+7EIBaNoJM/DAUfazYdn7rhbqTo1ZwqyTNyCVKFAo1v58XoJyyIeI5NU647rpOjnVKFgko9tL9M8pWxI+7xjaEwjrv18mnlMTozSI2GizMRIpurfi5xGWo+iwGxGFAd60ZuI/3mdDMMrPxdxmiGP2exRmEmCCZkUQHpCcYZyZAhlSpishA2oogxNTXNfnmZRbds04y72sExa5zXXqbl3F9X6ddFRGY7gGE7BhUuowy00oAkMUniBV3iznq1368P6nK2WrOLmEOZgff0C1yeaGg==</latexit><latexit sha1_base64="r7M0B23doF+D22FvoYEeiwjhYGk=">AAACCHicbVBLSgNBFHwTf3H8RV26aQyCG8OMCLoMunEZwSRCZgg9nZ6kSc+H7jdiGHIBD+BWj+BO3HoLT+A17CSzMIkFD4qq93hFBakUGh3n2yqtrK6tb5Q37a3tnd29yv5BSyeZYrzJEpmoh4BqLkXMmyhQ8odUcRoFkreD4c3Ebz9ypUUS3+Mo5X5E+7EIBaNoJM/DAUfazYdn7rhbqTo1ZwqyTNyCVKFAo1v58XoJyyIeI5NU647rpOjnVKFgko9tL9M8pWxI+7xjaEwjrv18mnlMTozSI2GizMRIpurfi5xGWo+iwGxGFAd60ZuI/3mdDMMrPxdxmiGP2exRmEmCCZkUQHpCcYZyZAhlSpishA2oogxNTXNfnmZRbds04y72sExa5zXXqbl3F9X6ddFRGY7gGE7BhUuowy00oAkMUniBV3iznq1368P6nK2WrOLmEOZgff0C1yeaGg==</latexit><latexit sha1_base64="r7M0B23doF+D22FvoYEeiwjhYGk=">AAACCHicbVBLSgNBFHwTf3H8RV26aQyCG8OMCLoMunEZwSRCZgg9nZ6kSc+H7jdiGHIBD+BWj+BO3HoLT+A17CSzMIkFD4qq93hFBakUGh3n2yqtrK6tb5Q37a3tnd29yv5BSyeZYrzJEpmoh4BqLkXMmyhQ8odUcRoFkreD4c3Ebz9ypUUS3+Mo5X5E+7EIBaNoJM/DAUfazYdn7rhbqTo1ZwqyTNyCVKFAo1v58XoJyyIeI5NU647rpOjnVKFgko9tL9M8pWxI+7xjaEwjrv18mnlMTozSI2GizMRIpurfi5xGWo+iwGxGFAd60ZuI/3mdDMMrPxdxmiGP2exRmEmCCZkUQHpCcYZyZAhlSpishA2oogxNTXNfnmZRbds04y72sExa5zXXqbl3F9X6ddFRGY7gGE7BhUuowy00oAkMUniBV3iznq1368P6nK2WrOLmEOZgff0C1yeaGg==</latexit><latexit sha1_base64="r7M0B23doF+D22FvoYEeiwjhYGk=">AAACCHicbVBLSgNBFHwTf3H8RV26aQyCG8OMCLoMunEZwSRCZgg9nZ6kSc+H7jdiGHIBD+BWj+BO3HoLT+A17CSzMIkFD4qq93hFBakUGh3n2yqtrK6tb5Q37a3tnd29yv5BSyeZYrzJEpmoh4BqLkXMmyhQ8odUcRoFkreD4c3Ebz9ypUUS3+Mo5X5E+7EIBaNoJM/DAUfazYdn7rhbqTo1ZwqyTNyCVKFAo1v58XoJyyIeI5NU647rpOjnVKFgko9tL9M8pWxI+7xjaEwjrv18mnlMTozSI2GizMRIpurfi5xGWo+iwGxGFAd60ZuI/3mdDMMrPxdxmiGP2exRmEmCCZkUQHpCcYZyZAhlSpishA2oogxNTXNfnmZRbds04y72sExa5zXXqbl3F9X6ddFRGY7gGE7BhUuowy00oAkMUniBV3iznq1368P6nK2WrOLmEOZgff0C1yeaGg==</latexit>

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Puneet Dokania !9

Final Objective Again (RWalk)(combining Fisher and Optimization path )

L̃k(✓) = Lk(✓) + �X

i

(F✓k�1i

+ stk�1

t0 )(✓i � ✓k�1i )2

<latexit sha1_base64="o21L6dKS7GY02FM+C+0DR80xsL0=">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</latexit><latexit sha1_base64="o21L6dKS7GY02FM+C+0DR80xsL0=">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</latexit><latexit sha1_base64="o21L6dKS7GY02FM+C+0DR80xsL0=">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</latexit><latexit sha1_base64="o21L6dKS7GY02FM+C+0DR80xsL0=">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</latexit>

✓0

✓1

✓k�1<latexit sha1_base64="r7M0B23doF+D22FvoYEeiwjhYGk=">AAACCHicbVBLSgNBFHwTf3H8RV26aQyCG8OMCLoMunEZwSRCZgg9nZ6kSc+H7jdiGHIBD+BWj+BO3HoLT+A17CSzMIkFD4qq93hFBakUGh3n2yqtrK6tb5Q37a3tnd29yv5BSyeZYrzJEpmoh4BqLkXMmyhQ8odUcRoFkreD4c3Ebz9ypUUS3+Mo5X5E+7EIBaNoJM/DAUfazYdn7rhbqTo1ZwqyTNyCVKFAo1v58XoJyyIeI5NU647rpOjnVKFgko9tL9M8pWxI+7xjaEwjrv18mnlMTozSI2GizMRIpurfi5xGWo+iwGxGFAd60ZuI/3mdDMMrPxdxmiGP2exRmEmCCZkUQHpCcYZyZAhlSpishA2oogxNTXNfnmZRbds04y72sExa5zXXqbl3F9X6ddFRGY7gGE7BhUuowy00oAkMUniBV3iznq1368P6nK2WrOLmEOZgff0C1yeaGg==</latexit><latexit sha1_base64="r7M0B23doF+D22FvoYEeiwjhYGk=">AAACCHicbVBLSgNBFHwTf3H8RV26aQyCG8OMCLoMunEZwSRCZgg9nZ6kSc+H7jdiGHIBD+BWj+BO3HoLT+A17CSzMIkFD4qq93hFBakUGh3n2yqtrK6tb5Q37a3tnd29yv5BSyeZYrzJEpmoh4BqLkXMmyhQ8odUcRoFkreD4c3Ebz9ypUUS3+Mo5X5E+7EIBaNoJM/DAUfazYdn7rhbqTo1ZwqyTNyCVKFAo1v58XoJyyIeI5NU647rpOjnVKFgko9tL9M8pWxI+7xjaEwjrv18mnlMTozSI2GizMRIpurfi5xGWo+iwGxGFAd60ZuI/3mdDMMrPxdxmiGP2exRmEmCCZkUQHpCcYZyZAhlSpishA2oogxNTXNfnmZRbds04y72sExa5zXXqbl3F9X6ddFRGY7gGE7BhUuowy00oAkMUniBV3iznq1368P6nK2WrOLmEOZgff0C1yeaGg==</latexit><latexit sha1_base64="r7M0B23doF+D22FvoYEeiwjhYGk=">AAACCHicbVBLSgNBFHwTf3H8RV26aQyCG8OMCLoMunEZwSRCZgg9nZ6kSc+H7jdiGHIBD+BWj+BO3HoLT+A17CSzMIkFD4qq93hFBakUGh3n2yqtrK6tb5Q37a3tnd29yv5BSyeZYrzJEpmoh4BqLkXMmyhQ8odUcRoFkreD4c3Ebz9ypUUS3+Mo5X5E+7EIBaNoJM/DAUfazYdn7rhbqTo1ZwqyTNyCVKFAo1v58XoJyyIeI5NU647rpOjnVKFgko9tL9M8pWxI+7xjaEwjrv18mnlMTozSI2GizMRIpurfi5xGWo+iwGxGFAd60ZuI/3mdDMMrPxdxmiGP2exRmEmCCZkUQHpCcYZyZAhlSpishA2oogxNTXNfnmZRbds04y72sExa5zXXqbl3F9X6ddFRGY7gGE7BhUuowy00oAkMUniBV3iznq1368P6nK2WrOLmEOZgff0C1yeaGg==</latexit><latexit sha1_base64="r7M0B23doF+D22FvoYEeiwjhYGk=">AAACCHicbVBLSgNBFHwTf3H8RV26aQyCG8OMCLoMunEZwSRCZgg9nZ6kSc+H7jdiGHIBD+BWj+BO3HoLT+A17CSzMIkFD4qq93hFBakUGh3n2yqtrK6tb5Q37a3tnd29yv5BSyeZYrzJEpmoh4BqLkXMmyhQ8odUcRoFkreD4c3Ebz9ypUUS3+Mo5X5E+7EIBaNoJM/DAUfazYdn7rhbqTo1ZwqyTNyCVKFAo1v58XoJyyIeI5NU647rpOjnVKFgko9tL9M8pWxI+7xjaEwjrv18mnlMTozSI2GizMRIpurfi5xGWo+iwGxGFAd60ZuI/3mdDMMrPxdxmiGP2exRmEmCCZkUQHpCcYZyZAhlSpishA2oogxNTXNfnmZRbds04y72sExa5zXXqbl3F9X6ddFRGY7gGE7BhUuowy00oAkMUniBV3iznq1368P6nK2WrOLmEOZgff0C1yeaGg==</latexit>

• If no Fisher and Euclidean distance = Path Integral [Zenke et al, ICML17]

Page 42: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !9

Final Objective Again (RWalk)(combining Fisher and Optimization path )

L̃k(✓) = Lk(✓) + �X

i

(F✓k�1i

+ stk�1

t0 )(✓i � ✓k�1i )2

<latexit sha1_base64="o21L6dKS7GY02FM+C+0DR80xsL0=">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</latexit><latexit sha1_base64="o21L6dKS7GY02FM+C+0DR80xsL0=">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</latexit><latexit sha1_base64="o21L6dKS7GY02FM+C+0DR80xsL0=">AAACnXicbVFda9swFJW9deuybk23xz5ULBQaSoNdOrqXQdno6EMYHSxNIU6MLN80IvIH0vVoEPot+137BfsbkxOXNu0uSBydc+4HV0kphcYg+OP5z55vvHi5+ar1euvN2+32zrsrXVSKw4AXslDXCdMgRQ4DFCjhulTAskTCMJl/rfXhL1BaFPlPXJQwzthNLqaCM3RU3P4doZApmL6dzOlBhDNA1qWfaf/h85BG0pVMGY10lcWiVuAWl92NgtSab7FZmWMxMfOj0FpbZ927ElmBNTo2GAd24u7G1b3r4qoe0fUa3ckxjdudoBcsgz4FYQM6pInLuP03SgteZZAjl0zrURiUODZMoeASbCuqNJSMz9kNjBzMWQZ6bJZDWrrvmJROC+VOjnTJPswwLNN6kSXOmTGc6cdaTf5PG1U4/TQ2Ii8rhJyvGk0rSbGg9a/QVCjgKBcOMK6Em5XyGVOMo/u7tS63q1FbLbeZ8PEenoKr414Y9MIfJ52zL82ONsku+UAOSEhOyRm5IJdkQLi34R16J95Hf88/9/v+95XV95qc92Qt/OE/6cfMAQ==</latexit><latexit sha1_base64="o21L6dKS7GY02FM+C+0DR80xsL0=">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</latexit>

✓0

✓1

✓k�1<latexit sha1_base64="r7M0B23doF+D22FvoYEeiwjhYGk=">AAACCHicbVBLSgNBFHwTf3H8RV26aQyCG8OMCLoMunEZwSRCZgg9nZ6kSc+H7jdiGHIBD+BWj+BO3HoLT+A17CSzMIkFD4qq93hFBakUGh3n2yqtrK6tb5Q37a3tnd29yv5BSyeZYrzJEpmoh4BqLkXMmyhQ8odUcRoFkreD4c3Ebz9ypUUS3+Mo5X5E+7EIBaNoJM/DAUfazYdn7rhbqTo1ZwqyTNyCVKFAo1v58XoJyyIeI5NU647rpOjnVKFgko9tL9M8pWxI+7xjaEwjrv18mnlMTozSI2GizMRIpurfi5xGWo+iwGxGFAd60ZuI/3mdDMMrPxdxmiGP2exRmEmCCZkUQHpCcYZyZAhlSpishA2oogxNTXNfnmZRbds04y72sExa5zXXqbl3F9X6ddFRGY7gGE7BhUuowy00oAkMUniBV3iznq1368P6nK2WrOLmEOZgff0C1yeaGg==</latexit><latexit sha1_base64="r7M0B23doF+D22FvoYEeiwjhYGk=">AAACCHicbVBLSgNBFHwTf3H8RV26aQyCG8OMCLoMunEZwSRCZgg9nZ6kSc+H7jdiGHIBD+BWj+BO3HoLT+A17CSzMIkFD4qq93hFBakUGh3n2yqtrK6tb5Q37a3tnd29yv5BSyeZYrzJEpmoh4BqLkXMmyhQ8odUcRoFkreD4c3Ebz9ypUUS3+Mo5X5E+7EIBaNoJM/DAUfazYdn7rhbqTo1ZwqyTNyCVKFAo1v58XoJyyIeI5NU647rpOjnVKFgko9tL9M8pWxI+7xjaEwjrv18mnlMTozSI2GizMRIpurfi5xGWo+iwGxGFAd60ZuI/3mdDMMrPxdxmiGP2exRmEmCCZkUQHpCcYZyZAhlSpishA2oogxNTXNfnmZRbds04y72sExa5zXXqbl3F9X6ddFRGY7gGE7BhUuowy00oAkMUniBV3iznq1368P6nK2WrOLmEOZgff0C1yeaGg==</latexit><latexit sha1_base64="r7M0B23doF+D22FvoYEeiwjhYGk=">AAACCHicbVBLSgNBFHwTf3H8RV26aQyCG8OMCLoMunEZwSRCZgg9nZ6kSc+H7jdiGHIBD+BWj+BO3HoLT+A17CSzMIkFD4qq93hFBakUGh3n2yqtrK6tb5Q37a3tnd29yv5BSyeZYrzJEpmoh4BqLkXMmyhQ8odUcRoFkreD4c3Ebz9ypUUS3+Mo5X5E+7EIBaNoJM/DAUfazYdn7rhbqTo1ZwqyTNyCVKFAo1v58XoJyyIeI5NU647rpOjnVKFgko9tL9M8pWxI+7xjaEwjrv18mnlMTozSI2GizMRIpurfi5xGWo+iwGxGFAd60ZuI/3mdDMMrPxdxmiGP2exRmEmCCZkUQHpCcYZyZAhlSpishA2oogxNTXNfnmZRbds04y72sExa5zXXqbl3F9X6ddFRGY7gGE7BhUuowy00oAkMUniBV3iznq1368P6nK2WrOLmEOZgff0C1yeaGg==</latexit><latexit sha1_base64="r7M0B23doF+D22FvoYEeiwjhYGk=">AAACCHicbVBLSgNBFHwTf3H8RV26aQyCG8OMCLoMunEZwSRCZgg9nZ6kSc+H7jdiGHIBD+BWj+BO3HoLT+A17CSzMIkFD4qq93hFBakUGh3n2yqtrK6tb5Q37a3tnd29yv5BSyeZYrzJEpmoh4BqLkXMmyhQ8odUcRoFkreD4c3Ebz9ypUUS3+Mo5X5E+7EIBaNoJM/DAUfazYdn7rhbqTo1ZwqyTNyCVKFAo1v58XoJyyIeI5NU647rpOjnVKFgko9tL9M8pWxI+7xjaEwjrv18mnlMTozSI2GizMRIpurfi5xGWo+iwGxGFAd60ZuI/3mdDMMrPxdxmiGP2exRmEmCCZkUQHpCcYZyZAhlSpishA2oogxNTXNfnmZRbds04y72sExa5zXXqbl3F9X6ddFRGY7gGE7BhUuowy00oAkMUniBV3iznq1368P6nK2WrOLmEOZgff0C1yeaGg==</latexit>

• If no Fisher and Euclidean distance = Path Integral [Zenke et al, ICML17]

• If no optimization path score• EWC [Kirkpatrick et al, PNAS16] with only one set of Fisher (similar idea

got accepted in ICML18 [Schwarz et al, ICML18])

Page 43: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !9

Final Objective Again (RWalk)(combining Fisher and Optimization path )

L̃k(✓) = Lk(✓) + �X

i

(F✓k�1i

+ stk�1

t0 )(✓i � ✓k�1i )2

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✓0

✓1

✓k�1<latexit sha1_base64="r7M0B23doF+D22FvoYEeiwjhYGk=">AAACCHicbVBLSgNBFHwTf3H8RV26aQyCG8OMCLoMunEZwSRCZgg9nZ6kSc+H7jdiGHIBD+BWj+BO3HoLT+A17CSzMIkFD4qq93hFBakUGh3n2yqtrK6tb5Q37a3tnd29yv5BSyeZYrzJEpmoh4BqLkXMmyhQ8odUcRoFkreD4c3Ebz9ypUUS3+Mo5X5E+7EIBaNoJM/DAUfazYdn7rhbqTo1ZwqyTNyCVKFAo1v58XoJyyIeI5NU647rpOjnVKFgko9tL9M8pWxI+7xjaEwjrv18mnlMTozSI2GizMRIpurfi5xGWo+iwGxGFAd60ZuI/3mdDMMrPxdxmiGP2exRmEmCCZkUQHpCcYZyZAhlSpishA2oogxNTXNfnmZRbds04y72sExa5zXXqbl3F9X6ddFRGY7gGE7BhUuowy00oAkMUniBV3iznq1368P6nK2WrOLmEOZgff0C1yeaGg==</latexit><latexit sha1_base64="r7M0B23doF+D22FvoYEeiwjhYGk=">AAACCHicbVBLSgNBFHwTf3H8RV26aQyCG8OMCLoMunEZwSRCZgg9nZ6kSc+H7jdiGHIBD+BWj+BO3HoLT+A17CSzMIkFD4qq93hFBakUGh3n2yqtrK6tb5Q37a3tnd29yv5BSyeZYrzJEpmoh4BqLkXMmyhQ8odUcRoFkreD4c3Ebz9ypUUS3+Mo5X5E+7EIBaNoJM/DAUfazYdn7rhbqTo1ZwqyTNyCVKFAo1v58XoJyyIeI5NU647rpOjnVKFgko9tL9M8pWxI+7xjaEwjrv18mnlMTozSI2GizMRIpurfi5xGWo+iwGxGFAd60ZuI/3mdDMMrPxdxmiGP2exRmEmCCZkUQHpCcYZyZAhlSpishA2oogxNTXNfnmZRbds04y72sExa5zXXqbl3F9X6ddFRGY7gGE7BhUuowy00oAkMUniBV3iznq1368P6nK2WrOLmEOZgff0C1yeaGg==</latexit><latexit sha1_base64="r7M0B23doF+D22FvoYEeiwjhYGk=">AAACCHicbVBLSgNBFHwTf3H8RV26aQyCG8OMCLoMunEZwSRCZgg9nZ6kSc+H7jdiGHIBD+BWj+BO3HoLT+A17CSzMIkFD4qq93hFBakUGh3n2yqtrK6tb5Q37a3tnd29yv5BSyeZYrzJEpmoh4BqLkXMmyhQ8odUcRoFkreD4c3Ebz9ypUUS3+Mo5X5E+7EIBaNoJM/DAUfazYdn7rhbqTo1ZwqyTNyCVKFAo1v58XoJyyIeI5NU647rpOjnVKFgko9tL9M8pWxI+7xjaEwjrv18mnlMTozSI2GizMRIpurfi5xGWo+iwGxGFAd60ZuI/3mdDMMrPxdxmiGP2exRmEmCCZkUQHpCcYZyZAhlSpishA2oogxNTXNfnmZRbds04y72sExa5zXXqbl3F9X6ddFRGY7gGE7BhUuowy00oAkMUniBV3iznq1368P6nK2WrOLmEOZgff0C1yeaGg==</latexit><latexit sha1_base64="r7M0B23doF+D22FvoYEeiwjhYGk=">AAACCHicbVBLSgNBFHwTf3H8RV26aQyCG8OMCLoMunEZwSRCZgg9nZ6kSc+H7jdiGHIBD+BWj+BO3HoLT+A17CSzMIkFD4qq93hFBakUGh3n2yqtrK6tb5Q37a3tnd29yv5BSyeZYrzJEpmoh4BqLkXMmyhQ8odUcRoFkreD4c3Ebz9ypUUS3+Mo5X5E+7EIBaNoJM/DAUfazYdn7rhbqTo1ZwqyTNyCVKFAo1v58XoJyyIeI5NU647rpOjnVKFgko9tL9M8pWxI+7xjaEwjrv18mnlMTozSI2GizMRIpurfi5xGWo+iwGxGFAd60ZuI/3mdDMMrPxdxmiGP2exRmEmCCZkUQHpCcYZyZAhlSpishA2oogxNTXNfnmZRbds04y72sExa5zXXqbl3F9X6ddFRGY7gGE7BhUuowy00oAkMUniBV3iznq1368P6nK2WrOLmEOZgff0C1yeaGg==</latexit>

• If no Fisher and Euclidean distance = Path Integral [Zenke et al, ICML17]

• If no optimization path score• EWC [Kirkpatrick et al, PNAS16] with only one set of Fisher (similar idea

got accepted in ICML18 [Schwarz et al, ICML18])• Fisher updated using moving average and batch statistics

• efficient as no need to pass the entire data• comes as by-product

Page 44: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !9

Final Objective Again (RWalk)(combining Fisher and Optimization path )

L̃k(✓) = Lk(✓) + �X

i

(F✓k�1i

+ stk�1

t0 )(✓i � ✓k�1i )2

<latexit sha1_base64="o21L6dKS7GY02FM+C+0DR80xsL0=">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</latexit><latexit sha1_base64="o21L6dKS7GY02FM+C+0DR80xsL0=">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</latexit><latexit sha1_base64="o21L6dKS7GY02FM+C+0DR80xsL0=">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</latexit><latexit sha1_base64="o21L6dKS7GY02FM+C+0DR80xsL0=">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</latexit>

✓0

✓1

✓k�1<latexit sha1_base64="r7M0B23doF+D22FvoYEeiwjhYGk=">AAACCHicbVBLSgNBFHwTf3H8RV26aQyCG8OMCLoMunEZwSRCZgg9nZ6kSc+H7jdiGHIBD+BWj+BO3HoLT+A17CSzMIkFD4qq93hFBakUGh3n2yqtrK6tb5Q37a3tnd29yv5BSyeZYrzJEpmoh4BqLkXMmyhQ8odUcRoFkreD4c3Ebz9ypUUS3+Mo5X5E+7EIBaNoJM/DAUfazYdn7rhbqTo1ZwqyTNyCVKFAo1v58XoJyyIeI5NU647rpOjnVKFgko9tL9M8pWxI+7xjaEwjrv18mnlMTozSI2GizMRIpurfi5xGWo+iwGxGFAd60ZuI/3mdDMMrPxdxmiGP2exRmEmCCZkUQHpCcYZyZAhlSpishA2oogxNTXNfnmZRbds04y72sExa5zXXqbl3F9X6ddFRGY7gGE7BhUuowy00oAkMUniBV3iznq1368P6nK2WrOLmEOZgff0C1yeaGg==</latexit><latexit sha1_base64="r7M0B23doF+D22FvoYEeiwjhYGk=">AAACCHicbVBLSgNBFHwTf3H8RV26aQyCG8OMCLoMunEZwSRCZgg9nZ6kSc+H7jdiGHIBD+BWj+BO3HoLT+A17CSzMIkFD4qq93hFBakUGh3n2yqtrK6tb5Q37a3tnd29yv5BSyeZYrzJEpmoh4BqLkXMmyhQ8odUcRoFkreD4c3Ebz9ypUUS3+Mo5X5E+7EIBaNoJM/DAUfazYdn7rhbqTo1ZwqyTNyCVKFAo1v58XoJyyIeI5NU647rpOjnVKFgko9tL9M8pWxI+7xjaEwjrv18mnlMTozSI2GizMRIpurfi5xGWo+iwGxGFAd60ZuI/3mdDMMrPxdxmiGP2exRmEmCCZkUQHpCcYZyZAhlSpishA2oogxNTXNfnmZRbds04y72sExa5zXXqbl3F9X6ddFRGY7gGE7BhUuowy00oAkMUniBV3iznq1368P6nK2WrOLmEOZgff0C1yeaGg==</latexit><latexit sha1_base64="r7M0B23doF+D22FvoYEeiwjhYGk=">AAACCHicbVBLSgNBFHwTf3H8RV26aQyCG8OMCLoMunEZwSRCZgg9nZ6kSc+H7jdiGHIBD+BWj+BO3HoLT+A17CSzMIkFD4qq93hFBakUGh3n2yqtrK6tb5Q37a3tnd29yv5BSyeZYrzJEpmoh4BqLkXMmyhQ8odUcRoFkreD4c3Ebz9ypUUS3+Mo5X5E+7EIBaNoJM/DAUfazYdn7rhbqTo1ZwqyTNyCVKFAo1v58XoJyyIeI5NU647rpOjnVKFgko9tL9M8pWxI+7xjaEwjrv18mnlMTozSI2GizMRIpurfi5xGWo+iwGxGFAd60ZuI/3mdDMMrPxdxmiGP2exRmEmCCZkUQHpCcYZyZAhlSpishA2oogxNTXNfnmZRbds04y72sExa5zXXqbl3F9X6ddFRGY7gGE7BhUuowy00oAkMUniBV3iznq1368P6nK2WrOLmEOZgff0C1yeaGg==</latexit><latexit sha1_base64="r7M0B23doF+D22FvoYEeiwjhYGk=">AAACCHicbVBLSgNBFHwTf3H8RV26aQyCG8OMCLoMunEZwSRCZgg9nZ6kSc+H7jdiGHIBD+BWj+BO3HoLT+A17CSzMIkFD4qq93hFBakUGh3n2yqtrK6tb5Q37a3tnd29yv5BSyeZYrzJEpmoh4BqLkXMmyhQ8odUcRoFkreD4c3Ebz9ypUUS3+Mo5X5E+7EIBaNoJM/DAUfazYdn7rhbqTo1ZwqyTNyCVKFAo1v58XoJyyIeI5NU647rpOjnVKFgko9tL9M8pWxI+7xjaEwjrv18mnlMTozSI2GizMRIpurfi5xGWo+iwGxGFAd60ZuI/3mdDMMrPxdxmiGP2exRmEmCCZkUQHpCcYZyZAhlSpishA2oogxNTXNfnmZRbds04y72sExa5zXXqbl3F9X6ddFRGY7gGE7BhUuowy00oAkMUniBV3iznq1368P6nK2WrOLmEOZgff0C1yeaGg==</latexit>

• If no Fisher and Euclidean distance = Path Integral [Zenke et al, ICML17]

• If no optimization path score• EWC [Kirkpatrick et al, PNAS16] with only one set of Fisher (similar idea

got accepted in ICML18 [Schwarz et al, ICML18])• Fisher updated using moving average and batch statistics

• efficient as no need to pass the entire data• comes as by-product

• Fisher and Scores individually normalized to [0,1]• makes lambda less sensitive to the num of tasks

Page 45: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !10

Handling Forgetting and Intransigence

Page 46: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !10

Handling Forgetting and Intransigence

L̃k(✓) = Lk(✓) + �X

i

(F✓k�1i

+ stk�1

t0 )(✓i � ✓k�1i )2

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• Encodes previous knowledge• Handles forgetting

Page 47: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !10

Handling Forgetting and Intransigence

• Handling Intransigence (inability to learn)? Big problem for single-head evaluation• Recall single-head is evaluated over all the labels seen• Requires learning discrimination b/w previous and new labels

L̃k(✓) = Lk(✓) + �X

i

(F✓k�1i

+ stk�1

t0 )(✓i � ✓k�1i )2

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• Encodes previous knowledge• Handles forgetting

Page 48: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !10

Handling Forgetting and Intransigence

• Handling Intransigence (inability to learn)? Big problem for single-head evaluation• Recall single-head is evaluated over all the labels seen• Requires learning discrimination b/w previous and new labels

• Store few samples from previous tasks: • Uniform• Plane distance based: Better if closer to the boundary• Entropy based: Higher entropy, more difficult the sample• Mean of features (MoF)

L̃k(✓) = Lk(✓) + �X

i

(F✓k�1i

+ stk�1

t0 )(✓i � ✓k�1i )2

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• Encodes previous knowledge• Handles forgetting

Page 49: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !11

Quantitative Evaluation of Incremental Learning

Page 50: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !11

Quantitative Evaluation of Incremental Learning

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Page 51: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !11

Quantitative Evaluation of Incremental Learning

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• Standard Approach: Compute accuracy at the end of all the tasks

Page 52: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !11

Quantitative Evaluation of Incremental Learning

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• Standard Approach: Compute accuracy at the end of all the tasks

• Doesn’t capture the behaviour of the model throughout the learning path

Page 53: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !11

Quantitative Evaluation of Incremental Learning

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• Standard Approach: Compute accuracy at the end of all the tasks

• Doesn’t capture the behaviour of the model throughout the learning path

• Doesn’t tell us anything about Forgetting and Instrasigence

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Puneet Dokania !12

Forgetting

Page 55: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania

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T1 = {y1, y2}<latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit><latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit><latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit><latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit>

D1<latexit sha1_base64="q69qAC9QCbzeFL5i4zpxpEWkU9k=">AAAB9HicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMuiLlxWsA9oh3InTdvQTGZMMoUy9DvcuFDErR/jzr8x085CWw8EDufcyz05QSy4Nq777RTW1jc2t4rbpZ3dvf2D8uFRU0eJoqxBIxGpdoCaCS5Zw3AjWDtWDMNAsFYwvs381oQpzSP5aKYx80McSj7gFI2V/G6IZkRRpHezntcrV9yqOwdZJV5OKpCj3it/dfsRTUImDRWodcdzY+OnqAyngs1K3USzGOkYh6xjqcSQaT+dh56RM6v0ySBS9klD5urvjRRDradhYCezkHrZy8T/vE5iBtd+ymWcGCbp4tAgEcREJGuA9Lli1IipJUgVt1kJHaFCamxPJVuCt/zlVdK8qHpu1Xu4rNRu8jqKcAKncA4eXEEN7qEODaDwBM/wCm/OxHlx3p2PxWjByXeO4Q+czx+iYZH+</latexit><latexit sha1_base64="q69qAC9QCbzeFL5i4zpxpEWkU9k=">AAAB9HicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMuiLlxWsA9oh3InTdvQTGZMMoUy9DvcuFDErR/jzr8x085CWw8EDufcyz05QSy4Nq777RTW1jc2t4rbpZ3dvf2D8uFRU0eJoqxBIxGpdoCaCS5Zw3AjWDtWDMNAsFYwvs381oQpzSP5aKYx80McSj7gFI2V/G6IZkRRpHezntcrV9yqOwdZJV5OKpCj3it/dfsRTUImDRWodcdzY+OnqAyngs1K3USzGOkYh6xjqcSQaT+dh56RM6v0ySBS9klD5urvjRRDradhYCezkHrZy8T/vE5iBtd+ymWcGCbp4tAgEcREJGuA9Lli1IipJUgVt1kJHaFCamxPJVuCt/zlVdK8qHpu1Xu4rNRu8jqKcAKncA4eXEEN7qEODaDwBM/wCm/OxHlx3p2PxWjByXeO4Q+czx+iYZH+</latexit><latexit sha1_base64="q69qAC9QCbzeFL5i4zpxpEWkU9k=">AAAB9HicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMuiLlxWsA9oh3InTdvQTGZMMoUy9DvcuFDErR/jzr8x085CWw8EDufcyz05QSy4Nq777RTW1jc2t4rbpZ3dvf2D8uFRU0eJoqxBIxGpdoCaCS5Zw3AjWDtWDMNAsFYwvs381oQpzSP5aKYx80McSj7gFI2V/G6IZkRRpHezntcrV9yqOwdZJV5OKpCj3it/dfsRTUImDRWodcdzY+OnqAyngs1K3USzGOkYh6xjqcSQaT+dh56RM6v0ySBS9klD5urvjRRDradhYCezkHrZy8T/vE5iBtd+ymWcGCbp4tAgEcREJGuA9Lli1IipJUgVt1kJHaFCamxPJVuCt/zlVdK8qHpu1Xu4rNRu8jqKcAKncA4eXEEN7qEODaDwBM/wCm/OxHlx3p2PxWjByXeO4Q+czx+iYZH+</latexit><latexit sha1_base64="q69qAC9QCbzeFL5i4zpxpEWkU9k=">AAAB9HicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMuiLlxWsA9oh3InTdvQTGZMMoUy9DvcuFDErR/jzr8x085CWw8EDufcyz05QSy4Nq777RTW1jc2t4rbpZ3dvf2D8uFRU0eJoqxBIxGpdoCaCS5Zw3AjWDtWDMNAsFYwvs381oQpzSP5aKYx80McSj7gFI2V/G6IZkRRpHezntcrV9yqOwdZJV5OKpCj3it/dfsRTUImDRWodcdzY+OnqAyngs1K3USzGOkYh6xjqcSQaT+dh56RM6v0ySBS9klD5urvjRRDradhYCezkHrZy8T/vE5iBtd+ymWcGCbp4tAgEcREJGuA9Lli1IipJUgVt1kJHaFCamxPJVuCt/zlVdK8qHpu1Xu4rNRu8jqKcAKncA4eXEEN7qEODaDwBM/wCm/OxHlx3p2PxWjByXeO4Q+czx+iYZH+</latexit>

✓2<latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit><latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit><latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit><latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit>

T2 = {y3, y4}<latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit><latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit><latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit><latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit>

D2<latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit><latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit><latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit><latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit>

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T3 = {y5, y6}<latexit sha1_base64="LwxbD5bgl32pINRhEeIeNWmb/8I=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJL43ghFNy4r9AVNCJPptB06eTAzEUPIr7hxoYhbf8Sdf+O0zUJbD1w4nHMv997jx5xJZVnfxtLyyuraemmjvLm1vbNr7lXaMkoEoS0S8Uh0fSwpZyFtKaY47caC4sDntOOP7yZ+55EKyaKwqdKYugEehmzACFZa8sxK0ztDN8jJUu/iBKXepZN7ZtWqWVOgRWIXpAoFGp755fQjkgQ0VIRjKXu2FSs3w0IxwmledhJJY0zGeEh7moY4oNLNprfn6EgrfTSIhK5Qoan6eyLDgZRp4OvOAKuRnPcm4n9eL1GDazdjYZwoGpLZokHCkYrQJAjUZ4ISxVNNMBFM34rICAtMlI6rrEOw519eJO3Tmm3V7Ifzav22iKMEB3AIx2DDFdThHhrQAgJP8Ayv8GbkxovxbnzMWpeMYmYf/sD4/AGV5ZLZ</latexit><latexit sha1_base64="LwxbD5bgl32pINRhEeIeNWmb/8I=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJL43ghFNy4r9AVNCJPptB06eTAzEUPIr7hxoYhbf8Sdf+O0zUJbD1w4nHMv997jx5xJZVnfxtLyyuraemmjvLm1vbNr7lXaMkoEoS0S8Uh0fSwpZyFtKaY47caC4sDntOOP7yZ+55EKyaKwqdKYugEehmzACFZa8sxK0ztDN8jJUu/iBKXepZN7ZtWqWVOgRWIXpAoFGp755fQjkgQ0VIRjKXu2FSs3w0IxwmledhJJY0zGeEh7moY4oNLNprfn6EgrfTSIhK5Qoan6eyLDgZRp4OvOAKuRnPcm4n9eL1GDazdjYZwoGpLZokHCkYrQJAjUZ4ISxVNNMBFM34rICAtMlI6rrEOw519eJO3Tmm3V7Ifzav22iKMEB3AIx2DDFdThHhrQAgJP8Ayv8GbkxovxbnzMWpeMYmYf/sD4/AGV5ZLZ</latexit><latexit sha1_base64="LwxbD5bgl32pINRhEeIeNWmb/8I=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJL43ghFNy4r9AVNCJPptB06eTAzEUPIr7hxoYhbf8Sdf+O0zUJbD1w4nHMv997jx5xJZVnfxtLyyuraemmjvLm1vbNr7lXaMkoEoS0S8Uh0fSwpZyFtKaY47caC4sDntOOP7yZ+55EKyaKwqdKYugEehmzACFZa8sxK0ztDN8jJUu/iBKXepZN7ZtWqWVOgRWIXpAoFGp755fQjkgQ0VIRjKXu2FSs3w0IxwmledhJJY0zGeEh7moY4oNLNprfn6EgrfTSIhK5Qoan6eyLDgZRp4OvOAKuRnPcm4n9eL1GDazdjYZwoGpLZokHCkYrQJAjUZ4ISxVNNMBFM34rICAtMlI6rrEOw519eJO3Tmm3V7Ifzav22iKMEB3AIx2DDFdThHhrQAgJP8Ayv8GbkxovxbnzMWpeMYmYf/sD4/AGV5ZLZ</latexit><latexit sha1_base64="LwxbD5bgl32pINRhEeIeNWmb/8I=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJL43ghFNy4r9AVNCJPptB06eTAzEUPIr7hxoYhbf8Sdf+O0zUJbD1w4nHMv997jx5xJZVnfxtLyyuraemmjvLm1vbNr7lXaMkoEoS0S8Uh0fSwpZyFtKaY47caC4sDntOOP7yZ+55EKyaKwqdKYugEehmzACFZa8sxK0ztDN8jJUu/iBKXepZN7ZtWqWVOgRWIXpAoFGp755fQjkgQ0VIRjKXu2FSs3w0IxwmledhJJY0zGeEh7moY4oNLNprfn6EgrfTSIhK5Qoan6eyLDgZRp4OvOAKuRnPcm4n9eL1GDazdjYZwoGpLZokHCkYrQJAjUZ4ISxVNNMBFM34rICAtMlI6rrEOw519eJO3Tmm3V7Ifzav22iKMEB3AIx2DDFdThHhrQAgJP8Ayv8GbkxovxbnzMWpeMYmYf/sD4/AGV5ZLZ</latexit>

D3<latexit sha1_base64="62hRsAjW7tKVI0FX4k//oGPjLlY=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclRkVdFnUhcsK9gHtUDLpbRuayYxJplCGfocbF4q49WPc+Tdm2llo64HA4Zx7uScniAXXxnW/nZXVtfWNzcJWcXtnd2+/dHDY0FGiGNZZJCLVCqhGwSXWDTcCW7FCGgYCm8HoNvObY1SaR/LRTGL0QzqQvM8ZNVbyOyE1Q0ZFejftXnRLZbfizkCWiZeTMuSodUtfnV7EkhClYYJq3fbc2PgpVYYzgdNiJ9EYUzaiA2xbKmmI2k9noafk1Co90o+UfdKQmfp7I6Wh1pMwsJNZSL3oZeJ/Xjsx/Ws/5TJODEo2P9RPBDERyRogPa6QGTGxhDLFbVbChlRRZmxPRVuCt/jlZdI4r3huxXu4LFdv8joKcAwncAYeXEEV7qEGdWDwBM/wCm/O2Hlx3p2P+eiKk+8cwR84nz+laZIA</latexit><latexit sha1_base64="62hRsAjW7tKVI0FX4k//oGPjLlY=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclRkVdFnUhcsK9gHtUDLpbRuayYxJplCGfocbF4q49WPc+Tdm2llo64HA4Zx7uScniAXXxnW/nZXVtfWNzcJWcXtnd2+/dHDY0FGiGNZZJCLVCqhGwSXWDTcCW7FCGgYCm8HoNvObY1SaR/LRTGL0QzqQvM8ZNVbyOyE1Q0ZFejftXnRLZbfizkCWiZeTMuSodUtfnV7EkhClYYJq3fbc2PgpVYYzgdNiJ9EYUzaiA2xbKmmI2k9noafk1Co90o+UfdKQmfp7I6Wh1pMwsJNZSL3oZeJ/Xjsx/Ws/5TJODEo2P9RPBDERyRogPa6QGTGxhDLFbVbChlRRZmxPRVuCt/jlZdI4r3huxXu4LFdv8joKcAwncAYeXEEV7qEGdWDwBM/wCm/O2Hlx3p2P+eiKk+8cwR84nz+laZIA</latexit><latexit sha1_base64="62hRsAjW7tKVI0FX4k//oGPjLlY=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclRkVdFnUhcsK9gHtUDLpbRuayYxJplCGfocbF4q49WPc+Tdm2llo64HA4Zx7uScniAXXxnW/nZXVtfWNzcJWcXtnd2+/dHDY0FGiGNZZJCLVCqhGwSXWDTcCW7FCGgYCm8HoNvObY1SaR/LRTGL0QzqQvM8ZNVbyOyE1Q0ZFejftXnRLZbfizkCWiZeTMuSodUtfnV7EkhClYYJq3fbc2PgpVYYzgdNiJ9EYUzaiA2xbKmmI2k9noafk1Co90o+UfdKQmfp7I6Wh1pMwsJNZSL3oZeJ/Xjsx/Ws/5TJODEo2P9RPBDERyRogPa6QGTGxhDLFbVbChlRRZmxPRVuCt/jlZdI4r3huxXu4LFdv8joKcAwncAYeXEEV7qEGdWDwBM/wCm/O2Hlx3p2P+eiKk+8cwR84nz+laZIA</latexit><latexit sha1_base64="62hRsAjW7tKVI0FX4k//oGPjLlY=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclRkVdFnUhcsK9gHtUDLpbRuayYxJplCGfocbF4q49WPc+Tdm2llo64HA4Zx7uScniAXXxnW/nZXVtfWNzcJWcXtnd2+/dHDY0FGiGNZZJCLVCqhGwSXWDTcCW7FCGgYCm8HoNvObY1SaR/LRTGL0QzqQvM8ZNVbyOyE1Q0ZFejftXnRLZbfizkCWiZeTMuSodUtfnV7EkhClYYJq3fbc2PgpVYYzgdNiJ9EYUzaiA2xbKmmI2k9noafk1Co90o+UfdKQmfp7I6Wh1pMwsJNZSL3oZeJ/Xjsx/Ws/5TJODEo2P9RPBDERyRogPa6QGTGxhDLFbVbChlRRZmxPRVuCt/jlZdI4r3huxXu4LFdv8joKcAwncAYeXEEV7qEGdWDwBM/wCm/O2Hlx3p2P+eiKk+8cwR84nz+laZIA</latexit>

!12

Forgetting

Page 56: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania

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T1 = {y1, y2}<latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit><latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit><latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit><latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit>

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✓2<latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit><latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit><latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit><latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit>

T2 = {y3, y4}<latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit><latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit><latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit><latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit>

D2<latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit><latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit><latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit><latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit>

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D3<latexit sha1_base64="62hRsAjW7tKVI0FX4k//oGPjLlY=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclRkVdFnUhcsK9gHtUDLpbRuayYxJplCGfocbF4q49WPc+Tdm2llo64HA4Zx7uScniAXXxnW/nZXVtfWNzcJWcXtnd2+/dHDY0FGiGNZZJCLVCqhGwSXWDTcCW7FCGgYCm8HoNvObY1SaR/LRTGL0QzqQvM8ZNVbyOyE1Q0ZFejftXnRLZbfizkCWiZeTMuSodUtfnV7EkhClYYJq3fbc2PgpVYYzgdNiJ9EYUzaiA2xbKmmI2k9noafk1Co90o+UfdKQmfp7I6Wh1pMwsJNZSL3oZeJ/Xjsx/Ws/5TJODEo2P9RPBDERyRogPa6QGTGxhDLFbVbChlRRZmxPRVuCt/jlZdI4r3huxXu4LFdv8joKcAwncAYeXEEV7qEGdWDwBM/wCm/O2Hlx3p2P+eiKk+8cwR84nz+laZIA</latexit><latexit sha1_base64="62hRsAjW7tKVI0FX4k//oGPjLlY=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclRkVdFnUhcsK9gHtUDLpbRuayYxJplCGfocbF4q49WPc+Tdm2llo64HA4Zx7uScniAXXxnW/nZXVtfWNzcJWcXtnd2+/dHDY0FGiGNZZJCLVCqhGwSXWDTcCW7FCGgYCm8HoNvObY1SaR/LRTGL0QzqQvM8ZNVbyOyE1Q0ZFejftXnRLZbfizkCWiZeTMuSodUtfnV7EkhClYYJq3fbc2PgpVYYzgdNiJ9EYUzaiA2xbKmmI2k9noafk1Co90o+UfdKQmfp7I6Wh1pMwsJNZSL3oZeJ/Xjsx/Ws/5TJODEo2P9RPBDERyRogPa6QGTGxhDLFbVbChlRRZmxPRVuCt/jlZdI4r3huxXu4LFdv8joKcAwncAYeXEEV7qEGdWDwBM/wCm/O2Hlx3p2P+eiKk+8cwR84nz+laZIA</latexit><latexit sha1_base64="62hRsAjW7tKVI0FX4k//oGPjLlY=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclRkVdFnUhcsK9gHtUDLpbRuayYxJplCGfocbF4q49WPc+Tdm2llo64HA4Zx7uScniAXXxnW/nZXVtfWNzcJWcXtnd2+/dHDY0FGiGNZZJCLVCqhGwSXWDTcCW7FCGgYCm8HoNvObY1SaR/LRTGL0QzqQvM8ZNVbyOyE1Q0ZFejftXnRLZbfizkCWiZeTMuSodUtfnV7EkhClYYJq3fbc2PgpVYYzgdNiJ9EYUzaiA2xbKmmI2k9noafk1Co90o+UfdKQmfp7I6Wh1pMwsJNZSL3oZeJ/Xjsx/Ws/5TJODEo2P9RPBDERyRogPa6QGTGxhDLFbVbChlRRZmxPRVuCt/jlZdI4r3huxXu4LFdv8joKcAwncAYeXEEV7qEGdWDwBM/wCm/O2Hlx3p2P+eiKk+8cwR84nz+laZIA</latexit><latexit sha1_base64="62hRsAjW7tKVI0FX4k//oGPjLlY=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclRkVdFnUhcsK9gHtUDLpbRuayYxJplCGfocbF4q49WPc+Tdm2llo64HA4Zx7uScniAXXxnW/nZXVtfWNzcJWcXtnd2+/dHDY0FGiGNZZJCLVCqhGwSXWDTcCW7FCGgYCm8HoNvObY1SaR/LRTGL0QzqQvM8ZNVbyOyE1Q0ZFejftXnRLZbfizkCWiZeTMuSodUtfnV7EkhClYYJq3fbc2PgpVYYzgdNiJ9EYUzaiA2xbKmmI2k9noafk1Co90o+UfdKQmfp7I6Wh1pMwsJNZSL3oZeJ/Xjsx/Ws/5TJODEo2P9RPBDERyRogPa6QGTGxhDLFbVbChlRRZmxPRVuCt/jlZdI4r3huxXu4LFdv8joKcAwncAYeXEEV7qEGdWDwBM/wCm/O2Hlx3p2P+eiKk+8cwR84nz+laZIA</latexit>

f31 =

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!12

Forgetting

Page 57: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania

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T1 = {y1, y2}<latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit><latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit><latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit><latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit>

D1<latexit sha1_base64="q69qAC9QCbzeFL5i4zpxpEWkU9k=">AAAB9HicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMuiLlxWsA9oh3InTdvQTGZMMoUy9DvcuFDErR/jzr8x085CWw8EDufcyz05QSy4Nq777RTW1jc2t4rbpZ3dvf2D8uFRU0eJoqxBIxGpdoCaCS5Zw3AjWDtWDMNAsFYwvs381oQpzSP5aKYx80McSj7gFI2V/G6IZkRRpHezntcrV9yqOwdZJV5OKpCj3it/dfsRTUImDRWodcdzY+OnqAyngs1K3USzGOkYh6xjqcSQaT+dh56RM6v0ySBS9klD5urvjRRDradhYCezkHrZy8T/vE5iBtd+ymWcGCbp4tAgEcREJGuA9Lli1IipJUgVt1kJHaFCamxPJVuCt/zlVdK8qHpu1Xu4rNRu8jqKcAKncA4eXEEN7qEODaDwBM/wCm/OxHlx3p2PxWjByXeO4Q+czx+iYZH+</latexit><latexit sha1_base64="q69qAC9QCbzeFL5i4zpxpEWkU9k=">AAAB9HicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMuiLlxWsA9oh3InTdvQTGZMMoUy9DvcuFDErR/jzr8x085CWw8EDufcyz05QSy4Nq777RTW1jc2t4rbpZ3dvf2D8uFRU0eJoqxBIxGpdoCaCS5Zw3AjWDtWDMNAsFYwvs381oQpzSP5aKYx80McSj7gFI2V/G6IZkRRpHezntcrV9yqOwdZJV5OKpCj3it/dfsRTUImDRWodcdzY+OnqAyngs1K3USzGOkYh6xjqcSQaT+dh56RM6v0ySBS9klD5urvjRRDradhYCezkHrZy8T/vE5iBtd+ymWcGCbp4tAgEcREJGuA9Lli1IipJUgVt1kJHaFCamxPJVuCt/zlVdK8qHpu1Xu4rNRu8jqKcAKncA4eXEEN7qEODaDwBM/wCm/OxHlx3p2PxWjByXeO4Q+czx+iYZH+</latexit><latexit sha1_base64="q69qAC9QCbzeFL5i4zpxpEWkU9k=">AAAB9HicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMuiLlxWsA9oh3InTdvQTGZMMoUy9DvcuFDErR/jzr8x085CWw8EDufcyz05QSy4Nq777RTW1jc2t4rbpZ3dvf2D8uFRU0eJoqxBIxGpdoCaCS5Zw3AjWDtWDMNAsFYwvs381oQpzSP5aKYx80McSj7gFI2V/G6IZkRRpHezntcrV9yqOwdZJV5OKpCj3it/dfsRTUImDRWodcdzY+OnqAyngs1K3USzGOkYh6xjqcSQaT+dh56RM6v0ySBS9klD5urvjRRDradhYCezkHrZy8T/vE5iBtd+ymWcGCbp4tAgEcREJGuA9Lli1IipJUgVt1kJHaFCamxPJVuCt/zlVdK8qHpu1Xu4rNRu8jqKcAKncA4eXEEN7qEODaDwBM/wCm/OxHlx3p2PxWjByXeO4Q+czx+iYZH+</latexit><latexit sha1_base64="q69qAC9QCbzeFL5i4zpxpEWkU9k=">AAAB9HicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMuiLlxWsA9oh3InTdvQTGZMMoUy9DvcuFDErR/jzr8x085CWw8EDufcyz05QSy4Nq777RTW1jc2t4rbpZ3dvf2D8uFRU0eJoqxBIxGpdoCaCS5Zw3AjWDtWDMNAsFYwvs381oQpzSP5aKYx80McSj7gFI2V/G6IZkRRpHezntcrV9yqOwdZJV5OKpCj3it/dfsRTUImDRWodcdzY+OnqAyngs1K3USzGOkYh6xjqcSQaT+dh56RM6v0ySBS9klD5urvjRRDradhYCezkHrZy8T/vE5iBtd+ymWcGCbp4tAgEcREJGuA9Lli1IipJUgVt1kJHaFCamxPJVuCt/zlVdK8qHpu1Xu4rNRu8jqKcAKncA4eXEEN7qEODaDwBM/wCm/OxHlx3p2PxWjByXeO4Q+czx+iYZH+</latexit>

✓2<latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit><latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit><latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit><latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit>

T2 = {y3, y4}<latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit><latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit><latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit><latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit>

D2<latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit><latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit><latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit><latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit>

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f31 =

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!12

Forgetting

Page 58: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania

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T1 = {y1, y2}<latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit><latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit><latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit><latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit>

D1<latexit sha1_base64="q69qAC9QCbzeFL5i4zpxpEWkU9k=">AAAB9HicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMuiLlxWsA9oh3InTdvQTGZMMoUy9DvcuFDErR/jzr8x085CWw8EDufcyz05QSy4Nq777RTW1jc2t4rbpZ3dvf2D8uFRU0eJoqxBIxGpdoCaCS5Zw3AjWDtWDMNAsFYwvs381oQpzSP5aKYx80McSj7gFI2V/G6IZkRRpHezntcrV9yqOwdZJV5OKpCj3it/dfsRTUImDRWodcdzY+OnqAyngs1K3USzGOkYh6xjqcSQaT+dh56RM6v0ySBS9klD5urvjRRDradhYCezkHrZy8T/vE5iBtd+ymWcGCbp4tAgEcREJGuA9Lli1IipJUgVt1kJHaFCamxPJVuCt/zlVdK8qHpu1Xu4rNRu8jqKcAKncA4eXEEN7qEODaDwBM/wCm/OxHlx3p2PxWjByXeO4Q+czx+iYZH+</latexit><latexit sha1_base64="q69qAC9QCbzeFL5i4zpxpEWkU9k=">AAAB9HicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMuiLlxWsA9oh3InTdvQTGZMMoUy9DvcuFDErR/jzr8x085CWw8EDufcyz05QSy4Nq777RTW1jc2t4rbpZ3dvf2D8uFRU0eJoqxBIxGpdoCaCS5Zw3AjWDtWDMNAsFYwvs381oQpzSP5aKYx80McSj7gFI2V/G6IZkRRpHezntcrV9yqOwdZJV5OKpCj3it/dfsRTUImDRWodcdzY+OnqAyngs1K3USzGOkYh6xjqcSQaT+dh56RM6v0ySBS9klD5urvjRRDradhYCezkHrZy8T/vE5iBtd+ymWcGCbp4tAgEcREJGuA9Lli1IipJUgVt1kJHaFCamxPJVuCt/zlVdK8qHpu1Xu4rNRu8jqKcAKncA4eXEEN7qEODaDwBM/wCm/OxHlx3p2PxWjByXeO4Q+czx+iYZH+</latexit><latexit sha1_base64="q69qAC9QCbzeFL5i4zpxpEWkU9k=">AAAB9HicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMuiLlxWsA9oh3InTdvQTGZMMoUy9DvcuFDErR/jzr8x085CWw8EDufcyz05QSy4Nq777RTW1jc2t4rbpZ3dvf2D8uFRU0eJoqxBIxGpdoCaCS5Zw3AjWDtWDMNAsFYwvs381oQpzSP5aKYx80McSj7gFI2V/G6IZkRRpHezntcrV9yqOwdZJV5OKpCj3it/dfsRTUImDRWodcdzY+OnqAyngs1K3USzGOkYh6xjqcSQaT+dh56RM6v0ySBS9klD5urvjRRDradhYCezkHrZy8T/vE5iBtd+ymWcGCbp4tAgEcREJGuA9Lli1IipJUgVt1kJHaFCamxPJVuCt/zlVdK8qHpu1Xu4rNRu8jqKcAKncA4eXEEN7qEODaDwBM/wCm/OxHlx3p2PxWjByXeO4Q+czx+iYZH+</latexit><latexit sha1_base64="q69qAC9QCbzeFL5i4zpxpEWkU9k=">AAAB9HicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMuiLlxWsA9oh3InTdvQTGZMMoUy9DvcuFDErR/jzr8x085CWw8EDufcyz05QSy4Nq777RTW1jc2t4rbpZ3dvf2D8uFRU0eJoqxBIxGpdoCaCS5Zw3AjWDtWDMNAsFYwvs381oQpzSP5aKYx80McSj7gFI2V/G6IZkRRpHezntcrV9yqOwdZJV5OKpCj3it/dfsRTUImDRWodcdzY+OnqAyngs1K3USzGOkYh6xjqcSQaT+dh56RM6v0ySBS9klD5urvjRRDradhYCezkHrZy8T/vE5iBtd+ymWcGCbp4tAgEcREJGuA9Lli1IipJUgVt1kJHaFCamxPJVuCt/zlVdK8qHpu1Xu4rNRu8jqKcAKncA4eXEEN7qEODaDwBM/wCm/OxHlx3p2PxWjByXeO4Q+czx+iYZH+</latexit>

✓2<latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit><latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit><latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit><latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit>

T2 = {y3, y4}<latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit><latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit><latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit><latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit>

D2<latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit><latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit><latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit><latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit>

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a11<latexit sha1_base64="45NZwI5lMdpP6iyoZ+EoOIHA+ZY=">AAAB7HicbVBNSwMxEJ2tX7V+VT16CRbBU9mIoMeiF48V3LbQriWbZtvQbLIkWaEs/Q1ePCji1R/kzX9j2u5BWx8MPN6bYWZelApurO9/e6W19Y3NrfJ2ZWd3b/+genjUMirTlAVUCaU7ETFMcMkCy61gnVQzkkSCtaPx7cxvPzFtuJIPdpKyMCFDyWNOiXVSQPr4EferNb/uz4FWCS5IDQo0+9Wv3kDRLGHSUkGM6WI/tWFOtOVUsGmllxmWEjomQ9Z1VJKEmTCfHztFZ04ZoFhpV9Kiufp7IieJMZMkcp0JsSOz7M3E/7xuZuPrMOcyzSyTdLEozgSyCs0+RwOuGbVi4gihmrtbER0RTah1+VRcCHj55VXSuqhjv47vL2uNmyKOMpzAKZwDhitowB00IQAKHJ7hFd486b14797HorXkFTPH8Afe5w8Ng44s</latexit><latexit sha1_base64="45NZwI5lMdpP6iyoZ+EoOIHA+ZY=">AAAB7HicbVBNSwMxEJ2tX7V+VT16CRbBU9mIoMeiF48V3LbQriWbZtvQbLIkWaEs/Q1ePCji1R/kzX9j2u5BWx8MPN6bYWZelApurO9/e6W19Y3NrfJ2ZWd3b/+genjUMirTlAVUCaU7ETFMcMkCy61gnVQzkkSCtaPx7cxvPzFtuJIPdpKyMCFDyWNOiXVSQPr4EferNb/uz4FWCS5IDQo0+9Wv3kDRLGHSUkGM6WI/tWFOtOVUsGmllxmWEjomQ9Z1VJKEmTCfHztFZ04ZoFhpV9Kiufp7IieJMZMkcp0JsSOz7M3E/7xuZuPrMOcyzSyTdLEozgSyCs0+RwOuGbVi4gihmrtbER0RTah1+VRcCHj55VXSuqhjv47vL2uNmyKOMpzAKZwDhitowB00IQAKHJ7hFd486b14797HorXkFTPH8Afe5w8Ng44s</latexit><latexit sha1_base64="45NZwI5lMdpP6iyoZ+EoOIHA+ZY=">AAAB7HicbVBNSwMxEJ2tX7V+VT16CRbBU9mIoMeiF48V3LbQriWbZtvQbLIkWaEs/Q1ePCji1R/kzX9j2u5BWx8MPN6bYWZelApurO9/e6W19Y3NrfJ2ZWd3b/+genjUMirTlAVUCaU7ETFMcMkCy61gnVQzkkSCtaPx7cxvPzFtuJIPdpKyMCFDyWNOiXVSQPr4EferNb/uz4FWCS5IDQo0+9Wv3kDRLGHSUkGM6WI/tWFOtOVUsGmllxmWEjomQ9Z1VJKEmTCfHztFZ04ZoFhpV9Kiufp7IieJMZMkcp0JsSOz7M3E/7xuZuPrMOcyzSyTdLEozgSyCs0+RwOuGbVi4gihmrtbER0RTah1+VRcCHj55VXSuqhjv47vL2uNmyKOMpzAKZwDhitowB00IQAKHJ7hFd486b14797HorXkFTPH8Afe5w8Ng44s</latexit><latexit sha1_base64="45NZwI5lMdpP6iyoZ+EoOIHA+ZY=">AAAB7HicbVBNSwMxEJ2tX7V+VT16CRbBU9mIoMeiF48V3LbQriWbZtvQbLIkWaEs/Q1ePCji1R/kzX9j2u5BWx8MPN6bYWZelApurO9/e6W19Y3NrfJ2ZWd3b/+genjUMirTlAVUCaU7ETFMcMkCy61gnVQzkkSCtaPx7cxvPzFtuJIPdpKyMCFDyWNOiXVSQPr4EferNb/uz4FWCS5IDQo0+9Wv3kDRLGHSUkGM6WI/tWFOtOVUsGmllxmWEjomQ9Z1VJKEmTCfHztFZ04ZoFhpV9Kiufp7IieJMZMkcp0JsSOz7M3E/7xuZuPrMOcyzSyTdLEozgSyCs0+RwOuGbVi4gihmrtbER0RTah1+VRcCHj55VXSuqhjv47vL2uNmyKOMpzAKZwDhitowB00IQAKHJ7hFd486b14797HorXkFTPH8Afe5w8Ng44s</latexit>

max(a11, a21)� a31

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f31 =

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!12

Forgetting

Page 59: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania

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D2<latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit><latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit><latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit><latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit>

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a11<latexit sha1_base64="45NZwI5lMdpP6iyoZ+EoOIHA+ZY=">AAAB7HicbVBNSwMxEJ2tX7V+VT16CRbBU9mIoMeiF48V3LbQriWbZtvQbLIkWaEs/Q1ePCji1R/kzX9j2u5BWx8MPN6bYWZelApurO9/e6W19Y3NrfJ2ZWd3b/+genjUMirTlAVUCaU7ETFMcMkCy61gnVQzkkSCtaPx7cxvPzFtuJIPdpKyMCFDyWNOiXVSQPr4EferNb/uz4FWCS5IDQo0+9Wv3kDRLGHSUkGM6WI/tWFOtOVUsGmllxmWEjomQ9Z1VJKEmTCfHztFZ04ZoFhpV9Kiufp7IieJMZMkcp0JsSOz7M3E/7xuZuPrMOcyzSyTdLEozgSyCs0+RwOuGbVi4gihmrtbER0RTah1+VRcCHj55VXSuqhjv47vL2uNmyKOMpzAKZwDhitowB00IQAKHJ7hFd486b14797HorXkFTPH8Afe5w8Ng44s</latexit><latexit sha1_base64="45NZwI5lMdpP6iyoZ+EoOIHA+ZY=">AAAB7HicbVBNSwMxEJ2tX7V+VT16CRbBU9mIoMeiF48V3LbQriWbZtvQbLIkWaEs/Q1ePCji1R/kzX9j2u5BWx8MPN6bYWZelApurO9/e6W19Y3NrfJ2ZWd3b/+genjUMirTlAVUCaU7ETFMcMkCy61gnVQzkkSCtaPx7cxvPzFtuJIPdpKyMCFDyWNOiXVSQPr4EferNb/uz4FWCS5IDQo0+9Wv3kDRLGHSUkGM6WI/tWFOtOVUsGmllxmWEjomQ9Z1VJKEmTCfHztFZ04ZoFhpV9Kiufp7IieJMZMkcp0JsSOz7M3E/7xuZuPrMOcyzSyTdLEozgSyCs0+RwOuGbVi4gihmrtbER0RTah1+VRcCHj55VXSuqhjv47vL2uNmyKOMpzAKZwDhitowB00IQAKHJ7hFd486b14797HorXkFTPH8Afe5w8Ng44s</latexit><latexit sha1_base64="45NZwI5lMdpP6iyoZ+EoOIHA+ZY=">AAAB7HicbVBNSwMxEJ2tX7V+VT16CRbBU9mIoMeiF48V3LbQriWbZtvQbLIkWaEs/Q1ePCji1R/kzX9j2u5BWx8MPN6bYWZelApurO9/e6W19Y3NrfJ2ZWd3b/+genjUMirTlAVUCaU7ETFMcMkCy61gnVQzkkSCtaPx7cxvPzFtuJIPdpKyMCFDyWNOiXVSQPr4EferNb/uz4FWCS5IDQo0+9Wv3kDRLGHSUkGM6WI/tWFOtOVUsGmllxmWEjomQ9Z1VJKEmTCfHztFZ04ZoFhpV9Kiufp7IieJMZMkcp0JsSOz7M3E/7xuZuPrMOcyzSyTdLEozgSyCs0+RwOuGbVi4gihmrtbER0RTah1+VRcCHj55VXSuqhjv47vL2uNmyKOMpzAKZwDhitowB00IQAKHJ7hFd486b14797HorXkFTPH8Afe5w8Ng44s</latexit><latexit sha1_base64="45NZwI5lMdpP6iyoZ+EoOIHA+ZY=">AAAB7HicbVBNSwMxEJ2tX7V+VT16CRbBU9mIoMeiF48V3LbQriWbZtvQbLIkWaEs/Q1ePCji1R/kzX9j2u5BWx8MPN6bYWZelApurO9/e6W19Y3NrfJ2ZWd3b/+genjUMirTlAVUCaU7ETFMcMkCy61gnVQzkkSCtaPx7cxvPzFtuJIPdpKyMCFDyWNOiXVSQPr4EferNb/uz4FWCS5IDQo0+9Wv3kDRLGHSUkGM6WI/tWFOtOVUsGmllxmWEjomQ9Z1VJKEmTCfHztFZ04ZoFhpV9Kiufp7IieJMZMkcp0JsSOz7M3E/7xuZuPrMOcyzSyTdLEozgSyCs0+RwOuGbVi4gihmrtbER0RTah1+VRcCHj55VXSuqhjv47vL2uNmyKOMpzAKZwDhitowB00IQAKHJ7hFd486b14797HorXkFTPH8Afe5w8Ng44s</latexit>

max(a11, a21)� a31

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f31 =

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!12

Forgetting

PBT (f31 < 0)

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• PBT (Positive Backward Transfer): Learning task k helped improve knowledge about previous task j (j<k)

Page 60: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania

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max(a11, a21)� a31

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f31 =

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!12

Forgetting

PBT (f31 < 0)

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• PBT (Positive Backward Transfer): Learning task k helped improve knowledge about previous task j (j<k)

NBT (f31 > 0)

<latexit sha1_base64="jFWpVzbNETbkbtSe3vhGmcfesAA=">AAACCXicbVC7SgNBFJ2NrxhfUUubwSDEJuyqoJWE2FhJhLwgiWF2cjcZMvtg5q4YlrQ2/oqNhSK2/oGdf+PkUWjigQuHc+6dufe4kRQabfvbSi0tr6yupdczG5tb2zvZ3b2aDmPFocpDGaqGyzRIEUAVBUpoRAqY70qou4OrsV+/B6VFGFRwGEHbZ71AeIIzNFInS1sIDzh5J1HQHSU3pQrNex3n7pReUvt41Mnm7II9AV0kzozkyAzlTvar1Q157EOAXDKtm44dYTthCgWXMMq0Yg0R4wPWg6ahAfNBt5PJBiN6ZJQu9UJlKkA6UX9PJMzXeui7ptNn2Nfz3lj8z2vG6F20ExFEMULApx95saQY0nEstCsUcJRDQxhXwuxKeZ8pxtGElzEhOPMnL5LaScGxC87tWa5YmsWRJgfkkOSJQ85JkVyTMqkSTh7JM3klb9aT9WK9Wx/T1pQ1m9knf2B9/gCCmZjg</latexit><latexit sha1_base64="jFWpVzbNETbkbtSe3vhGmcfesAA=">AAACCXicbVC7SgNBFJ2NrxhfUUubwSDEJuyqoJWE2FhJhLwgiWF2cjcZMvtg5q4YlrQ2/oqNhSK2/oGdf+PkUWjigQuHc+6dufe4kRQabfvbSi0tr6yupdczG5tb2zvZ3b2aDmPFocpDGaqGyzRIEUAVBUpoRAqY70qou4OrsV+/B6VFGFRwGEHbZ71AeIIzNFInS1sIDzh5J1HQHSU3pQrNex3n7pReUvt41Mnm7II9AV0kzozkyAzlTvar1Q157EOAXDKtm44dYTthCgWXMMq0Yg0R4wPWg6ahAfNBt5PJBiN6ZJQu9UJlKkA6UX9PJMzXeui7ptNn2Nfz3lj8z2vG6F20ExFEMULApx95saQY0nEstCsUcJRDQxhXwuxKeZ8pxtGElzEhOPMnL5LaScGxC87tWa5YmsWRJgfkkOSJQ85JkVyTMqkSTh7JM3klb9aT9WK9Wx/T1pQ1m9knf2B9/gCCmZjg</latexit><latexit sha1_base64="jFWpVzbNETbkbtSe3vhGmcfesAA=">AAACCXicbVC7SgNBFJ2NrxhfUUubwSDEJuyqoJWE2FhJhLwgiWF2cjcZMvtg5q4YlrQ2/oqNhSK2/oGdf+PkUWjigQuHc+6dufe4kRQabfvbSi0tr6yupdczG5tb2zvZ3b2aDmPFocpDGaqGyzRIEUAVBUpoRAqY70qou4OrsV+/B6VFGFRwGEHbZ71AeIIzNFInS1sIDzh5J1HQHSU3pQrNex3n7pReUvt41Mnm7II9AV0kzozkyAzlTvar1Q157EOAXDKtm44dYTthCgWXMMq0Yg0R4wPWg6ahAfNBt5PJBiN6ZJQu9UJlKkA6UX9PJMzXeui7ptNn2Nfz3lj8z2vG6F20ExFEMULApx95saQY0nEstCsUcJRDQxhXwuxKeZ8pxtGElzEhOPMnL5LaScGxC87tWa5YmsWRJgfkkOSJQ85JkVyTMqkSTh7JM3klb9aT9WK9Wx/T1pQ1m9knf2B9/gCCmZjg</latexit><latexit sha1_base64="jFWpVzbNETbkbtSe3vhGmcfesAA=">AAACCXicbVC7SgNBFJ2NrxhfUUubwSDEJuyqoJWE2FhJhLwgiWF2cjcZMvtg5q4YlrQ2/oqNhSK2/oGdf+PkUWjigQuHc+6dufe4kRQabfvbSi0tr6yupdczG5tb2zvZ3b2aDmPFocpDGaqGyzRIEUAVBUpoRAqY70qou4OrsV+/B6VFGFRwGEHbZ71AeIIzNFInS1sIDzh5J1HQHSU3pQrNex3n7pReUvt41Mnm7II9AV0kzozkyAzlTvar1Q157EOAXDKtm44dYTthCgWXMMq0Yg0R4wPWg6ahAfNBt5PJBiN6ZJQu9UJlKkA6UX9PJMzXeui7ptNn2Nfz3lj8z2vG6F20ExFEMULApx95saQY0nEstCsUcJRDQxhXwuxKeZ8pxtGElzEhOPMnL5LaScGxC87tWa5YmsWRJgfkkOSJQ85JkVyTMqkSTh7JM3klb9aT9WK9Wx/T1pQ1m9knf2B9/gCCmZjg</latexit>

• NBT (Negative Backward Transfer): Learning task k forced the model to forget some information about previous task j (j<k)

Page 61: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !13

Intransigence (Inability to learn)

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Puneet Dokania

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T1 = {y1, y2}<latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit><latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit><latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit><latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit>

D1<latexit sha1_base64="q69qAC9QCbzeFL5i4zpxpEWkU9k=">AAAB9HicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMuiLlxWsA9oh3InTdvQTGZMMoUy9DvcuFDErR/jzr8x085CWw8EDufcyz05QSy4Nq777RTW1jc2t4rbpZ3dvf2D8uFRU0eJoqxBIxGpdoCaCS5Zw3AjWDtWDMNAsFYwvs381oQpzSP5aKYx80McSj7gFI2V/G6IZkRRpHezntcrV9yqOwdZJV5OKpCj3it/dfsRTUImDRWodcdzY+OnqAyngs1K3USzGOkYh6xjqcSQaT+dh56RM6v0ySBS9klD5urvjRRDradhYCezkHrZy8T/vE5iBtd+ymWcGCbp4tAgEcREJGuA9Lli1IipJUgVt1kJHaFCamxPJVuCt/zlVdK8qHpu1Xu4rNRu8jqKcAKncA4eXEEN7qEODaDwBM/wCm/OxHlx3p2PxWjByXeO4Q+czx+iYZH+</latexit><latexit sha1_base64="q69qAC9QCbzeFL5i4zpxpEWkU9k=">AAAB9HicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMuiLlxWsA9oh3InTdvQTGZMMoUy9DvcuFDErR/jzr8x085CWw8EDufcyz05QSy4Nq777RTW1jc2t4rbpZ3dvf2D8uFRU0eJoqxBIxGpdoCaCS5Zw3AjWDtWDMNAsFYwvs381oQpzSP5aKYx80McSj7gFI2V/G6IZkRRpHezntcrV9yqOwdZJV5OKpCj3it/dfsRTUImDRWodcdzY+OnqAyngs1K3USzGOkYh6xjqcSQaT+dh56RM6v0ySBS9klD5urvjRRDradhYCezkHrZy8T/vE5iBtd+ymWcGCbp4tAgEcREJGuA9Lli1IipJUgVt1kJHaFCamxPJVuCt/zlVdK8qHpu1Xu4rNRu8jqKcAKncA4eXEEN7qEODaDwBM/wCm/OxHlx3p2PxWjByXeO4Q+czx+iYZH+</latexit><latexit sha1_base64="q69qAC9QCbzeFL5i4zpxpEWkU9k=">AAAB9HicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMuiLlxWsA9oh3InTdvQTGZMMoUy9DvcuFDErR/jzr8x085CWw8EDufcyz05QSy4Nq777RTW1jc2t4rbpZ3dvf2D8uFRU0eJoqxBIxGpdoCaCS5Zw3AjWDtWDMNAsFYwvs381oQpzSP5aKYx80McSj7gFI2V/G6IZkRRpHezntcrV9yqOwdZJV5OKpCj3it/dfsRTUImDRWodcdzY+OnqAyngs1K3USzGOkYh6xjqcSQaT+dh56RM6v0ySBS9klD5urvjRRDradhYCezkHrZy8T/vE5iBtd+ymWcGCbp4tAgEcREJGuA9Lli1IipJUgVt1kJHaFCamxPJVuCt/zlVdK8qHpu1Xu4rNRu8jqKcAKncA4eXEEN7qEODaDwBM/wCm/OxHlx3p2PxWjByXeO4Q+czx+iYZH+</latexit><latexit sha1_base64="q69qAC9QCbzeFL5i4zpxpEWkU9k=">AAAB9HicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMuiLlxWsA9oh3InTdvQTGZMMoUy9DvcuFDErR/jzr8x085CWw8EDufcyz05QSy4Nq777RTW1jc2t4rbpZ3dvf2D8uFRU0eJoqxBIxGpdoCaCS5Zw3AjWDtWDMNAsFYwvs381oQpzSP5aKYx80McSj7gFI2V/G6IZkRRpHezntcrV9yqOwdZJV5OKpCj3it/dfsRTUImDRWodcdzY+OnqAyngs1K3USzGOkYh6xjqcSQaT+dh56RM6v0ySBS9klD5urvjRRDradhYCezkHrZy8T/vE5iBtd+ymWcGCbp4tAgEcREJGuA9Lli1IipJUgVt1kJHaFCamxPJVuCt/zlVdK8qHpu1Xu4rNRu8jqKcAKncA4eXEEN7qEODaDwBM/wCm/OxHlx3p2PxWjByXeO4Q+czx+iYZH+</latexit>

✓2<latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit><latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit><latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit><latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit>

T2 = {y3, y4}<latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit><latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit><latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit><latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit>

D2<latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit><latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit><latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit><latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit>

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T3 = {y5, y6}<latexit sha1_base64="LwxbD5bgl32pINRhEeIeNWmb/8I=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJL43ghFNy4r9AVNCJPptB06eTAzEUPIr7hxoYhbf8Sdf+O0zUJbD1w4nHMv997jx5xJZVnfxtLyyuraemmjvLm1vbNr7lXaMkoEoS0S8Uh0fSwpZyFtKaY47caC4sDntOOP7yZ+55EKyaKwqdKYugEehmzACFZa8sxK0ztDN8jJUu/iBKXepZN7ZtWqWVOgRWIXpAoFGp755fQjkgQ0VIRjKXu2FSs3w0IxwmledhJJY0zGeEh7moY4oNLNprfn6EgrfTSIhK5Qoan6eyLDgZRp4OvOAKuRnPcm4n9eL1GDazdjYZwoGpLZokHCkYrQJAjUZ4ISxVNNMBFM34rICAtMlI6rrEOw519eJO3Tmm3V7Ifzav22iKMEB3AIx2DDFdThHhrQAgJP8Ayv8GbkxovxbnzMWpeMYmYf/sD4/AGV5ZLZ</latexit><latexit sha1_base64="LwxbD5bgl32pINRhEeIeNWmb/8I=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJL43ghFNy4r9AVNCJPptB06eTAzEUPIr7hxoYhbf8Sdf+O0zUJbD1w4nHMv997jx5xJZVnfxtLyyuraemmjvLm1vbNr7lXaMkoEoS0S8Uh0fSwpZyFtKaY47caC4sDntOOP7yZ+55EKyaKwqdKYugEehmzACFZa8sxK0ztDN8jJUu/iBKXepZN7ZtWqWVOgRWIXpAoFGp755fQjkgQ0VIRjKXu2FSs3w0IxwmledhJJY0zGeEh7moY4oNLNprfn6EgrfTSIhK5Qoan6eyLDgZRp4OvOAKuRnPcm4n9eL1GDazdjYZwoGpLZokHCkYrQJAjUZ4ISxVNNMBFM34rICAtMlI6rrEOw519eJO3Tmm3V7Ifzav22iKMEB3AIx2DDFdThHhrQAgJP8Ayv8GbkxovxbnzMWpeMYmYf/sD4/AGV5ZLZ</latexit><latexit sha1_base64="LwxbD5bgl32pINRhEeIeNWmb/8I=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJL43ghFNy4r9AVNCJPptB06eTAzEUPIr7hxoYhbf8Sdf+O0zUJbD1w4nHMv997jx5xJZVnfxtLyyuraemmjvLm1vbNr7lXaMkoEoS0S8Uh0fSwpZyFtKaY47caC4sDntOOP7yZ+55EKyaKwqdKYugEehmzACFZa8sxK0ztDN8jJUu/iBKXepZN7ZtWqWVOgRWIXpAoFGp755fQjkgQ0VIRjKXu2FSs3w0IxwmledhJJY0zGeEh7moY4oNLNprfn6EgrfTSIhK5Qoan6eyLDgZRp4OvOAKuRnPcm4n9eL1GDazdjYZwoGpLZokHCkYrQJAjUZ4ISxVNNMBFM34rICAtMlI6rrEOw519eJO3Tmm3V7Ifzav22iKMEB3AIx2DDFdThHhrQAgJP8Ayv8GbkxovxbnzMWpeMYmYf/sD4/AGV5ZLZ</latexit><latexit sha1_base64="LwxbD5bgl32pINRhEeIeNWmb/8I=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJL43ghFNy4r9AVNCJPptB06eTAzEUPIr7hxoYhbf8Sdf+O0zUJbD1w4nHMv997jx5xJZVnfxtLyyuraemmjvLm1vbNr7lXaMkoEoS0S8Uh0fSwpZyFtKaY47caC4sDntOOP7yZ+55EKyaKwqdKYugEehmzACFZa8sxK0ztDN8jJUu/iBKXepZN7ZtWqWVOgRWIXpAoFGp755fQjkgQ0VIRjKXu2FSs3w0IxwmledhJJY0zGeEh7moY4oNLNprfn6EgrfTSIhK5Qoan6eyLDgZRp4OvOAKuRnPcm4n9eL1GDazdjYZwoGpLZokHCkYrQJAjUZ4ISxVNNMBFM34rICAtMlI6rrEOw519eJO3Tmm3V7Ifzav22iKMEB3AIx2DDFdThHhrQAgJP8Ayv8GbkxovxbnzMWpeMYmYf/sD4/AGV5ZLZ</latexit>

D3<latexit sha1_base64="62hRsAjW7tKVI0FX4k//oGPjLlY=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclRkVdFnUhcsK9gHtUDLpbRuayYxJplCGfocbF4q49WPc+Tdm2llo64HA4Zx7uScniAXXxnW/nZXVtfWNzcJWcXtnd2+/dHDY0FGiGNZZJCLVCqhGwSXWDTcCW7FCGgYCm8HoNvObY1SaR/LRTGL0QzqQvM8ZNVbyOyE1Q0ZFejftXnRLZbfizkCWiZeTMuSodUtfnV7EkhClYYJq3fbc2PgpVYYzgdNiJ9EYUzaiA2xbKmmI2k9noafk1Co90o+UfdKQmfp7I6Wh1pMwsJNZSL3oZeJ/Xjsx/Ws/5TJODEo2P9RPBDERyRogPa6QGTGxhDLFbVbChlRRZmxPRVuCt/jlZdI4r3huxXu4LFdv8joKcAwncAYeXEEV7qEGdWDwBM/wCm/O2Hlx3p2P+eiKk+8cwR84nz+laZIA</latexit><latexit sha1_base64="62hRsAjW7tKVI0FX4k//oGPjLlY=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclRkVdFnUhcsK9gHtUDLpbRuayYxJplCGfocbF4q49WPc+Tdm2llo64HA4Zx7uScniAXXxnW/nZXVtfWNzcJWcXtnd2+/dHDY0FGiGNZZJCLVCqhGwSXWDTcCW7FCGgYCm8HoNvObY1SaR/LRTGL0QzqQvM8ZNVbyOyE1Q0ZFejftXnRLZbfizkCWiZeTMuSodUtfnV7EkhClYYJq3fbc2PgpVYYzgdNiJ9EYUzaiA2xbKmmI2k9noafk1Co90o+UfdKQmfp7I6Wh1pMwsJNZSL3oZeJ/Xjsx/Ws/5TJODEo2P9RPBDERyRogPa6QGTGxhDLFbVbChlRRZmxPRVuCt/jlZdI4r3huxXu4LFdv8joKcAwncAYeXEEV7qEGdWDwBM/wCm/O2Hlx3p2P+eiKk+8cwR84nz+laZIA</latexit><latexit sha1_base64="62hRsAjW7tKVI0FX4k//oGPjLlY=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclRkVdFnUhcsK9gHtUDLpbRuayYxJplCGfocbF4q49WPc+Tdm2llo64HA4Zx7uScniAXXxnW/nZXVtfWNzcJWcXtnd2+/dHDY0FGiGNZZJCLVCqhGwSXWDTcCW7FCGgYCm8HoNvObY1SaR/LRTGL0QzqQvM8ZNVbyOyE1Q0ZFejftXnRLZbfizkCWiZeTMuSodUtfnV7EkhClYYJq3fbc2PgpVYYzgdNiJ9EYUzaiA2xbKmmI2k9noafk1Co90o+UfdKQmfp7I6Wh1pMwsJNZSL3oZeJ/Xjsx/Ws/5TJODEo2P9RPBDERyRogPa6QGTGxhDLFbVbChlRRZmxPRVuCt/jlZdI4r3huxXu4LFdv8joKcAwncAYeXEEV7qEGdWDwBM/wCm/O2Hlx3p2P+eiKk+8cwR84nz+laZIA</latexit><latexit sha1_base64="62hRsAjW7tKVI0FX4k//oGPjLlY=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclRkVdFnUhcsK9gHtUDLpbRuayYxJplCGfocbF4q49WPc+Tdm2llo64HA4Zx7uScniAXXxnW/nZXVtfWNzcJWcXtnd2+/dHDY0FGiGNZZJCLVCqhGwSXWDTcCW7FCGgYCm8HoNvObY1SaR/LRTGL0QzqQvM8ZNVbyOyE1Q0ZFejftXnRLZbfizkCWiZeTMuSodUtfnV7EkhClYYJq3fbc2PgpVYYzgdNiJ9EYUzaiA2xbKmmI2k9noafk1Co90o+UfdKQmfp7I6Wh1pMwsJNZSL3oZeJ/Xjsx/Ws/5TJODEo2P9RPBDERyRogPa6QGTGxhDLFbVbChlRRZmxPRVuCt/jlZdI4r3huxXu4LFdv8joKcAwncAYeXEEV7qEGdWDwBM/wCm/O2Hlx3p2P+eiKk+8cwR84nz+laZIA</latexit>

!13

Intransigence (Inability to learn)

Page 63: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania

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T1 = {y1, y2}<latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit><latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit><latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit><latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit>

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✓2<latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit><latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit><latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit><latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit>

T2 = {y3, y4}<latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit><latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit><latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit><latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit>

D2<latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit><latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit><latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit><latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit>

✓3<latexit sha1_base64="sEfrZCRNHJ1LHhcgS2bOY0dpI5M=">AAAB73icbVBNS8NAEJ3Ur1q/qh69BIvgqSQq6LHoxWMFWwttKJvtpF262cTdiVBK/4QXD4p49e9489+4bXPQ1gcDj/dmmJkXplIY8rxvp7Cyura+UdwsbW3v7O6V9w+aJsk0xwZPZKJbITMohcIGCZLYSjWyOJT4EA5vpv7DE2ojEnVPoxSDmPWViARnZKVWhwZIrHveLVe8qjeDu0z8nFQgR71b/ur0Ep7FqIhLZkzb91IKxkyT4BInpU5mMGV8yPrYtlSxGE0wnt07cU+s0nOjRNtS5M7U3xNjFhszikPbGTMamEVvKv7ntTOKroKxUGlGqPh8UZRJlxJ3+rzbExo5yZEljGthb3X5gGnGyUZUsiH4iy8vk+ZZ1feq/t1FpXadx1GEIziGU/DhEmpwC3VoAAcJz/AKb86j8+K8Ox/z1oKTzxzCHzifP9Bvj84=</latexit><latexit sha1_base64="sEfrZCRNHJ1LHhcgS2bOY0dpI5M=">AAAB73icbVBNS8NAEJ3Ur1q/qh69BIvgqSQq6LHoxWMFWwttKJvtpF262cTdiVBK/4QXD4p49e9489+4bXPQ1gcDj/dmmJkXplIY8rxvp7Cyura+UdwsbW3v7O6V9w+aJsk0xwZPZKJbITMohcIGCZLYSjWyOJT4EA5vpv7DE2ojEnVPoxSDmPWViARnZKVWhwZIrHveLVe8qjeDu0z8nFQgR71b/ur0Ep7FqIhLZkzb91IKxkyT4BInpU5mMGV8yPrYtlSxGE0wnt07cU+s0nOjRNtS5M7U3xNjFhszikPbGTMamEVvKv7ntTOKroKxUGlGqPh8UZRJlxJ3+rzbExo5yZEljGthb3X5gGnGyUZUsiH4iy8vk+ZZ1feq/t1FpXadx1GEIziGU/DhEmpwC3VoAAcJz/AKb86j8+K8Ox/z1oKTzxzCHzifP9Bvj84=</latexit><latexit sha1_base64="sEfrZCRNHJ1LHhcgS2bOY0dpI5M=">AAAB73icbVBNS8NAEJ3Ur1q/qh69BIvgqSQq6LHoxWMFWwttKJvtpF262cTdiVBK/4QXD4p49e9489+4bXPQ1gcDj/dmmJkXplIY8rxvp7Cyura+UdwsbW3v7O6V9w+aJsk0xwZPZKJbITMohcIGCZLYSjWyOJT4EA5vpv7DE2ojEnVPoxSDmPWViARnZKVWhwZIrHveLVe8qjeDu0z8nFQgR71b/ur0Ep7FqIhLZkzb91IKxkyT4BInpU5mMGV8yPrYtlSxGE0wnt07cU+s0nOjRNtS5M7U3xNjFhszikPbGTMamEVvKv7ntTOKroKxUGlGqPh8UZRJlxJ3+rzbExo5yZEljGthb3X5gGnGyUZUsiH4iy8vk+ZZ1feq/t1FpXadx1GEIziGU/DhEmpwC3VoAAcJz/AKb86j8+K8Ox/z1oKTzxzCHzifP9Bvj84=</latexit><latexit sha1_base64="sEfrZCRNHJ1LHhcgS2bOY0dpI5M=">AAAB73icbVBNS8NAEJ3Ur1q/qh69BIvgqSQq6LHoxWMFWwttKJvtpF262cTdiVBK/4QXD4p49e9489+4bXPQ1gcDj/dmmJkXplIY8rxvp7Cyura+UdwsbW3v7O6V9w+aJsk0xwZPZKJbITMohcIGCZLYSjWyOJT4EA5vpv7DE2ojEnVPoxSDmPWViARnZKVWhwZIrHveLVe8qjeDu0z8nFQgR71b/ur0Ep7FqIhLZkzb91IKxkyT4BInpU5mMGV8yPrYtlSxGE0wnt07cU+s0nOjRNtS5M7U3xNjFhszikPbGTMamEVvKv7ntTOKroKxUGlGqPh8UZRJlxJ3+rzbExo5yZEljGthb3X5gGnGyUZUsiH4iy8vk+ZZ1feq/t1FpXadx1GEIziGU/DhEmpwC3VoAAcJz/AKb86j8+K8Ox/z1oKTzxzCHzifP9Bvj84=</latexit>

T3 = {y5, y6}<latexit sha1_base64="LwxbD5bgl32pINRhEeIeNWmb/8I=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJL43ghFNy4r9AVNCJPptB06eTAzEUPIr7hxoYhbf8Sdf+O0zUJbD1w4nHMv997jx5xJZVnfxtLyyuraemmjvLm1vbNr7lXaMkoEoS0S8Uh0fSwpZyFtKaY47caC4sDntOOP7yZ+55EKyaKwqdKYugEehmzACFZa8sxK0ztDN8jJUu/iBKXepZN7ZtWqWVOgRWIXpAoFGp755fQjkgQ0VIRjKXu2FSs3w0IxwmledhJJY0zGeEh7moY4oNLNprfn6EgrfTSIhK5Qoan6eyLDgZRp4OvOAKuRnPcm4n9eL1GDazdjYZwoGpLZokHCkYrQJAjUZ4ISxVNNMBFM34rICAtMlI6rrEOw519eJO3Tmm3V7Ifzav22iKMEB3AIx2DDFdThHhrQAgJP8Ayv8GbkxovxbnzMWpeMYmYf/sD4/AGV5ZLZ</latexit><latexit sha1_base64="LwxbD5bgl32pINRhEeIeNWmb/8I=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJL43ghFNy4r9AVNCJPptB06eTAzEUPIr7hxoYhbf8Sdf+O0zUJbD1w4nHMv997jx5xJZVnfxtLyyuraemmjvLm1vbNr7lXaMkoEoS0S8Uh0fSwpZyFtKaY47caC4sDntOOP7yZ+55EKyaKwqdKYugEehmzACFZa8sxK0ztDN8jJUu/iBKXepZN7ZtWqWVOgRWIXpAoFGp755fQjkgQ0VIRjKXu2FSs3w0IxwmledhJJY0zGeEh7moY4oNLNprfn6EgrfTSIhK5Qoan6eyLDgZRp4OvOAKuRnPcm4n9eL1GDazdjYZwoGpLZokHCkYrQJAjUZ4ISxVNNMBFM34rICAtMlI6rrEOw519eJO3Tmm3V7Ifzav22iKMEB3AIx2DDFdThHhrQAgJP8Ayv8GbkxovxbnzMWpeMYmYf/sD4/AGV5ZLZ</latexit><latexit sha1_base64="LwxbD5bgl32pINRhEeIeNWmb/8I=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJL43ghFNy4r9AVNCJPptB06eTAzEUPIr7hxoYhbf8Sdf+O0zUJbD1w4nHMv997jx5xJZVnfxtLyyuraemmjvLm1vbNr7lXaMkoEoS0S8Uh0fSwpZyFtKaY47caC4sDntOOP7yZ+55EKyaKwqdKYugEehmzACFZa8sxK0ztDN8jJUu/iBKXepZN7ZtWqWVOgRWIXpAoFGp755fQjkgQ0VIRjKXu2FSs3w0IxwmledhJJY0zGeEh7moY4oNLNprfn6EgrfTSIhK5Qoan6eyLDgZRp4OvOAKuRnPcm4n9eL1GDazdjYZwoGpLZokHCkYrQJAjUZ4ISxVNNMBFM34rICAtMlI6rrEOw519eJO3Tmm3V7Ifzav22iKMEB3AIx2DDFdThHhrQAgJP8Ayv8GbkxovxbnzMWpeMYmYf/sD4/AGV5ZLZ</latexit><latexit sha1_base64="LwxbD5bgl32pINRhEeIeNWmb/8I=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJL43ghFNy4r9AVNCJPptB06eTAzEUPIr7hxoYhbf8Sdf+O0zUJbD1w4nHMv997jx5xJZVnfxtLyyuraemmjvLm1vbNr7lXaMkoEoS0S8Uh0fSwpZyFtKaY47caC4sDntOOP7yZ+55EKyaKwqdKYugEehmzACFZa8sxK0ztDN8jJUu/iBKXepZN7ZtWqWVOgRWIXpAoFGp755fQjkgQ0VIRjKXu2FSs3w0IxwmledhJJY0zGeEh7moY4oNLNprfn6EgrfTSIhK5Qoan6eyLDgZRp4OvOAKuRnPcm4n9eL1GDazdjYZwoGpLZokHCkYrQJAjUZ4ISxVNNMBFM34rICAtMlI6rrEOw519eJO3Tmm3V7Ifzav22iKMEB3AIx2DDFdThHhrQAgJP8Ayv8GbkxovxbnzMWpeMYmYf/sD4/AGV5ZLZ</latexit>

D3<latexit sha1_base64="62hRsAjW7tKVI0FX4k//oGPjLlY=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclRkVdFnUhcsK9gHtUDLpbRuayYxJplCGfocbF4q49WPc+Tdm2llo64HA4Zx7uScniAXXxnW/nZXVtfWNzcJWcXtnd2+/dHDY0FGiGNZZJCLVCqhGwSXWDTcCW7FCGgYCm8HoNvObY1SaR/LRTGL0QzqQvM8ZNVbyOyE1Q0ZFejftXnRLZbfizkCWiZeTMuSodUtfnV7EkhClYYJq3fbc2PgpVYYzgdNiJ9EYUzaiA2xbKmmI2k9noafk1Co90o+UfdKQmfp7I6Wh1pMwsJNZSL3oZeJ/Xjsx/Ws/5TJODEo2P9RPBDERyRogPa6QGTGxhDLFbVbChlRRZmxPRVuCt/jlZdI4r3huxXu4LFdv8joKcAwncAYeXEEV7qEGdWDwBM/wCm/O2Hlx3p2P+eiKk+8cwR84nz+laZIA</latexit><latexit sha1_base64="62hRsAjW7tKVI0FX4k//oGPjLlY=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclRkVdFnUhcsK9gHtUDLpbRuayYxJplCGfocbF4q49WPc+Tdm2llo64HA4Zx7uScniAXXxnW/nZXVtfWNzcJWcXtnd2+/dHDY0FGiGNZZJCLVCqhGwSXWDTcCW7FCGgYCm8HoNvObY1SaR/LRTGL0QzqQvM8ZNVbyOyE1Q0ZFejftXnRLZbfizkCWiZeTMuSodUtfnV7EkhClYYJq3fbc2PgpVYYzgdNiJ9EYUzaiA2xbKmmI2k9noafk1Co90o+UfdKQmfp7I6Wh1pMwsJNZSL3oZeJ/Xjsx/Ws/5TJODEo2P9RPBDERyRogPa6QGTGxhDLFbVbChlRRZmxPRVuCt/jlZdI4r3huxXu4LFdv8joKcAwncAYeXEEV7qEGdWDwBM/wCm/O2Hlx3p2P+eiKk+8cwR84nz+laZIA</latexit><latexit sha1_base64="62hRsAjW7tKVI0FX4k//oGPjLlY=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclRkVdFnUhcsK9gHtUDLpbRuayYxJplCGfocbF4q49WPc+Tdm2llo64HA4Zx7uScniAXXxnW/nZXVtfWNzcJWcXtnd2+/dHDY0FGiGNZZJCLVCqhGwSXWDTcCW7FCGgYCm8HoNvObY1SaR/LRTGL0QzqQvM8ZNVbyOyE1Q0ZFejftXnRLZbfizkCWiZeTMuSodUtfnV7EkhClYYJq3fbc2PgpVYYzgdNiJ9EYUzaiA2xbKmmI2k9noafk1Co90o+UfdKQmfp7I6Wh1pMwsJNZSL3oZeJ/Xjsx/Ws/5TJODEo2P9RPBDERyRogPa6QGTGxhDLFbVbChlRRZmxPRVuCt/jlZdI4r3huxXu4LFdv8joKcAwncAYeXEEV7qEGdWDwBM/wCm/O2Hlx3p2P+eiKk+8cwR84nz+laZIA</latexit><latexit sha1_base64="62hRsAjW7tKVI0FX4k//oGPjLlY=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclRkVdFnUhcsK9gHtUDLpbRuayYxJplCGfocbF4q49WPc+Tdm2llo64HA4Zx7uScniAXXxnW/nZXVtfWNzcJWcXtnd2+/dHDY0FGiGNZZJCLVCqhGwSXWDTcCW7FCGgYCm8HoNvObY1SaR/LRTGL0QzqQvM8ZNVbyOyE1Q0ZFejftXnRLZbfizkCWiZeTMuSodUtfnV7EkhClYYJq3fbc2PgpVYYzgdNiJ9EYUzaiA2xbKmmI2k9noafk1Co90o+UfdKQmfp7I6Wh1pMwsJNZSL3oZeJ/Xjsx/Ws/5TJODEo2P9RPBDERyRogPa6QGTGxhDLFbVbChlRRZmxPRVuCt/jlZdI4r3huxXu4LFdv8joKcAwncAYeXEEV7qEGdWDwBM/wCm/O2Hlx3p2P+eiKk+8cwR84nz+laZIA</latexit>

a35<latexit sha1_base64="D0JYKjNDf1BdnL+Se4tfX6VDh+U=">AAAB/3icbVDJSgNBEO2JW4xbVPDipTEInsKMC3oMevEYwSyQxNDTU5M06VnorhHDOAd/xYsHRbz6G978GzvLQRMfFDzeq+rqem4shUbb/rZyC4tLyyv51cLa+sbmVnF7p66jRHGo8UhGqukyDVKEUEOBEpqxAha4Ehru4GrkN+5BaRGFtziMoROwXih8wRkaqVvcayM84PidVIGXpax7dneSdYslu2yPQeeJMyUlMkW1W/xqexFPAgiRS6Z1y7Fj7KRMoeASskI70RAzPmA9aBkasgB0Jx3vzeihUTzqR8pUiHSs/p5IWaD1MHBNZ8Cwr2e9kfif10rQv+ikIowThJBPFvmJpBjRURjUEwo4yqEhjCth/kp5nynG0URWMCE4syfPk/px2bHLzs1pqXI5jSNP9skBOSIOOScVck2qpEY4eSTP5JW8WU/Wi/VufUxac9Z0Zpf8gfX5A6D7lng=</latexit><latexit sha1_base64="D0JYKjNDf1BdnL+Se4tfX6VDh+U=">AAAB/3icbVDJSgNBEO2JW4xbVPDipTEInsKMC3oMevEYwSyQxNDTU5M06VnorhHDOAd/xYsHRbz6G978GzvLQRMfFDzeq+rqem4shUbb/rZyC4tLyyv51cLa+sbmVnF7p66jRHGo8UhGqukyDVKEUEOBEpqxAha4Ehru4GrkN+5BaRGFtziMoROwXih8wRkaqVvcayM84PidVIGXpax7dneSdYslu2yPQeeJMyUlMkW1W/xqexFPAgiRS6Z1y7Fj7KRMoeASskI70RAzPmA9aBkasgB0Jx3vzeihUTzqR8pUiHSs/p5IWaD1MHBNZ8Cwr2e9kfif10rQv+ikIowThJBPFvmJpBjRURjUEwo4yqEhjCth/kp5nynG0URWMCE4syfPk/px2bHLzs1pqXI5jSNP9skBOSIOOScVck2qpEY4eSTP5JW8WU/Wi/VufUxac9Z0Zpf8gfX5A6D7lng=</latexit><latexit sha1_base64="D0JYKjNDf1BdnL+Se4tfX6VDh+U=">AAAB/3icbVDJSgNBEO2JW4xbVPDipTEInsKMC3oMevEYwSyQxNDTU5M06VnorhHDOAd/xYsHRbz6G978GzvLQRMfFDzeq+rqem4shUbb/rZyC4tLyyv51cLa+sbmVnF7p66jRHGo8UhGqukyDVKEUEOBEpqxAha4Ehru4GrkN+5BaRGFtziMoROwXih8wRkaqVvcayM84PidVIGXpax7dneSdYslu2yPQeeJMyUlMkW1W/xqexFPAgiRS6Z1y7Fj7KRMoeASskI70RAzPmA9aBkasgB0Jx3vzeihUTzqR8pUiHSs/p5IWaD1MHBNZ8Cwr2e9kfif10rQv+ikIowThJBPFvmJpBjRURjUEwo4yqEhjCth/kp5nynG0URWMCE4syfPk/px2bHLzs1pqXI5jSNP9skBOSIOOScVck2qpEY4eSTP5JW8WU/Wi/VufUxac9Z0Zpf8gfX5A6D7lng=</latexit><latexit sha1_base64="D0JYKjNDf1BdnL+Se4tfX6VDh+U=">AAAB/3icbVDJSgNBEO2JW4xbVPDipTEInsKMC3oMevEYwSyQxNDTU5M06VnorhHDOAd/xYsHRbz6G978GzvLQRMfFDzeq+rqem4shUbb/rZyC4tLyyv51cLa+sbmVnF7p66jRHGo8UhGqukyDVKEUEOBEpqxAha4Ehru4GrkN+5BaRGFtziMoROwXih8wRkaqVvcayM84PidVIGXpax7dneSdYslu2yPQeeJMyUlMkW1W/xqexFPAgiRS6Z1y7Fj7KRMoeASskI70RAzPmA9aBkasgB0Jx3vzeihUTzqR8pUiHSs/p5IWaD1MHBNZ8Cwr2e9kfif10rQv+ikIowThJBPFvmJpBjRURjUEwo4yqEhjCth/kp5nynG0URWMCE4syfPk/px2bHLzs1pqXI5jSNP9skBOSIOOScVck2qpEY4eSTP5JW8WU/Wi/VufUxac9Z0Zpf8gfX5A6D7lng=</latexit>

!13

Intransigence (Inability to learn)

I35 =<latexit sha1_base64="uh4WliMZrrT847n/n1qRqJ62eVY=">AAACA3icbVC7SgNBFL0bX3F9RS1thgQhVdhVRBshaKNdBPOAZA2zk9lkyOzsMjMrhpDSD7DVT7ATWz9EsLDzN5xkU5jEAwOHc+7lnjl+zJnSjvNpZZaWV1bXsuv2xubW9k5ud6+mokQSWiURj2TDx4pyJmhVM81pI5YUhz6ndb9/Ofbr91QqFolbPYipF+KuYAEjWBupft0+uTtG5+1cwSk5E6BF4k5JoZwvfn0DQKWd+2l1IpKEVGjCsVJN14m1N8RSM8LpyG4lisaY9HGXNg0VOKTKG07ijtChUTooiKR5QqOJ+ndjiEOlBqFvJkOse2reG4v/ec1EB2fekIk40VSQ9FCQcKQjNP476jBJieYDQzCRzGRFpIclJto0NHPlIY1q26YZd76HRVI7KrlOyb0xFV1AiiwcQB6K4MIplOEKKlAFAn14gmd4sR6tV+vNek9HM9Z0Zx9mYH38AtjBmWM=</latexit><latexit sha1_base64="kS2wCYmQzo1ZaK/bmYEEZGdXcp4=">AAACA3icbVC7SgNBFL0bX3F9RS1thgQhVdhVJDZC0Ea7COYByRpmJ7PJkNkHM7NiWFL6AbbmE+zE1g/wE0R7f8NJ1sIkHhg4nHMv98xxI86ksqwPI7O0vLK6ll03Nza3tndyu3t1GcaC0BoJeSiaLpaUs4DWFFOcNiNBse9y2nAHFxO/cUeFZGFwo4YRdXzcC5jHCFZaalx1Tm6P0VknV7BK1hRokdi/pFDJF78+y+/jaif33e6GJPZpoAjHUrZsK1JOgoVihNOR2Y4ljTAZ4B5taRpgn0onmcYdoUOtdJEXCv0Chabq340E+1IOfVdP+lj15bw3Ef/zWrHyTp2EBVGsaEDSQ17MkQrR5O+oywQlig81wUQwnRWRPhaYKN3QzJX7NKpp6mbs+R4WSf2oZFsl+1pXdA4psnAAeSiCDWWowCVUoQYEBvAITzA2Hoxn48V4TUczxu/OPszAePsBGDKa+Q==</latexit><latexit sha1_base64="kS2wCYmQzo1ZaK/bmYEEZGdXcp4=">AAACA3icbVC7SgNBFL0bX3F9RS1thgQhVdhVJDZC0Ea7COYByRpmJ7PJkNkHM7NiWFL6AbbmE+zE1g/wE0R7f8NJ1sIkHhg4nHMv98xxI86ksqwPI7O0vLK6ll03Nza3tndyu3t1GcaC0BoJeSiaLpaUs4DWFFOcNiNBse9y2nAHFxO/cUeFZGFwo4YRdXzcC5jHCFZaalx1Tm6P0VknV7BK1hRokdi/pFDJF78+y+/jaif33e6GJPZpoAjHUrZsK1JOgoVihNOR2Y4ljTAZ4B5taRpgn0onmcYdoUOtdJEXCv0Chabq340E+1IOfVdP+lj15bw3Ef/zWrHyTp2EBVGsaEDSQ17MkQrR5O+oywQlig81wUQwnRWRPhaYKN3QzJX7NKpp6mbs+R4WSf2oZFsl+1pXdA4psnAAeSiCDWWowCVUoQYEBvAITzA2Hoxn48V4TUczxu/OPszAePsBGDKa+Q==</latexit><latexit sha1_base64="pfv2YEIxMVNRMBoAjelX8nf5U0E=">AAACA3icbVDLSsNAFL2prxpfUZduBovgqiSK6EYoutFdBfuANpbJdNIOnUzCzEQsoUs/wK1+gjtx64f4Bf6G0zYL23pg4HDOvdwzJ0g4U9p1v63C0vLK6lpx3d7Y3NrecXb36ipOJaE1EvNYNgOsKGeC1jTTnDYTSXEUcNoIBtdjv/FIpWKxuNfDhPoR7gkWMoK1kRq3nbOHU3TZcUpu2Z0ALRIvJyXIUe04P+1uTNKICk04VqrluYn2Myw1I5yO7HaqaILJAPdoy1CBI6r8bBJ3hI6M0kVhLM0TGk3UvxsZjpQaRoGZjLDuq3lvLP7ntVIdXvgZE0mqqSDTQ2HKkY7R+O+oyyQlmg8NwUQykxWRPpaYaNPQzJWnaVTbNs148z0skvpJ2XPL3p1bqlzlHRXhAA7hGDw4hwrcQBVqQGAAL/AKb9az9W59WJ/T0YKV7+zDDKyvX5g0lx0=</latexit>

Page 64: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania

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D2<latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit><latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit><latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit><latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit>

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D = [3i=1Di

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!13

Intransigence (Inability to learn)

I35 =<latexit sha1_base64="uh4WliMZrrT847n/n1qRqJ62eVY=">AAACA3icbVC7SgNBFL0bX3F9RS1thgQhVdhVRBshaKNdBPOAZA2zk9lkyOzsMjMrhpDSD7DVT7ATWz9EsLDzN5xkU5jEAwOHc+7lnjl+zJnSjvNpZZaWV1bXsuv2xubW9k5ud6+mokQSWiURj2TDx4pyJmhVM81pI5YUhz6ndb9/Ofbr91QqFolbPYipF+KuYAEjWBupft0+uTtG5+1cwSk5E6BF4k5JoZwvfn0DQKWd+2l1IpKEVGjCsVJN14m1N8RSM8LpyG4lisaY9HGXNg0VOKTKG07ijtChUTooiKR5QqOJ+ndjiEOlBqFvJkOse2reG4v/ec1EB2fekIk40VSQ9FCQcKQjNP476jBJieYDQzCRzGRFpIclJto0NHPlIY1q26YZd76HRVI7KrlOyb0xFV1AiiwcQB6K4MIplOEKKlAFAn14gmd4sR6tV+vNek9HM9Z0Zx9mYH38AtjBmWM=</latexit><latexit sha1_base64="kS2wCYmQzo1ZaK/bmYEEZGdXcp4=">AAACA3icbVC7SgNBFL0bX3F9RS1thgQhVdhVJDZC0Ea7COYByRpmJ7PJkNkHM7NiWFL6AbbmE+zE1g/wE0R7f8NJ1sIkHhg4nHMv98xxI86ksqwPI7O0vLK6ll03Nza3tndyu3t1GcaC0BoJeSiaLpaUs4DWFFOcNiNBse9y2nAHFxO/cUeFZGFwo4YRdXzcC5jHCFZaalx1Tm6P0VknV7BK1hRokdi/pFDJF78+y+/jaif33e6GJPZpoAjHUrZsK1JOgoVihNOR2Y4ljTAZ4B5taRpgn0onmcYdoUOtdJEXCv0Chabq340E+1IOfVdP+lj15bw3Ef/zWrHyTp2EBVGsaEDSQ17MkQrR5O+oywQlig81wUQwnRWRPhaYKN3QzJX7NKpp6mbs+R4WSf2oZFsl+1pXdA4psnAAeSiCDWWowCVUoQYEBvAITzA2Hoxn48V4TUczxu/OPszAePsBGDKa+Q==</latexit><latexit sha1_base64="kS2wCYmQzo1ZaK/bmYEEZGdXcp4=">AAACA3icbVC7SgNBFL0bX3F9RS1thgQhVdhVJDZC0Ea7COYByRpmJ7PJkNkHM7NiWFL6AbbmE+zE1g/wE0R7f8NJ1sIkHhg4nHMv98xxI86ksqwPI7O0vLK6ll03Nza3tndyu3t1GcaC0BoJeSiaLpaUs4DWFFOcNiNBse9y2nAHFxO/cUeFZGFwo4YRdXzcC5jHCFZaalx1Tm6P0VknV7BK1hRokdi/pFDJF78+y+/jaif33e6GJPZpoAjHUrZsK1JOgoVihNOR2Y4ljTAZ4B5taRpgn0onmcYdoUOtdJEXCv0Chabq340E+1IOfVdP+lj15bw3Ef/zWrHyTp2EBVGsaEDSQ17MkQrR5O+oywQlig81wUQwnRWRPhaYKN3QzJX7NKpp6mbs+R4WSf2oZFsl+1pXdA4psnAAeSiCDWWowCVUoQYEBvAITzA2Hoxn48V4TUczxu/OPszAePsBGDKa+Q==</latexit><latexit sha1_base64="pfv2YEIxMVNRMBoAjelX8nf5U0E=">AAACA3icbVDLSsNAFL2prxpfUZduBovgqiSK6EYoutFdBfuANpbJdNIOnUzCzEQsoUs/wK1+gjtx64f4Bf6G0zYL23pg4HDOvdwzJ0g4U9p1v63C0vLK6lpx3d7Y3NrecXb36ipOJaE1EvNYNgOsKGeC1jTTnDYTSXEUcNoIBtdjv/FIpWKxuNfDhPoR7gkWMoK1kRq3nbOHU3TZcUpu2Z0ALRIvJyXIUe04P+1uTNKICk04VqrluYn2Myw1I5yO7HaqaILJAPdoy1CBI6r8bBJ3hI6M0kVhLM0TGk3UvxsZjpQaRoGZjLDuq3lvLP7ntVIdXvgZE0mqqSDTQ2HKkY7R+O+oyyQlmg8NwUQykxWRPpaYaNPQzJWnaVTbNs148z0skvpJ2XPL3p1bqlzlHRXhAA7hGDw4hwrcQBVqQGAAL/AKb9az9W59WJ/T0YKV7+zDDKyvX5g0lx0=</latexit>

Page 65: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania

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D = [3i=1Di

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✓⇤<latexit sha1_base64="ZgGLxwiTVh36uGTFt5Dvp6p74lQ=">AAAB73icbVBNS8NAEN3Ur1q/qh69LBZBPJREBD0WvXisYD+gjWWznbRLN5u4OxFK6J/w4kERr/4db/4bt20O2vpg4PHeDDPzgkQKg6777RRWVtfWN4qbpa3tnd298v5B08Sp5tDgsYx1O2AGpFDQQIES2okGFgUSWsHoZuq3nkAbEat7HCfgR2ygRCg4Qyu1uzgEZA9nvXLFrboz0GXi5aRCctR75a9uP+ZpBAq5ZMZ0PDdBP2MaBZcwKXVTAwnjIzaAjqWKRWD8bHbvhJ5YpU/DWNtSSGfq74mMRcaMo8B2RgyHZtGbiv95nRTDKz8TKkkRFJ8vClNJMabT52lfaOAox5YwroW9lfIh04yjjahkQ/AWX14mzfOq51a9u4tK7TqPo0iOyDE5JR65JDVyS+qkQTiR5Jm8kjfn0Xlx3p2PeWvByWcOyR84nz/BRo/E</latexit><latexit sha1_base64="ZgGLxwiTVh36uGTFt5Dvp6p74lQ=">AAAB73icbVBNS8NAEN3Ur1q/qh69LBZBPJREBD0WvXisYD+gjWWznbRLN5u4OxFK6J/w4kERr/4db/4bt20O2vpg4PHeDDPzgkQKg6777RRWVtfWN4qbpa3tnd298v5B08Sp5tDgsYx1O2AGpFDQQIES2okGFgUSWsHoZuq3nkAbEat7HCfgR2ygRCg4Qyu1uzgEZA9nvXLFrboz0GXi5aRCctR75a9uP+ZpBAq5ZMZ0PDdBP2MaBZcwKXVTAwnjIzaAjqWKRWD8bHbvhJ5YpU/DWNtSSGfq74mMRcaMo8B2RgyHZtGbiv95nRTDKz8TKkkRFJ8vClNJMabT52lfaOAox5YwroW9lfIh04yjjahkQ/AWX14mzfOq51a9u4tK7TqPo0iOyDE5JR65JDVyS+qkQTiR5Jm8kjfn0Xlx3p2PeWvByWcOyR84nz/BRo/E</latexit><latexit sha1_base64="ZgGLxwiTVh36uGTFt5Dvp6p74lQ=">AAAB73icbVBNS8NAEN3Ur1q/qh69LBZBPJREBD0WvXisYD+gjWWznbRLN5u4OxFK6J/w4kERr/4db/4bt20O2vpg4PHeDDPzgkQKg6777RRWVtfWN4qbpa3tnd298v5B08Sp5tDgsYx1O2AGpFDQQIES2okGFgUSWsHoZuq3nkAbEat7HCfgR2ygRCg4Qyu1uzgEZA9nvXLFrboz0GXi5aRCctR75a9uP+ZpBAq5ZMZ0PDdBP2MaBZcwKXVTAwnjIzaAjqWKRWD8bHbvhJ5YpU/DWNtSSGfq74mMRcaMo8B2RgyHZtGbiv95nRTDKz8TKkkRFJ8vClNJMabT52lfaOAox5YwroW9lfIh04yjjahkQ/AWX14mzfOq51a9u4tK7TqPo0iOyDE5JR65JDVyS+qkQTiR5Jm8kjfn0Xlx3p2PeWvByWcOyR84nz/BRo/E</latexit><latexit sha1_base64="ZgGLxwiTVh36uGTFt5Dvp6p74lQ=">AAAB73icbVBNS8NAEN3Ur1q/qh69LBZBPJREBD0WvXisYD+gjWWznbRLN5u4OxFK6J/w4kERr/4db/4bt20O2vpg4PHeDDPzgkQKg6777RRWVtfWN4qbpa3tnd298v5B08Sp5tDgsYx1O2AGpFDQQIES2okGFgUSWsHoZuq3nkAbEat7HCfgR2ygRCg4Qyu1uzgEZA9nvXLFrboz0GXi5aRCctR75a9uP+ZpBAq5ZMZ0PDdBP2MaBZcwKXVTAwnjIzaAjqWKRWD8bHbvhJ5YpU/DWNtSSGfq74mMRcaMo8B2RgyHZtGbiv95nRTDKz8TKkkRFJ8vClNJMabT52lfaOAox5YwroW9lfIh04yjjahkQ/AWX14mzfOq51a9u4tK7TqPo0iOyDE5JR65JDVyS+qkQTiR5Jm8kjfn0Xlx3p2PeWvByWcOyR84nz/BRo/E</latexit>

!13

Intransigence (Inability to learn)

I35 =<latexit sha1_base64="uh4WliMZrrT847n/n1qRqJ62eVY=">AAACA3icbVC7SgNBFL0bX3F9RS1thgQhVdhVRBshaKNdBPOAZA2zk9lkyOzsMjMrhpDSD7DVT7ATWz9EsLDzN5xkU5jEAwOHc+7lnjl+zJnSjvNpZZaWV1bXsuv2xubW9k5ud6+mokQSWiURj2TDx4pyJmhVM81pI5YUhz6ndb9/Ofbr91QqFolbPYipF+KuYAEjWBupft0+uTtG5+1cwSk5E6BF4k5JoZwvfn0DQKWd+2l1IpKEVGjCsVJN14m1N8RSM8LpyG4lisaY9HGXNg0VOKTKG07ijtChUTooiKR5QqOJ+ndjiEOlBqFvJkOse2reG4v/ec1EB2fekIk40VSQ9FCQcKQjNP476jBJieYDQzCRzGRFpIclJto0NHPlIY1q26YZd76HRVI7KrlOyb0xFV1AiiwcQB6K4MIplOEKKlAFAn14gmd4sR6tV+vNek9HM9Z0Zx9mYH38AtjBmWM=</latexit><latexit sha1_base64="kS2wCYmQzo1ZaK/bmYEEZGdXcp4=">AAACA3icbVC7SgNBFL0bX3F9RS1thgQhVdhVJDZC0Ea7COYByRpmJ7PJkNkHM7NiWFL6AbbmE+zE1g/wE0R7f8NJ1sIkHhg4nHMv98xxI86ksqwPI7O0vLK6ll03Nza3tndyu3t1GcaC0BoJeSiaLpaUs4DWFFOcNiNBse9y2nAHFxO/cUeFZGFwo4YRdXzcC5jHCFZaalx1Tm6P0VknV7BK1hRokdi/pFDJF78+y+/jaif33e6GJPZpoAjHUrZsK1JOgoVihNOR2Y4ljTAZ4B5taRpgn0onmcYdoUOtdJEXCv0Chabq340E+1IOfVdP+lj15bw3Ef/zWrHyTp2EBVGsaEDSQ17MkQrR5O+oywQlig81wUQwnRWRPhaYKN3QzJX7NKpp6mbs+R4WSf2oZFsl+1pXdA4psnAAeSiCDWWowCVUoQYEBvAITzA2Hoxn48V4TUczxu/OPszAePsBGDKa+Q==</latexit><latexit sha1_base64="kS2wCYmQzo1ZaK/bmYEEZGdXcp4=">AAACA3icbVC7SgNBFL0bX3F9RS1thgQhVdhVJDZC0Ea7COYByRpmJ7PJkNkHM7NiWFL6AbbmE+zE1g/wE0R7f8NJ1sIkHhg4nHMv98xxI86ksqwPI7O0vLK6ll03Nza3tndyu3t1GcaC0BoJeSiaLpaUs4DWFFOcNiNBse9y2nAHFxO/cUeFZGFwo4YRdXzcC5jHCFZaalx1Tm6P0VknV7BK1hRokdi/pFDJF78+y+/jaif33e6GJPZpoAjHUrZsK1JOgoVihNOR2Y4ljTAZ4B5taRpgn0onmcYdoUOtdJEXCv0Chabq340E+1IOfVdP+lj15bw3Ef/zWrHyTp2EBVGsaEDSQ17MkQrR5O+oywQlig81wUQwnRWRPhaYKN3QzJX7NKpp6mbs+R4WSf2oZFsl+1pXdA4psnAAeSiCDWWowCVUoQYEBvAITzA2Hoxn48V4TUczxu/OPszAePsBGDKa+Q==</latexit><latexit sha1_base64="pfv2YEIxMVNRMBoAjelX8nf5U0E=">AAACA3icbVDLSsNAFL2prxpfUZduBovgqiSK6EYoutFdBfuANpbJdNIOnUzCzEQsoUs/wK1+gjtx64f4Bf6G0zYL23pg4HDOvdwzJ0g4U9p1v63C0vLK6lpx3d7Y3NrecXb36ipOJaE1EvNYNgOsKGeC1jTTnDYTSXEUcNoIBtdjv/FIpWKxuNfDhPoR7gkWMoK1kRq3nbOHU3TZcUpu2Z0ALRIvJyXIUe04P+1uTNKICk04VqrluYn2Myw1I5yO7HaqaILJAPdoy1CBI6r8bBJ3hI6M0kVhLM0TGk3UvxsZjpQaRoGZjLDuq3lvLP7ntVIdXvgZE0mqqSDTQ2HKkY7R+O+oyyQlmg8NwUQykxWRPpaYaNPQzJWnaVTbNs148z0skvpJ2XPL3p1bqlzlHRXhAA7hGDw4hwrcQBVqQGAAL/AKb9az9W59WJ/T0YKV7+zDDKyvX5g0lx0=</latexit>

a⇤5 � a35<latexit sha1_base64="tkqz8D5WgwhOWeOrKAkBGlvk13o=">AAACHHicbVDLSgNBEOyN7/iKehRkUAQRDLuK6FH04jGCiYEkhtlJxwyZfTDTKwlLbn6HH+BVP8GbeBUED978DSeJB2MsGCiquqea8mMlDbnuu5OZmJyanpmdy84vLC4t51ZWSyZKtMCiiFSkyz43qGSIRZKksBxr5IGv8Mpvn/X9q1vURkbhJXVjrAX8JpRNKThZqZ7b4PXD6122x6qEHRr8l2ps9NK+ftCr57bcvDsAGyfeD9k62dz5+ASAQj33VW1EIgkwJKG4MRXPjamWck1SKOxlq4nBmIs2v8GKpSEP0NTSQW6PbVulwZqRti8kNlB/b6Q8MKYb+HYy4NQyf72++J9XSah5XEtlGCeEoRgGNRPFKGL9UlhDahSkupZwoaW9lYkW11yQrW4kpTM8NZu1zXh/exgnpf285+a9C1vRKQwxC+uwCTvgwRGcwDkUoAgC7uABHuHJuXeenRfndTiacX521mAEzts3s8mjig==</latexit><latexit sha1_base64="yWXxcZLUOoRN4ki9W7ZNYjnQVOg=">AAACHHicbVDJSgNBFOyJW4xb1KMgTUQIgmFGkXgMevEYwSyQxNDTeYmNPQvdbyRhyM2/EPwAr/oJXkS8CqJ3f8POctDEgoai6r2uR7mhFBpt+8NKzMzOzS8kF1NLyyura+n1jbIOIsWhxAMZqKrLNEjhQwkFSqiGCpjnSqi416cDv3IDSovAv8BeCA2PdXzRFpyhkZrpbdY8utyj+7SO0MXhf7GCVj8e6If9ZnrHztlD0GnijMlOIZP9+sy/3BWb6e96K+CRBz5yybSuOXaIjZgpFFxCP1WPNISMX7MO1Az1mQe6EQ9z+3TXKC3aDpR5PtKh+nsjZp7WPc81kx7DKz3pDcT/vFqE7eNGLPwwQvD5KKgdSYoBHZRCW0IBR9kzhHElzK2UXzHFOJrq/qR0R6emUqYZZ7KHaVI+yDl2zjk3FZ2QEZJki2RIljgkTwrkjBRJiXBySx7II3my7q1n69V6G40mrPHOJvkD6/0H8yulIA==</latexit><latexit sha1_base64="yWXxcZLUOoRN4ki9W7ZNYjnQVOg=">AAACHHicbVDJSgNBFOyJW4xb1KMgTUQIgmFGkXgMevEYwSyQxNDTeYmNPQvdbyRhyM2/EPwAr/oJXkS8CqJ3f8POctDEgoai6r2uR7mhFBpt+8NKzMzOzS8kF1NLyyura+n1jbIOIsWhxAMZqKrLNEjhQwkFSqiGCpjnSqi416cDv3IDSovAv8BeCA2PdXzRFpyhkZrpbdY8utyj+7SO0MXhf7GCVj8e6If9ZnrHztlD0GnijMlOIZP9+sy/3BWb6e96K+CRBz5yybSuOXaIjZgpFFxCP1WPNISMX7MO1Az1mQe6EQ9z+3TXKC3aDpR5PtKh+nsjZp7WPc81kx7DKz3pDcT/vFqE7eNGLPwwQvD5KKgdSYoBHZRCW0IBR9kzhHElzK2UXzHFOJrq/qR0R6emUqYZZ7KHaVI+yDl2zjk3FZ2QEZJki2RIljgkTwrkjBRJiXBySx7II3my7q1n69V6G40mrPHOJvkD6/0H8yulIA==</latexit><latexit sha1_base64="h1113Jy2NSfys6kbXumfQsjEOw0=">AAACHHicbVBLSgNBFOyJvzj+oi4FaQyCCIYZRXQZdOMygvlAEkNP5yVp0vOh+40kDNl5Dg/gVo/gTtwKnsBr2JlkYaIFDUXVe12P8iIpNDrOl5VZWFxaXsmu2mvrG5tbue2dig5jxaHMQxmqmsc0SBFAGQVKqEUKmO9JqHr967FffQClRRjc4TCCps+6gegIztBIrdw+a53fH9MT2kAYYPpfoqA9Ssb62aiVyzsFJwX9S9wpyZMpSq3cd6Md8tiHALlkWtddJ8JmwhQKLmFkN2INEeN91oW6oQHzQTeTNHdED43Spp1QmRcgTdXfGwnztR76npn0Gfb0vDcW//PqMXYum4kIohgh4JOgTiwphnRcCm0LBRzl0BDGlTC3Ut5jinE01c2kDCan2rZpxp3v4S+pnBZcp+DeOvni1bSjLNkjB+SIuOSCFMkNKZEy4eSRPJMX8mo9WW/Wu/UxGc1Y051dMgPr8wdzPKFE</latexit>

Page 66: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania

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T1 = {y1, y2}<latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit><latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit><latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit><latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit>

D1<latexit sha1_base64="q69qAC9QCbzeFL5i4zpxpEWkU9k=">AAAB9HicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMuiLlxWsA9oh3InTdvQTGZMMoUy9DvcuFDErR/jzr8x085CWw8EDufcyz05QSy4Nq777RTW1jc2t4rbpZ3dvf2D8uFRU0eJoqxBIxGpdoCaCS5Zw3AjWDtWDMNAsFYwvs381oQpzSP5aKYx80McSj7gFI2V/G6IZkRRpHezntcrV9yqOwdZJV5OKpCj3it/dfsRTUImDRWodcdzY+OnqAyngs1K3USzGOkYh6xjqcSQaT+dh56RM6v0ySBS9klD5urvjRRDradhYCezkHrZy8T/vE5iBtd+ymWcGCbp4tAgEcREJGuA9Lli1IipJUgVt1kJHaFCamxPJVuCt/zlVdK8qHpu1Xu4rNRu8jqKcAKncA4eXEEN7qEODaDwBM/wCm/OxHlx3p2PxWjByXeO4Q+czx+iYZH+</latexit><latexit sha1_base64="q69qAC9QCbzeFL5i4zpxpEWkU9k=">AAAB9HicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMuiLlxWsA9oh3InTdvQTGZMMoUy9DvcuFDErR/jzr8x085CWw8EDufcyz05QSy4Nq777RTW1jc2t4rbpZ3dvf2D8uFRU0eJoqxBIxGpdoCaCS5Zw3AjWDtWDMNAsFYwvs381oQpzSP5aKYx80McSj7gFI2V/G6IZkRRpHezntcrV9yqOwdZJV5OKpCj3it/dfsRTUImDRWodcdzY+OnqAyngs1K3USzGOkYh6xjqcSQaT+dh56RM6v0ySBS9klD5urvjRRDradhYCezkHrZy8T/vE5iBtd+ymWcGCbp4tAgEcREJGuA9Lli1IipJUgVt1kJHaFCamxPJVuCt/zlVdK8qHpu1Xu4rNRu8jqKcAKncA4eXEEN7qEODaDwBM/wCm/OxHlx3p2PxWjByXeO4Q+czx+iYZH+</latexit><latexit sha1_base64="q69qAC9QCbzeFL5i4zpxpEWkU9k=">AAAB9HicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMuiLlxWsA9oh3InTdvQTGZMMoUy9DvcuFDErR/jzr8x085CWw8EDufcyz05QSy4Nq777RTW1jc2t4rbpZ3dvf2D8uFRU0eJoqxBIxGpdoCaCS5Zw3AjWDtWDMNAsFYwvs381oQpzSP5aKYx80McSj7gFI2V/G6IZkRRpHezntcrV9yqOwdZJV5OKpCj3it/dfsRTUImDRWodcdzY+OnqAyngs1K3USzGOkYh6xjqcSQaT+dh56RM6v0ySBS9klD5urvjRRDradhYCezkHrZy8T/vE5iBtd+ymWcGCbp4tAgEcREJGuA9Lli1IipJUgVt1kJHaFCamxPJVuCt/zlVdK8qHpu1Xu4rNRu8jqKcAKncA4eXEEN7qEODaDwBM/wCm/OxHlx3p2PxWjByXeO4Q+czx+iYZH+</latexit><latexit sha1_base64="q69qAC9QCbzeFL5i4zpxpEWkU9k=">AAAB9HicbVDLSgMxFL1TX7W+qi7dBIvgqsyIoMuiLlxWsA9oh3InTdvQTGZMMoUy9DvcuFDErR/jzr8x085CWw8EDufcyz05QSy4Nq777RTW1jc2t4rbpZ3dvf2D8uFRU0eJoqxBIxGpdoCaCS5Zw3AjWDtWDMNAsFYwvs381oQpzSP5aKYx80McSj7gFI2V/G6IZkRRpHezntcrV9yqOwdZJV5OKpCj3it/dfsRTUImDRWodcdzY+OnqAyngs1K3USzGOkYh6xjqcSQaT+dh56RM6v0ySBS9klD5urvjRRDradhYCezkHrZy8T/vE5iBtd+ymWcGCbp4tAgEcREJGuA9Lli1IipJUgVt1kJHaFCamxPJVuCt/zlVdK8qHpu1Xu4rNRu8jqKcAKncA4eXEEN7qEODaDwBM/wCm/OxHlx3p2PxWjByXeO4Q+czx+iYZH+</latexit>

✓2<latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit><latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit><latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit><latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit>

T2 = {y3, y4}<latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit><latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit><latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit><latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit>

D2<latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit><latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit><latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit><latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit>

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D = [3i=1Di

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!13

Intransigence (Inability to learn)

PFT (I35 < 0)<latexit sha1_base64="cidcbnM6hInI2GcfUNWcZcryXxk=">AAAB9XicbVDLSgNBEOyNrxhfUY9eBoMQL2HXB3rwEBREbxHygmQTZiezyZDZ2WVmVglL/sOLB0W8+i/e/BsnyR40saChqOqmu8uLOFPatr+tzNLyyupadj23sbm1vZPf3aurMJaE1kjIQ9n0sKKcCVrTTHPajCTFgcdpwxveTPzGI5WKhaKqRxF1A9wXzGcEayN1KrfV4n33vHOKrpB93M0X7JI9BVokTkoKkKLSzX+1eyGJAyo04ViplmNH2k2w1IxwOs61Y0UjTIa4T1uGChxQ5SbTq8foyCg95IfSlNBoqv6eSHCg1CjwTGeA9UDNexPxP68Va//STZiIYk0FmS3yY450iCYRoB6TlGg+MgQTycytiAywxESboHImBGf+5UVSPyk5dsl5OCuUr9M4snAAh1AEBy6gDHdQgRoQkPAMr/BmPVkv1rv1MWvNWOnMPvyB9fkDNh2QWw==</latexit><latexit sha1_base64="cidcbnM6hInI2GcfUNWcZcryXxk=">AAAB9XicbVDLSgNBEOyNrxhfUY9eBoMQL2HXB3rwEBREbxHygmQTZiezyZDZ2WVmVglL/sOLB0W8+i/e/BsnyR40saChqOqmu8uLOFPatr+tzNLyyupadj23sbm1vZPf3aurMJaE1kjIQ9n0sKKcCVrTTHPajCTFgcdpwxveTPzGI5WKhaKqRxF1A9wXzGcEayN1KrfV4n33vHOKrpB93M0X7JI9BVokTkoKkKLSzX+1eyGJAyo04ViplmNH2k2w1IxwOs61Y0UjTIa4T1uGChxQ5SbTq8foyCg95IfSlNBoqv6eSHCg1CjwTGeA9UDNexPxP68Va//STZiIYk0FmS3yY450iCYRoB6TlGg+MgQTycytiAywxESboHImBGf+5UVSPyk5dsl5OCuUr9M4snAAh1AEBy6gDHdQgRoQkPAMr/BmPVkv1rv1MWvNWOnMPvyB9fkDNh2QWw==</latexit><latexit sha1_base64="cidcbnM6hInI2GcfUNWcZcryXxk=">AAAB9XicbVDLSgNBEOyNrxhfUY9eBoMQL2HXB3rwEBREbxHygmQTZiezyZDZ2WVmVglL/sOLB0W8+i/e/BsnyR40saChqOqmu8uLOFPatr+tzNLyyupadj23sbm1vZPf3aurMJaE1kjIQ9n0sKKcCVrTTHPajCTFgcdpwxveTPzGI5WKhaKqRxF1A9wXzGcEayN1KrfV4n33vHOKrpB93M0X7JI9BVokTkoKkKLSzX+1eyGJAyo04ViplmNH2k2w1IxwOs61Y0UjTIa4T1uGChxQ5SbTq8foyCg95IfSlNBoqv6eSHCg1CjwTGeA9UDNexPxP68Va//STZiIYk0FmS3yY450iCYRoB6TlGg+MgQTycytiAywxESboHImBGf+5UVSPyk5dsl5OCuUr9M4snAAh1AEBy6gDHdQgRoQkPAMr/BmPVkv1rv1MWvNWOnMPvyB9fkDNh2QWw==</latexit><latexit sha1_base64="cidcbnM6hInI2GcfUNWcZcryXxk=">AAAB9XicbVDLSgNBEOyNrxhfUY9eBoMQL2HXB3rwEBREbxHygmQTZiezyZDZ2WVmVglL/sOLB0W8+i/e/BsnyR40saChqOqmu8uLOFPatr+tzNLyyupadj23sbm1vZPf3aurMJaE1kjIQ9n0sKKcCVrTTHPajCTFgcdpwxveTPzGI5WKhaKqRxF1A9wXzGcEayN1KrfV4n33vHOKrpB93M0X7JI9BVokTkoKkKLSzX+1eyGJAyo04ViplmNH2k2w1IxwOs61Y0UjTIa4T1uGChxQ5SbTq8foyCg95IfSlNBoqv6eSHCg1CjwTGeA9UDNexPxP68Va//STZiIYk0FmS3yY450iCYRoB6TlGg+MgQTycytiAywxESboHImBGf+5UVSPyk5dsl5OCuUr9M4snAAh1AEBy6gDHdQgRoQkPAMr/BmPVkv1rv1MWvNWOnMPvyB9fkDNh2QWw==</latexit>

• PFT (Positive Forward Transfer): Incrementally learning task k improves model’s knowledge about it.

I35 =<latexit sha1_base64="uh4WliMZrrT847n/n1qRqJ62eVY=">AAACA3icbVC7SgNBFL0bX3F9RS1thgQhVdhVRBshaKNdBPOAZA2zk9lkyOzsMjMrhpDSD7DVT7ATWz9EsLDzN5xkU5jEAwOHc+7lnjl+zJnSjvNpZZaWV1bXsuv2xubW9k5ud6+mokQSWiURj2TDx4pyJmhVM81pI5YUhz6ndb9/Ofbr91QqFolbPYipF+KuYAEjWBupft0+uTtG5+1cwSk5E6BF4k5JoZwvfn0DQKWd+2l1IpKEVGjCsVJN14m1N8RSM8LpyG4lisaY9HGXNg0VOKTKG07ijtChUTooiKR5QqOJ+ndjiEOlBqFvJkOse2reG4v/ec1EB2fekIk40VSQ9FCQcKQjNP476jBJieYDQzCRzGRFpIclJto0NHPlIY1q26YZd76HRVI7KrlOyb0xFV1AiiwcQB6K4MIplOEKKlAFAn14gmd4sR6tV+vNek9HM9Z0Zx9mYH38AtjBmWM=</latexit><latexit sha1_base64="kS2wCYmQzo1ZaK/bmYEEZGdXcp4=">AAACA3icbVC7SgNBFL0bX3F9RS1thgQhVdhVJDZC0Ea7COYByRpmJ7PJkNkHM7NiWFL6AbbmE+zE1g/wE0R7f8NJ1sIkHhg4nHMv98xxI86ksqwPI7O0vLK6ll03Nza3tndyu3t1GcaC0BoJeSiaLpaUs4DWFFOcNiNBse9y2nAHFxO/cUeFZGFwo4YRdXzcC5jHCFZaalx1Tm6P0VknV7BK1hRokdi/pFDJF78+y+/jaif33e6GJPZpoAjHUrZsK1JOgoVihNOR2Y4ljTAZ4B5taRpgn0onmcYdoUOtdJEXCv0Chabq340E+1IOfVdP+lj15bw3Ef/zWrHyTp2EBVGsaEDSQ17MkQrR5O+oywQlig81wUQwnRWRPhaYKN3QzJX7NKpp6mbs+R4WSf2oZFsl+1pXdA4psnAAeSiCDWWowCVUoQYEBvAITzA2Hoxn48V4TUczxu/OPszAePsBGDKa+Q==</latexit><latexit sha1_base64="kS2wCYmQzo1ZaK/bmYEEZGdXcp4=">AAACA3icbVC7SgNBFL0bX3F9RS1thgQhVdhVJDZC0Ea7COYByRpmJ7PJkNkHM7NiWFL6AbbmE+zE1g/wE0R7f8NJ1sIkHhg4nHMv98xxI86ksqwPI7O0vLK6ll03Nza3tndyu3t1GcaC0BoJeSiaLpaUs4DWFFOcNiNBse9y2nAHFxO/cUeFZGFwo4YRdXzcC5jHCFZaalx1Tm6P0VknV7BK1hRokdi/pFDJF78+y+/jaif33e6GJPZpoAjHUrZsK1JOgoVihNOR2Y4ljTAZ4B5taRpgn0onmcYdoUOtdJEXCv0Chabq340E+1IOfVdP+lj15bw3Ef/zWrHyTp2EBVGsaEDSQ17MkQrR5O+oywQlig81wUQwnRWRPhaYKN3QzJX7NKpp6mbs+R4WSf2oZFsl+1pXdA4psnAAeSiCDWWowCVUoQYEBvAITzA2Hoxn48V4TUczxu/OPszAePsBGDKa+Q==</latexit><latexit sha1_base64="pfv2YEIxMVNRMBoAjelX8nf5U0E=">AAACA3icbVDLSsNAFL2prxpfUZduBovgqiSK6EYoutFdBfuANpbJdNIOnUzCzEQsoUs/wK1+gjtx64f4Bf6G0zYL23pg4HDOvdwzJ0g4U9p1v63C0vLK6lpx3d7Y3NrecXb36ipOJaE1EvNYNgOsKGeC1jTTnDYTSXEUcNoIBtdjv/FIpWKxuNfDhPoR7gkWMoK1kRq3nbOHU3TZcUpu2Z0ALRIvJyXIUe04P+1uTNKICk04VqrluYn2Myw1I5yO7HaqaILJAPdoy1CBI6r8bBJ3hI6M0kVhLM0TGk3UvxsZjpQaRoGZjLDuq3lvLP7ntVIdXvgZE0mqqSDTQ2HKkY7R+O+oyyQlmg8NwUQykxWRPpaYaNPQzJWnaVTbNs148z0skvpJ2XPL3p1bqlzlHRXhAA7hGDw4hwrcQBVqQGAAL/AKb9az9W59WJ/T0YKV7+zDDKyvX5g0lx0=</latexit>

a⇤5 � a35<latexit sha1_base64="tkqz8D5WgwhOWeOrKAkBGlvk13o=">AAACHHicbVDLSgNBEOyN7/iKehRkUAQRDLuK6FH04jGCiYEkhtlJxwyZfTDTKwlLbn6HH+BVP8GbeBUED978DSeJB2MsGCiquqea8mMlDbnuu5OZmJyanpmdy84vLC4t51ZWSyZKtMCiiFSkyz43qGSIRZKksBxr5IGv8Mpvn/X9q1vURkbhJXVjrAX8JpRNKThZqZ7b4PXD6122x6qEHRr8l2ps9NK+ftCr57bcvDsAGyfeD9k62dz5+ASAQj33VW1EIgkwJKG4MRXPjamWck1SKOxlq4nBmIs2v8GKpSEP0NTSQW6PbVulwZqRti8kNlB/b6Q8MKYb+HYy4NQyf72++J9XSah5XEtlGCeEoRgGNRPFKGL9UlhDahSkupZwoaW9lYkW11yQrW4kpTM8NZu1zXh/exgnpf285+a9C1vRKQwxC+uwCTvgwRGcwDkUoAgC7uABHuHJuXeenRfndTiacX521mAEzts3s8mjig==</latexit><latexit sha1_base64="yWXxcZLUOoRN4ki9W7ZNYjnQVOg=">AAACHHicbVDJSgNBFOyJW4xb1KMgTUQIgmFGkXgMevEYwSyQxNDTeYmNPQvdbyRhyM2/EPwAr/oJXkS8CqJ3f8POctDEgoai6r2uR7mhFBpt+8NKzMzOzS8kF1NLyyura+n1jbIOIsWhxAMZqKrLNEjhQwkFSqiGCpjnSqi416cDv3IDSovAv8BeCA2PdXzRFpyhkZrpbdY8utyj+7SO0MXhf7GCVj8e6If9ZnrHztlD0GnijMlOIZP9+sy/3BWb6e96K+CRBz5yybSuOXaIjZgpFFxCP1WPNISMX7MO1Az1mQe6EQ9z+3TXKC3aDpR5PtKh+nsjZp7WPc81kx7DKz3pDcT/vFqE7eNGLPwwQvD5KKgdSYoBHZRCW0IBR9kzhHElzK2UXzHFOJrq/qR0R6emUqYZZ7KHaVI+yDl2zjk3FZ2QEZJki2RIljgkTwrkjBRJiXBySx7II3my7q1n69V6G40mrPHOJvkD6/0H8yulIA==</latexit><latexit sha1_base64="yWXxcZLUOoRN4ki9W7ZNYjnQVOg=">AAACHHicbVDJSgNBFOyJW4xb1KMgTUQIgmFGkXgMevEYwSyQxNDTeYmNPQvdbyRhyM2/EPwAr/oJXkS8CqJ3f8POctDEgoai6r2uR7mhFBpt+8NKzMzOzS8kF1NLyyura+n1jbIOIsWhxAMZqKrLNEjhQwkFSqiGCpjnSqi416cDv3IDSovAv8BeCA2PdXzRFpyhkZrpbdY8utyj+7SO0MXhf7GCVj8e6If9ZnrHztlD0GnijMlOIZP9+sy/3BWb6e96K+CRBz5yybSuOXaIjZgpFFxCP1WPNISMX7MO1Az1mQe6EQ9z+3TXKC3aDpR5PtKh+nsjZp7WPc81kx7DKz3pDcT/vFqE7eNGLPwwQvD5KKgdSYoBHZRCW0IBR9kzhHElzK2UXzHFOJrq/qR0R6emUqYZZ7KHaVI+yDl2zjk3FZ2QEZJki2RIljgkTwrkjBRJiXBySx7II3my7q1n69V6G40mrPHOJvkD6/0H8yulIA==</latexit><latexit sha1_base64="h1113Jy2NSfys6kbXumfQsjEOw0=">AAACHHicbVBLSgNBFOyJvzj+oi4FaQyCCIYZRXQZdOMygvlAEkNP5yVp0vOh+40kDNl5Dg/gVo/gTtwKnsBr2JlkYaIFDUXVe12P8iIpNDrOl5VZWFxaXsmu2mvrG5tbue2dig5jxaHMQxmqmsc0SBFAGQVKqEUKmO9JqHr967FffQClRRjc4TCCps+6gegIztBIrdw+a53fH9MT2kAYYPpfoqA9Ssb62aiVyzsFJwX9S9wpyZMpSq3cd6Md8tiHALlkWtddJ8JmwhQKLmFkN2INEeN91oW6oQHzQTeTNHdED43Spp1QmRcgTdXfGwnztR76npn0Gfb0vDcW//PqMXYum4kIohgh4JOgTiwphnRcCm0LBRzl0BDGlTC3Ut5jinE01c2kDCan2rZpxp3v4S+pnBZcp+DeOvni1bSjLNkjB+SIuOSCFMkNKZEy4eSRPJMX8mo9WW/Wu/UxGc1Y051dMgPr8wdzPKFE</latexit>

Page 67: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania

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T1 = {y1, y2}<latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit><latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit><latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit><latexit sha1_base64="310ONmf9g1hSqfo8S9kcVQPBsXc=">AAAB+3icbVDLSsNAFJ34rPUV69LNYBFcSMkUQTdC0Y3LCn1BE8JkOmmHTiZhZiKGkF9x40IRt/6IO//GaZuFth64cDjnXu69J0g4U9pxvq219Y3Nre3KTnV3b//g0D6q9VScSkK7JOaxHARYUc4E7WqmOR0kkuIo4LQfTO9mfv+RSsVi0dFZQr0IjwULGcHaSL5d6/gI3kA3z3x0ATO/6Ra+XXcazhxwlaCS1EGJtm9/uaOYpBEVmnCs1BA5ifZyLDUjnBZVN1U0wWSKx3RoqMARVV4+v72AZ0YZwTCWpoSGc/X3RI4jpbIoMJ0R1hO17M3E/7xhqsNrL2ciSTUVZLEoTDnUMZwFAUdMUqJ5ZggmkplbIZlgiYk2cVVNCGj55VXSazaQ00APl/XWbRlHBZyAU3AOELgCLXAP2qALCHgCz+AVvFmF9WK9Wx+L1jWrnDkGf2B9/gCGe5LP</latexit>

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✓2<latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit><latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit><latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit><latexit sha1_base64="7/pSNJ56+9MBYfOPbWbW9A9Ekos=">AAAB73icbVDLSgNBEOz1GeMr6tHLYBA8hd0g6DHoxWME84BkCbOTTjJk9uFMrxCW/IQXD4p49Xe8+TdOkj1oYkFDUdVNd1eQKGnIdb+dtfWNza3twk5xd2//4LB0dNw0caoFNkSsYt0OuEElI2yQJIXtRCMPA4WtYHw781tPqI2MoweaJOiHfBjJgRScrNTu0giJ96q9UtmtuHOwVeLlpAw56r3SV7cfizTEiITixnQ8NyE/45qkUDgtdlODCRdjPsSOpREP0fjZ/N4pO7dKnw1ibSsiNld/T2Q8NGYSBrYz5DQyy95M/M/rpDS49jMZJSlhJBaLBqliFLPZ86wvNQpSE0u40NLeysSIay7IRlS0IXjLL6+SZrXiuRXv/rJcu8njKMApnMEFeHAFNbiDOjRAgIJneIU359F5cd6dj0XrmpPPnMAfOJ8/zuuPzQ==</latexit>

T2 = {y3, y4}<latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit><latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit><latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit><latexit sha1_base64="K921TP0wLZxhIdktYCuyq9z/AZ4=">AAAB+3icbVDLSsNAFL3xWesr1qWbwSK4kJLUgm6EohuXFfqCJoTJdNoOnTyYmYgh5FfcuFDErT/izr9x2mahrQcuHM65l3vv8WPOpLKsb2NtfWNza7u0U97d2z84NI8qXRklgtAOiXgk+j6WlLOQdhRTnPZjQXHgc9rzp3czv/dIhWRR2FZpTN0Aj0M2YgQrLXlmpe3V0Q1ystS7vECp13Byz6xaNWsOtErsglShQMszv5xhRJKAhopwLOXAtmLlZlgoRjjNy04iaYzJFI/pQNMQB1S62fz2HJ1pZYhGkdAVKjRXf09kOJAyDXzdGWA1kcveTPzPGyRqdO1mLIwTRUOyWDRKOFIRmgWBhkxQoniqCSaC6VsRmWCBidJxlXUI9vLLq6Rbr9lWzX5oVJu3RRwlOIFTOAcbrqAJ99CCDhB4gmd4hTcjN16Md+Nj0bpmFDPH8AfG5w+OMJLU</latexit>

D2<latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit><latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit><latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit><latexit sha1_base64="kkMnEJJTL4WoIFiQkDJLkJ60BFg=">AAAB9HicbVDLSgMxFL3js9ZX1aWbYBFclZki6LKoC5cV7APaoWTS2zY0kxmTTKEM/Q43LhRx68e482/MtLPQ1gOBwzn3ck9OEAuujet+O2vrG5tb24Wd4u7e/sFh6ei4qaNEMWywSESqHVCNgktsGG4EtmOFNAwEtoLxbea3Jqg0j+Sjmcboh3Qo+YAzaqzkd0NqRoyK9G7Wq/ZKZbfizkFWiZeTMuSo90pf3X7EkhClYYJq3fHc2PgpVYYzgbNiN9EYUzamQ+xYKmmI2k/noWfk3Cp9MoiUfdKQufp7I6Wh1tMwsJNZSL3sZeJ/Xicxg2s/5TJODEq2ODRIBDERyRogfa6QGTG1hDLFbVbCRlRRZmxPRVuCt/zlVdKsVjy34j1clms3eR0FOIUzuAAPrqAG91CHBjB4gmd4hTdn4rw4787HYnTNyXdO4A+czx+j5ZH/</latexit>

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D = [3i=1Di

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!13

Intransigence (Inability to learn)

PFT (I35 < 0)<latexit sha1_base64="cidcbnM6hInI2GcfUNWcZcryXxk=">AAAB9XicbVDLSgNBEOyNrxhfUY9eBoMQL2HXB3rwEBREbxHygmQTZiezyZDZ2WVmVglL/sOLB0W8+i/e/BsnyR40saChqOqmu8uLOFPatr+tzNLyyupadj23sbm1vZPf3aurMJaE1kjIQ9n0sKKcCVrTTHPajCTFgcdpwxveTPzGI5WKhaKqRxF1A9wXzGcEayN1KrfV4n33vHOKrpB93M0X7JI9BVokTkoKkKLSzX+1eyGJAyo04ViplmNH2k2w1IxwOs61Y0UjTIa4T1uGChxQ5SbTq8foyCg95IfSlNBoqv6eSHCg1CjwTGeA9UDNexPxP68Va//STZiIYk0FmS3yY450iCYRoB6TlGg+MgQTycytiAywxESboHImBGf+5UVSPyk5dsl5OCuUr9M4snAAh1AEBy6gDHdQgRoQkPAMr/BmPVkv1rv1MWvNWOnMPvyB9fkDNh2QWw==</latexit><latexit sha1_base64="cidcbnM6hInI2GcfUNWcZcryXxk=">AAAB9XicbVDLSgNBEOyNrxhfUY9eBoMQL2HXB3rwEBREbxHygmQTZiezyZDZ2WVmVglL/sOLB0W8+i/e/BsnyR40saChqOqmu8uLOFPatr+tzNLyyupadj23sbm1vZPf3aurMJaE1kjIQ9n0sKKcCVrTTHPajCTFgcdpwxveTPzGI5WKhaKqRxF1A9wXzGcEayN1KrfV4n33vHOKrpB93M0X7JI9BVokTkoKkKLSzX+1eyGJAyo04ViplmNH2k2w1IxwOs61Y0UjTIa4T1uGChxQ5SbTq8foyCg95IfSlNBoqv6eSHCg1CjwTGeA9UDNexPxP68Va//STZiIYk0FmS3yY450iCYRoB6TlGg+MgQTycytiAywxESboHImBGf+5UVSPyk5dsl5OCuUr9M4snAAh1AEBy6gDHdQgRoQkPAMr/BmPVkv1rv1MWvNWOnMPvyB9fkDNh2QWw==</latexit><latexit sha1_base64="cidcbnM6hInI2GcfUNWcZcryXxk=">AAAB9XicbVDLSgNBEOyNrxhfUY9eBoMQL2HXB3rwEBREbxHygmQTZiezyZDZ2WVmVglL/sOLB0W8+i/e/BsnyR40saChqOqmu8uLOFPatr+tzNLyyupadj23sbm1vZPf3aurMJaE1kjIQ9n0sKKcCVrTTHPajCTFgcdpwxveTPzGI5WKhaKqRxF1A9wXzGcEayN1KrfV4n33vHOKrpB93M0X7JI9BVokTkoKkKLSzX+1eyGJAyo04ViplmNH2k2w1IxwOs61Y0UjTIa4T1uGChxQ5SbTq8foyCg95IfSlNBoqv6eSHCg1CjwTGeA9UDNexPxP68Va//STZiIYk0FmS3yY450iCYRoB6TlGg+MgQTycytiAywxESboHImBGf+5UVSPyk5dsl5OCuUr9M4snAAh1AEBy6gDHdQgRoQkPAMr/BmPVkv1rv1MWvNWOnMPvyB9fkDNh2QWw==</latexit><latexit sha1_base64="cidcbnM6hInI2GcfUNWcZcryXxk=">AAAB9XicbVDLSgNBEOyNrxhfUY9eBoMQL2HXB3rwEBREbxHygmQTZiezyZDZ2WVmVglL/sOLB0W8+i/e/BsnyR40saChqOqmu8uLOFPatr+tzNLyyupadj23sbm1vZPf3aurMJaE1kjIQ9n0sKKcCVrTTHPajCTFgcdpwxveTPzGI5WKhaKqRxF1A9wXzGcEayN1KrfV4n33vHOKrpB93M0X7JI9BVokTkoKkKLSzX+1eyGJAyo04ViplmNH2k2w1IxwOs61Y0UjTIa4T1uGChxQ5SbTq8foyCg95IfSlNBoqv6eSHCg1CjwTGeA9UDNexPxP68Va//STZiIYk0FmS3yY450iCYRoB6TlGg+MgQTycytiAywxESboHImBGf+5UVSPyk5dsl5OCuUr9M4snAAh1AEBy6gDHdQgRoQkPAMr/BmPVkv1rv1MWvNWOnMPvyB9fkDNh2QWw==</latexit>

• PFT (Positive Forward Transfer): Incrementally learning task k improves model’s knowledge about it.

I35 =<latexit sha1_base64="uh4WliMZrrT847n/n1qRqJ62eVY=">AAACA3icbVC7SgNBFL0bX3F9RS1thgQhVdhVRBshaKNdBPOAZA2zk9lkyOzsMjMrhpDSD7DVT7ATWz9EsLDzN5xkU5jEAwOHc+7lnjl+zJnSjvNpZZaWV1bXsuv2xubW9k5ud6+mokQSWiURj2TDx4pyJmhVM81pI5YUhz6ndb9/Ofbr91QqFolbPYipF+KuYAEjWBupft0+uTtG5+1cwSk5E6BF4k5JoZwvfn0DQKWd+2l1IpKEVGjCsVJN14m1N8RSM8LpyG4lisaY9HGXNg0VOKTKG07ijtChUTooiKR5QqOJ+ndjiEOlBqFvJkOse2reG4v/ec1EB2fekIk40VSQ9FCQcKQjNP476jBJieYDQzCRzGRFpIclJto0NHPlIY1q26YZd76HRVI7KrlOyb0xFV1AiiwcQB6K4MIplOEKKlAFAn14gmd4sR6tV+vNek9HM9Z0Zx9mYH38AtjBmWM=</latexit><latexit sha1_base64="kS2wCYmQzo1ZaK/bmYEEZGdXcp4=">AAACA3icbVC7SgNBFL0bX3F9RS1thgQhVdhVJDZC0Ea7COYByRpmJ7PJkNkHM7NiWFL6AbbmE+zE1g/wE0R7f8NJ1sIkHhg4nHMv98xxI86ksqwPI7O0vLK6ll03Nza3tndyu3t1GcaC0BoJeSiaLpaUs4DWFFOcNiNBse9y2nAHFxO/cUeFZGFwo4YRdXzcC5jHCFZaalx1Tm6P0VknV7BK1hRokdi/pFDJF78+y+/jaif33e6GJPZpoAjHUrZsK1JOgoVihNOR2Y4ljTAZ4B5taRpgn0onmcYdoUOtdJEXCv0Chabq340E+1IOfVdP+lj15bw3Ef/zWrHyTp2EBVGsaEDSQ17MkQrR5O+oywQlig81wUQwnRWRPhaYKN3QzJX7NKpp6mbs+R4WSf2oZFsl+1pXdA4psnAAeSiCDWWowCVUoQYEBvAITzA2Hoxn48V4TUczxu/OPszAePsBGDKa+Q==</latexit><latexit sha1_base64="kS2wCYmQzo1ZaK/bmYEEZGdXcp4=">AAACA3icbVC7SgNBFL0bX3F9RS1thgQhVdhVJDZC0Ea7COYByRpmJ7PJkNkHM7NiWFL6AbbmE+zE1g/wE0R7f8NJ1sIkHhg4nHMv98xxI86ksqwPI7O0vLK6ll03Nza3tndyu3t1GcaC0BoJeSiaLpaUs4DWFFOcNiNBse9y2nAHFxO/cUeFZGFwo4YRdXzcC5jHCFZaalx1Tm6P0VknV7BK1hRokdi/pFDJF78+y+/jaif33e6GJPZpoAjHUrZsK1JOgoVihNOR2Y4ljTAZ4B5taRpgn0onmcYdoUOtdJEXCv0Chabq340E+1IOfVdP+lj15bw3Ef/zWrHyTp2EBVGsaEDSQ17MkQrR5O+oywQlig81wUQwnRWRPhaYKN3QzJX7NKpp6mbs+R4WSf2oZFsl+1pXdA4psnAAeSiCDWWowCVUoQYEBvAITzA2Hoxn48V4TUczxu/OPszAePsBGDKa+Q==</latexit><latexit sha1_base64="pfv2YEIxMVNRMBoAjelX8nf5U0E=">AAACA3icbVDLSsNAFL2prxpfUZduBovgqiSK6EYoutFdBfuANpbJdNIOnUzCzEQsoUs/wK1+gjtx64f4Bf6G0zYL23pg4HDOvdwzJ0g4U9p1v63C0vLK6lpx3d7Y3NrecXb36ipOJaE1EvNYNgOsKGeC1jTTnDYTSXEUcNoIBtdjv/FIpWKxuNfDhPoR7gkWMoK1kRq3nbOHU3TZcUpu2Z0ALRIvJyXIUe04P+1uTNKICk04VqrluYn2Myw1I5yO7HaqaILJAPdoy1CBI6r8bBJ3hI6M0kVhLM0TGk3UvxsZjpQaRoGZjLDuq3lvLP7ntVIdXvgZE0mqqSDTQ2HKkY7R+O+oyyQlmg8NwUQykxWRPpaYaNPQzJWnaVTbNs148z0skvpJ2XPL3p1bqlzlHRXhAA7hGDw4hwrcQBVqQGAAL/AKb9az9W59WJ/T0YKV7+zDDKyvX5g0lx0=</latexit>

a⇤5 � a35<latexit sha1_base64="tkqz8D5WgwhOWeOrKAkBGlvk13o=">AAACHHicbVDLSgNBEOyN7/iKehRkUAQRDLuK6FH04jGCiYEkhtlJxwyZfTDTKwlLbn6HH+BVP8GbeBUED978DSeJB2MsGCiquqea8mMlDbnuu5OZmJyanpmdy84vLC4t51ZWSyZKtMCiiFSkyz43qGSIRZKksBxr5IGv8Mpvn/X9q1vURkbhJXVjrAX8JpRNKThZqZ7b4PXD6122x6qEHRr8l2ps9NK+ftCr57bcvDsAGyfeD9k62dz5+ASAQj33VW1EIgkwJKG4MRXPjamWck1SKOxlq4nBmIs2v8GKpSEP0NTSQW6PbVulwZqRti8kNlB/b6Q8MKYb+HYy4NQyf72++J9XSah5XEtlGCeEoRgGNRPFKGL9UlhDahSkupZwoaW9lYkW11yQrW4kpTM8NZu1zXh/exgnpf285+a9C1vRKQwxC+uwCTvgwRGcwDkUoAgC7uABHuHJuXeenRfndTiacX521mAEzts3s8mjig==</latexit><latexit sha1_base64="yWXxcZLUOoRN4ki9W7ZNYjnQVOg=">AAACHHicbVDJSgNBFOyJW4xb1KMgTUQIgmFGkXgMevEYwSyQxNDTeYmNPQvdbyRhyM2/EPwAr/oJXkS8CqJ3f8POctDEgoai6r2uR7mhFBpt+8NKzMzOzS8kF1NLyyura+n1jbIOIsWhxAMZqKrLNEjhQwkFSqiGCpjnSqi416cDv3IDSovAv8BeCA2PdXzRFpyhkZrpbdY8utyj+7SO0MXhf7GCVj8e6If9ZnrHztlD0GnijMlOIZP9+sy/3BWb6e96K+CRBz5yybSuOXaIjZgpFFxCP1WPNISMX7MO1Az1mQe6EQ9z+3TXKC3aDpR5PtKh+nsjZp7WPc81kx7DKz3pDcT/vFqE7eNGLPwwQvD5KKgdSYoBHZRCW0IBR9kzhHElzK2UXzHFOJrq/qR0R6emUqYZZ7KHaVI+yDl2zjk3FZ2QEZJki2RIljgkTwrkjBRJiXBySx7II3my7q1n69V6G40mrPHOJvkD6/0H8yulIA==</latexit><latexit sha1_base64="yWXxcZLUOoRN4ki9W7ZNYjnQVOg=">AAACHHicbVDJSgNBFOyJW4xb1KMgTUQIgmFGkXgMevEYwSyQxNDTeYmNPQvdbyRhyM2/EPwAr/oJXkS8CqJ3f8POctDEgoai6r2uR7mhFBpt+8NKzMzOzS8kF1NLyyura+n1jbIOIsWhxAMZqKrLNEjhQwkFSqiGCpjnSqi416cDv3IDSovAv8BeCA2PdXzRFpyhkZrpbdY8utyj+7SO0MXhf7GCVj8e6If9ZnrHztlD0GnijMlOIZP9+sy/3BWb6e96K+CRBz5yybSuOXaIjZgpFFxCP1WPNISMX7MO1Az1mQe6EQ9z+3TXKC3aDpR5PtKh+nsjZp7WPc81kx7DKz3pDcT/vFqE7eNGLPwwQvD5KKgdSYoBHZRCW0IBR9kzhHElzK2UXzHFOJrq/qR0R6emUqYZZ7KHaVI+yDl2zjk3FZ2QEZJki2RIljgkTwrkjBRJiXBySx7II3my7q1n69V6G40mrPHOJvkD6/0H8yulIA==</latexit><latexit sha1_base64="h1113Jy2NSfys6kbXumfQsjEOw0=">AAACHHicbVBLSgNBFOyJvzj+oi4FaQyCCIYZRXQZdOMygvlAEkNP5yVp0vOh+40kDNl5Dg/gVo/gTtwKnsBr2JlkYaIFDUXVe12P8iIpNDrOl5VZWFxaXsmu2mvrG5tbue2dig5jxaHMQxmqmsc0SBFAGQVKqEUKmO9JqHr967FffQClRRjc4TCCps+6gegIztBIrdw+a53fH9MT2kAYYPpfoqA9Ssb62aiVyzsFJwX9S9wpyZMpSq3cd6Md8tiHALlkWtddJ8JmwhQKLmFkN2INEeN91oW6oQHzQTeTNHdED43Spp1QmRcgTdXfGwnztR76npn0Gfb0vDcW//PqMXYum4kIohgh4JOgTiwphnRcCm0LBRzl0BDGlTC3Ut5jinE01c2kDCan2rZpxp3v4S+pnBZcp+DeOvni1bSjLNkjB+SIuOSCFMkNKZEy4eSRPJMX8mo9WW/Wu/UxGc1Y051dMgPr8wdzPKFE</latexit>

NFT (I35 > 0)<latexit sha1_base64="hrF8p2qBeTu+WpB/ZTiVbPW3qts=">AAACCHicbVDJSgNBEO2JW4xb1KMHG4MQL2HGBT1JUBC9SIRskMTQ06kkTXoWumvEMOToxV/x4kERr36CN//GznLQ6IOCx3tV3VXPDaXQaNtfVmJmdm5+IbmYWlpeWV1Lr2+UdRApDiUeyEBVXaZBCh9KKFBCNVTAPFdCxe2dD/3KHSgtAr+I/RAaHuv4oi04QyM109t1hHscvRMraA3i64ti9qp5dHtAT6m9N2imM3bOHoH+Jc6EZMgEhWb6s94KeOSBj1wyrWuOHWIjZgoFlzBI1SMNIeM91oGaoT7zQDfi0QIDumuUFm0HypSPdKT+nIiZp3Xfc02nx7Crp72h+J9Xi7B90oiFH0YIPh9/1I4kxYAOU6EtoYCj7BvCuBJmV8q7TDGOJruUCcGZPvkvKe/nHDvn3Bxm8meTOJJki+yQLHHIMcmTS1IgJcLJA3kiL+TVerSerTfrfdyasCYzm+QXrI9vAuaYoQ==</latexit><latexit sha1_base64="hrF8p2qBeTu+WpB/ZTiVbPW3qts=">AAACCHicbVDJSgNBEO2JW4xb1KMHG4MQL2HGBT1JUBC9SIRskMTQ06kkTXoWumvEMOToxV/x4kERr36CN//GznLQ6IOCx3tV3VXPDaXQaNtfVmJmdm5+IbmYWlpeWV1Lr2+UdRApDiUeyEBVXaZBCh9KKFBCNVTAPFdCxe2dD/3KHSgtAr+I/RAaHuv4oi04QyM109t1hHscvRMraA3i64ti9qp5dHtAT6m9N2imM3bOHoH+Jc6EZMgEhWb6s94KeOSBj1wyrWuOHWIjZgoFlzBI1SMNIeM91oGaoT7zQDfi0QIDumuUFm0HypSPdKT+nIiZp3Xfc02nx7Crp72h+J9Xi7B90oiFH0YIPh9/1I4kxYAOU6EtoYCj7BvCuBJmV8q7TDGOJruUCcGZPvkvKe/nHDvn3Bxm8meTOJJki+yQLHHIMcmTS1IgJcLJA3kiL+TVerSerTfrfdyasCYzm+QXrI9vAuaYoQ==</latexit><latexit sha1_base64="hrF8p2qBeTu+WpB/ZTiVbPW3qts=">AAACCHicbVDJSgNBEO2JW4xb1KMHG4MQL2HGBT1JUBC9SIRskMTQ06kkTXoWumvEMOToxV/x4kERr36CN//GznLQ6IOCx3tV3VXPDaXQaNtfVmJmdm5+IbmYWlpeWV1Lr2+UdRApDiUeyEBVXaZBCh9KKFBCNVTAPFdCxe2dD/3KHSgtAr+I/RAaHuv4oi04QyM109t1hHscvRMraA3i64ti9qp5dHtAT6m9N2imM3bOHoH+Jc6EZMgEhWb6s94KeOSBj1wyrWuOHWIjZgoFlzBI1SMNIeM91oGaoT7zQDfi0QIDumuUFm0HypSPdKT+nIiZp3Xfc02nx7Crp72h+J9Xi7B90oiFH0YIPh9/1I4kxYAOU6EtoYCj7BvCuBJmV8q7TDGOJruUCcGZPvkvKe/nHDvn3Bxm8meTOJJki+yQLHHIMcmTS1IgJcLJA3kiL+TVerSerTfrfdyasCYzm+QXrI9vAuaYoQ==</latexit><latexit sha1_base64="hrF8p2qBeTu+WpB/ZTiVbPW3qts=">AAACCHicbVDJSgNBEO2JW4xb1KMHG4MQL2HGBT1JUBC9SIRskMTQ06kkTXoWumvEMOToxV/x4kERr36CN//GznLQ6IOCx3tV3VXPDaXQaNtfVmJmdm5+IbmYWlpeWV1Lr2+UdRApDiUeyEBVXaZBCh9KKFBCNVTAPFdCxe2dD/3KHSgtAr+I/RAaHuv4oi04QyM109t1hHscvRMraA3i64ti9qp5dHtAT6m9N2imM3bOHoH+Jc6EZMgEhWb6s94KeOSBj1wyrWuOHWIjZgoFlzBI1SMNIeM91oGaoT7zQDfi0QIDumuUFm0HypSPdKT+nIiZp3Xfc02nx7Crp72h+J9Xi7B90oiFH0YIPh9/1I4kxYAOU6EtoYCj7BvCuBJmV8q7TDGOJruUCcGZPvkvKe/nHDvn3Bxm8meTOJJki+yQLHHIMcmTS1IgJcLJA3kiL+TVerSerTfrfdyasCYzm+QXrI9vAuaYoQ==</latexit>

• NFT (Negative Forward Transfer): Incrementally learning task k had negative influence on it.

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Puneet Dokania !14

Experimental Settings

• Incremental MNIST• Split into five disjoint subsets • Network: MLP

• Incremental CIFAR-100• Split into ten disjoint subset• Network: CNN

• Optimizer: Adam, batch size: 64

Page 69: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !15

Results

For MNIST and CIFAR, 10 (0.2%) and 25(5%) samples are used from the previous tasks using mean of features (MoF) sampling. Baselines where samples are used are appended with ’-S’.

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Puneet Dokania !16

Forgetting vs Intransigence Trade-off (MNIST)

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Puneet Dokania !17

Few open problems and insights(based on our recent analysis work)

Page 72: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !17

Few open problems and insights(based on our recent analysis work)

• ResNets? • Need more data

Page 73: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !17

Few open problems and insights(based on our recent analysis work)

• ResNets? • Need more data

• Use generative models• Encoder-Decoder type to learn data-distribution?

Page 74: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !17

Few open problems and insights(based on our recent analysis work)

• ResNets? • Need more data

• Use generative models• Encoder-Decoder type to learn data-distribution?

• Saddle Point?

Page 75: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !17

Few open problems and insights(based on our recent analysis work)

• ResNets? • Need more data

• Use generative models• Encoder-Decoder type to learn data-distribution?

• Saddle Point?• Order of tasks, subset of labels?

Page 76: Puneet K. Dokania · Puneet Dokania!1 Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence (ECCV18) Puneet K. Dokania (University of Oxford) 7th Aug,

Puneet Dokania !17

Few open problems and insights(based on our recent analysis work)

• ResNets? • Need more data

• Use generative models• Encoder-Decoder type to learn data-distribution?

• Saddle Point?• Order of tasks, subset of labels?• Judge when to stop training on more tasks? Saturate?