Tianxiao Li, Wenping Zhou a*, Wei Sheng, Fan Li and Weizhe ...
Blank Language Modelspeople.csail.mit.edu/tianxiao/papers/emnlp20_blm_slides.pdf · BLM - Overview...
Transcript of Blank Language Modelspeople.csail.mit.edu/tianxiao/papers/emnlp20_blm_slides.pdf · BLM - Overview...
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Blank Language ModelsTianxiao Shen* Victor Quach* Regina Barzilay Tommi Jaakkola (*: equal contribution)
mailto:[email protected]
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Left-to-Right Language Model
They also have ice
They also have ice
cream
…
Generate from scratch
Start with partially specified text
• text editing
• template filling
• text restoration
• …
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Blank Language Model (BLM)
Fine-grained control over generation location
Respect preceding and following context
Variable number of missing tokens
Output: They also have ice cream which is really good .Input: They also have which .
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BLM - Overview
• Dynamic canvas where “ ” controls where tokens can be placed
• At each step,
1. select a “ ”
2. predict a word w
3. replace that blank with “w”, “ w”, “w ”, or “ w ”
• Stop when there is no “ ”
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BLM - Overview
They also have which .
• Dynamic canvas where “ ” controls where tokens can be placed
• At each step,
1. select a “ ”
2. predict a word w
3. replace that blank with “w”, “ w”, “w ”, or “ w ”
• Stop when there is no “ ”
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BLM - Overview
really
They also have which .
• Dynamic canvas where “ ” controls where tokens can be placed
• At each step,
1. select a “ ”
2. predict a word w
3. replace that blank with “w”, “ w”, “w ”, or “ w ”
• Stop when there is no “ ”
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BLM - Overview
They also have which really .
• Dynamic canvas where “ ” controls where tokens can be placed
• At each step,
1. select a “ ”
2. predict a word w
3. replace that blank with “w”, “ w”, “w ”, or “ w ”
• Stop when there is no “ ”
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BLM - Overview
ice
They also have which really .
• Dynamic canvas where “ ” controls where tokens can be placed
• At each step,
1. select a “ ”
2. predict a word w
3. replace that blank with “w”, “ w”, “w ”, or “ w ”
• Stop when there is no “ ”
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BLM - Overview
They also have ice which really .
• Dynamic canvas where “ ” controls where tokens can be placed
• At each step,
1. select a “ ”
2. predict a word w
3. replace that blank with “w”, “ w”, “w ”, or “ w ”
• Stop when there is no “ ”
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BLM - Overview
is
They also have ice which really .
• Dynamic canvas where “ ” controls where tokens can be placed
• At each step,
1. select a “ ”
2. predict a word w
3. replace that blank with “w”, “ w”, “w ”, or “ w ”
• Stop when there is no “ ”
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BLM - Overview
They also have ice which is really .
• Dynamic canvas where “ ” controls where tokens can be placed
• At each step,
1. select a “ ”
2. predict a word w
3. replace that blank with “w”, “ w”, “w ”, or “ w ”
• Stop when there is no “ ”
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BLM - Overview
cream
They also have ice which is really .
• Dynamic canvas where “ ” controls where tokens can be placed
• At each step,
1. select a “ ”
2. predict a word w
3. replace that blank with “w”, “ w”, “w ”, or “ w ”
• Stop when there is no “ ”
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BLM - Overview
good
They also have ice cream which is really .
• Dynamic canvas where “ ” controls where tokens can be placed
• At each step,
1. select a “ ”
2. predict a word w
3. replace that blank with “w”, “ w”, “w ”, or “ w ”
• Stop when there is no “ ”
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BLM - Overview
They also have ice cream which is really good .
• Dynamic canvas where “ ” controls where tokens can be placed
• At each step,
1. select a “ ”
2. predict a word w
3. replace that blank with “w”, “ w”, “w ”, or “ w ”
• Stop when there is no “ ”
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BLM - Overview
• Dynamic canvas where “ ” controls where tokens can be placed
• At each step,
1. select a “ ”
2. predict a word w
3. replace that blank with “w”, “ w”, “w ”, or “ w ”
• Stop when there is no “ ”Grammar
• Nonterminal:
• Terminals: w V
• Production rules: ? w ?
(dist. depends on model and context)
∈
→
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BLM - Architecture
alsoThey have ____ which ____
Transformer
.
Linear & Softmax1) Choose a blank 2) Predict a word
3) Create new blanks
Linear & Softmax
really
MLP
Fill and repeat
really
really
really____
really
____
________
✓
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Trajectory: generating process from an initial “ ” to complete text
BLM - Likelihood
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BLM - Likelihood
A sentence with words can be realized by trajectories, each trajectory corresponds to a different word insertion order
x
AAAB6HicbVDLSgNBEOyNrxhfUY9eBoPgKexKQL0FBPGYgHlAsoTZSW8yZnZ2mZkVwxLw7sWDIl79JG/+jZPHQaMFDUVVN91dQSK4Nq775eRWVtfWN/Kbha3tnd294v5BU8epYthgsYhVO6AaBZfYMNwIbCcKaRQIbAWjq6nfukeleSxvzThBP6IDyUPOqLFS/aFXLLlldwbyl3gLUoIFar3iZ7cfszRCaZigWnc8NzF+RpXhTOCk0E01JpSN6AA7lkoaofaz2aETcmKVPgljZUsaMlN/TmQ00nocBbYzomaol72p+J/XSU144WdcJqlByeaLwlQQE5Pp16TPFTIjxpZQpri9lbAhVZQZm03BhuAtv/yXNM/KXqV8Wa+UqteP8zjycATHcAoenEMVbqAGDWCA8AQv8OrcOc/Om/M+b805iwgP4Recj28RXI2M
n
AAAB6HicbVDLSgNBEOyNrxhfUY9eBoPgKexKQL0FBPGYgHlAsoTZSW8yZnZ2mZkVwhLw7sWDIl79JG/+jZPHQRMLGoqqbrq7gkRwbVz328mtrW9sbuW3Czu7e/sHxcOjpo5TxbDBYhGrdkA1Ci6xYbgR2E4U0igQ2ApGN1O/9YhK81jem3GCfkQHkoecUWOluuwVS27ZnYGsEm9BSrBArVf86vZjlkYoDRNU647nJsbPqDKcCZwUuqnGhLIRHWDHUkkj1H42O3RCzqzSJ2GsbElDZurviYxGWo+jwHZG1Az1sjcV//M6qQmv/IzLJDUo2XxRmApiYjL9mvS5QmbE2BLKFLe3EjakijJjsynYELzll1dJ86LsVcrX9Uqpevs0jyMPJ3AK5+DBJVThDmrQAAYIz/AKb86D8+K8Ox/z1pyziPAY/sD5/AECNI2C
n!
AAAB6XicbVDLSgNBEOyNrxhfUY9eRoPgKexKQL0FBPEYxTwgWcLsZDYZMju7zPQKYQn4AV48KOLVP/Lm3zh5HDSxoKGo6qa7K0ikMOi6305uZXVtfSO/Wdja3tndK+4fNEycasbrLJaxbgXUcCkUr6NAyVuJ5jQKJG8Gw+uJ33zk2ohYPeAo4X5E+0qEglG00r067hZLbtmdgiwTb05KMEetW/zq9GKWRlwhk9SYtucm6GdUo2CSjwud1PCEsiHt87alikbc+Nn00jE5tUqPhLG2pZBM1d8TGY2MGUWB7YwoDsyiNxH/89ophpd+JlSSIldstihMJcGYTN4mPaE5QzmyhDIt7K2EDaimDG04BRuCt/jyMmmcl71K+equUqrePM3iyMMRnMAZeHABVbiFGtSBQQjP8ApvztB5cd6dj1lrzplHeAh/4Hz+AFmKja0=
p(x; ✓) =X
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p(x,�; ✓) =X
�2Sn
n�1Y
t=0
p(ax,�t |cx,�t ; ✓)
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
order action, canvas at step t
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
1 2 3 4 5 6 7 8 9 10
3
1
10
6
2
8
4
7
5
9
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BLM - Training
log p(x; ✓) = logX
�2Sn
n�1Y
t=0
p(ax,�t |cx,�t ; ✓)
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intractable
log
1
m
mX
i=1
ai
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1
m
mX
i=1
log ai
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
� log(n!) + 1n!
X
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n�1X
t=0
log p(ax,�t |cx,�t ; ✓)
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BLM - Training
log p(x; ✓) = logX
�2Sn
n�1Y
t=0
p(ax,�t |cx,�t ; ✓) intractable
log
1
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mX
i=1
ai
!>=
1
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mX
i=1
log ai
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�2Sn
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t=0
log p(ax,�t |cx,�t ; ✓)
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1. Uniformly sample from
2. Uniformly sample from to
3. Construct canvas
4. Compute estimated loss
cx,�t
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� log(n!)� n · log p(ax,�t |cx,�t ; ✓)
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t
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0
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n� 1
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
�
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
Sn
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
one action loss per pass :(
-
BLM - Training
� log(n!) + 1n!
X
�2Sn
n�1X
t=0
log p(ax,�t |cx,�t ; ✓)
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
depends only on the first elements of
—> combine into one pass loss calculations of trajectories that are the samecx,�t
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
t
AAAFqnicrVRbb9MwFM62Bka4dfDIi0dV0Wpr1UyTgKGiSQjEC9K4tB2q28hx3NRa4kTxCVoVLPHT+A288W9wk4616yZWwFKk4+9cvu+cE9mNAy6h1fq5tr5RMm/c3Lxl3b5z99798taDrozShLIOjYIoOXaJZAEXrAMcAnYcJ4yEbsB67smrqb/3hSWSR+ITTGI2CIkv+IhTAhpytja+V3EQ+Siunb7AMGZA6qiNcgjLNHQyLLkfEswF+ugIhXCcRJ6TQbulhplo2EpnkmF2ulvEKQe+0oUrOitr5UQ4YCOo4VFCaGarLFQFC2/bahgi4nCccH8MdfRSq7giKlenQ3VFn+W3mtiuo53zBLGtrpCfg3PqZ81fu4Ucs6q6mFXVBSywqovBVrXxW1EDCUy9CFYkac+3tCT4zz3+PduZ3pDA2HXRa2fOnNE4mX0ASrMsO2DHVupSfO9ATFOmu++vJK/4GwZa5fye/13l/9NyLRU52Wx1Qq+uAYu7O1e1uh6nXGk1W/lBy4Y9MyrG7Bw55R/Yi2gaMgE0IFL27VYMg4wkwGnAlIVTyWJCT4jP+toUJGRykOVPjUJVjXhoFCX6E4BydD4jI6GUk9DVkdNpyIu+KXiZr5/C6Nkg4yJOgQlaEI3SAEGEpu8W8njCKAQTbRCacK0V0THRAwX9ull6CPbFlpeN7l7T3m8+f79fOXzzrRjHpvHIeGzUDNt4ahwab40jo2PQ0pPSu1K31DN3zQ/mZ7NfhK6vzUb40Fg4pvcLKDjk3w==
�
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
t
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
t+ 1
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
in the first steps but different at the step
-
BLM - Training depends only on the first elements of
—> combine into one pass loss calculations of trajectories that are the samecx,�t
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
t
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
�
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
t
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
t+ 1
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in the first steps but different at the step
� log(n!) +n�1X
t=0
1
n!
X
�2Sn
log p(ax,�t |cx,�t ; ✓)
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
= log(n!) + n · EtE�1:tE�t+1E�t+2:n [log p(ax,�t |c
x,�t ; ✓)]
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
= log(n!) + EtE�1:t
2
4 nn� t
X
�t+1
log p(ax,�t |cx,�t ; ✓)
3
5
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
-
BLM - Training
= log(n!) + EtE�1:t
2
4 nn� t
X
�t+1
log p(ax,�t |cx,�t ; ✓)
3
5
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
1. Uniformly sample from to
2. Uniformly sample
3. Construct canvas
4. Compute estimated loss
cx,�t
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
t
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
0
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
n� 1
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
�1:t
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
� log(n!)� nn� t
X
�t+1
log p(ax,�t |cx,�t ; ✓)
AAAGEXicrVRNb9NAEHVLDMV8pXDksiWySFQSxVUloCioEgJxLIK0leLEWm82zqr22vKOUSOzEr+AC3+FCwcQ4sqNG/+GtZ1Sp2lFQ1nJ1uzbmXlvZlbrRj4T0G7/Wlq+VNEvX1m5aly7fuPmrerq7V0RJjGhXRL6YbzvYkF9xmkXGPh0P4opDlyf7rkHz7Lzvbc0Fizkb2AS0X6APc5GjGBQkLNauW/afuihqH74xIYxBdxAHZRDtkgCJ7UF8wJsM45eO1wiO4rDoZNCpy0HKW9aUkXiQXr4oPCTDrwjM1t0lNbIiWyfjqBuj2JMUkumgSxYWMeSgwBhh9kx88bQQE+VijO8cnXKVWX0aL6r87UGWj8O4GvyDPk5WFI/Lf7cJeSYk1pbIA1TpTRMlcYwYV39ZqMMs/lHWhNxmwxDWJTNo+Xq5rT/vdzF+DoltiPFAYax66LnTslMy21QLPMHqh9SnopvbPEsJLsGvYXkFRejr1SWR35xlf9Py7lU5GTT0XE1uibMzu5Y1T/oaaLSlZvhuDCFU621W+18oXnDmho1bbp2nOpPexiSJKAciI+F6FntCPopjoERn0rDTgSNMDnAHu0pk+OAin6av2gSmQoZolEYq48DytFyRIoDISaBqzyzTouTZxl42lkvgdGjfsp4lADlpCAaJT6CEGXPIxqymBLwJ8rAJGZKKyJjrBoJ6hE1VBOskyXPG7sbLWuz9fjVZm37xfuiHSvaXe2eVtcs7aG2rb3UdrSuRiofKp8qXypf9Y/6Z/2b/r1wXV6atvCONrP0H78Bf9EM+g==
n/2 action losses per pass :)
-
BLM - Training
They also have ice cream which is really good .
1 2 3 4 5 6 7 8 9 10x =
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
AAAB63icbVBNSwMxEJ2tX7V+VT16CRbBU8mKoheh6MVjBWsL7VKyabYNTbJLkhXK0r/gxYMiXv1D3vw3Zts9aOuDgcd7M8zMCxPBjcX42yutrK6tb5Q3K1vbO7t71f2DRxOnmrIWjUWsOyExTHDFWpZbwTqJZkSGgrXD8W3ut5+YNjxWD3aSsECSoeIRp8Tmkrr2cb9aw3U8A1omfkFqUKDZr371BjFNJVOWCmJM18eJDTKiLaeCTSu91LCE0DEZsq6jikhmgmx26xSdOGWAoli7UhbN1N8TGZHGTGToOiWxI7Po5eJ/Xje10VWQcZWklik6XxSlAtkY5Y+jAdeMWjFxhFDN3a2Ijogm1Lp4Ki4Ef/HlZfJ4Vvcv6vj+vNa4KeIowxEcwyn4cAkNuIMmtIDCCJ7hFd486b14797HvLXkFTOH8Afe5w84oI2y
n = 10
1. Uniformly sample from to
2. Uniformly sample
3. Construct canvas
4. Compute estimated loss
cx,�t
AAADbXiclVJbixMxFE6nXtbx1l3xwQuStRRb3JYZWVCRyoIIPq5odxeadkjTzDRskhmSM7JlnCf/oW/+BV/8C6bTqttdF/RA4Mt3bt9JziSTwkIQfKt59UuXr1zduOZfv3Hz1u3G5taBTXPD+IClMjVHE2q5FJoPQIDkR5nhVE0kP5wcv1n4Dz9xY0WqP8I84yNFEy1iwSg4KtqsfWkRmSY4a5+8IjDjQDu4jyuK2FxFBbEiUZQIjT9EusQkM+k0KqAflONCd8PSZdJxcbKzjCsj+MzWrvhXWb9qRCSPoU1iQ1kRloUql11EPyzHCtNIECOSGXTwa6figqhKnQt1FRNe3dp6u4Of/knQ2+UF8ivylPrV8P88QsX5636/1f0toos1YdMU/qtu1GgGvaAyfB6EK9BEK9uPGl/JNGW54hqYpNYOwyCDUUENCCZ56ZPc8oyyY5rwoYOaKm5HRbUtJW45Zorj1LijAVfs6YyCKmvnauIiFYWZPetbkH/zDXOIX4wKobMcuGbLRnEuMaR4sXp4KgxnIOcOUGaE04rZjLovA7egvnuE8OzI58HBs16423v5fre593b1HBvoAXqM2ihEz9Eeeof20QCx2nev4d3z7ns/6nfrD+uPlqFebZVzB61Z/clP4VEWPg==
t
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
0
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
n� 1
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
�1:t
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
� log(n!)� nn� t
X
�t+1
log p(ax,�t |cx,�t ; ✓)
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
n/2 action losses per pass :)
-
BLM - Training
t = 5
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
They also have ice cream which is really good .
1 2 3 4 5 6 7 8 9 10x =
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
AAAB63icbVBNSwMxEJ2tX7V+VT16CRbBU8mKoheh6MVjBWsL7VKyabYNTbJLkhXK0r/gxYMiXv1D3vw3Zts9aOuDgcd7M8zMCxPBjcX42yutrK6tb5Q3K1vbO7t71f2DRxOnmrIWjUWsOyExTHDFWpZbwTqJZkSGgrXD8W3ut5+YNjxWD3aSsECSoeIRp8Tmkrr2cb9aw3U8A1omfkFqUKDZr371BjFNJVOWCmJM18eJDTKiLaeCTSu91LCE0DEZsq6jikhmgmx26xSdOGWAoli7UhbN1N8TGZHGTGToOiWxI7Po5eJ/Xje10VWQcZWklik6XxSlAtkY5Y+jAdeMWjFxhFDN3a2Ijogm1Lp4Ki4Ef/HlZfJ4Vvcv6vj+vNa4KeIowxEcwyn4cAkNuIMmtIDCCJ7hFd486b14797HvLXkFTOH8Afe5w84oI2y
n = 10
1. Uniformly sample from to
2. Uniformly sample
3. Construct canvas
4. Compute estimated loss
cx,�t
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
t
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
0
AAADcHiclVJtixMxEE63vpzrW8/7IqiYWgqt2rIrBypSORDBjyfau4OmXdI0uw2XZJdkVq6s+9Uf6Dd/hF/8Babbqtc7D3QgMHnmmZlnkplmUlgIgm81r37p8pWrW9f86zdu3rrd2L5zYNPcMD5kqUzN0ZRaLoXmQxAg+VFmOFVTyQ+nx2+W8cNP3FiR6o+wyPhY0USLWDAKDoq2a1/aRKYJzjonrwjMOdAuHuAKIjZXUUGsSBQlQuMPkS4xyUw6iwoYBOWk0L2wdJl0Upw8XfHKCD6zjSv+VdavGhHJY+iQ2FBWhGWhylUXMQjLicI0EsSIZA5d/NqpuIBVqXNUVzHh1a2jm1385E+CbpYXyK/AU+rXw//zCBXmB357k+K3e7919LAmbJbCf5WOGq2gH1SGzzvh2mmhte1Hja9klrJccQ1MUmtHYZDBuKAGBJO89ElueUbZMU34yLmaKm7HRbUwJW47ZIbj1LijAVfo6YyCKmsXauqYisLcno0twb/FRjnEL8aF0FkOXLNVoziXGFK83D48E4YzkAvnUGaE04rZnLpfA7ejvnuE8OzI552DZ/1wt//y/W5r7+36ObbQPfQIdVCInqM99A7toyFite/ejnffe+D9qN+tP6w3V1Svts7ZQRtWf/wTUQIWuw==
n� 1
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
�1:t
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
� log(n!)� nn� t
X
�t+1
log p(ax,�t |cx,�t ; ✓)
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
n/2 action losses per pass :)
-
BLM - Training
t = 5
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
They also have ice cream which is really good .
1 2 3 4 5 6 7 8 9 10x =
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
�1:t = (6, 2, 1, 3, 10)
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
AAAB63icbVBNSwMxEJ2tX7V+VT16CRbBU8mKoheh6MVjBWsL7VKyabYNTbJLkhXK0r/gxYMiXv1D3vw3Zts9aOuDgcd7M8zMCxPBjcX42yutrK6tb5Q3K1vbO7t71f2DRxOnmrIWjUWsOyExTHDFWpZbwTqJZkSGgrXD8W3ut5+YNjxWD3aSsECSoeIRp8Tmkrr2cb9aw3U8A1omfkFqUKDZr371BjFNJVOWCmJM18eJDTKiLaeCTSu91LCE0DEZsq6jikhmgmx26xSdOGWAoli7UhbN1N8TGZHGTGToOiWxI7Po5eJ/Xje10VWQcZWklik6XxSlAtkY5Y+jAdeMWjFxhFDN3a2Ijogm1Lp4Ki4Ef/HlZfJ4Vvcv6vj+vNa4KeIowxEcwyn4cAkNuIMmtIDCCJ7hFd486b14797HvLXkFTOH8Afe5w84oI2y
n = 10
1. Uniformly sample from to
2. Uniformly sample
3. Construct canvas
4. Compute estimated loss
cx,�t
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
t
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
0
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
n� 1
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
�1:t
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
� log(n!)� nn� t
X
�t+1
log p(ax,�t |cx,�t ; ✓)
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
n/2 action losses per pass :)
-
BLM - Training
t = 5
AAAGHHicrVTLbtNAFHVLAsU8msKSzZQoUqKSyI6KgKKgCoTEsgjSVopTazwZO6PaY8tzjRqZ+RA2/AobFiDEhgUSf8PYcanTtKKhjGTrzn2dcx8aJ/KZAMP4tbR8pVK9em3lun7j5q3bq7W1O7siTGJC+yT0w3jfwYL6jNM+MPDpfhRTHDg+3XMOX2T2vXc0Fizkb2ES0WGAPc5cRjAolb1W6TYsP/RQ1Dx6asGYAm6hHspVlkgCO7UE8wJsMY7e2FwiK4rDkZ1Cz5AHKW+bUkXig/TowdRP2vCezFzRcVo9B7J86kLTcmNMUlOmgZyisJ4pDwKEbWbFzBtDCz1TLM7xytkpV5XRo/mtyddbaOMkgK/Lc+jnyhL7ovgLl5Dr7NTcAqk3VEq9odLoDdhQv9kovdH+Q62NuEVGISyK5tFydXPc/17uYni9Etox4wDD2HHQS7skpuU2KJR5g+qHlGfqu1s8C8nWYLAQveliDBXL8sgvz/L/cbkQixysGB1Xo2vD7OxOWP0LnzYq7dwMyKUx1Kb3TEOH3kO7Vjc6Rn7QvGAWQl0rzo5d+2GNQpIElAPxsRAD04hgmOIYGPGp1K1E0AiTQ+zRgRI5DqgYpvnjJlFDaUbIDWP1cUC5thyR4kCISeAoz6zp4rQtU55lGyTgPh6mjEcJUE6mQG7iIwhR9lKiEYspAX+iBExiprgiMsaqpaDeU101wTxd8ryw2+2Ym50nrzfr28+Ldqxo97T7WlMztUfatvZK29H6Gql8qHyqfKl8rX6sfq5+q36fui4vFTF3tZlT/fkbAV4PNA==
alsoThey have ____ which ____ .cx,�t
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
They also have ice cream which is really good .
1 2 3 4 5 6 7 8 9 10x =
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
�1:t = (6, 2, 1, 3, 10)
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
(6, 2, 1, 3, 10)
AAAB+XicbVDLSgMxFL1TX7W+Rl26CRahQhlm2lrtrujGZQX7gHYomTRtQzMPkkyhDP0TNy4UceufuPNvTF+g1gP3cjjnXnJzvIgzqWz7y0htbG5t76R3M3v7B4dH5vFJQ4axILROQh6Klocl5SygdcUUp61IUOx7nDa90d3Mb46pkCwMHtUkoq6PBwHrM4KVlrqmmSvnUSGPnDwq6m5fds2sbdlzINsqF68KlRJyVsqKZGGJWtf87PRCEvs0UIRjKduOHSk3wUIxwuk004kljTAZ4QFtaxpgn0o3mV8+RRda6aF+KHQFCs3VnxsJ9qWc+J6e9LEayr/eTPzPa8eqf+MmLIhiRQOyeKgfc6RCNIsB9ZigRPGJJpgIpm9FZIgFJkqHldEhrH15nTQKllOyKg+lbPV2GUcazuAccuDANVThHmpQBwJjeIIXeDUS49l4M94XoyljuXMKv2B8fAMl45Aj
AAAB63icbVBNSwMxEJ2tX7V+VT16CRbBU8mKoheh6MVjBWsL7VKyabYNTbJLkhXK0r/gxYMiXv1D3vw3Zts9aOuDgcd7M8zMCxPBjcX42yutrK6tb5Q3K1vbO7t71f2DRxOnmrIWjUWsOyExTHDFWpZbwTqJZkSGgrXD8W3ut5+YNjxWD3aSsECSoeIRp8Tmkrr2cb9aw3U8A1omfkFqUKDZr371BjFNJVOWCmJM18eJDTKiLaeCTSu91LCE0DEZsq6jikhmgmx26xSdOGWAoli7UhbN1N8TGZHGTGToOiWxI7Po5eJ/Xje10VWQcZWklik6XxSlAtkY5Y+jAdeMWjFxhFDN3a2Ijogm1Lp4Ki4Ef/HlZfJ4Vvcv6vj+vNa4KeIowxEcwyn4cAkNuIMmtIDCCJ7hFd486b14797HvLXkFTOH8Afe5w84oI2y
n = 10
1. Uniformly sample from to
2. Uniformly sample
3. Construct canvas
4. Compute estimated loss
cx,�t
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
t
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
0
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
n� 1
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
�1:t
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
� log(n!)� nn� t
X
�t+1
log p(ax,�t |cx,�t ; ✓)
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
n/2 action losses per pass :)
-
BLM - Training
t = 5
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
Transformer
alsoThey have ____ which ____ .cx,�t
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
ice ____ ____ cream
is ____ ____ really ____
____ goodax,�t
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
They also have ice cream which is really good .
1 2 3 4 5 6 7 8 9 10x =
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
�1:t = (6, 2, 1, 3, 10)
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
(6, 2, 1, 3, 10)
AAAB+XicbVDLSgMxFL1TX7W+Rl26CRahQhlm2lrtrujGZQX7gHYomTRtQzMPkkyhDP0TNy4UceufuPNvTF+g1gP3cjjnXnJzvIgzqWz7y0htbG5t76R3M3v7B4dH5vFJQ4axILROQh6Klocl5SygdcUUp61IUOx7nDa90d3Mb46pkCwMHtUkoq6PBwHrM4KVlrqmmSvnUSGPnDwq6m5fds2sbdlzINsqF68KlRJyVsqKZGGJWtf87PRCEvs0UIRjKduOHSk3wUIxwuk004kljTAZ4QFtaxpgn0o3mV8+RRda6aF+KHQFCs3VnxsJ9qWc+J6e9LEayr/eTPzPa8eqf+MmLIhiRQOyeKgfc6RCNIsB9ZigRPGJJpgIpm9FZIgFJkqHldEhrH15nTQKllOyKg+lbPV2GUcazuAccuDANVThHmpQBwJjeIIXeDUS49l4M94XoyljuXMKv2B8fAMl45Aj
AAAB63icbVBNSwMxEJ2tX7V+VT16CRbBU8mKoheh6MVjBWsL7VKyabYNTbJLkhXK0r/gxYMiXv1D3vw3Zts9aOuDgcd7M8zMCxPBjcX42yutrK6tb5Q3K1vbO7t71f2DRxOnmrIWjUWsOyExTHDFWpZbwTqJZkSGgrXD8W3ut5+YNjxWD3aSsECSoeIRp8Tmkrr2cb9aw3U8A1omfkFqUKDZr371BjFNJVOWCmJM18eJDTKiLaeCTSu91LCE0DEZsq6jikhmgmx26xSdOGWAoli7UhbN1N8TGZHGTGToOiWxI7Po5eJ/Xje10VWQcZWklik6XxSlAtkY5Y+jAdeMWjFxhFDN3a2Ijogm1Lp4Ki4Ef/HlZfJ4Vvcv6vj+vNa4KeIowxEcwyn4cAkNuIMmtIDCCJ7hFd486b14797HvLXkFTOH8Afe5w84oI2y
n = 10
1. Uniformly sample from to
2. Uniformly sample
3. Construct canvas
4. Compute estimated loss
cx,�t
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
t
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
0
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
n� 1
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
�1:t
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
� log(n!)� nn� t
X
�t+1
log p(ax,�t |cx,�t ; ✓)
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
n/2 action losses per pass :)
-
BLM - Inference
Simple greedy decoding or beam search to fill in the blanks in input
not search for sentence with the maximum marginal likelihood ,
but for sentence and trajectory that have the maximum joint likelihood
p(x; ✓)
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
p(x,�; ✓)
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
x
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
x
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
�
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
Note:
-
Experiments
Input: They also have which . Output: They also have ice cream which is really good .
Input: τε εγγονον εισαι???????σοφιαι Output: τε εγγονον εισαιου του σοφιαι
Input: The employees were super nice and efficient ! Output: The employees were rude and unprofessional !
Output: They also have ice cream which is really good.
Text infilling
Ancient text restoration
Sentiment transfer
Language modeling
-
Text Infilling
Dataset: Yahoo Answers (100K documents, max length 200 words)
Test data: randomly mask tokens with ratio , contiguous masked tokens —> “ ”
Metrics:
• Accuracy:
• Fluency:
r
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
BLEU score against original document
perplexity evaluated by a pre-trained left-to-right LM
-
Text Infilling
Baselines:
• BERT+LM
- use BERT representation of each blank as seed for a left-to-right LM that learns to
generate tokens in the corresponding blank
- at test time, multiple blanks are filled in one after another
-
Text Infilling
Baselines:
• BERT+LM
• Masked Language Model (MLM) with oracle length
- replace blanks with the target number of ⟨mask⟩ tokens
- fill masks autoregressively by most-confident-first heuristic
-
Text Infilling
Baselines:
• BERT+LM
• Masked Language Model (MLM) with oracle length
• Insertion Transformer (Stern et al., 2019)
- not allow users to specify where to insert
- force it to generate at valid locations, disable ⟨eos⟩ unless all blanks are filled,
prioritize slots that haven’t been filled yet; otherwise failure rate > 88%
-
Text Infilling
Baselines:
• BERT+LM
• Masked Language Model (MLM) with oracle length
• Insertion Transformer (Stern et al., 2019)
• Seq2seq-full (Donahue et al., 2020)
- output the full document from input
- may miss existing tokens in input or generate tokens in incorrect locations
• Seq2seq-fill (Donahue et al., 2020)
- output tokens to be placed in blanks, using ‘|’ to indicate separation
- may not generate the correct number of ‘|’
-
Text Infilling
Baselines:
• BERT+LM
• Masked Language Model (MLM) with oracle length
• Insertion Transformer (Stern et al., 2019)
• Seq2seq-full (Donahue et al., 2020)
- output the full document from input
- may miss existing tokens in input or generate tokens in incorrect locations
• Seq2seq-fill (Donahue et al., 2020)
- output tokens to be placed in blanks, using ‘|’ to indicate separation
- may not generate the correct number of ‘|’
failure rate from 15% to 47%
-
Text Infilling
BLEU
20
30
40
50
60
70
80
90
Mask ratio10% 20% 30% 40% 50%
BERT+LM MLM (oracle length) InsT BLM
-
Text Infilling
Perp
lexi
ty
0
10
20
30
40
50
60
Mask ratio10% 20% 30% 40% 50%
BERT+LM MLM (oracle length) InsT BLM
original data
-
Text Infilling
when time flies , where does it go ? to the center of the earth to be recycled came made into new time .
when time flies , where does it go ? from the center of the earth to be recycled converted made into new time .
when time flies , where does it go ? for the center of the earth has to be recycled and made into new time .
when time flies , where does it go ? for the center of the earth to be recycled and made into new time .
Original
Blanked
BERT+LM
MLM (oracle len)
InsT
BLM
when time flies , where does it go ? to the center of the universe to be recycled and made into new time .
when time flies , does it go ? the center of the to be recycled made into new time .
Mask ratio 10%
-
Text Infilling
when time flies , where does it go ? to the center of the universe to be recycled and made into new time .
when time , where ? the of universe to recycled made into .
when time is , where to ? i need to find the way of the universe to be recycled and made into a lot .
when time is , where is the universe ? from the creation of the universe to be recycled and made into the universe .
when time was created , where was it ? what was the name of the universe to be recycled and made into space .
when time was created , where did it come from ? it was the first part of the universe to be recycled and made into space .
Original
Blanked
BERT+LM
MLM (oracle len)
InsT
BLM
Mask ratio 50%
-
Ancient Text Restoration
Dataset (Assael et al., 2019): ancient Greek inscriptions (18M characters/3M words)
• number of characters to recover is assumed to be known
l 2 {0, · · · , t� 1}
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
t� 1� l
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
Length-aware BLM (L-BLM)
• [t] denotes blank of length t
• predict length of the new left blank,
new right blank has length
Baselines (Assael et al., 2019):
• Pythia: character-level seq2seq model to fill in one slot at a time
• Pythia-word: use both character and word representations
-
Ancient Text Restoration
Cha
ract
er e
rror r
ate
20
25
30
35
40
45
50
55
60
1% 25% 40% 50%
Human Pythia Pythia-word L-BLM
Single-slot Multi-slot
Mask ratio
-
Sentiment Transfer
Two-step approach:
1. Remove expressions of high polarity
- train a sentiment classifier and mask words with attention weight above average
2. Complete the partial sentence with expressions of the target sentiment
- train two instances of BLM, one for each sentiment
everyone that i spoke with was very helpful and kind .
everyone that i spoke with was rude and unprofessional .
there is definitely not enough room in that part of the venue .
there is always enough parking in that part of the venue .
it is n’t terrible , but it is n’t very good either .
it is n’t fancy , but it is still very good either .
Input
BLM
Input
BLM
Input
BLM
-
Sentiment Transfer
30
40
50
60
70
80
90
100
Accuracy
MLM (Wu et al. 2019) BLM
10
12
14
16
18
20
22
BLEU
Yelp reviews
-
Language Modeling
To compute , use Monte-Carlo estimate
• estimated perplexity is likely to be higher than actual perplexity
• as increases, it converges to actual perplexity
p(x; ✓) =X
�2Sn
p(x,�; ✓)
AAAGvXicrVRbb9MwFM7GWka4bfDIi8cUqdOSNSkdu6DAJATicQh2keo2OK6bmjlOFDuwKUTiN8IT/wYn7Vi6bmJjWEpycnx8vu9cfPyYUSFt+9fM7K25Wv32/B397r37Dx4uLD7aF1GaYLKHIxYlhz4ShFFO9iSVjBzGCUG