Local Representation Alignment: A Biologically Motivated Algorithm

for Training Neural Systems

Alexander G. Ororbia II

The Neural Adaptive Computing (NAC) Laboratory

Rochester Institute of Technology

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Collaborators

• The Pennsylvania State University• Dr. C. Lee Giles

• Dr. Daniel Kifer

• Rochester Institute of Technology (RIT)• Dr. Ifeoma Nwogu (Computer Vision)

• Dr. Travis Desell (Neuro-evolution, distributed computing)

• Students• Ankur Mali (PhD student, Penn State, co-advised w/ Dr. C. Lee Giles)

• Timothy Zee (PhD student, RIT, co-advised w/ Dr. Ifeoma Nwogu)

• Abdelrahman Elsiad (PhD student, RIT, co-advised w/ Dr. Travis Desell)

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Objectives

• Context: Credit assignment & algorithmic alternatives• Backpropagation of errors (backprop)• Feedback alignment algorithms• Target propagation (TP) • Contrastive Hebbian learning (CHL)

• Discrepancy Reduction – a family of learning procedures• Error-Driven Local Representation Alignment (LRA/LRA-E)• Adaptive Noise Difference Target Propagation (DTP-σ)

• Experimental Results & Variations

• Conclusions3

Equilibrium propagation (EP)

Contrastive Divergence (CD)

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Backprop, CHL, LRA

SGD, Adam, RMSprop

MSE, MAE, CNLL

MNISTMLP, AE, BM, RNN

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MLP = Multilayer perceptronAE = AutoencoderBM = Boltzmann machine

Problems with Backprop

Global optimization, back-prop through whole graph.

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• The global feedback pathway• Vanishing/exploding gradients• In recurrent networks, this is worse!!

• The weight transport problem• High sensitivity to initialization• Activation constraints/conditions

• Requires system to be fully differentiable → difficulty in handling discrete-valued functions

• Requires sufficiently linearity →adversarial samples

Feedforward InferenceIllustration: forward propagation in a multilayer perceptron (MLP) to collect activities

(Shared across most algorithms, i.e., backprop, random feedback alignment, direct feedback alignment, local representation alignment)

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Backpropagation of Errors

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Conducting credit assignment using the activities produced by the inference pass 14

Pass error signal back through post-activations (get derivatives w.r.t. pre-activitions)

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Pass error signal back through (incoming) synaptic weights to get error signal transmitted to post-activations in layer below

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Repeat the previous steps, layer by layer (recursive treatment of backprop procedure)

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Random Feedback Alignment

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Pass error signal back through post-activations (get derivatives w.r.t. pre-activitions)

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Pass error signal back through fixed, random alignment weights (replaces backprop’s step of passing error through transpose of feedforward weights)

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Repeat previous steps (similar to backprop)

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Direct Feedback Alignment

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Pass error signal back through post-activations (get derivatives w.r.t. pre-activitions)

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Pass error signal along first set of direct alignment weights to second layer

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Pass error signal along next set of direct alignment weights to first layer

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Treat the signals propagated along direct alignment connections as proxies for error derivatives and run them through post-activations in each layer, respectively

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Random Feedback Alignment: Direct Feedback Alignment:

Backpropagation of Errors:

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Global versus Local Signals

Global optimization, back-prop through whole graph. Local optimization, back-prop through sub-graphs.

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Global versus Local Signals

Global optimization, back-prop through whole graph. Local optimization, back-prop through sub-graphs.

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Global feedback pathway

Will these yield coherent models?

Equilibrium Propagation

38Negative phase Positive phase

The Discrepancy Reduction Family

• General process (Ororbia et. al., 2017 Adapt)• 1) Search for latent representations that better explain input/output (targets)

• 2) Reduce mismatch between currently “guessed” representations & target representations• Sum of internal, local losses (in nats) → total discrepancy (akin to “pseudo-energy”)

• Coordinated local learning rules

• Algorithms• Difference target propagation (DTP) (Lee et. al., 2014)• DTP-σ (Ororbia et. al., 2019)• LRA (Ororbia et. al., 2018, Ororbia et. al., 2019)• Others – targets could come from an external, interacting process

• NPC (neural predictive coding, Ororbia et. al., 2017/2018/2019)

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Adaptive Noise Difference Target Propagation (DTP-σ)

Image adapted from (Lillicrap et al., 2018)

zL zL˄

z L-1z L-1˄

g(z )Lg(z )L˄

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Error-Driven Local Representation Alignment (LRA-E)

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Transmit error along error feedback weights, and error correct the post-activations using the transmitted displacement/delta

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Calculate local error in layer below, measuring discrepancy between original post-activation and error-corrected post-activation

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Repeat the past several steps, error-correcting each layer further down within the network/system

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Optional…substitute & repeat!

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Aligning Local Representations• Credit assignment by optimizing subgraphs linked by error units

The Cauchy local loss:48

Aligning Local Representations• Credit assignment by optimizing subgraphs linked by error units,

motivated/inspired by (Rao & Ballard, 1999)

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Aligning Local Representations• Credit assignment by optimizing subgraphs linked by error units,

motivated/inspired by (Rao & Ballard, 1999)

There is more than one way to compute these changes 50

Some Experimental Results

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Experimental Results

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MNIST

Fashion MNIST

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3

Trousers

Dress

Shirt

(Ororbia et al., 2018 Bio)

Acquired Filters

Third level filters acquired, after a single pass through the data, by tanh network trained by a) backprop, b) LRA.

Backprop LRA

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Visualization of Topmost Post-Activities

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Angle between LRA, DFA, & DTP-σ against Backprop

Measuring Total Discrepancy in LRA-E

Equilibrium Propagation (8 layers):MNIST: 59.03% Fashion MNIST: 67.33%Equilibrium Propagation (3 layers):MNIST: 6.00% Fashion MNIST: 16.71%

Training Deep (& Thin) Networks

(Ororbia et al., 2018 Credit)

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Training Networks from Null Initialization

LWTA: SLWTA:

(Ororbia et al., 2018 Credit) 57

Training Stochastic Networks

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If time permits…let’s talk about modeling time…

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Training Neural Temporal/Recurrent Models

The Parallel Temporal Neural Coding Network (P-TNCN) (Ororbia et al., 2018)

(Ororbia et al., 2018 Continual)

• Integrating LRA into recurrent networks – result = Temporal Neural Coding Network

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Removing Back-Propagation through Time!• Each step in time entails: 1) generate hypothesis, 2) error correction in light of evidence

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Conclusions

• Backprop has issues, alignment algorithms fix one issue• Other algorithms such as DTP or EP are slow….

• Discrepancy reduction• Local representation alignment• Adaptive noise difference target propagation (DTP-σ)

• Showed promising results, stable and performant compared to alternatives such as Equilibrium Propagation & alignment algorithms• Can work with non-differentiable operators (discrete/stochastic)

• Can be used to train recurrent/temporal models too!64

Questions?

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References• (Ororbia et al., 2018, Credit) -- Alexander G. Ororbia II, Ankur Mali, Daniel Kifer,

and C. Lee Giles. “Deep Credit Assignment by Aligning Local Distributed Representations”. arXiv:1803.01834 [cs.LG].

• (Ororbia et al., 2018, Continual) -- Alexander G. Ororbia II , Ankur Mali, C. Lee Giles, and Daniel Kifer. “Continual Learning of Recurrent Neural Networks by Locally Aligning Distributed Representations”. arXiv:1810.07411 [cs.LG].

• (Ororbia et al., 2017, Adapt) -- Alexander G. Ororbia II , Patrick Haffner, David Reitter, and C. Lee Giles. “Learning to Adapt by Minimizing Discrepancy”. arXiv:1711.11542 [cs.LG].

• (Ororbia et al., 2018, Lifelong) -- Alexander G. Ororbia II , Ankur Mali, Daniel Kifer, and C. Lee Giles. “Lifelong Neural Predictive Coding: Sparsity Yields Less Forgetting when Learning Cumulatively”. arXiv:1905.10696 [cs.LG].

• (Ororbia et al., 2018, Bio) -- Alexander G. Ororbia II and Ankur Mali. “Biologically Motivated Algorithms for Propagating Local Target Representations”. In: Thirty-Third AAAI Conference on Artificial Intelligence.

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