[Paper Review] Towards Biologically Plausible Deep Learning

Yoshua Bengio, Dong-Hyun Lee+3 more|arXiv (Cornell University)|Feb 14, 2015

Neural dynamics and brain function37 references296 citations

TL;DR

This paper proposes a biologically plausible learning framework for deep neural networks by interpreting Spike-Timing-Dependent Plasticity (STDP) as stochastic gradient descent on a variational objective, enabling credit assignment without backpropagation. It shows that approximate inference via neural dynamics and denoising auto-encoder training can replace backpropagation while achieving competitive generative modeling performance.

ABSTRACT

Neuroscientists have long criticised deep learning algorithms as incompatible with current knowledge of neurobiology. We explore more biologically plausible versions of deep representation learning, focusing here mostly on unsupervised learning but developing a learning mechanism that could account for supervised, unsupervised and reinforcement learning. The starting point is that the basic learning rule believed to govern synaptic weight updates (Spike-Timing-Dependent Plasticity) arises out of a simple update rule that makes a lot of sense from a machine learning point of view and can be interpreted as gradient descent on some objective function so long as the neuronal dynamics push firing rates towards better values of the objective function (be it supervised, unsupervised, or reward-driven). The second main idea is that this corresponds to a form of the variational EM algorithm, i.e., with approximate rather than exact posteriors, implemented by neural dynamics. Another contribution of this paper is that the gradients required for updating the hidden states in the above variational interpretation can be estimated using an approximation that only requires propagating activations forward and backward, with pairs of layers learning to form a denoising auto-encoder. Finally, we extend the theory about the probabilistic interpretation of auto-encoders to justify improved sampling schemes based on the generative interpretation of denoising auto-encoders, and we validate all these ideas on generative learning tasks.

Motivation & Objective

• To address the biological implausibility of back-propagation in deep learning, particularly its reliance on symmetric weights and precise error signal propagation.
• To provide a machine learning interpretation of STDP that supports efficient credit assignment across deep networks.
• To unify supervised, unsupervised, and reinforcement learning under a common framework based on neural dynamics and variational inference.
• To demonstrate that denoising auto-encoders trained via forward and backward activation propagation can approximate gradient updates without backpropagation.
• To validate the approach on generative modeling tasks, showing improved likelihood and sample quality through iterative inference.

Proposed method

• Interprets STDP as stochastic gradient descent on a variational objective function, where feedback signals modulate neuronal firing rates to align with gradient directions.
• Models neural dynamics as approximate inference in a probabilistic graphical model, with hidden states updated to maximize the joint likelihood of data and hidden variables.
• Uses a denoising auto-encoder structure where pairs of layers learn to reconstruct corrupted inputs, enabling gradient estimation via forward and backward propagation without weight tying.
• Applies a variational EM framework with approximate posteriors, where the E-step is implemented by neural dynamics and the M-step by weight updates based on STDP.
• Introduces a modified inference procedure that fills in missing inputs by iteratively maximizing the likelihood of visible inputs given hidden states.
• Employs noise injection in the inference process to approximate MCMC sampling, improving sample quality beyond standard variational inference.

Experimental results

Research questions

• RQ1 Can STDP be interpreted as a form of stochastic gradient descent that supports credit assignment in deep networks?
• RQ2 How can neural dynamics be used to implement approximate inference in a probabilistic model without exact MCMC sampling?
• RQ3 Can denoising auto-encoders trained via forward and backward propagation replace backpropagation in deep learning?
• RQ4 Does iterative inference based on variational EM with noise injection improve generative model quality?
• RQ5 Can this framework unify supervised, unsupervised, and reinforcement learning under a single biologically plausible mechanism?

Key findings

• STDP can be interpreted as stochastic gradient descent on a variational objective, providing a biologically plausible mechanism for credit assignment in deep networks.
• Neural dynamics that push firing rates toward better objective values correspond to approximate inference in a probabilistic model, avoiding the need for exact MCMC sampling.
• The proposed method achieves competitive performance on generative learning tasks, with improved joint likelihood and sample quality compared to standard variational inference.
• Iterative inference using the model's own dynamics leads to effective missing-data imputation, as demonstrated in the reconstruction of corrupted inputs.
• Denoising auto-encoder training with forward and backward activation propagation approximates gradient updates without requiring symmetric weights or error backpropagation.
• Noise injection during inference enhances sampling quality, suggesting a path to MCMC-like inference within a biologically plausible framework.