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Jeffrey Krichmar

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2 papers

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AAAI Conference 2024 Conference Paper

Understanding and Improving Optimization in Predictive Coding Networks

Nicholas Alonso
Jeffrey Krichmar
Emre Neftci

Backpropagation (BP), the standard learning algorithm for artificial neural networks, is often considered biologically implausible. In contrast, the standard learning algorithm for predictive coding (PC) models in neuroscience, known as the inference learning algorithm (IL), is a promising, bio-plausible alternative. However, several challenges and questions hinder IL's application to real-world problems. For example, IL is computationally demanding, and without memory-intensive optimizers like Adam, IL may converge to poor local minima. Moreover, although IL can reduce loss more quickly than BP, the reasons for these speedups or their robustness remains unclear. In this paper, we tackle these challenges by 1) altering the standard implementation of PC circuits to substantially reduce computation, 2) developing a novel optimizer that improves the convergence of IL without increasing memory usage, and 3) establishing theoretical results that help elucidate the conditions under which IL is sensitive to second and higher-order information.

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NeurIPS Conference 2022 Conference Paper

A Theoretical Framework for Inference Learning

Nick Alonso
Beren Millidge
Jeffrey Krichmar
Emre O Neftci

Backpropagation (BP) is the most successful and widely used algorithm in deep learning. However, the computations required by BP are challenging to reconcile with known neurobiology. This difficulty has stimulated interest in more biologically plausible alternatives to BP. One such algorithm is the inference learning algorithm (IL). IL trains predictive coding models of neural circuits and has achieved equal performance to BP on supervised and auto-associative tasks. In contrast to BP, however, the mathematical foundations of IL are not well-understood. Here, we develop a novel theoretical framework for IL. Our main result is that IL closely approximates an optimization method known as implicit stochastic gradient descent (implicit SGD), which is distinct from the explicit SGD implemented by BP. Our results further show how the standard implementation of IL can be altered to better approximate implicit SGD. Our novel implementation considerably improves the stability of IL across learning rates, which is consistent with our theory, as a key property of implicit SGD is its stability. We provide extensive simulation results that further support our theoretical interpretations and find IL achieves quicker convergence when trained with mini-batch size one while performing competitively with BP for larger mini-batches when combined with Adam.

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