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Predictive Coding Approximates Backprop along Arbitrary Computation Graphs (2006.04182v5)

Published 7 Jun 2020 in cs.LG and cs.NE

Abstract: Backpropagation of error (backprop) is a powerful algorithm for training machine learning architectures through end-to-end differentiation. However, backprop is often criticised for lacking biological plausibility. Recently, it has been shown that backprop in multilayer-perceptrons (MLPs) can be approximated using predictive coding, a biologically-plausible process theory of cortical computation which relies only on local and Hebbian updates. The power of backprop, however, lies not in its instantiation in MLPs, but rather in the concept of automatic differentiation which allows for the optimisation of any differentiable program expressed as a computation graph. Here, we demonstrate that predictive coding converges asymptotically (and in practice rapidly) to exact backprop gradients on arbitrary computation graphs using only local learning rules. We apply this result to develop a straightforward strategy to translate core machine learning architectures into their predictive coding equivalents. We construct predictive coding CNNs, RNNs, and the more complex LSTMs, which include a non-layer-like branching internal graph structure and multiplicative interactions. Our models perform equivalently to backprop on challenging machine learning benchmarks, while utilising only local and (mostly) Hebbian plasticity. Our method raises the potential that standard machine learning algorithms could in principle be directly implemented in neural circuitry, and may also contribute to the development of completely distributed neuromorphic architectures.

Citations (111)

Summary

  • The paper demonstrates that predictive coding converges to backpropagation gradients using local operations and Hebbian updates.
  • It extends the framework to arbitrary computation graphs, enabling optimization of various neural architectures such as CNNs, RNNs, and LSTMs.
  • The authors provide theoretical proofs and benchmark validations on datasets like SVHN and CIFAR, bridging neuroscience and machine learning.

Summary of "Predictive Coding Approximates Backprop along Arbitrary Computation Graphs"

The paper by Millidge, Tschantz, and Buckley presents a significant exploration into the potential compatibility between predictive coding and backpropagation. It investigates the hypothesis that predictive coding can serve as an approximation to backpropagation across arbitrary computation graphs, providing an alternative computational model rooted in biological plausibility. The authors propose that predictive coding, long considered a theory for cortical computation, can converge asymptotically to backpropagation gradients using only local operations and Hebbian learning, which are more akin to neural mechanisms observed in biological systems.

Main Contributions

  1. Integration of Predictive Coding with Machine Learning Architectures: The paper successfully integrates predictive coding with standard machine learning architectures such as convolutional neural networks (CNNs), recurrent neural networks (RNNs), and long short-term memory networks (LSTMs). These implementations demonstrate that predictive coding can achieve performance comparable to backpropagation on established benchmarks like SVHN and CIFAR.
  2. Extension to Arbitrary Computation Graphs: Predictive coding is extended beyond simple hierarchical structures to operate effectively over arbitrary computation graphs. This means any differentiable architecture capable of being expressed as a computation graph, ranging from standard feedforward networks to more complex programs, could theoretically be optimized using predictive coding.
  3. Theoretical Proofs and Practical Implications: The authors provide theoretical proofs that establish the conditions under which predictive coding not only approximates but can become equivalent to backpropagation gradients. This equivalence is achieved without the need for global synchronization or non-local information, resolving long-standing criticisms regarding the biological implausibility of backpropagation.

Implications and Future Directions

  • Biological Plausibility: This work substantially bolsters the argument that machine learning algorithms, specifically those involving gradient-based optimization, could be directly implemented in neural circuitry. The reliance on local operations and Hebbian updates emphasizes a shift towards algorithms that mimic brain-like computations, potentially enhancing neuromorphic computing designs.
  • Distributed Neuromorphic Hardware: The findings suggest a pathway for developing entirely distributed neuromorphic hardware that can compute in parallel, mimicking biological processes more closely than traditional neural network training methods. This could lead to efficient real-time learning processes applicable in edge devices and other resource-constrained environments.
  • Scalability and Computational Cost: While equivalent performance to backpropagation was observed, the current implementation incurs significant computational overhead due to iterative convergence processes. Future work should focus on reducing this overhead, possibly through parallelization or more efficient convergence strategies, to make predictive coding a competitive alternative.
  • Integration with Neuroscience: The paper opens the door to further interdisciplinary studies that integrate neuroscience with artificial intelligence. The predictive coding framework provides a strong premise for testing neuroscientific models of learning and adaptation in computing environments, potentially leading to new insights into cognitive processes like perception and decision-making.

Conclusion

The research conducted by Millidge et al. provokes thoughtful consideration of alternative computational paradigms that align more closely with biological systems. By demonstrating predictive coding's potential to replicate backpropagation's effectiveness across complex computation graphs, the paper sets a foundation for developing machine learning methods rooted deeply in the principles of neurobiology. It represents a step toward harmonizing artificial intelligence methodologies with the intricate functionalities of the brain, fostering innovations in both fields. Future research inspired by these results could lead to the creation of more adaptable, efficient, and biologically consonant learning systems.

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