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Predictive Coding: Towards a Future of Deep Learning beyond Backpropagation?

Beren Millidge, Tommaso Salvatori, Yuhang Song, Rafal Bogacz, Thomas Lukasiewicz

TL;DR

The paper surveys predictive coding as a neuroscience-inspired alternative to backpropagation, highlighting its local learning and energy-based updates. It shows theoretical connections to backpropagation and variational inference, and demonstrates that predictive coding networks can match or approach BP on standard benchmarks while offering greater flexibility and parallelizability. It also covers extensions to associative memories, graph-structured networks, and control/robotics, illustrating broad applicability. The authors argue that PCN-based architectures, especially on neuromorphic hardware, may enable scalable, brain-like learning beyond backpropagation.

Abstract

The backpropagation of error algorithm used to train deep neural networks has been fundamental to the successes of deep learning. However, it requires sequential backward updates and non-local computations, which make it challenging to parallelize at scale and is unlike how learning works in the brain. Neuroscience-inspired learning algorithms, however, such as \emph{predictive coding}, which utilize local learning, have the potential to overcome these limitations and advance beyond current deep learning technologies. While predictive coding originated in theoretical neuroscience as a model of information processing in the cortex, recent work has developed the idea into a general-purpose algorithm able to train neural networks using only local computations. In this survey, we review works that have contributed to this perspective and demonstrate the close theoretical connections between predictive coding and backpropagation, as well as works that highlight the multiple advantages of using predictive coding models over backpropagation-trained neural networks. Specifically, we show the substantially greater flexibility of predictive coding networks against equivalent deep neural networks, which can function as classifiers, generators, and associative memories simultaneously, and can be defined on arbitrary graph topologies. Finally, we review direct benchmarks of predictive coding networks on machine learning classification tasks, as well as its close connections to control theory and applications in robotics.

Predictive Coding: Towards a Future of Deep Learning beyond Backpropagation?

TL;DR

The paper surveys predictive coding as a neuroscience-inspired alternative to backpropagation, highlighting its local learning and energy-based updates. It shows theoretical connections to backpropagation and variational inference, and demonstrates that predictive coding networks can match or approach BP on standard benchmarks while offering greater flexibility and parallelizability. It also covers extensions to associative memories, graph-structured networks, and control/robotics, illustrating broad applicability. The authors argue that PCN-based architectures, especially on neuromorphic hardware, may enable scalable, brain-like learning beyond backpropagation.

Abstract

The backpropagation of error algorithm used to train deep neural networks has been fundamental to the successes of deep learning. However, it requires sequential backward updates and non-local computations, which make it challenging to parallelize at scale and is unlike how learning works in the brain. Neuroscience-inspired learning algorithms, however, such as \emph{predictive coding}, which utilize local learning, have the potential to overcome these limitations and advance beyond current deep learning technologies. While predictive coding originated in theoretical neuroscience as a model of information processing in the cortex, recent work has developed the idea into a general-purpose algorithm able to train neural networks using only local computations. In this survey, we review works that have contributed to this perspective and demonstrate the close theoretical connections between predictive coding and backpropagation, as well as works that highlight the multiple advantages of using predictive coding models over backpropagation-trained neural networks. Specifically, we show the substantially greater flexibility of predictive coding networks against equivalent deep neural networks, which can function as classifiers, generators, and associative memories simultaneously, and can be defined on arbitrary graph topologies. Finally, we review direct benchmarks of predictive coding networks on machine learning classification tasks, as well as its close connections to control theory and applications in robotics.
Paper Structure (10 sections, 6 equations, 4 figures)

This paper contains 10 sections, 6 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Overview of Predictive Coding
  3. Predictive Coding Networks
  4. Predictive Coding as Variational Inference
  5. Predictive Coding and Backpropagation
  6. Performance of Predictive Coding
  7. Associative Memories
  8. Learning on Arbitrary Graph Topologies
  9. Predictive Coding for Control and Robotics
  10. Summary and Open Challenges

Figures (4)

  • Figure 1: (a): A multilayer PCN trained on a data point of MNIST. Here, the neural activities of a specific layer predict the ones of the previous layer in a forward direction. The error in this prediction is then propagated back down the hierarchy. (b) Difference between the update rules of BP (left) and PC (right). Particularly, the loss function of BP defines an error only on the output layer, and this error is minimized via gradient descent. In very deep networks, this causes weights to be updated to minimize an error that could be dozens of layers away. By contract PC minimizes a local energy function for each layer.
  • Figure 2: (a) Historical and conceptual sketch of the results unifying predictive coding (PC) and backpropagation (BP). (b) Sketch of a generative PCN. In contrast to networks trained for classification, the input image is presented in the first layer of the network. The energy minimization updates the weights to get zero (or low) error on it. (c) Examples of generated MNIST and FashionMNIST using a generative PCN. (d) Examples of reconstructed (left) and denoised (right) MNIST and FashionMNIST images using a generative PCN. Figures (c,d) are taken from the original papers, i.e., ororbia20 and salvatori2022learning, respectively.
  • Figure 3: Examples of retrieved ImageNet pictures when presenting a corrupted key with gaussian noise of mean zero and variance $\eta = 2.0$ (left) and an incomplete key, where only $\frac{1}{4}$ of the original pixels were provided. Particularly, $100$ images were stored in this example.
  • Figure 4: (a) Difference in topology between an ANN (left) and a sketch of a network of structural connections that link distinct neuronal elements in a brain (right). Figure taken from salvatori2022learning. (b) Graphical representation of the joint minimization of free energy by action and control to enable a simultaneous state estimation and action selection in a robotic grasping task with a humanoid robot. Figure taken from oliver2021empirical.