[Paper Review] Predictive Coding: a Theoretical and Experimental Review

Beren Millidge, Anil K. Seth+1 more|arXiv (Cornell University)|Jul 27, 2021

Neural dynamics and brain functionNeuroscience164 references26 citations

TL;DR

This paper surveys predictive coding as a Bayesian variational inference framework, reviews its mathematical structure, neural implementation, and connections to machine learning and control theory.

ABSTRACT

Predictive coding offers a potentially unifying account of cortical function -- postulating that the core function of the brain is to minimize prediction errors with respect to a generative model of the world. The theory is closely related to the Bayesian brain framework and, over the last two decades, has gained substantial influence in the fields of theoretical and cognitive neuroscience. A large body of research has arisen based on both empirically testing improved and extended theoretical and mathematical models of predictive coding, as well as in evaluating their potential biological plausibility for implementation in the brain and the concrete neurophysiological and psychological predictions made by the theory. Despite this enduring popularity, however, no comprehensive review of predictive coding theory, and especially of recent developments in this field, exists. Here, we provide a comprehensive review both of the core mathematical structure and logic of predictive coding, thus complementing recent tutorials in the literature. We also review a wide range of classic and recent work within the framework, ranging from the neurobiologically realistic microcircuits that could implement predictive coding, to the close relationship between predictive coding and the widely-used backpropagation of error algorithm, as well as surveying the close relationships between predictive coding and modern machine learning techniques.

Motivation & Objective

• Summarize the core mathematical structure and logic of predictive coding within a probabilistic (variational) framework.
• Survey neurobiological plausibility and proposed cortical microcircuit implementations.
• Review connections between predictive coding and machine learning methods, including backpropagation and normalizing flows.
• Explore extensions to dynamics, precision, and action/active inference.

Proposed method

• Frame predictive coding as variational inference with Gaussian generative models.
• Derive predictive coding update rules from the variational free energy. Define prediction errors and their role in updating states and parameters.
• Discuss EM-like alternating optimization for learning the generative model alongside the posterior.
• Relate predictive coding to classical algorithms (Kalman filtering, backpropagation) and to active inference.

Experimental results

Research questions

• RQ1 How can predictive coding be formulated as an approximate Bayesian/inference process?
• RQ2 What are the mathematical mechanisms by which predictive coding minimizes prediction error across a hierarchy?
• RQ3 How can predictive coding be implemented in biologically plausible neural microcircuits?
• RQ4 What is the relationship between predictive coding and established machine learning methods like backpropagation and normalizing flows?
• RQ5 How do dynamics, precision, and action integrate into the predictive coding framework? (including active inference)

Key findings

• Predictive coding can be recast as variational inference minimizing a free energy bound.
• The energy term reduces to a sum of weighted prediction errors, linking perception and learning.
• Gradient-descent updates yield concrete rules for state and parameter learning in a hierarchical model.
• The framework interfaces with established algorithms like Kalman filtering and backpropagation under certain assumptions.
• Extensions to dynamics, precision, and action connect predictive coding to active inference and control theory.