[Paper Review] What does the free energy principle tell us about the brain?

Samuel J. Gershman|arXiv (Cornell University)|Jan 23, 2019

Neuroscience, Education and Cognitive Function5 citations

TL;DR

This paper clarifies the free energy principle (FEP) as a unifying framework for brain function, showing it reduces to Bayesian inference, predictive coding, and active inference under specific assumptions. It demonstrates that FEP's distinctive predictions emerge only when assumptions—such as exact posterior inference, deterministic outcomes, or utility-log probability correspondence—deviate from standard models, enabling falsifiable distinctions from alternative theories.

ABSTRACT

The free energy principle has been proposed as a unifying account of brain function. It is closely related, and in some cases subsumes, earlier unifying ideas such as Bayesian inference, predictive coding, and active learning. This article clarifies these connections, teasing apart distinctive and shared predictions.

Motivation & Objective

• To clarify the theoretical claims of the free energy principle (FEP) and distinguish them from related theories like Bayesian inference and predictive coding.
• To identify the specific assumptions under which FEP makes unique, falsifiable predictions, rather than being a tautological principle.
• To evaluate FEP’s empirical credibility by deconstructing its assumptions and linking them to testable neural and behavioral predictions.
• To assess the conditions under which FEP diverges from standard models such as information gain policies or Bayesian decision theory.
• To demonstrate that FEP's distinctive contributions arise only when assumptions like exact inference or utility-log probability correspondence are violated.

Proposed method

• Deconstructs FEP by analyzing its core components: generative models, variational inference, and free energy minimization.
• Compares FEP to Bayesian brain hypothesis using Bayes' rule: $ p(s|o) = \frac{p(o|s)p(s)}{p(o)} $, showing equivalence when the variational family includes the exact posterior.
• Analyzes predictive coding as a special case of FEP, arising under restricted variational families and specific optimization schemes.
• Examines active inference via expected free energy $ \mathcal{G} $, contrasting it with information gain $ \mathcal{I} $, especially under stochastic vs. deterministic outcomes.
• Applies the planning as inference framework, interpreting utility as log prior probability $ u(o) = \log p(o|\pi) $, linking FEP to Bayesian decision theory.
• Uses Kullback-Leibler divergence $ \mathcal{D}[p(s|o,\pi) \| p(s|\pi)] $ to formalize information gain and epistemic value in active inference.

Experimental results

Research questions

• RQ1 Under what conditions does the free energy principle make predictions distinct from the Bayesian brain hypothesis?
• RQ2 When does predictive coding emerge as a consequence of the free energy principle, and what assumptions are required?
• RQ3 How does active inference differ from a pure information gain policy, particularly when observations are stochastic?
• RQ4 In what scenarios does FEP diverge from standard Bayesian decision theory, and what are the empirical implications?
• RQ5 To what extent is the planning as inference interpretation of FEP a notational variant of Bayesian decision theory, and when does it yield novel predictions?

Key findings

• When the variational family includes the exact posterior, minimizing free energy is equivalent to exact Bayesian inference, making FEP indistinguishable from the Bayesian brain hypothesis in passive observation settings.
• Predictive coding arises only under specific restrictions of the variational family and a particular optimization scheme, not as a generic consequence of FEP.
• In active inference, when the posterior is exact and outcomes are deterministic, FEP reduces to an information gain policy; however, with stochastic outcomes, it induces risk-averse behavior not captured by information gain alone.
• When utilities are interpreted as log prior probabilities, FEP reduces to planning as inference, a form of Bayesian utility maximization, making its predictions indistinguishable from standard Bayesian decision theory.
• FEP makes distinctive predictions only when utilities do not correspond to log probabilities, or when algorithmic approximations or neural implementations differ from standard models.
• The theory's empirical testability depends on verifying its underlying assumptions, such as the structure of the generative model, the quality of the variational approximation, and the nature of action-outcome dependencies.