Some Interesting Observations on the Free Energy Principle

Biehl et al. (2021) present some interesting observations on an early formulation of the free energy principle. We use these observations to scaffold a discussion of the technical arguments that underwrite the free energy principle. This discussion focuses on solenoidal coupling between various (subsets of) states in sparsely coupled systems that possess a Markov blanket—and the distinction between exact and approximate Bayesian inference, implied by the ensuing Bayesian mechanics.

A Memory Constrained Approximate Bayesian Inference Approach Using Incremental Construction of Clique Trees

<div>The complexity of inference using the belief propagation algorithms increases exponentially with the maximum clique size. We describe an approximate inference approach when there are clique size limitations due to memory constraints using incremental construction of clique trees.<br></div>

A Memory Constrained Approximate Bayesian Inference Approach Using Incremental Construction of Clique Trees

<div>The complexity of inference using the belief propagation algorithms increases exponentially with the maximum clique size. We describe an approximate inference approach when there are clique size limitations due to memory constraints using incremental construction of clique trees.<br></div>

A recurrent cortical model can parsimoniously explain the effect of expectations on sensory processes

The effect of prior knowledge and expectations on perceptual and decision-making processes have been extensively studied. Yet, the computational mechanisms underlying those effects have been a controversial issue. Recently, using a recursive Bayesian updating scheme, unmet expectations have been shown to entail further computations, and consequently delay perceptual processes. Here we take a step further and model these empirical findings with a recurrent cortical model, which was previously suggested to approximate Bayesian inference (Heeger, 2017). Our model fitting results show that the cortical model can successfully predict the behavioral effects of expectation. That is, when the actual sensory input does not match with the expectations, the sensory process needs to be completed with additional, and consequently longer, computations. We suggest that this process underlies the delay in perceptual thresholds in unmet expectations. Overall our findings demonstrate that a parsimonious recurrent cortical model can explain the effects of expectation on sensory processes.