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The free energy principle (FEP), as an encompassing framework and a unifiedbrain theory, has been widely applied to account for various problems in fieldssuch as cognitive science, neuroscience, social interaction, and hermeneutics.As a computational model deeply rooted in math and statistics, FEP posits anoptimization problem based on variational Bayes, which is solved either bydynamic programming or expectation maximization in practice. However, thereseems to be a bottleneck in extending the FEP to machine learning andimplementing such models with neural networks. This paper gives a preliminaryattempt at bridging FEP and machine learning, via a classical neural networkmodel, the Helmholtz machine. As a variational machine learning model, theHelmholtz machine is optimized by minimizing its free energy, the sameobjective as FEP. Although the Helmholtz machine is not temporal, it gives anideal parallel to the vanilla FEP and the hierarchical model of the brain,under which the active inference and predictive coding could be formulatedcoherently. Besides a detailed theoretical discussion, the paper also presentsa preliminary experiment to validate the hypothesis. By fine-tuning the trainedneural network through active inference, the model performance is promoted toaccuracy above 99\%. In the meantime, the data distribution is continuouslydeformed to a salience that conforms to the model representation, as a resultof active sampling.

A Neural Network Implementation for Free Energy Principle