A Neural Network Implementation for Free Energy Principle
Jingwei Liu
The free energy principle (FEP), as an encompassing framework and a unified
brain theory, has been widely applied to account for various problems in fields
such as cognitive science, neuroscience, social interaction, and hermeneutics.
As a computational model deeply rooted in math and statistics, FEP posits an
optimization problem based on variational Bayes, which is solved either by
dynamic programming or expectation maximization in practice. However, there
seems to be a bottleneck in extending the FEP to machine learning and
implementing such models with neural networks. This paper gives a preliminary
attempt at bridging FEP and machine learning, via a classical neural network
model, the Helmholtz machine. As a variational machine learning model, the
Helmholtz machine is optimized by minimizing its free energy, the same
objective as FEP. Although the Helmholtz machine is not temporal, it gives an
ideal parallel to the vanilla FEP and the hierarchical model of the brain,
under which the active inference and predictive coding could be formulated
coherently. Besides a detailed theoretical discussion, the paper also presents
a preliminary experiment to validate the hypothesis. By fine-tuning the trained
neural network through active inference, the model performance is promoted to
accuracy above 99\%. In the meantime, the data distribution is continuously
deformed to a salience that conforms to the model representation, as a result
of active sampling.