Principled Pruning of Bayesian Neural Networks through Variational Free Energy Minimization

TL;DR

This paper introduces a principled Bayesian neural network pruning method based on variational free energy minimization, offering a theoretically sound, iterative approach that outperforms existing pruning techniques in model performance.

Contribution

The paper formulates Bayesian model reduction for neural network pruning and develops an iterative algorithm that reduces approximation errors and improves upon current methods.

Findings

Better model performance compared to state-of-the-art pruning methods

Clear stopping criterion for pruning process

Effective on UCI datasets with various inference algorithms

Abstract

Bayesian model reduction provides an efficient approach for comparing the performance of all nested sub-models of a model, without re-evaluating any of these sub-models. Until now, Bayesian model reduction has been applied mainly in the computational neuroscience community on simple models. In this paper, we formulate and apply Bayesian model reduction to perform principled pruning of Bayesian neural networks, based on variational free energy minimization. Direct application of Bayesian model reduction, however, gives rise to approximation errors. Therefore, a novel iterative pruning algorithm is presented to alleviate the problems arising with naive Bayesian model reduction, as supported experimentally on the publicly available UCI datasets for different inference algorithms. This novel parameter pruning scheme solves the shortcomings of current state-of-the-art pruning methods that are used by the signal processing community. The proposed approach has a clear stopping criterion and minimizes the same objective that is used during training. Next to these benefits, our experiments indicate better model performance in comparison to state-of-the-art pruning schemes.