Modern neural networks are often massively overparameterized leading to high compute costs during training and at inference. One effective method to improve both the compute and energy efficiency of neural networks while maintaining good performance is structured pruning, where full network structures (e.g.

In this work, we address this challenge by proposing BMRS: B ayesian M odel R eduction for S tructured pruning.

This technical note considers the sampling of outcomes that provide the greatest amount of information about the structure of underlying world models. This generalisation furnishes a principled approach to structure learning under a plausible set of generative models or hypotheses. In active inference, policies - i.e., combinations of actions - are selected based on their expected free energy, which comprises expected information gain and value. Information gain corresponds to the KL divergence between predictive posteriors with, and without, the consequences of action. Posteriors over models can be evaluated quickly and efficiently using Bayesian Model Reduction, based upon accumulated posterior beliefs about model parameters. The ensuing information gain can then be used to select actions that disambiguate among alternative models, in the spirit of optimal experimental design. We illustrate this kind of active selection or reasoning using partially observed discrete models; namely, a 'three-ball' paradigm used previously to describe artificial insight and 'aha moments' via (synthetic) introspection or sleep. We focus on the sample efficiency afforded by seeking outcomes that resolve the greatest uncertainty about the world model, under which outcomes are generated.

Modern neural networks are often massively overparameterized leading to high compute costs during training and at inference. One effective method to improve both the compute and energy efficiency of neural networks while maintaining good performance is structured pruning, where full network structures (e.g. In this work, we propose Bayesian Model Reduction for Structured pruning (BMRS), a fully end-to-end Bayesian method of structured pruning. BMRS is based on two recent methods: Bayesian structured pruning with multiplicative noise, and Bayesian model reduction (BMR), a method which allows efficient comparison of Bayesian models under a change in prior. We present two realizations of BMRS derived from different priors which yield different structured pruning characteristics: 1) BMRSN with the truncated log-normal prior, which offers reliable compression rates and accuracy without the need for tuning any thresholds and 2) BMRSU with the truncated log-uniform prior that can achieve more aggressive compression based on the boundaries of truncation.

Modern neural networks are often massively overparameterized leading to high compute costs during training and at inference. One effective method to improve both the compute and energy efficiency of neural networks while maintaining good performance is structured pruning, where full network structures (e.g. neurons or convolutional filters) that have limited impact on the model output are removed. In this work, we propose Bayesian Model Reduction for Structured pruning (BMRS), a fully end-to-end Bayesian method of structured pruning. BMRS is based on two recent methods: Bayesian structured pruning with multiplicative noise, and Bayesian model reduction (BMR), a method which allows efficient comparison of Bayesian models under a change in prior. We present two realizations of BMRS derived from different priors which yield different structured pruning characteristics: 1) BMRS_N with the truncated log-normal prior, which offers reliable compression rates and accuracy without the need for tuning any thresholds and 2) BMRS_U with the truncated log-uniform prior that can achieve more aggressive compression based on the boundaries of truncation. Overall, we find that BMRS offers a theoretically grounded approach to structured pruning of neural networks yielding both high compression rates and accuracy. Experiments on multiple datasets and neural networks of varying complexity showed that the two BMRS methods offer a competitive performance-efficiency trade-off compared to other pruning methods.

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.

Deep learning's immense capabilities are often constrained by the complexity of its models, leading to an increasing demand for effective sparsification techniques. Bayesian sparsification for deep learning emerges as a crucial approach, facilitating the design of models that are both computationally efficient and competitive in terms of performance across various deep learning applications. The state-of-the-art -- in Bayesian sparsification of deep neural networks -- combines structural shrinkage priors on model weights with an approximate inference scheme based on stochastic variational inference. However, model inversion of the full generative model is exceptionally computationally demanding, especially when compared to standard deep learning of point estimates. In this context, we advocate for the use of Bayesian model reduction (BMR) as a more efficient alternative for pruning of model weights. As a generalization of the Savage-Dickey ratio, BMR allows a post-hoc elimination of redundant model weights based on the posterior estimates under a straightforward (non-hierarchical) generative model. Our comparative study highlights the advantages of the BMR method relative to established approaches based on hierarchical horseshoe priors over model weights. We illustrate the potential of BMR across various deep learning architectures, from classical networks like LeNet to modern frameworks such as Vision Transformers and MLP-Mixers.