Bayesian Compression for Deep Learning (1705.08665v4)

Abstract: Compression and computational efficiency in deep learning have become a problem of great significance. In this work, we argue that the most principled and effective way to attack this problem is by adopting a Bayesian point of view, where through sparsity inducing priors we prune large parts of the network. We introduce two novelties in this paper: 1) we use hierarchical priors to prune nodes instead of individual weights, and 2) we use the posterior uncertainties to determine the optimal fixed point precision to encode the weights. Both factors significantly contribute to achieving the state of the art in terms of compression rates, while still staying competitive with methods designed to optimize for speed or energy efficiency.

• The paper introduces hierarchical priors and uncertainty-based precision tuning to prune entire nodes and optimize weight encoding.
• It leverages a variational Bayesian framework to achieve significant compression while maintaining speed and energy efficiency on models like LeNet and VGG.
• Empirical results demonstrate state-of-the-art compression rates, offering practical solutions for fixed-point deployment in constrained hardware environments.

Bayesian Compression for Deep Learning: A Detailed Examination

The paper "Bayesian Compression for Deep Learning" addresses the critical issue of compressing deep neural networks to enhance their computational efficiency and applicability in real-world scenarios. Neural networks, though highly successful, pose challenges due to their extensive energy consumption and impracticality for real-time applications and bandwidth-limited channels. This work proposes a Bayesian approach to compress these networks by employing sparsity-inducing priors, significantly contributing to achieving superior compression rates while maintaining competitiveness in speed and energy efficiency.

Core Contributions

The paper introduces two key innovations in the field of Bayesian neural network pruning:

1. Hierarchical Priors for Node Pruning: Rather than targeting individual weights, the authors utilize hierarchical priors to prune entire nodes, thereby simplifying coding schemes and improving network efficiency.
2. Posterior Uncertainty for Precision Determination: The work leverages posterior uncertainties to deduce the optimal fixed-point precision required to encode the weights, facilitating effective compression and practical implementation.

These advancements enable the realization of state-of-the-art compression rates, showing compatibility with competitive speed and energy-efficient methods.

Methodological Framework

The authors integrate variational Bayesian approximation within a model compression framework. The Minimum Description Length (MDL) principle emerges as a thematic underpinning, promoting models that minimize the sum of model complexity and data misfit costs.

Two prior settings are pivotal:

• Normal-Jeffreys Prior: An improper log-uniform prior leading to a sparsity-inducing distribution favorable for group node pruning. The Gaussian variational approximation is used here for efficient inference.
• Horseshoe Prior: A half-Cauchy prior promoting "global-local" shrinkage, where local shrinkage parameters allow for certain weights to naturally escape the global regularization effect.

Each framework provides a distinct pathway to probabilistically prune network nodes and reduce unnecessary computational overhead.

Empirical Results and Findings

The paper extensively evaluates the proposed Bayesian compression methods on recognized architectures like LeNet and VGG, demonstrating notable compression and speed capabilities:

• The Bayesian compression methods achieved remarkable performance in terms of compression rates, outperforming contemporary methods like Sparse VD and Generalized Dropout.
• Specific layers were reduced in size, optimizing the architectures without hampering accuracy, showcasing efficient pruning mechanism through probabilistic modeling.
• The models learned to adaptively assign bit precision to weights, illustrating practical solutions for fixed-point deployment in constrained hardware environments.

Implications and Future Directions

The research offers a pragmatic look into optimizing neural networks for deployment in resource-constrained environments, contributing to energy-efficient AI solutions. This Bayesian perspective not only maximizes compression efficiency but also aligns weight precision with practical hardware requirements.

Looking forward, future developments may explore more intricate posterior approximations beyond mean-field variational methods to enhance variance accuracy. Furthermore, extending these Bayesian compression techniques to other model types and exploring integration with hardware-level optimizations could yield further enhancements in real-world applications.

In conclusion, this paper provides a significant stride towards addressing computational inefficiency in deep learning through a principled Bayesian framework, emphasizing the balance between network performance and compression.