A Bregman Learning Framework for Sparse Neural Networks

• URL: http://arxiv.org/abs/2105.04319v1
• Date: Mon, 10 May 2021 12:56:01 GMT
• Title: A Bregman Learning Framework for Sparse Neural Networks
• Authors: Leon Bungert, Tim Roith, Daniel Tenbrinck, Martin Burger
• Abstract summary: We propose a learning framework based on Bregman iterations to train sparse neural networks. We derive a baseline algorithm called LinBreg, an accelerated version using momentum, and AdaBreg, which is a Bregmanized generalization of the Adam algorithm.
• Score: 1.7778609937758323
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a learning framework based on stochastic Bregman iterations to train sparse neural networks with an inverse scale space approach. We derive a baseline algorithm called LinBreg, an accelerated version using momentum, and AdaBreg, which is a Bregmanized generalization of the Adam algorithm. In contrast to established methods for sparse training the proposed family of algorithms constitutes a regrowth strategy for neural networks that is solely optimization-based without additional heuristics. Our Bregman learning framework starts the training with very few initial parameters, successively adding only significant ones to obtain a sparse and expressive network. The proposed approach is extremely easy and efficient, yet supported by the rich mathematical theory of inverse scale space methods. We derive a statistically profound sparse parameter initialization strategy and provide a rigorous stochastic convergence analysis of the loss decay and additional convergence proofs in the convex regime. Using only 3.4% of the parameters of ResNet-18 we achieve 90.2% test accuracy on CIFAR-10, compared to 93.6% using the dense network. Our algorithm also unveils an autoencoder architecture for a denoising task. The proposed framework also has a huge potential for integrating sparse backpropagation and resource-friendly training.

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