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.

提出一种基于随机Bregman迭代的学习框架，用于训练稀疏神经网络，采用逆比例空间方法。该方法具有很高的效率和易实现性，且在ResNet-18的参数中仅用了3.4%，达到90.2%的CIFAR-10测试准确率。同时，利用该框架还可以进行稀疏反向传播和资源友好型训练。

基于Bregman学习框架的稀疏神经网络