Papers › A Bregman Learning Framework for Sparse Neural Networks

A Bregman Learning Framework for Sparse Neural Networks

10 May 2021arXiv:2105.04319archive 2025-07-28

Leon Bungert, Tim Roith, Daniel Tenbrinck, Martin Burger

We propose a learning framework based on stochastic Bregman iterations, also known as mirror descent, 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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ResNet18 TimRoith/BregmanLearning/models/resnet.py official repository unverified MIT (permissive) · bef7c3588a8a1920 · report
ResNet34 TimRoith/BregmanLearning/models/resnet.py official repository unverified MIT (permissive) · 3a99b51deb632de7 · report
ResNet50 TimRoith/BregmanLearning/models/resnet.py official repository unverified MIT (permissive) · 32785cbfb4305fcb · report
get_data_set TimRoith/BregmanLearning/utils/datasets.py official repository unverified MIT (permissive) · 24fbacb4a8fa7e6b · report
get_encoder_mnist TimRoith/BregmanLearning/utils/datasets.py official repository unverified MIT (permissive) · 77482de815b7636c · report
get_mnist TimRoith/BregmanLearning/utils/datasets.py official repository unverified MIT (permissive) · 2f27d73dd37f8bdc · report
net_sparsity TimRoith/BregmanLearning/models/aux_funs.py official repository unverified MIT (permissive) · f1b6a227e496d8f0 · report
node_sparsity TimRoith/BregmanLearning/models/aux_funs.py official repository unverified MIT (permissive) · 8c9c1fb9fd88bac7 · report
print_sparsity TimRoith/BregmanLearning/models/aux_funs.py official repository unverified MIT (permissive) · e3035503849b4b24 · report

Tasks

DenoisingImage Classification

Results from the paper archive 2025-07-28

TaskDatasetModelMetricValueRank at snapshotLeaderboardReport
Image Classification CIFAR-10 ResNet Percentage correct 92.3 #182 of 265 Archive leaderboard report

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Adam

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