Structured Channel Network Pruning with Bi-Sparse Matrix Factorization

As the need for more accurate and powerful Convolutional Neural Networks (CNNs) increases, so too does the size, execution time, memory footprint, and power consumption. To overcome this, solutions such as pruning have been proposed with their own metrics and methodologies, or criteria, for how weights should be removed. These solutions do not share a common implementation and are difficult to implement and compare. In this work, we introduce Combine, a criterion- based pruning solution and demonstrate that it is fast and effective framework for iterative pruning, demonstrate that criterion have differing effects on different models, create a standard language for comparing criterion functions, and propose a few novel criterion functions. We show the capacity of these criterion functions and the framework on VGG inspired models, pruning up to 79% of filters while retaining or improving accuracy, and reducing the computations needed by the network by up to 68%.

Unstructured pruning at extreme sparsity often suffers from representational collapse, causing sharp drops in accuracy. To address this, we study Backbone Contrastive Pruning (BaCP), which regularizes the sparse network's embedding space by aligning it with pretrained, fine-tuned, and historical snapshot models. Building on the contrastive decomposition of the CAP framework (Xu et al., 2022), we provide a rigorous matched-budget characterization of this approach across multiple pruning criteria. Evaluated across 90 settings, BaCP improves accuracy substantially in extreme sparsity regimes where standard pruning fails, and is close to baseline where representations remain intact.

Muon has emerged as a strong optimizer for neural network training and admits an interpretation as steepest descent under a spectral-norm geometry. Yet we find that Muon-trained Transformers can degrade sharply when their MLP hidden channels are pruned after training. To reconcile Muon's optimization performance with structured compressibility, we introduce Budget Muon (BMuon), which modifies Muon's spectral geometry so that hidden channels across blocks compete for a shared allocation budget. The resulting oracle is exactly normalized steepest descent under a family of norms that interpolate between Muon's geometry and structured sparse geometries. Our principal sparsity control is an interpretable global channel-allocation budget, rather than a setting-dependent sparsity-penalty coefficient. For linear factorization models, we show that Muon admits minimum-cost exact representations with redundant hidden width, whereas under the BMuon oracle geometry and a sufficiently scarce budget, every minimum-cost representation is width-minimal. For practical training, we derive a minorization-maximization surrogate for the exact allocation problem. On ImageNet-1K with ViT-S/16, BMuon improves over Muon under gradual structured MLP pruning, and its learned allocations provide a more effective pruning criterion than weight magnitude. On a 1B-parameter LLaMA-style model trained on FineWeb, BMuon improves over Muon under post-training MLP channel pruning.