STARFISH: faST Accuracy Recovery in pruned networks From Internal State Healing

We study a Marchenko--Pastur (MP) random-matrix approach to pruning deep neural networks with very small post-pruning fine-tuning budgets. The main practical contribution is accuracy retention under short calibration and fine-tuning schedules, rather than a long post-pruning reoptimization pipeline. The theory gives deterministic data-path certificates: if the removed component $R$ has small propagated logit effect $L_s \| R ψ_1(s) \|_\infty$, pruning decreases an elastic-net objective and preserves samples whose dense margin exceeds twice the perturbation. The zero-budget case gives perfect pruning; a prune--restore extension models weight restoration inside a fixed sparse-execution pattern; and an additive $L_2$-regularized model shows admissible random-like components vanish at the training limit, with persistent spikes stabilizing as the MP bulk collapses. Under iid-Gaussian sufficient conditions, the fitted MP edge $σ_+$ gives a high-probability layerwise budget signal. On ImageNet-1k, after only three distillation epochs, ViT-B/16 $2{:}4{+}$ToMe reaches $83.41\%$ top-1 ($-1.70$ pp from dense) at $59.81\%$ sparse-execution MAC reduction, with $1.388\times$ best-observed A40 native-$2{:}4$ backend speedup for the same checkpoint and ToMe graph; a separate no-ToMe A100 endpoint gives $2.705\times$. At structured sparsity, ViT-B/16 $6{:}12$ reaches $83.74\%$, ViT-L/16 $8{:}16$ dense+permutation reaches $85.33\%$ ($-0.51$ pp), and ConvNeXtV2-Base $12{:}16$ reaches $86.35\%$ ($-0.37$ pp). For CNNs, ResNet50 $8{:}16$ dense+permutation reaches $75.87\%$ ($-0.26$ pp), and ResNet152d CAST-conv+permutation reaches $81.33\%$ ($-1.53$ pp) at ${\sim}50\%$ MAC accounting with a $1.62\times$ A40 im2col$+2{:}4$ sparse-GEMM audit.

Network pruning is used to reduce inference latency and power consumption in large neural networks. However, most methods focus on empirical results at the expense of understanding the pruning process. We introduce Hyperflux, a novel $L_0$ method which models pruning as a continuously evolving system determined by flux, the gradient response to a weight's removal, and pressure, a global regularization driving weights toward pruning. By exploiting this model, Hyperflux's pruning behavior becomes understandable at both microscopic (weight regrowth/pruning) and macroscopic (sparsity convergence, etc.) levels. We also introduce a novel pressure scheduler that reliably targets desired sparsities. Hyperflux achieves competitive results with ResNet-50, VGG-19 and DeiT-T/S on CIFAR-10, CIFAR-100 and ImageNet datasets.

Weight pruning is a common technique for compressing large neural networks. We focus on the challenging post-training one-shot setting, where a pre-trained model is compressed without any retraining. Existing one-shot pruning methods typically optimize a single objective, such as a layer-wise reconstruction loss or a second-order Taylor approximation of the training loss. We highlight that neither objective alone is consistently the most effective across architectures and sparsity levels. Motivated by this insight, we propose MOONSHOT, a general and flexible framework that extends any single-objective pruning method into a multi-objective formulation by jointly optimizing both the layer-wise reconstruction error and second-order Taylor approximation of the training loss. MOONSHOT acts as a wrapper around existing pruning algorithms. To enable this integration while maintaining scalability to billion-parameter models, we propose modeling decisions and introduce an efficient procedure for computing the inverse Hessian, preserving the efficiency of state-of-the-art one-shot pruners. When combined with state-of-the-art pruning methods on Llama-3.2 and Llama-2 models, MOONSHOT reduces C4 perplexity by up to 32.6% at 2:4 sparsity and improves zero-shot mean accuracy across seven classification benchmarks by up to 4.9 points. On Vision Transformers, it improves accuracy on ImageNet-1k by over 5 points at 70% sparsity, and on ResNet-50, it yields a 4-point gain at 90% sparsity.