Finding Sparse Subnetworks in One Training Cycle via Progressive Magnitude-Based Pruning

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.

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.

We study compute reduction in neural networks through a unified partial versus full computation view, captured by one-shot magnitude pruning in the static regime and early exit in the adaptive regime. In an asymptotic single-neuron model, we prove a concentration theorem for one-shot magnitude pruning with explicit rates. We also introduce the conditional perceptron for early exit and show that its excess generalization error decays as a power of the compute gap, with an exponent that grows to infinity as the alignment between partial and full computations tends to one. We then extend the analysis to deep networks, characterizing how pruning-induced distortions accumulate with depth and deriving a corresponding compute-accuracy tradeoff for frozen-backbone early exit under a neural network Gaussian process model. Numerical simulations corroborate the predicted scaling laws.