Relative Repairability: A Calibration-Based Diagnostic for High-Sparsity Post-Pruning Allocation

Unstructured magnitude pruning at high sparsity can reduce neural network accuracy to near-random performance, while labeled retraining may be unavailable in practical deployment settings. Label-free post-pruning repair methods can partially recover collapsed sparse models, but their effectiveness depends on the sparse model left by the upstream pruning allocation. This paper studies how sparsity allocation shapes post-repair recoverability under a fixed activation-statistic repair backend. We compare ERK and LAMP allocations under the same label-free repair protocol across CIFAR-10, CIFAR-100, and Imagenette with ResNet-18, ResNet-34, and ResNet-50 at sparsities from 90% to 95.5%. The results show that allocation choice can substantially change post-repair accuracy at the same global sparsity, and that the preferred allocation varies with architecture, dataset difficulty, and sparsity level. We identify a repair-sensitive transition regime in which BatchNorm recalibration begins to fail, while activation-statistic repair still recovers nontrivial accuracy. Additional validation on ImageNet-100 and DenseNet-121 shows that the location and width of this recoverable regime depend on data scale and connectivity structure. These findings suggest that pruning allocation and post-pruning repair should be studied jointly, since the allocation determines how much activation signal remains available for label-free recovery.

One-shot magnitude pruning can cause severe accuracy collapse in the high-sparsity regime, even when the pruning mask preserves the largest weights. We argue that this failure reflects a granularity mismatch in post-pruning repair. Under global magnitude pruning, nearly collapsed channels can coexist with channels that retain informative activation variance within the same layer. Existing layer-wise activation repair methods apply a single correction to the whole layer, and can therefore over-amplify damaged channels while trying to restore the layer-level signal. We propose Adaptive Signal Resuscitation (ASR), a training-free channel-wise repair method that matches the granularity of repair to the granularity of damage. ASR estimates a variance-matching correction for each output channel and stabilizes it with a data-driven shrinkage rule, suppressing unreliable corrections for channels with weak post-pruning signal while preserving corrections for healthier channels. Applied before BatchNorm recalibration, ASR requires only forward passes on a small calibration set and no retraining. Across three datasets, four convolutional architectures, and both unstructured and structured sparsity settings, ASR generally improves over layer-wise repair, with the clearest gains in high-sparsity regimes. On ResNet-50 at 90% sparsity, ASR recovers 55.6% top-1 accuracy on CIFAR-10, compared with 41.0% for layer-wise repair and 28.0% for BatchNorm-only recalibration. Ablations show that naive channel-wise variance matching is insufficient, and that shrinkage stabilizes post-pruning repair.

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.