Spiking Layer-Adaptive Magnitude-based Pruning

Deploying spiking neural networks (SNNs) on neuromorphic hardware demands aggressive synaptic pruning while preserving temporal computation integrity. Existing strategies either neglect neuronal criticality or rely on convex relaxations of the inherently combinatorial pruning problem whose fractional masks, upon binarisation, destroy accuracy at moderate-to-high sparsity. We present Criticality-Constrained Quadratic Pruning (CQP), a native PyTorch pipeline that fuses weight magnitude with surrogate-gradient criticality into an analytically exact importance metric, eliminating the rounding artefacts endemic to solver-based approaches. We formally characterise a continuous-relaxation trap wherein OSQP-solver fractional masks overshoot the intended sparsity by up to 12 percentage points (pp), precipitating a 44 pp accuracy collapse. We identify and remediate a zombie-weight failure mode in which Adam's first-moment tensors resurrect pruned synapses, violating the binary sparsity guarantee. An iterative schedule - prune, fine-tune with gradient masking, recompute criticality, and repeat - eliminates gradient staleness at high sparsity. A KL-divergence temporal analysis identifies a redundant simulation timestep, enabling a free 10% theoretical energy reduction without weight modification. On MNIST (60,000 training examples), CQP yields 95.6% accuracy at 90% sparsity versus 93.4% for magnitude pruning (+2.2 pp). A criticality-threshold sweep reveals an empirical criticality cliff: accuracy falls from 87.0% to 14.4% as the threshold reaches tau = 0.9, constituting a quantitative SNN-level analogue of the Critical Brain Hypothesis. Combined weight sparsification and temporal truncation yield a compound 73% reduction in per-inference energy at 70% sparsity, confirming the practical value of the proposed pipeline for neuromorphic deployment.

Activation-energy pruning -- removing weights whose product of magnitude and cumulative pre-synaptic spike count falls below a threshold -- was established as an effective unsupervised personalization strategy for conventional deep neural networks~\citep{BINGHAM2025101242}. This paper asks what happens when the same criterion is applied to spiking neural networks (SNNs), where activation energy is not merely a useful heuristic but a literal physical quantity proportional to the metabolic cost of each synapse. The answer is surprising on three counts. First, gradient-based pruning methods that perform competitively on conventional networks (SNIP, GraSP, magnitude pruning) consistently underperform on SNNs, collapsing to near-chance accuracy by $σ= 0.2$ sparsity across all tested architectures and datasets. We trace this to a systematic incompatibility between surrogate-gradient saliency estimation and the binary spike-train representation, though we cannot rule out that alternative surrogate choices or hyperparameter settings might partially mitigate the effect. Second, activation-energy pruning applied to a neuromorphic benchmark improves over the source model at high sparsity ($98.4 \pm 0.4\%$ vs.\ $97.2 \pm 0.7\%$ at $σ= 0.8$ on N-MNIST), a phenomenon with no counterpart in the conventional network setting. We interpret this result as consistent with experience-dependent cortical specialisation: removing connections active only for non-target classes may reduce cross-class interference and produce a cleaner target representation, though we note this is an interpretive analogy rather than a mechanistic demonstration.

Spiking Neural Networks (SNNs) encode information through binary spikes and compute in an event-driven manner, offering an energy-efficient paradigm for machine intelligence. However, high-performance SNNs incur substantial memory and timestep-wise computation costs that hinder deployment on resource-constrained devices. Quantization and pruning provide complementary routes to reducing these costs, yet both make their decisions with local criteria that overlook temporal task feedback in quantization and inter-channel dependencies in pruning. Consequently, optimizing either criterion can still yield suboptimal compression performance. We refer to this discrepancy as criterion-behavior mismatch and propose Behavior-Aligned SNN Compression (BASC), a unified framework with two lightweight modules. For quantization, the scale is applied to synaptic current at every timestep and therefore shifts spike timing. Temporal-Behavior Scale Correction (TSC) makes the scale learnable under a temporal loss, allowing firing behavior to inform scale optimization. For pruning, channel importance depends on how channels jointly drive the membrane potential across the firing threshold. Boundary-Level Inter-Channel Correction (BIC) uses channelwise importance scores for initial selection and inter-channel information to re-evaluate only channels near the pruning threshold. Extensive experiments on static and neuromorphic benchmarks show that lower-bit BASC models match or outperform higher-bit baselines and retain this accuracy advantage after structured pruning, while further reducing model storage and synaptic operations.