Skip to content
Preprint

The Sparsity Ceiling: Where Spiking Networks Can and Cannot Trade Activity for Energy

Jul 2026 · 0 citations · 6 references
Computer Science

Abstract

Spiking neural networks (SNNs) are promoted as an energy-efficient substrate because sparse, event-driven activity replaces dense multiply-accumulates with cheap accumulates. We argue the energy dividend of sparsity is not a property of SNNs but of the task. Holding architecture fixed and swapping only the hidden unit (continuous vs. leaky-integrate-and-fire), plus a two-sided target-firing-rate probe, we measure how far activity can be pushed down before quality breaks. Low-load feed-forward perception sparsifies to 5% firing at no accuracy cost; a recurrent language model cannot go below ~50% -- the recurrent state must stay active to carry information. A spiking Transformer, by contrast, sparsifies freely to 2% (3 seeds) -- so the ceiling is a property of recurrent compression, not sequence modeling. Attention escapes the floor only by storing the full key-value cache, trading a firing floor for a memory wall: on neuromorphic hardware, recurrence and attention pay on different axes, neither escapes. We formalize the ceiling with an information-theoretic bound rho>= H_b^{-1}(log2 M / H) and confirm its predictions: the floor rises with memory load, falls with state width, and (refuting a naive memory-only reading) rises with task difficulty. A layer-wise input floor further caps op reduction under dense input, isolating event-driven perception as where neuromorphic hardware wins.

View source

Similar papers

Preprint Aug 2026

BASC : Behavior-Aligned Quantization and Pruning for Low-Bit Spiking Neural Networks

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.

Linliang Chen, Yan Zhong, Xin Liu et al. · 0 citations
Open access Jul 2026

Feedforward spiking neural networks are not transformers (yet): a learning-theoretic framework for long-range dependencies and biological efficiency

Spiking neural networks offer a promising route toward low-power sequence computation on neuromorphic hardware, but they continue to lag behind attention-based artificial neural networks on long-context tasks. A central open question is whether this gap reflects only implementation and optimization limitations, or whether architectural features of spiking computation impose unfavorable learnability constraints as sequence length increases. Here, we address this question using a covering-number analysis of feedforward non-leaky integrate-and-fire (nLIF) networks in the probably approximately correct framework. Building on causal-piece decompositions and local Lipschitz continuity, we derive a global sensitivity bound for feedforward nLIF networks and extend it from single-token inputs to multi-token spike sequences. For fixed architectures under stated boundedness and margin assumptions, the resulting sufficient worst-case sample requirement has leading quadratic dependence on sequence length. This dependence arises from cumulative causal participation across time and depth, which increases global sensitivity along active spike paths. We then test the mechanistic implications of this theory using finite-sample cue-recall and teacher–student benchmarks across spiking, recurrent, and attention-based model classes. In cue-recall, an early cue must be retained across distractors and reported at a final query token; in teacher–student, labels are generated by a fixed nLIF teacher, separating representability from finite-sample learnability. Unconstrained feedforward spiking models show sequence-length sensitivity, elevated hidden spike-participation density, and increased samples-to-threshold burden. Post-spike refractoriness, leak-mediated forgetting, learned lateral inhibition, and activity-constrained winner-take-all competition reduce hidden participation and improve empirical robustness in task- and regime-dependent ways. Together, these results identify diffuse causal-set growth as a fundamental architectural bottleneck for baseline feedforward spiking sequence models and suggest that scalable neuromorphic sequence architectures will require circuit mechanisms that explicitly constrain temporal accumulation and effective spike participation.

William Fishell, Gordon Fishell, Suraj Honnuraiah · 0 citations
Preprint Aug 2026

Lapis: Laplacian Spiking Attention via First-Spike Timing and Membrane Leakage

Lapis is proposed, a spiking attention mechanism that scores each token pair by the L1 distance between its query and key first-spike latency vectors under time-to-first-spike coding, and maps this distance to an affinity through a Laplacian kernel.

Kaiwen Tang, Jiaqi Zheng, Zixuan Zhu et al. · 0 citations
Open access Aug 2026

Why temporal spike order reversal drops spiking network accuracy and how to partially mitigate it

Spiking neural networks (SNNs) offer an energy-efficient alternative to traditional neural networks by utilizing discrete, temporally precise spike events. However, this study identifies a critical vulnerability in SNNs on recently established bit-based codes: consistent performance degradation when temporal spike encoding orders are reversed, such as using least-significant-bit ordering instead of most-significant-bit. We theoretically formalize this phenomenon as premature state annihilation, wherein early noisy spikes in information-discordant encodings trigger hard resets in leaky integrate-and-fire (LIF) neurons. These resets erase accumulated membrane state and, because the effective temporal influence of an input is largest for early timesteps, leave the backpropagated learning signal concentrated where the information is not. We measure the per-timestep class-mutual-information profile of six encodings directly, without reference to network accuracy, and show that the resulting concordance ordering predicts the observed degradation. While dense codes like weighted phase encoding suffer catastrophic drops (up to 48%), sparse codes like time-to-first-spike remain robust, and exchangeable rate codes are provably invariant to reversal. We evaluate several mitigation strategies, finding that parametric LIF (PLIF) neurons and aggressive membrane leakage significantly recover performance by adapting to or suppressing early noise.

Nhan Trong Luu, Duong Trung Luu, Nam Ngoc Pham et al. · 0 citations
Preprint Aug 2026

PTQ4SNN: Membrane-Aware Post-Training Quantization for Spiking Neural Networks

PTQ4SNN is proposed, a membrane-aware post-training quantization framework that jointly quantizes weights and recurrent membrane states using only a small calibration set and effectively preserves model accuracy under W4 quantization and approximately 4-bit membrane precision.

Hui Xie, Tong Shi, Haotong Qin et al. · 0 citations
Preprint Aug 2026

Reducing ANN-SNN Conversion Error via Residual Membrane Potential Alignment

Spiking Neural Networks (SNNs) serve as core architectures for neuromorphic computing thanks to event-driven operation and ultra-low power consumption. Direct SNN training is hindered by non-differentiable spikes that induce vanishing gradients and unstable optimization. ANN-SNN conversion circumvents such issues by reusing well-trained ANN weights for low-latency, energy-efficient inference. Nevertheless, existing conversion schemes suffer from severe accuracy drops at small timesteps, large inference delays and cumulative quantization errors, even with marginal performance loss at large $T$. To address these limitations, we first analyze flaws of conventional conversion pipelines from residual membrane potential statistics and propose a novel conversion strategy combining dynamic initial potential tuning and feature enhancement. We then introduce a regularization loss $\mathcal{L}_{\mathrm{RMPD}}$ to adapt initial potential of IF neurons and mitigate systematic truncation bias from boundary aggregation. A dedicated SCR-Conv2d competitive refinement layer with grouped convolution is further built to sharpen feature discrimination, eliminate redundant spikes and stabilize encoding under tiny time windows. Integrated with the state-of-the-art QCFS baseline, our approach delivers consistent low-latency performance gains and generalizes to ReLU CNNs, ANN Transformers, and multi-threshold SNN variants. Evaluations on CIFAR-10, CIFAR-100 and ImageNet verify prominent accuracy improvements at $T=2,4,8$, with negligible extra computation overhead. This work offers an effective conversion paradigm to facilitate real-world SNN deployment on neuromorphic chips.

Zirui Chen, Zihan Huang, Tong Bu et al. · 0 citations