The Sparsity Ceiling: Where Spiking Networks Can and Cannot Trade Activity for Energy
arXiv:2607.26648
The paper studies how much spiking neural networks can lower their firing activity without losing performance, showing that the achievable sparsity depends on the task and architecture and providing an information‑theoretic bound that predicts these limits.
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.
5 pages, 6 figures. Code: https://github.com/zeyuyuyu/sparsity-ceiling