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

2026-07-29

AI Summary

This study investigates the theoretical limits of energy efficiency in spiking neural networks (SNNs) through sparse activity across diverse tasks. By fixing the network architecture and solely substituting hidden unit types—continuous versus leaky integrate-and-fire (LIF) neurons—the authors introduce a bidirectional target firing rate probe to systematically measure the minimal activity level achievable without performance degradation. They propose, for the first time, the concept of a “sparsity ceiling” and derive an information-theoretic lower bound ρ ≥ H_b⁻¹(log₂M / H), demonstrating that this limit is governed by a task’s memory load, state width, and intrinsic difficulty rather than model architecture. Experiments reveal that feedforward perceptual tasks can operate at as low as 5% firing rates, recurrent language models exhibit a floor near 50%, and Spiking Transformers achieve sparsity down to 2%, confirming that the sparsity ceiling is dictated by the inherent complexity of the task itself.

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.

Problem

• spiking neural networks
• sparsity ceiling
• energy efficiency
• recurrent computation
• information-theoretic bound

Innovation

• spiking neural networks
• sparsity ceiling
• energy efficiency
• information-theoretic bound
• neuromorphic computing