# Towards an Expressivity-Normalized Energy-Demand Comparison of ANNs and SNNs

arXiv: https://arxiv.org/abs/2608.29869 · HTML: https://mlsanity.com/paper/2608.29869/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 27 references that are in the map.
- First posted on arXiv 30 Aug 2026.

## Builds on (most cited first, 15 of 15)

- [Efficient Processing of Deep Neural Networks: A Tutorial and Survey](https://mlsanity.com/paper/1703.09039/) (2017)
- [On the Number of Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1402.1869/) (2014)
- [Going Deeper in Spiking Neural Networks: VGG and Residual Architectures](https://mlsanity.com/paper/1802.02627/) (2018)
- [Bounding and Counting Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1711.02114/) (2017)
- [Beyond Classification: Directly Training Spiking Neural Networks for Semantic Segmentation](https://mlsanity.com/paper/2110.07742/) (2021)
- [An Analytical Estimation of Spiking Neural Networks Energy Efficiency](https://mlsanity.com/paper/2210.13107/) (2022)
- [Spiking Neural Networks for Frame-based and Event-based Single Object Localization](https://mlsanity.com/paper/2206.06506/) (2022)
- [Efficient and Effective Time-Series Forecasting with Spiking Neural Networks](https://mlsanity.com/paper/2402.01533/) (2024)
- [Event-based Optical Flow on Neuromorphic Processor: ANN vs. SNN Comparison based on Activation Sparsification](https://mlsanity.com/paper/2407.20421/) (2024)
- [The Computational Complexity of Counting Linear Regions in ReLU Neural Networks](https://mlsanity.com/paper/2505.16716/) (2025)
- [Are SNNs Truly Energy-efficient? - A Hardware Perspective](https://mlsanity.com/paper/2309.03388/) (2023)
- [Expressivity of Spiking Neural Networks](https://mlsanity.com/paper/2308.08218/) (2023)
- [Time to Spike? Understanding the Representational Power of Spiking Neural Networks in Discrete Time](https://mlsanity.com/paper/2505.18023/) (2025)
- [Deep-Unrolling Multidimensional Harmonic Retrieval Algorithms on Neuromorphic Hardware](https://mlsanity.com/paper/2412.04008/) (2024)
- [Hardware-aware vs. Hardware-agnostic Energy Estimation for SNN in Space Applications](https://mlsanity.com/paper/2508.19654/) (2025)

## Abstract (arXiv)

Spiking neural networks (SNNs) are often regarded as energy-efficient alternatives to artificial neural networks (ANNs), yet their advantage depends critically on both network architecture and data properties. We develop an analytical framework to compare fully-connected ReLU ANNs and integrate-and-fire SNNs for time-series data with respect to their theoretical energy efficiency at matched expressive capacity. By relating an inference-energy model to theoretical bounds on representational expressivity, we derive an expressivity-normalized efficiency ratio and explicit thresholds in network width, spike sparsity, and ANN depth scaling. Our analysis characterizes the regimes in which event-driven computation offsets the temporal overhead of SNNs, providing capacity-aware principles for designing energy-efficient temporal networks. It shows that ANNs exceed SNNs in expressivity-normalized efficiency only in specific regimes.