# NEXUS: Bit-Exact ANN-to-SNN Equivalence via Neuromorphic Gate Circuits with Surrogate-Free Training

arXiv: https://arxiv.org/abs/2601.21279 · HTML: https://mlsanity.com/paper/2601.21279/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 26 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Builds on (most cited first, 12 of 12)

- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [Spatio-Temporal Backpropagation for Training High-performance Spiking Neural Networks](https://mlsanity.com/paper/1706.02609/) (2017)
- [SLAYER: Spike Layer Error Reassignment in Time](https://mlsanity.com/paper/1810.08646/) (2018)
- [Temporal Efficient Training of Spiking Neural Network via Gradient Re-weighting](https://mlsanity.com/paper/2202.11946/) (2022)
- [Enabling Deep Spiking Neural Networks with Hybrid Conversion and Spike Timing Dependent Backpropagation](https://mlsanity.com/paper/2005.01807/) (2020)
- [SpikeGPT: Generative Pre-trained Language Model with Spiking Neural Networks](https://mlsanity.com/paper/2302.13939/) (2023)
- [DIET-SNN: Direct Input Encoding With Leakage and Threshold Optimization in Deep Spiking Neural Networks](https://mlsanity.com/paper/2008.03658/) (2020)
- [SpikeLM: Towards General Spike-Driven Language Modeling via Elastic Bi-Spiking Mechanisms](https://mlsanity.com/paper/2406.03287/) (2024)
- [SpikeLLM: Scaling up Spiking Neural Network to Large Language Models via Saliency-based Spiking](https://mlsanity.com/paper/2407.04752/) (2024)
- [Spikformer V2: Join the High Accuracy Club on ImageNet with an SNN Ticket](https://mlsanity.com/paper/2401.02020/) (2024)
- [High-performance deep spiking neural networks with 0.3 spikes per neuron](https://mlsanity.com/paper/2306.08744/) (2023)
- [SpikeZIP-TF: Conversion is All You Need for Transformer-based SNN](https://mlsanity.com/paper/2406.03470/) (2024)

## Abstract (arXiv)

Spiking Neural Networks (SNNs) promise energy-efficient computing through event-driven sparsity, yet all existing approaches sacrifice accuracy by approximating continuous values with discrete spikes. We propose NEXUS, a framework that achieves bit-exact ANN-to-SNN equivalence -- not approximate, but mathematically identical outputs. Our key insight is constructing all arithmetic operations, both linear and nonlinear, from pure IF neuron logic gates that implement IEEE-754 compliant floating-point arithmetic. Through spatial bit encoding (zero encoding error by construction), hierarchical neuromorphic gate circuits (from basic logic gates to complete transformer layers), and surrogate-free STE training (exact identity mapping rather than heuristic approximation), NEXUS produces outputs identical to standard ANNs up to machine precision. Experiments on models up to LLaMA-2 70B demonstrate identical task accuracy (0.00% degradation) with mean ULP error of only 6.19, while achieving 27-168,000× energy reduction on neuromorphic hardware. Crucially, spatial bit encoding's single-timestep design renders the framework inherently immune to membrane potential leakage (100% accuracy across all decay factors β∈[0.1,1.0]), while tolerating synaptic noise up to σ=0.2 with >98% gate-level accuracy.