# Lyapunov-Guided Training for Hardware-Safe Neural Networks Under Fixed-Point Arithmetic

Source: [Lyapunov-Guided Training for Hardware-Safe Neural Networks Under Fixed-Point Arithmetic](<https://www.sota2.com/research/paper/6a4c882085dba69fef8b2942>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-07-08T05:00:20.838Z

Authors: Anis Hamadouche, Amir Hussain

Published: 2026-07-05T22:25:52.000Z

## Abstract

Low-precision neural networks are attractive for resource-constrained hardware, but fixed-point arithmetic introduces failure modes that are often hidden by idealised quantisation models. In particular, two's-complement overflow wrapping can corrupt hidden activations by changing both their magnitude and sign, leading to unstable numerical error propagation and severe accuracy degradation. This paper proposes a Lyapunov-stabilised quantisation framework for low-precision neural networks operating under hardware-style wrapping arithmetic. The hidden-state energy is monitored through a layerwise Lyapunov function, and a monotone projection is applied to enforce bounded and non-increasing state evolution across depth. The method is evaluated on MNIST using a compact patch-based transformer under post-training quantisation and quantisation-aware training with fixed-point bit-widths from 4 to 16 bits. Monte Carlo results show that unconstrained wrapped quantisation-aware training collapses to near-chance accuracy across 6-16 bits, with activation overflow rates exceeding 11%. In contrast, the proposed monotone Lyapunov projection suppresses activation overflow to below 0.012% and restores stable low-precision learning, achieving 86.55% accuracy at 12 bits. These results demonstrate that Lyapunov-based state control can act as a hardware-aware stabilisation mechanism for reliable fixed-point neural inference and training.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Image Classification on MNIST (test) (Accuracy, Loss, and Operational Metrics)](<https://www.sota2.com/research/sota/image-classification-on-mnist-test-accuracy-loss-and-operational-metrics.md>): Image Classification; MNIST (test); Accuracy: 86.95.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2607.04531>)

[PDF](<https://arxiv.org/pdf/2607.04531.pdf>)