Automated Numerical Stability Analysis of Deep Learning Operators

2026-07-28

AI Summary

This work addresses the susceptibility of deep learning operators to numerical instability under finite-precision arithmetic, which can lead to error accumulation and result corruption. For the first time, the CESTAC stochastic rounding error analysis method is systematically introduced into the deep learning domain. The authors propose a unified software framework that enables automatic detection of operator-level numerical instability, precise localization of instability sources, and end-to-end stability monitoring throughout both training and inference. The tool supports single-run verification and has successfully identified pollution operators responsible for numerical instability across diverse tasks, thereby ensuring efficient and reliable computation in deep learning systems.

Abstract

Finite-precision arithmetic unavoidably introduces numerical approximation errors. Numerical computations may use insufficient precision or an improper formulation, which leads to numerical instability. In this paper, we introduce the first unified software tool that integrates CESTAC for detecting the numerical stability of deep learning operators. Our developed software not only enables numerical validation with a single computation pass but also detects the sources of numerical instability and provides numerical stability monitoring during deep learning training and inference. We verified its effectiveness on the detection of polluted operators with injected numerical instabilities across various tasks. We believe that our developed method and tool provide valuable insights into developing numerically stable computing kernels, which are particularly critical for numerically stable and efficient deep learning training and inference.

Problem

• numerical stability
• deep learning operators
• finite-precision arithmetic
• numerical instability
• automated analysis

Innovation

• numerical stability
• CESTAC
• deep learning operators
• finite-precision arithmetic
• automated analysis