# Automated Numerical Stability Analysis of Deep Learning Operators

arXiv: https://arxiv.org/abs/2607.25494 · HTML: https://mlsanity.com/paper/2607.25494/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 60 references that are in the map.
- First posted on arXiv 28 Jul 2026.

## Builds on (most cited first, 17 of 17)

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- [Deep Speech: Scaling up end-to-end speech recognition](https://mlsanity.com/paper/1412.5567/) (2014)
- [Why Low-Precision Transformer Training Fails: An Analysis on Flash Attention](https://mlsanity.com/paper/2510.04212/) (2025)
- [To FP8 and Back Again: Quantifying Reduced Precision Effects on LLM Training Stability](https://mlsanity.com/paper/2405.18710/) (2024)
- [Numerical stability analysis of large language models](https://mlsanity.com/paper/2503.10251/) (2025)
- [Mixed precision accumulation for neural network inference guided by componentwise forward error analysis](https://mlsanity.com/paper/2503.15568/) (2025)
- [Grokking or Glitching? How Low-Precision Drives Slingshot Loss Spikes](https://mlsanity.com/paper/2605.06152/) (2026)
- [A Framework for Semi-Automatic Precision and Accuracy Analysis for Fast and Rigorous Deep Learning](https://mlsanity.com/paper/2002.03869/) (2020)
- [Fuzzy PyTorch: Rapid Numerical Variability Evaluation for Deep Learning Models](https://mlsanity.com/paper/2605.25991/) (2026)
- [AdaQAT: Adaptive Bit-Width Quantization-Aware Training](https://mlsanity.com/paper/2404.16876/) (2024)

## Abstract (arXiv)

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 a unified software tool for stochastic numerical validation of deep-learning operators. The tool follows CESTAC on supported exposed operations and uses an operator-level data-perturbation approximation for GEMM-like kernels. 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 tools provide valuable insights into developing numerically stable computing kernels, which are particularly critical for numerically stable and efficient deep learning training and inference.