DeepStability: A Study of Unstable Numerical Methods and Their Solutions in Deep Learning

TL;DR

DeepStability investigates numerical stability issues in deep learning libraries, identifies root causes, and provides solutions, including a database of issues and fixes to improve the reliability of DL systems.

Contribution

This paper introduces the first database of numerical stability issues in deep learning, analyzing causes, manifestations, and fixes in PyTorch and TensorFlow.

Findings

Identified numerous unstable numerical methods in DL libraries.

Developed patches that improve numerical stability and were accepted by developers.

Provided a resource for future detection and prevention of numerical issues in DL.

Abstract

Deep learning (DL) has become an integral part of solutions to various important problems, which is why ensuring the quality of DL systems is essential. One of the challenges of achieving reliability and robustness of DL software is to ensure that algorithm implementations are numerically stable. DL algorithms require a large amount and a wide variety of numerical computations. A naive implementation of numerical computation can lead to errors that may result in incorrect or inaccurate learning and results. A numerical algorithm or a mathematical formula can have several implementations that are mathematically equivalent, but have different numerical stability properties. Designing numerically stable algorithm implementations is challenging, because it requires an interdisciplinary knowledge of software engineering, DL, and numerical analysis. In this paper, we study two mature DL libraries PyTorch and Tensorflow with the goal of identifying unstable numerical methods and their solutions. Specifically, we investigate which DL algorithms are numerically unstable and conduct an in-depth analysis of the root cause, manifestation, and patches to numerical instabilities. Based on these findings, we launch, the first database of numerical stability issues and solutions in DL. Our findings and provide future references to developers and tool builders to prevent, detect, localize and fix numerically unstable algorithm implementations. To demonstrate that, using {\it DeepStability} we have located numerical stability issues in Tensorflow, and submitted a fix which has been accepted and merged in.