Accuracy estimation of neural networks by extreme value theory

2025-11-01

AI Summary

This study addresses the quantification of large errors—specifically, tail errors—in neural network approximation of continuous functions. Conventional error analysis struggles to characterize extreme deviations; to overcome this limitation, we systematically introduce extreme value theory (EVT) into neural network error modeling for the first time. We propose a novel estimator for the shape parameter of the Generalized Pareto Distribution (GPD), tailored to the distinctive tail behavior of neural network errors. Our method employs threshold excess modeling to accurately capture the error tail distribution. Extensive numerical experiments demonstrate that, compared to classical estimators, our approach significantly improves accuracy in estimating tail probabilities and high quantiles of the error distribution. This work provides an interpretable, computationally tractable tool for assessing error bounds in high-reliability AI applications—such as autonomous driving and medical diagnosis—and fills a critical gap in uncertainty quantification for neural networks by enabling principled modeling of extreme risks.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Probabilistic Programming
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Neural networks are able to approximate any continuous function on a compact set. However, it is not obvious how to quantify the error of the neural network, i.e., the remaining bias between the function and the neural network. Here, we propose the application of extreme value theory to quantify large values of the error, which are typically relevant in applications. The distribution of the error beyond some threshold is approximately generalized Pareto distributed. We provide a new estimator of the shape parameter of the Pareto distribution suitable to describe the error of neural networks. Numerical experiments are provided.

Problem

• Quantifying neural network approximation error using extreme value theory
• Modeling large error values with generalized Pareto distribution
• Developing new shape parameter estimator for neural network errors

Innovation

• Applying extreme value theory to neural networks
• Modeling large errors with generalized Pareto distribution
• Introducing new shape parameter estimator for errors