Hessian-based toolbox for reliable and interpretable machine learning in physics

TL;DR

This paper introduces a Hessian-based toolbox that enhances the interpretability and reliability of machine learning models in physics, providing insights into data influence, uncertainty, and extrapolation with a single Hessian computation.

Contribution

It presents a model-agnostic toolbox leveraging Hessian computations to improve interpretability and reliability in physics-related machine learning applications.

Findings

Provides influence of input data on predictions

Estimates uncertainty of model predictions

Offers an extrapolation score for model reliability

Abstract

Machine learning (ML) techniques applied to quantum many-body physics have emerged as a new research field. While the numerical power of this approach is undeniable, the most expressive ML algorithms, such as neural networks, are black boxes: The user does neither know the logic behind the model predictions nor the uncertainty of the model predictions. In this work, we present a toolbox for interpretability and reliability, agnostic of the model architecture. In particular, it provides a notion of the influence of the input data on the prediction at a given test point, an estimation of the uncertainty of the model predictions, and an extrapolation score for the model predictions. Such a toolbox only requires a single computation of the Hessian of the training loss function. Our work opens the road to the systematic use of interpretability and reliability methods in ML applied to physics and, more generally, science.