A Step Toward Interpretability: Smearing the Likelihood

TL;DR

This paper introduces a new method for interpreting machine learning models in particle physics by smoothing data to identify relevant energy scales, revealing insights into the model's reliance on various emission scales.

Contribution

It proposes a practical approach to interpretability through data smearing and demonstrates its effectiveness in analyzing scale sensitivity in jet classification.

Findings

Discrimination power increases as resolution decreases.

Scaling laws emerge from extreme value theory.

Likelihood sensitivity spans multiple emission scales.

Abstract

The problem of interpretability of machine learning architecture in particle physics has no agreed-upon definition, much less any proposed solution. We present a first modest step toward these goals by proposing a definition and corresponding practical method for isolation and identification of relevant physical energy scales exploited by the machine. This is accomplished by smearing or averaging over all input events that lie within a prescribed metric energy distance of one another and correspondingly renders any quantity measured on a finite, discrete dataset continuous over the dataspace. Within this approach, we are able to explicitly demonstrate that (approximate) scaling laws are a consequence of extreme value theory applied to analysis of the distribution of the irreducible minimal distance over which a machine must extrapolate given a finite dataset. As an example, we study quark versus gluon jet identification, construct the smeared likelihood, and show that discrimination power steadily increases as resolution decreases, indicating that the true likelihood for the problem is sensitive to emissions at all scales.