# A Step Toward Interpretability: Smearing the Likelihood

arXiv: https://arxiv.org/abs/2501.07643 · HTML: https://mlsanity.com/paper/2501.07643/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 115 references that are in the map.
- First posted on arXiv 13 Jan 2025.

## Builds on (most cited first, 21 of 21)

- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Scaling Laws for Autoregressive Generative Modeling](https://mlsanity.com/paper/2010.14701/) (2020)
- [Explaining Neural Scaling Laws](https://mlsanity.com/paper/2102.06701/) (2021)
- [A Constructive Prediction of the Generalization Error Across Scales](https://mlsanity.com/paper/1909.12673/) (2019)
- [The Principles of Deep Learning Theory](https://mlsanity.com/paper/2106.10165/) (2021)
- [Particle Transformer for Jet Tagging](https://mlsanity.com/paper/2202.03772/) (2022)
- [A Living Review of Machine Learning for Particle Physics](https://mlsanity.com/paper/2102.02770/) (2021)
- [Machine Learning in High Energy Physics Community White Paper](https://mlsanity.com/paper/1807.02876/) (2018)
- [On the Predictability of Pruning Across Scales](https://mlsanity.com/paper/2006.10621/) (2020)
- [Machine Learning for Anomaly Detection in Particle Physics](https://mlsanity.com/paper/2312.14190/) (2023)
- [Linearized Optimal Transport for Collider Events](https://mlsanity.com/paper/2008.08604/) (2020)
- [Aspen Open Jets: Unlocking LHC Data for Foundation Models in Particle Physics](https://mlsanity.com/paper/2412.10504/) (2024)
- [Particle Graph Autoencoders and Differentiable, Learned Energy Mover's Distance](https://mlsanity.com/paper/2111.12849/) (2021)
- [Snowmass 2021 Computational Frontier CompF03 Topical Group Report: Machine Learning](https://mlsanity.com/paper/2209.07559/) (2022)
- [Interpretable machine learning in Physics](https://mlsanity.com/paper/2203.08021/) (2022)
- [On the Topic of Jets: Disentangling Quarks and Gluons at Colliders](https://mlsanity.com/paper/1802.00008/) (2018)
- [A Theoretical-Empirical Approach to Estimating Sample Complexity of DNNs](https://mlsanity.com/paper/2105.01867/) (2021)
- [Finding NEEMo: Geometric Fitting using Neural Estimation of the Energy Mover's Distance](https://mlsanity.com/paper/2209.15624/) (2022)
- [Opening the black box of neural nets: case studies in stop/top discrimination](https://mlsanity.com/paper/1804.09278/) (2018)
- [Feature Selection with Distance Correlation](https://mlsanity.com/paper/2212.00046/) (2022)
- [Retrieval of Boost Invariant Symbolic Observables via Feature Importance](https://mlsanity.com/paper/2306.13496/) (2023)

## Built on by (most cited first, 1 of 1)

- [Non-Gaussianities in Collider Metric Binning](https://mlsanity.com/paper/2503.03809/) (2025)

## Abstract (arXiv)

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.