Machine Can Automatically Discover Parametric Functions to Model HEP Data

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The gist

The gist The iterative process can be automated by a machine using symbolic regression, which performs a data-driven search over function space without requiring prior knowledge of what an adequate

In short

The paper automates finding suitable mathematical functions to model binned data in high-energy physics (HEP) using symbolic regression. Instead of manual guessing, a machine searches vast function spaces to discover accurate models for spectra like dijet events. The resulting tool, SymbolFit, pairs this search with uncertainty modeling to provide statistically sound functions that can be used directly in analysis.

Key concepts

Symbolic Regression (SR)
A machine learning method that treats the functional form of a model as a 'trainable parameter.' It searches through mathematical operators and rules to dynamically construct candidate functions that best fit the data, eliminating the need for humans to pre-define what an adequate function should look like.
SymbolFit
A package designed to automate three modeling steps: searching for functions using SR, re-optimizing numerical constants with uncertainty estimates via LMFIT, and evaluating candidate functions based on metrics like $\chi^2/NDF$ or RMSE. It streamlines the process from initial guess to a statistically rigorous model.
Functional Form Search
The core search mechanism where the system explores a massive space of possible mathematical expressions connecting elementary operators. This data-driven approach allows the machine to discover complex, non-intuitive functional shapes that might be missed by human intuition alone.
Uncertainty Modeling
Because symbolic regression returns exact functions without inherent error measures, SymbolFit interfaces with LMFIT to re-optimize the numerical constants and calculate a covariance matrix. This step is crucial for HEP analyses as it provides the essential uncertainty information needed for statistical hypothesis testing.

Terminology used across episodes

This episode discusses

The paper

Machine Can Automatically Discover Parametric Functions to Model HEP Data · Read on arXiv

University of Pennsylvania University of European Organization for Nuclear Research University of Cambridge Institute for Artificial Intelligence and Fundamental Interactions University of Wisconsin-Madison University of California San Diego Massachusetts Institute of Technology Institute for Artificial Intelligence and Fundamental Interactions

In HEP data analyses, finding an adequate function to model binned data has largely relied on a manual process: guess a functional form by intuition, fit, examine, then repeat until successful. We show that this iterative process can be automated by a machine using symbolic regression, which performs a data-driven search over function space without requiring prior knowledge of what an adequate function should look like. We present the SymbolFit package, which pairs symbolic regression with uncertainty modeling to target HEP analysis use cases, and demonstrate it on the CMS and ATLAS Run 2 dijet spectra: 560 independent seeded runs across seven simple fit configurations generated over 1000 functions fitting the spectra with χ 2/NDF about 1, and 111 of the runs rediscovered the very dijet and UA2 functions used in published dijet searches.

Transcript

Introduction to the show: ident: AI Radio. Generated commentary on the latest Artificial Intelligence papers.

Tom: We're looking at the paper: "Machine Can Automatically Discover Parametric Functions to Model HEP Data".

Jane: The gist The iterative process can be automated by a machine using symbolic regression,

Tom: First, who's behind it and why it matters.

Paper summary: Tom: So, looking at the paper "Machine Can Automatically Discover Parametric Functions to Model HEP Data," the authors are essentially showing how symbolic regression can automate the creation of models for binned data in high-energy physics.

Jane: They demonstrate that this automated process can be used on CMS and ATLAS Run two dijet spectra, finding functions that match existing dijet and UA2 models <ref:2607.19750#pg1,CMS and ATLAS Run 2 dijet spectra>.

Lu: The implication is that we can potentially bypass the tedious manual guesswork of functional form selection in analysis, which is a major bottleneck right now.

Meng: For deployment, I still have questions about the practical implementation details regarding scaling this up to handle real-world data streams efficiently, as you'd need robust infrastructure for those symbolic operations.

Tom: The paper focuses on showing that the method works by demonstrating it on five hundred sixty independent seeded runs across seven configurations, achieving a chi squared over degrees of freedom of approximately one in many cases <ref:2607.19750#pg3>.

Jane: So, while they show success and relevance to existing models like the dijet function, we should keep in mind what they didn't cover.

Lu: They mention that the search is constrained by defining a set of elementary math operators and rules that connect them, which limits the types of functions it can discover to those defined by those rules.

Tom: That’s a key limitation; you can only find functions within the space they've defined, not some completely arbitrary mathematical expression.

Jane: So, for someone listening who isn't in HEP, the big change is seeing how an AI system can be used to automatically discover complex mathematical relationships from raw data without a human having to pre-define those relationships.

Meng: If this approach proves scalable and reliable outside of these specific benchmark spectra, then it could significantly speed up many other kinds of automated modeling tasks in production environments.

Tom: That's the core idea behind this work on "Machine Can Automatically Discover Parametric Functions to Model HEP Data." It’s about automating the discovery part of scientific modeling.

Conclusion: Tom: So, this paper is about using symbolic regression to automatically find mathematical functions that fit messy binned data in high-energy physics, specifically for things like dijet spectra.

Jane: It sounds like they're tackling the decades-old headache of manually guessing a function shape when you only have empirical data and no true underlying formula.

Lu: Exactly. The authors are proposing an automated search over function space, where the math operators and rules themselves become trainable parameters during the fit process.

Meng: But I always wonder about the cost to run this thing in production; does this symbolic search happen fast enough for a real-time analysis pipeline?

Tom: The paper shows they paired their symbolic regression engine, PySR, with an optimizer called LMFIT to handle those exact uncertainty measures needed for physics.

Jane: And the result is pretty neat—they tested it on CMS and ATLAS Run two dijet data and found functions that actually rediscovered known dijet and UA2 models.

Lu: That’s a significant result because it means the AI isn't just fitting random noise; it’s finding mathematically meaningful structures that already exist in the data.

Tom: It shifts the manual work from guessing *what* to do with the function to defining *how* the function can be built, which is a big mechanical change.

Jane: So, what does this mean for someone who just wants to understand this? It suggests that instead of spending weeks tweaking a curve by hand, we could let an AI search millions of mathematical possibilities for us.

Meng: If it works on these benchmark spectra, the question is whether it breaks when the data gets really complex or when you move to a completely different type of physics signal.

Tom: That’s the next thing we need to check—the generalization beyond those specific dijet setups and how robust those discovered functions are.

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