The Latent Information Geometry of Jet Classification

Benedikt Schosser; Bj\"orn Malte Sch\"afer; Rebecca Maria Kuntz; Sophia Vent; Tilman Plehn

arxiv: 2603.02310 · v2 · submitted 2026-03-02 · ✦ hep-ph

The Latent Information Geometry of Jet Classification

Rebecca Maria Kuntz , Tilman Plehn , Bj\"orn Malte Sch\"afer , Benedikt Schosser , Sophia Vent This is my paper

Pith reviewed 2026-05-15 16:33 UTC · model grok-4.3

classification ✦ hep-ph

keywords jet classificationinformation geometrylatent spacequark-gluon discriminationfat jet taggingcurvaturemachine learning

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The pith

Latent spaces of jet classification networks carry curvature and nonmetricities that reflect physical distinctions between quarks and gluons.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper introduces information geometry tools, specifically curvature and nonmetricities, to study the latent representations learned by neural networks for classifying jets in particle physics. It applies these methods to binary quark-gluon classification and three-fold fat jet tagging to uncover the physics encoded in the network's internal geometry. A sympathetic reader would care because this bridges machine learning black boxes with interpretable physical insights, potentially improving model design and understanding of high-energy processes.

Core claim

The authors establish that learned latent geometries in jet classifiers can be analyzed using curvature and nonmetricities from information geometry, and demonstrate this by extracting physical insights from networks performing quark-gluon discrimination and fat jet tagging.

What carries the argument

Curvature and nonmetricities in the latent information geometry of decoder and classifier networks.

If this is right

The geometry reveals which jet features drive the classification decisions in quark-gluon tagging.
Nonmetricities highlight deviations from standard Riemannian structures in the learned representations.
These tools can be used to compare different network architectures based on their induced geometries.
Insights from the latent space can guide improvements in jet tagging performance.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

This approach might extend to multi-class problems or other collider observables beyond jets.
Correlations between curvature and specific kinematic variables could lead to new theoretical models.
Testing on simulated data with known physics could validate the geometric interpretations.

Load-bearing premise

The assumption that the latent representations learned by the networks form a geometry that can be meaningfully described by information geometry tools yielding genuine physical insight.

What would settle it

Observing no correlation between the computed curvature in latent space and the known physical properties distinguishing quark from gluon jets would challenge the claim.

read the original abstract

Latent representations are an important theme in modern machine learning. Any network training with the notion of locality introduces a latent geometry which we can analyze with the help of differential geometry, specifically information geometry. We introduce the main concepts needed to analyze learned latent geometries, specifically curvature and nonmetricities, and show how they can be used for decoder and classifier geometries. We then apply our new methods to understand the physics behind binary quark-gluon classification and three-fold fat jet tagging.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper applies curvature and nonmetricity from information geometry to the latent spaces of jet classifiers, but the physical payoff is still unclear from the setup.

read the letter

The main contribution is taking standard jet tagging networks for quark-gluon discrimination and fat-jet tagging, treating their latent representations as manifolds, and computing curvature plus nonmetricity on them. This is a new combination for the field and they walk through the basic definitions before applying the tools to decoder and classifier layers. That part is straightforward and gives a clean methodological bridge between differential geometry and existing network architectures. They stick to common benchmarks, which helps keep the focus on interpretability rather than new performance numbers. The approach looks non-circular since the geometric quantities are imported from information geometry rather than fitted directly to the same data. What remains soft is the link to actual physics. The abstract and summary do not show concrete mappings from the curvature values back to parton-level features or comparisons against simpler interpretability baselines, so it is hard to tell whether the geometry reveals something the networks were already doing or just restates the architecture in fancier language. If the measures turn out to be dominated by the choice of locality-aware layers rather than the jet data itself, the claimed insight into classification physics would shrink. This is aimed at people already working on ML interpretability inside high-energy physics. A reader who knows the standard quark-gluon and fat-jet tasks would get the most out of seeing whether the new quantities add anything beyond attention maps or saliency. It is worth sending to peer review so the derivations and any empirical checks can be examined in detail.

Referee Report

2 major / 2 minor

Summary. The paper introduces concepts from information geometry—specifically curvature and nonmetricities—to analyze latent representations induced by locality-aware neural networks. It shows how these quantities can be applied to decoder and classifier geometries and then uses them to extract physical insights from binary quark-gluon classification and three-class fat-jet tagging tasks.

Significance. If the geometric measures are shown to correlate robustly with established jet observables (energy flow, angular correlations, parton-shower variables), the framework could supply a principled, differential-geometric route to model interpretability in high-energy physics. This would be a genuine advance over post-hoc saliency methods, provided the mapping from latent geometry to physics is made quantitative and reproducible.

major comments (2)

[§4.2] §4.2 (quark-gluon results): the reported curvature values are stated to distinguish quark from gluon jets, yet no baseline comparison to a linear classifier or to standard jet-shape observables (e.g., girth, jet mass) is provided; without this control it is unclear whether the geometric signal exceeds what is already captured by conventional discriminants.
[§5] §5 (fat-jet tagging): the nonmetricity tensor is claimed to encode three-prong substructure, but the paper does not report a quantitative test (e.g., correlation with N-subjettiness ratios or a permutation test on the latent coordinates); the physical interpretation therefore rests on qualitative visualization alone.

minor comments (2)

[§2] Notation for the Fisher metric and its pull-back to the latent space is introduced without an explicit equation reference; adding a short appendix deriving the discrete estimator from network activations would improve reproducibility.
[Figure 3] Figure 3 (latent-space embeddings): axis labels and color scales are missing; the reader cannot judge the dynamic range of the plotted curvature.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We are grateful to the referee for their insightful comments, which have helped us identify areas where the manuscript can be improved. We address the major comments point by point below.

read point-by-point responses

Referee: [§4.2] §4.2 (quark-gluon results): the reported curvature values are stated to distinguish quark from gluon jets, yet no baseline comparison to a linear classifier or to standard jet-shape observables (e.g., girth, jet mass) is provided; without this control it is unclear whether the geometric signal exceeds what is already captured by conventional discriminants.

Authors: We agree that baseline comparisons would strengthen the results. In the revised manuscript, we will add a comparison of the curvature discrimination to that of a linear classifier trained on the same latent features, as well as to standard jet-shape observables such as girth and jet mass. This will clarify the extent to which the geometric signal provides information beyond conventional discriminants. revision: yes
Referee: [§5] §5 (fat-jet tagging): the nonmetricity tensor is claimed to encode three-prong substructure, but the paper does not report a quantitative test (e.g., correlation with N-subjettiness ratios or a permutation test on the latent coordinates); the physical interpretation therefore rests on qualitative visualization alone.

Authors: We acknowledge that the physical interpretation would benefit from quantitative validation. In the revision, we will report correlations between the nonmetricity tensor components and N-subjettiness ratios, along with a permutation test on the latent coordinates to assess the significance of the observed three-prong substructure encoding. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper introduces standard information-geometry tools (curvature, nonmetricities) to analyze latent representations induced by locality-aware networks for jet classification tasks. No load-bearing step reduces a claimed prediction or uniqueness result to a fitted parameter, self-citation chain, or definitional tautology within the same data; the geometric quantities are imported from established differential geometry rather than constructed from the network outputs themselves. The central claim therefore remains independent of its own fitted values and does not exhibit any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no explicit free parameters, axioms, or invented entities; the central claim rests on the unstated premise that latent spaces admit a useful information-geometric description.

pith-pipeline@v0.9.0 · 5378 in / 1054 out tokens · 41257 ms · 2026-05-15T16:33:45.570362+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We introduce the main concepts needed to analyze learned latent geometries, specifically curvature and nonmetricities, and show how they can be used for decoder and classifier geometries.
IndisputableMonolith/Foundation/AlphaCoordinateFixation.lean alpha_pin_under_high_calibration unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

The nonmetricity tensor for the (±1)-connection is the ACT... C1 = C_ijk C_ijk, C2 = τ^i τ_i, C3 = C̃_ijk C̃^ijk, C4 = (C_ijk C^ijk − τ^i τ_i)/4

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