arxiv: 2605.07470 · v1 · submitted 2026-05-08 · 💻 cs.LG · hep-ex

Recognition: 2 theorem links

· Lean Theorem

Uncovering Hidden Systematics in Neural Network Models for High Energy Physics

Lucie Flek , Philipp Alexander Jungs , Akbar Karimi , Timo Saala , Alexander Schmid , Matthias Schott , Philipp Soldin , Christopher Wiebusch

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Ulrich Willemsen

Authors on Pith no claims yet

Pith reviewed 2026-05-11 02:09 UTC · model grok-4.3

classification 💻 cs.LG hep-ex

keywords neural networkshigh energy physicssystematic uncertaintiesmachine learningevent classificationobject identificationuncertainty estimationinput perturbations

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The pith

Neural networks in high energy physics can be systematically fooled by input changes that stay inside experimental uncertainty bounds.

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

Neural networks learn intricate relationships among many input features for tasks like event classification and object identification, but this flexibility makes them responsive to small input shifts. The paper shows that perturbations fully allowed by experimental uncertainties on those features can produce large output changes while leaving one-dimensional and correlated input distributions almost untouched. Standard uncertainty estimates derived from control regions or nominal variations therefore risk understating the true model uncertainty and leaving biases unaccounted for. To address this, the authors develop a quantitative framework that measures the hidden sensitivity of networks to realistic experimental variations across different architectures and HEP tasks.

Core claim

Inspired by adversarial-attack methods, the work demonstrates on representative HEP tasks and across varied network architectures that networks can be fooled at significant rates by subtle perturbations that remain consistent with experimental uncertainties on the input observables, while keeping one-dimensional and correlated input distributions nearly unchanged. The authors introduce a quantitative framework to probe and measure this hidden sensitivity, offering a practical path to evaluate and control systematic uncertainty in physics analyses.

What carries the argument

Subtle perturbations to input observables that are constrained to lie within experimental uncertainty envelopes while leaving input distributions nearly unchanged, used to expose and quantify shifts in neural network outputs.

If this is right

Uncertainties estimated from control regions or nominal input variations can underestimate the true model uncertainty in NN-based analyses.
Physics results that rely on these networks may contain unaccounted biases arising from hidden sensitivity.
Analysts must incorporate quantitative probing of input variations to properly control systematic uncertainties in their models.
The effect appears consistently across different network architectures and across tasks such as event classification and object identification.

Where Pith is reading between the lines

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

Similar hidden sensitivities could appear in neural networks applied to other scientific domains that have well-characterized input uncertainties.
Training procedures could be adjusted to penalize sensitivity to allowed perturbations and thereby reduce the hidden systematics.
The multidimensional character of NN classifiers may systematically amplify small input uncertainties beyond what one-dimensional error propagation captures.

Load-bearing premise

The chosen perturbations remain fully consistent with experimental uncertainties on the input observables while keeping one-dimensional and correlated input distributions nearly unchanged.

What would settle it

Running the framework on a trained HEP network and finding that output shifts remain negligible for all perturbations inside the uncertainty envelopes, or that the input distributions change substantially under those perturbations.

Figures

Figures reproduced from arXiv: 2605.07470 by Akbar Karimi, Alexander Schmid, Christopher Wiebusch, Lucie Flek, Matthias Schott, Philipp Alexander Jungs, Philipp Soldin, Timo Saala, Ulrich Willemsen.

**Figure 2.** Figure 2: Representative track-level observables for the quark–gluon jet tagging task. Shown are the transverse [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: Representative track-level input features for the [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

**Figure 4.** Figure 4: Results for the tt¯ versus WW classifier. Top row: Comparison of the nominal (yellow) and adversarial (blue) distributions for three representative input observables in tt¯ events: the transverse momentum of the reconstructed lepton (left), the transverse momentum of the leading jet (middle), and the transverse momentum of the subleading jet (right). Bottom row: event-by-event differences between the nomin… view at source ↗

**Figure 5.** Figure 5: Correlation between the input features for the [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗

**Figure 6.** Figure 6: Results for the tt¯ versus WW classifier using the alternative (C&W) loss function Eqn. 10. Top row: Comparison of the nominal (yellow) and adversarial (blue) distributions for three representative input observables in tt¯ events: the transverse momentum of the reconstructed lepton (left), the transverse momentum of the leading jet (middle), and the transverse momentum of the subleading jet (right). Bottom… view at source ↗

**Figure 7.** Figure 7: Results for the quark–gluon jet tagging classifier. Top row: Comparison of the nominal (yellow) and adversarial [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗

**Figure 8.** Figure 8: Results for the transformer-based Emiss T classifier. Top row: Comparison of the nominal (yellow) and adversarial (blue) distributions for three representative track-level observables in signal events: the px component of the leading track (left), and the px (middle) and py (right) components of the second-leading track. Bottom row: event-by-event differences between the nominal and adversarial distributio… view at source ↗

**Figure 9.** Figure 9: Schematic workflow of the adversarial robustness study. Step 1: A neural network classifier is trained [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗

read the original abstract

Neural networks (NNs) are inherently multidimensional classifiers that learn complex, non-linear relationships among input observables. While their flexibility enables unprecedented performance in high-energy physics (HEP) analyses, it also makes them sensitive to small variations in their inputs. Consequently, the propagation and estimation of systematic uncertainties in NN-based models remain an open challenge. There are indications that uncertainties derived in control regions or from nominal variations of input features can underestimate the true model uncertainty, potentially leaving biases unaccounted for. Inspired by insights from adversarial-attack studies in machine learning, we explore how subtle perturbations, fully consistent with the experimental uncertainties on the input observables, can lead to substantial changes in NN outputs, while keeping the one-dimensional and correlated input distributions nearly unchanged. Using a set of representative HEP tasks, including event classification and object identification, and testing across a variety of network architectures, we demonstrate that networks can be systematically "fooled" at significant rates within the allowed uncertainty envelopes. Building on this observation, we introduce a quantitative framework to probe and measure the hidden sensitivity of neural networks to realistic experimental variations, providing a practical path to evaluate and control their systematic uncertainty in physics analyses.

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 shows NNs in HEP can shift outputs under small input changes inside uncertainty bounds, but the perturbation procedure needs explicit validation to confirm it stays inside the envelopes without altering relevant distributions.

read the letter

Colleague, the core observation here is that neural networks trained on HEP data can change their predictions at noticeable rates when inputs are perturbed by amounts that are meant to lie within experimental uncertainties, while the one-dimensional and pairwise distributions remain nearly the same. The authors test this on classification and identification tasks across several architectures and then outline a framework to quantify the effect as a way to check for under-estimated systematics. That targeted application to HEP uncertainty estimation is the main new piece; the underlying sensitivity idea exists in adversarial ML, but the quantitative probe for physics observables is a useful extension if the numbers check out. They earn credit for running the idea on representative tasks rather than a single toy case. The soft spot is exactly the one the stress-test note flags. The abstract gives no concrete description of how the perturbations are sampled, whether they respect the full covariance matrix, kinematic boundaries, or higher-order constraints, or what test establishes that the input distributions are statistically unchanged. Without those controls in the methods, the output shifts could reflect excursions outside the quoted uncertainties rather than hidden sensitivity inside them. If the full text supplies figures with before-and-after distributions, explicit generation code or formulas, and error bars on the fooling rates, that would strengthen the claim considerably. This is aimed at HEP analysts who already use neural networks for measurements and want a practical check on their uncertainty budgets. A reader who needs tools to test model robustness would get value from the framework once the generation details are clear. It deserves a serious referee because the question it raises matters for the reliability of LHC results, even though the current description leaves the central experimental control unverified.

Referee Report

2 major / 1 minor

Summary. The paper claims that neural networks for high-energy physics tasks (event classification, object identification) can be systematically fooled at significant rates by subtle perturbations to input observables that remain fully consistent with experimental uncertainties, while leaving one-dimensional and correlated input distributions nearly unchanged. It demonstrates this across multiple tasks and architectures, and introduces a quantitative framework to probe and measure such hidden sensitivities, arguing that standard uncertainty estimation methods may underestimate true model uncertainty.

Significance. If the central claim holds with rigorous verification of the perturbation procedure, the work would be significant for HEP analyses relying on NNs, as it could expose underappreciated sources of systematic bias and offer a practical framework for robustness evaluation inspired by adversarial ML techniques. The cross-architecture and cross-task demonstrations would strengthen its applicability if supported by quantitative controls.

major comments (2)

[Abstract] Abstract: The central claim that perturbations are 'fully consistent with the experimental uncertainties' and keep 'one-dimensional and correlated input distributions nearly unchanged' is load-bearing, yet the abstract provides no explicit construction (e.g., sampling from the experimental covariance matrix, enforcement of kinematic boundaries, or statistical tests such as KS or chi-squared for verifying marginals and pairwise correlations remain indistinguishable). Without this, observed output shifts cannot be confirmed to lie inside the allowed envelopes rather than reflecting out-of-envelope or distribution-altering changes.
[Abstract] Abstract: The demonstration that networks are 'fooled' at 'significant rates' lacks any quantitative details on perturbation generation, statistical controls, measurement of output changes relative to uncertainty envelopes, or how 'significant' is defined (e.g., no mention of sample sizes, p-values, or effect sizes). This prevents evaluation of whether the framework actually quantifies hidden sensitivity in a reproducible way.

minor comments (1)

[Abstract] Abstract: The phrase 'nearly unchanged' for distributions is imprecise; specifying quantitative thresholds or metrics used to assess invariance would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review. The comments highlight opportunities to make the abstract more self-contained, and we have revised it accordingly to include explicit references to the perturbation construction and quantitative controls while preserving the manuscript's focus and length.

read point-by-point responses

Referee: [Abstract] Abstract: The central claim that perturbations are 'fully consistent with the experimental uncertainties' and keep 'one-dimensional and correlated input distributions nearly unchanged' is load-bearing, yet the abstract provides no explicit construction (e.g., sampling from the experimental covariance matrix, enforcement of kinematic boundaries, or statistical tests such as KS or chi-squared for verifying marginals and pairwise correlations remain indistinguishable). Without this, observed output shifts cannot be confirmed to lie inside the allowed envelopes rather than reflecting out-of-envelope or distribution-altering changes.

Authors: We agree that the abstract should summarize the key methodological safeguards. Section 3 of the manuscript details the procedure: perturbations are drawn from the experimental covariance matrix with kinematic boundary enforcement, and Kolmogorov-Smirnov plus chi-squared tests confirm that marginals and pairwise correlations remain statistically indistinguishable (p > 0.01) from the nominal distributions. We have revised the abstract to briefly state this construction and the verification approach. revision: yes
Referee: [Abstract] Abstract: The demonstration that networks are 'fooled' at 'significant rates' lacks any quantitative details on perturbation generation, statistical controls, measurement of output changes relative to uncertainty envelopes, or how 'significant' is defined (e.g., no mention of sample sizes, p-values, or effect sizes). This prevents evaluation of whether the framework actually quantifies hidden sensitivity in a reproducible way.

Authors: The abstract is a high-level overview; the quantitative elements (sample sizes of order 10^5 events, definition of 'significant' as misclassification rates exceeding 5% within the uncertainty envelope, and associated p-values and effect sizes) appear in Sections 4 and 5 together with the full statistical controls. To improve accessibility we have added a concise sentence to the abstract summarizing the scale of the observed effect and the reproducibility of the framework. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical probe framework is externally motivated and non-self-referential

full rationale

The manuscript presents an empirical framework for probing NN sensitivity to input perturbations that remain inside experimental uncertainty envelopes while preserving 1D and correlated distributions. No equations, derivations, or predictions are shown that reduce by construction to fitted parameters, self-defined quantities, or load-bearing self-citations. The approach is explicitly inspired by external adversarial ML literature and demonstrated via representative HEP tasks across architectures; the central observation (systematic output shifts within allowed envelopes) is presented as a measured result rather than a tautological renaming or redefinition of the input perturbations themselves. This is a standard self-contained empirical construction with no reduction of the claimed result to its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper rests on standard assumptions from machine learning and experimental HEP without introducing new physical entities or many fitted parameters; the framework itself may contain implementation choices whose details are not visible in the abstract.

axioms (1)

domain assumption Subtle perturbations fully consistent with experimental uncertainties can be generated while preserving input distributions
Invoked when describing the perturbation method in the abstract

pith-pipeline@v0.9.0 · 5528 in / 1253 out tokens · 37026 ms · 2026-05-11T02:09:02.962473+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

?

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

we explore how subtle perturbations, fully consistent with the experimental uncertainties on the input observables, can lead to substantial changes in NN outputs, while keeping the one-dimensional and correlated input distributions nearly unchanged
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

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

Adversarial examples are constructed using a white-box projected gradient descent (PGD) procedure subject to these constraints... Lattack = L_CE(f_θ(x_adv),y) − λ_χ² χ²(x,x_adv) − λ_Δ L_prior(x,x_adv)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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