arxiv: 2605.12490 · v1 · submitted 2026-05-12 · ✦ hep-ex

Recognition: 2 theorem links

· Lean Theorem

DNN predictions for pp reference p_T spectra at unmeasured sqrt{s}

Henner B\"usching, Jerome Jung, Maria A. Calmon Behling, Mario Kr\"uger

Pith reviewed 2026-05-13 02:33 UTC · model grok-4.3

classification ✦ hep-ex

keywords deep neural networkproton-proton collisionstransverse momentum spectraLHCextrapolationALICEreference spectraheavy-ion collisions

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The pith

Deep neural networks trained on ALICE data can predict proton-proton transverse-momentum spectra at unmeasured LHC energies.

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

The paper demonstrates a deep neural network approach to interpolate and extrapolate proton-proton reference transverse-momentum spectra to center-of-mass energies that have not yet been measured. These reference spectra are essential for studying the Quark-Gluon Plasma in heavy-ion collisions by providing a baseline at the same energy. The model uses data from ALICE measurements in LHC Runs 1 and 2 to generate predictions for Run 3 and future runs. If the extrapolation holds, it enables consistent analysis of new data without delays for dedicated reference measurements.

Core claim

A deep neural network, trained on measured pp p_T spectra at known sqrt(s) from ALICE, can interpolate between existing energies and extrapolate to higher unmeasured ones, providing reference spectra for heavy-ion studies at LHC Run 3 energies and beyond.

What carries the argument

A deep neural network that learns the dependence of transverse-momentum spectra on center-of-mass energy from existing data.

If this is right

The model supplies reference spectra for direct comparison in heavy-ion analyses at new energies.
It allows study of energy evolution of particle production without requiring measurements at every energy point.
Predictions can be used immediately for upcoming Run 3 data taking.
Variations in the network can help estimate uncertainties in the extrapolated spectra.

Where Pith is reading between the lines

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

The method could be extended to other particle observables or different collision types.
Direct measurements at the predicted energies will provide a test of the model's accuracy.
It may help in planning experiments by forecasting needed reference data.

Load-bearing premise

The energy dependence of the spectra follows a learnable pattern from the available measured points that generalizes to unmeasured higher energies.

What would settle it

A future measurement of pp transverse-momentum spectra at one of the unmeasured energies that deviates substantially from the DNN prediction would falsify the reliability of the extrapolation.

Figures

Figures reproduced from arXiv: 2605.12490 by Henner B\"usching, Jerome Jung, Maria A. Calmon Behling, Mario Kr\"uger.

**Figure 1.** Figure 1: pT spectra simulated with PYTHIA (left) and EPOS LHC (right) together with the corresponding predictions of the PYTHIA- and EPOS LHC-based DNNs. 5 Performance evaluation The extrapolation performance of the DNN architecture determined with PYTHIA (’PYTHIA-based DNN’) in the hyperparameter scan is evaluated using an independent dataset of EPOS LHC-simulated data [23], as the pT spectra in PYTHIA and EPOS … view at source ↗

**Figure 2.** Figure 2: pT spectra measured by ALICE [15] together with the corresponding predictions of the ALICE-based DNN model (left) and their ⟨dNch/dη⟩ and ⟨pT⟩ as a function of √ s (right). 6 Model application to ALICE data After selecting the model architecture based on the PYTHIA dataset and validating the performance with the EPOS LHC dataset, the final DNN ensemble (’ALICE-based DNN’) is trained on the ALICE dataset [… view at source ↗

**Figure 3.** Figure 3: Ratios of pT-differential cross sections at different energies to √ s = 5.02 TeV as predicted by the DNN, together with NLO pQCD calculations, PYTHIA simulations, and functional interpolations, summarized in [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: pp reference pT-differential cross sections at different energies constructed from the DNN-predicted cross section ratios to the baseline energy √ s = 5.02 TeV and a corresponding ALICE measurement [9]. 8 Summary In this paper, a DNN-based method for constructing pp reference pT spectra at unmeasured √ s is presented. The DNN is trained with inclusive charged-particle pT spectra measured by the ALICE col… view at source ↗

read the original abstract

Studies of the properties of the Quark-Gluon Plasma in high-energy heavy-ion collisions commonly facilitate proton-proton (pp) collisions at the same center-of-mass energy per nucleon pair as a reference measurement. In this paper, a deep neural network-based approach for interpolating and extrapolating pp reference transverse-momentum spectra to unmeasured energies is presented. The model is trained with ALICE data from LHC Runs 1 and 2 and provides predictions for center-of-mass energies relevant to LHC Run 3 and beyond.

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

A practical DNN tool for filling in missing pp reference spectra, but the extrapolation step rests on untested assumptions about what the network has actually learned.

read the letter

The paper trains a deep neural network on ALICE pp pT spectra from LHC Runs 1 and 2, then uses it to generate reference distributions at energies that have not yet been measured. That is the core new piece: a targeted application of standard DNN interpolation/extrapolation to a concrete need in heavy-ion analyses, where people constantly need pp baselines at the same sqrt(s) as their PbPb or pPb runs. If the outputs turn out reliable, it gives experimental groups a quick way to produce those references without waiting for new data or building new parametrizations from scratch. The training data are public, so the approach is at least reproducible in principle. That is the part worth noting positively. The rest of the work is mostly standard network training on binned spectra, with no indication of novel architecture or loss functions. The soft spot is exactly where the stress-test note points: there is no evidence in the abstract or described method that the authors performed held-out extrapolation tests, such as training on a subset of measured energies and checking against the remaining measured ones. Without those checks, or comparisons to pQCD calculations or existing functional forms, it is impossible to know whether the network is capturing the real energy dependence of hard scattering and fragmentation or simply fitting correlations that break at higher sqrt(s). The risk of unphysical high-pT tails or wrong normalizations is real for plain feed-forward networks, and the paper does not appear to constrain the outputs with any physics priors. This work is aimed at heavy-ion experimentalists who need reference spectra for Run 3 and future runs. A reader who already works with ALICE data and wants a fast generator might get some value, but only after the validation gaps are closed. It is coherent on its own terms and shows honest engagement with the practical problem, so it deserves a serious referee rather than a desk reject. I would send it out for review with the explicit request that the authors add extrapolation tests and uncertainty estimates before acceptance.

Referee Report

2 major / 1 minor

Summary. The paper presents a deep neural network (DNN) trained on ALICE pp p_T spectra from LHC Runs 1 and 2 to interpolate and extrapolate reference spectra to unmeasured center-of-mass energies √s relevant to Run 3 and beyond, for use in heavy-ion collision analyses.

Significance. If the extrapolation proves reliable, the method could supply practical reference spectra at new energies where direct measurements are unavailable, supporting QGP studies. The approach is self-contained, uses publicly referenced ALICE data, and avoids circular fitting to the same datasets, which are positive attributes. However, without reported validation or physics constraints, the practical significance remains limited.

major comments (2)

[Abstract] Abstract: the central claim that the DNN 'provides predictions' for unmeasured √s is load-bearing but unsupported by any reported validation metrics, error estimates, extrapolation tests (e.g., held-out energy prediction), or comparison to pQCD/parametrizations, leaving the reliability of the extrapolation unverified.
[Abstract] The weakest assumption—that a standard feed-forward DNN trained only on lower-energy spectra learns the true √s dependence without introducing unphysical tails or normalizations—is not addressed by any explicit test in the manuscript, which is required to substantiate the extrapolation claim.

minor comments (1)

Notation for input features (e.g., how √s and p_T are encoded) could be clarified for reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The major comments correctly identify that the current manuscript does not contain explicit validation of the extrapolation performance. We will revise the paper to include the requested tests, metrics, and comparisons, thereby strengthening the central claims.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that the DNN 'provides predictions' for unmeasured √s is load-bearing but unsupported by any reported validation metrics, error estimates, extrapolation tests (e.g., held-out energy prediction), or comparison to pQCD/parametrizations, leaving the reliability of the extrapolation unverified.

Authors: We agree that the abstract claim requires supporting evidence. In the revised manuscript we will add a validation section that reports quantitative metrics (e.g., χ² per degree of freedom and relative residuals) on held-out √s points, provides uncertainty bands derived from the DNN ensemble or dropout, and includes direct comparisons of the DNN predictions against available pQCD calculations and standard parametrizations at both interpolated and extrapolated energies. These additions will allow readers to assess the reliability of the predictions. revision: yes
Referee: [Abstract] The weakest assumption—that a standard feed-forward DNN trained only on lower-energy spectra learns the true √s dependence without introducing unphysical tails or normalizations—is not addressed by any explicit test in the manuscript, which is required to substantiate the extrapolation claim.

Authors: We acknowledge that no explicit test of this assumption is currently presented. The revised version will include dedicated checks: (i) inspection of predicted spectra at extrapolated √s for negative yields or unphysical high-p_T tails, (ii) verification that integrated yields remain consistent with measured trends, and (iii) a comparison of the learned √s scaling against both data and theoretical expectations. Should any unphysical features appear, we will discuss them and consider adding physics-informed regularisation or limiting the extrapolation range. revision: yes

Circularity Check

0 steps flagged

No circularity: DNN trained on external ALICE data for energy extrapolation

full rationale

The paper presents a supervised DNN model trained on publicly referenced ALICE pp p_T spectra from LHC Runs 1 and 2 to interpolate and extrapolate to unmeasured √s values. This is a standard data-driven regression setup with no self-definitional loops, no fitted parameters renamed as predictions, and no load-bearing self-citations or imported uniqueness theorems. The derivation chain consists of training on external measurements and applying the model forward; predictions are not equivalent to inputs by construction. The approach is self-contained against external benchmarks, with any validation concerns falling under correctness rather than circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard machine-learning assumptions that the spectra vary smoothly enough to be captured by a neural network and that the training data distribution is representative for extrapolation; no explicit free parameters or invented entities are named in the abstract.

axioms (1)

domain assumption Proton-proton transverse-momentum spectra at different center-of-mass energies can be learned and extrapolated by a deep neural network without large unmodeled physics effects
Implicit in the decision to use DNN regression for interpolation/extrapolation across energies.

pith-pipeline@v0.9.0 · 5392 in / 1185 out tokens · 59584 ms · 2026-05-13T02:33:17.760442+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
a deep neural network-based approach for interpolating and extrapolating pp reference transverse-momentum spectra... trained with ALICE data from LHC Runs 1 and 2
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
DNN predictions... no assumptions about the physical processes underlying the spectra’s energy dependence

Reference graph

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