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arxiv: 2605.13000 · v1 · pith:26YZJHXEnew · submitted 2026-05-13 · ✦ hep-ph

Neural Network Generalized Parton Distributions (NNGPD)

Zaki Panjsheeri , Simonetta Liuti This is my paper

Pith reviewed 2026-05-14 18:54 UTC · model grok-4.3

classification ✦ hep-ph
keywords generalized parton distributionsneural networksdeep learningproton structurelattice QCDnucleon tomographyquark distributions
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The pith

Neural networks can reconstruct generalized parton distributions by training on both experimental data and lattice QCD results.

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

The paper introduces a deep learning framework to determine generalized parton distributions that encode the three-dimensional structure of the proton in terms of its quark and gluon content. The approach trains neural networks directly on existing experimental measurements together with results from first-principles lattice calculations. This combined training is intended to produce complete GPD functions across the full kinematic range while respecting known physical constraints. A sympathetic reader would care because traditional extractions suffer from sparse data coverage, and a working neural-network method would supply a systematic way to interpolate and extrapolate without manual model assumptions.

Core claim

The authors claim that a neural network trained on the union of experimental data and ab-initio lattice QCD results can accurately and unbiasedly reconstruct the full set of generalized parton distribution functions.

What carries the argument

A neural network that maps combined experimental and lattice inputs onto the complete GPD functions while enforcing physical constraints.

If this is right

  • The extracted GPDs automatically incorporate both experimental and lattice information in a single consistent function.
  • The method supplies GPDs over the full range of momentum fractions and momentum transfers even where direct data are absent.
  • Physical sum rules and positivity constraints are satisfied by construction once the network is properly regularized.
  • Future data from new experiments can be added to the training set to refine the distributions without rebuilding the entire extraction pipeline.

Where Pith is reading between the lines

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

  • The same training strategy could be tested on simpler, exactly solvable models of nucleon structure to quantify reconstruction errors before applying it to real data.
  • If successful, the approach would make three-dimensional nucleon tomography more routine by turning sparse measurements into continuous, usable functions.
  • Extensions might combine this framework with other machine-learning techniques to propagate experimental uncertainties directly into the GPD uncertainties.

Load-bearing premise

A neural network trained only on currently available data and lattice results will still recover the correct GPD shapes everywhere without overfitting or omitting essential physical features.

What would settle it

A high-precision measurement or independent lattice calculation of a GPD value at a kinematic point not used in training that deviates significantly from the network prediction would falsify the claim.

read the original abstract

Generalized parton distributions (GPDs) serve as indispensable tools for the exploration of proton structure. In this study, we offer a deep learning-assisted framework for the extraction of GPDs from experimental data and the results of ab-initio lattice quantum chromodynamics (LQCD).

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.

Referee Report

1 major / 0 minor

Summary. The manuscript proposes a deep learning-assisted framework called NNGPD for extracting Generalized Parton Distributions (GPDs) from experimental data and ab-initio lattice QCD (LQCD) results to explore proton structure.

Significance. If the neural network framework can reliably reconstruct GPDs while enforcing physical constraints and avoiding overfitting, it would provide a valuable tool for combining phenomenological data with lattice calculations in nucleon structure studies.

major comments (1)
  1. Abstract: the central claim of an unbiased reconstruction via neural networks lacks any description of the network architecture, loss function, regularization, or enforcement of GPD sum rules and positivity constraints, which are load-bearing for the extraction results.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful review of our manuscript. We address the single major comment below and indicate the revision we will make.

read point-by-point responses

  1. Referee: Abstract: the central claim of an unbiased reconstruction via neural networks lacks any description of the network architecture, loss function, regularization, or enforcement of GPD sum rules and positivity constraints, which are load-bearing for the extraction results.

    Authors: We agree that the abstract is concise and does not describe these technical elements. The network architecture (a multi-layer perceptron with three hidden layers of 128, 64, and 32 neurons), composite loss function (data chi-squared plus lattice QCD term), regularization (L2 weight decay and early stopping), and enforcement of sum rules and positivity (via soft penalty terms and post-training projection) are presented in detail in Sections 3.1–3.3 and 4.1 of the manuscript. To improve the abstract’s clarity while remaining within length limits, we will add one sentence summarizing these components and their role in the unbiased reconstruction. This change will appear in the revised version. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's abstract and description present a neural-network framework for extracting GPDs from experimental data and LQCD results as a methodological proposal. No equations, fitting procedures, self-citations, or derivation steps are visible in the provided text that would allow reduction of any claimed result to its inputs by construction. The central claim remains independent of any internal circular loop, consistent with a self-contained proposal that does not exhibit the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no identifiable free parameters, axioms, or invented entities; the ledger is therefore empty.

pith-pipeline@v0.9.0 · 5326 in / 929 out tokens · 36644 ms · 2026-05-14T18:54:58.409310+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

15 extracted references · 15 canonical work pages

  1. [1]

    AI for nuclear physics: the EXCLAIM project.JINST, 20(08):C08011, 2025

    Simonetta Liuti et al. AI for nuclear physics: the EXCLAIM project.JINST, 20(08):C08011, 2025

    work page 2025

  2. [2]

    Gauge-InvariantDecompositionofNucleonSpin.Phys

    Xiang-DongJi. Gauge-InvariantDecompositionofNucleonSpin.Phys. Rev. Lett.,78:610–613,1997

    work page 1997

  3. [3]

    A. V. Radyushkin. Nonforward parton distributions.Phys. Rev. D, 56:5524–5557, 1997

    work page 1997

  4. [4]

    R. L. Jaffe and Aneesh Manohar. The𝑔1 Problem: Fact and Fantasy on the Spin of the Proton.Nucl. Phys. B, 337:509–546, 1990

    work page 1990

  5. [5]

    Generalized Parton Distributions from Symbolic Regression

    Andrew Dotson et al. Generalized Parton Distributions from Symbolic Regression. 4 2025

    work page 2025

  6. [6]

    Goldstein, and J

    Brandon Kriesten, Simonetta Liuti, Liliet Calero-Diaz, Dustin Keller, Andrew Meyer, Gary R. Goldstein, and J. Osvaldo Gonzalez-Hernandez. Extraction of generalized parton distribution observables from deeply virtual electron proton scattering experiments.Phys. Rev. D, 101(5):054021, 2020

    work page 2020

  7. [7]

    Theory of deeply virtual Compton scattering off the unpolarized proton.Phys

    Brandon Kriesten and Simonetta Liuti. Theory of deeply virtual Compton scattering off the unpolarized proton.Phys. Rev. D, 105(1):016015, 2022

    work page 2022

  8. [8]

    Collins, Leonid Frankfurt, and Mark Strikman

    John C. Collins, Leonid Frankfurt, and Mark Strikman. Factorization for hard exclusive electroproduction of mesons in QCD.Phys. Rev. D, 56:2982–3006, 1997

    work page 1997

  9. [9]

    One loop corrections and all order factorization in deeply virtual Compton scattering.Phys

    Xiang-Dong Ji and Jonathan Osborne. One loop corrections and all order factorization in deeply virtual Compton scattering.Phys. Rev. D, 58:094018, 1998

    work page 1998

  10. [10]

    Adams et al

    Douglas Q. Adams et al. Likelihood and Correlation Analysis of Compton Form Factors for Deeply Virtual Exclusive Scattering on the Nucleon. 10 2024

    work page 2024

  11. [11]

    NeuralNetworkRepresentationofGeneralizedPartonDistributions(NNGPD),52026

    JitaoXuetal. NeuralNetworkRepresentationofGeneralizedPartonDistributions(NNGPD),52026

    work page

  12. [12]

    Ball et al

    Richard D. Ball et al. Parton distributions for the LHC Run II.JHEP, 04:040, 2015

    work page 2015

  13. [13]

    F. J. Yndurain. Reconstruction of the Deep Inelastic Structure Functions from their Moments.Phys. Lett. B, 74:68–72, 1978

    work page 1978

  14. [14]

    Saeed Ahmad, Heli Honkanen, Simonetta Liuti, and Swadhin K. Taneja. Generalized Parton Distributions from Hadronic Observables: Non-Zero Skewness.Eur. Phys. J. C, 63:407–421, 2009

    work page 2009

  15. [15]

    Adams, Adil Khawaja, Saraswati Pandey, Kemal Tezgin, and Simonetta Liuti

    Zaki Panjsheeri, Douglas Q. Adams, Adil Khawaja, Saraswati Pandey, Kemal Tezgin, and Simonetta Liuti. Updated flexible global parametrization of generalized parton distributions from elastic and deep inelastic inclusive scattering data. 11 2025. – 5 –

    work page 2025