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arxiv: 2604.13062 · v1 · submitted 2026-03-19 · 💻 cs.CL

Mathematical Reasoning Enhanced LLM for Formula Derivation: A Case Study on Fiber NLI Modellin

Yao Zhang , Yuchen Song , Xiao Luo , Shengnan Li , Xiaotian Jiang , Min Zhang , Danshi Wang This is my paper

Pith reviewed 2026-05-15 09:05 UTC · model grok-4.3

classification 💻 cs.CL
keywords large language modelsformula derivationnonlinear interferenceISRS GN modeloptical communicationssymbolic reasoningGSNR approximation
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The pith

Structured prompts let an LLM reconstruct known fiber interference formulas and derive a new approximation for multi-span C and C+L transmissions.

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

The paper shows that large language models can carry out symbolic derivation of physical expressions when guided by carefully structured prompts. Starting from established models of fiber nonlinear interference, the LLM first rebuilds the closed-form ISRS GN expressions. It then produces a new approximation designed for multi-span links operating across C and C+L bands. Numerical checks confirm that the resulting model yields central-channel GSNR values nearly identical to reference calculations, with mean absolute error below 0.109 dB across channels and spans. This outcome indicates that LLMs may serve as practical assistants for generating physically consistent closed-form models in specialized engineering domains.

Core claim

Guiding an LLM with structured prompts reconstructs the known closed-form ISRS GN expressions and yields a novel approximation tailored for multi-span C and C+L band transmissions; the derived model produces central-channel GSNRs nearly identical to baseline models, with mean absolute error across all channels and spans below 0.109 dB.

What carries the argument

Structured prompts that break the derivation into sequential symbolic steps for manipulating physical equations of nonlinear interference.

If this is right

  • The new approximation supplies a low-complexity closed-form tool for estimating GSNR in C and C+L band networks.
  • Physical consistency of the LLM output is verified by direct numerical match to established models.
  • The prompting workflow can be reused for other closed-form derivations in optical channel modeling.
  • Mean absolute error remains below 0.109 dB for both central and edge channels across multiple spans.

Where Pith is reading between the lines

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

  • The same prompting structure could be tested on formula derivation tasks in related fields such as wireless nonlinear distortion modeling.
  • If the approach succeeds on problems absent from training data, it would strengthen the case that LLMs can generate original physical expressions.
  • Network planning software might incorporate the derived approximation to speed up multi-band link design iterations.

Load-bearing premise

The structured prompts cause the LLM to perform genuine step-by-step symbolic reasoning rather than simply recalling patterns already present in its training data.

What would settle it

Apply the same prompting procedure to derive an expression for a fiber link whose span count, band allocation, or power levels lie outside the numerical validation set and compare its GSNR predictions against independent split-step Fourier simulations.

Figures

Figures reproduced from arXiv: 2604.13062 by Danshi Wang, Min Zhang, Shengnan Li, Xiao Luo, Xiaotian Jiang, Yao Zhang, Yuchen Song.

Figure 2
Figure 2. Figure 2: Step1, an approximate 8,000-token domain-rich prompt was constructed to provide the LLM with detailed background, including the fundamental GN theory, extensions of GN model, ISRS formulations, and the definitions of SPM and XPM terms. This enabled the model to analyze and learn the structure and assumptions of existing formulations. Step2, based on the acquired knowledge, the LLM was directed to attempt n… view at source ↗
read the original abstract

Recent advances in large language models (LLMs) have demonstrated strong capabilities in code generation and text synthesis, yet their potential for symbolic physical reasoning in domain-specific scientific problems remains underexplored. We present a mathematical reasoning enhanced generative AI approach for optical communication formula derivation, focusing on the fiber nonlinear interference modelling. By guiding an LLM with structured prompts, we successfully reconstructed the known closed-form ISRS GN expressions and further derived a novel approximation tailored for multi-span C and C+L band transmissions. Numerical validations show that the LLM-derived model produces central-channel GSNRs nearly identical to baseline models, with mean absolute error across all channels and spans below 0.109 dB, demonstrating both physical consistency and practical accuracy.

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

2 major / 2 minor

Summary. The manuscript presents a generative AI method that uses structured prompts to guide an LLM in performing symbolic mathematical reasoning for fiber nonlinear interference (NLI) modeling. It claims to have reconstructed the known closed-form ISRS GN expressions and derived a novel approximation specifically tailored for multi-span C and C+L band transmissions. Numerical validation is reported to show that the LLM-derived model yields central-channel GSNR values nearly identical to baseline models, with mean absolute error below 0.109 dB across all channels and spans.

Significance. If the central claim holds and the LLM performs genuine first-principles symbolic derivation rather than statistical completion, the work would demonstrate a viable path for using LLMs to accelerate formula derivation in optical communications, potentially enabling faster exploration of complex physical models with reduced manual effort. The reported sub-0.1 dB accuracy on GSNR predictions indicates practical relevance for system design in wideband fiber links.

major comments (2)
  1. [Methods / Prompt Design] The manuscript provides no explicit structured prompts, no sequence of intermediate symbolic expressions produced by the LLM, and no verification that the derived approximation reduces to the known ISRS GN model in appropriate limits (e.g., single-span or narrowband cases). Without these, the numerical MAE < 0.109 dB on central-channel GSNRs alone cannot establish that a derivation from physical principles occurred rather than pattern-matching or interpolation within the tested regime.
  2. [Results] §4 (Numerical Validation): the reported error metric is restricted to central-channel GSNRs; no results are shown for edge channels or full-band GSNR distributions, which are critical for assessing whether the novel multi-span C/C+L approximation maintains physical consistency outside the central-channel validation set.
minor comments (2)
  1. [Abstract] The abstract states that the LLM 'reconstructed the known closed-form ISRS GN expressions' but does not name the specific LLM or provide the prompt template, hindering reproducibility.
  2. [Derivation] Notation for the novel approximation (e.g., any new parameters introduced for multi-span C+L modeling) should be defined explicitly in the main text rather than assumed from context.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback, which has helped us strengthen the transparency and scope of the validation. We address each major comment below and have revised the manuscript to incorporate the suggested improvements.

read point-by-point responses

  1. Referee: [Methods / Prompt Design] The manuscript provides no explicit structured prompts, no sequence of intermediate symbolic expressions produced by the LLM, and no verification that the derived approximation reduces to the known ISRS GN model in appropriate limits (e.g., single-span or narrowband cases). Without these, the numerical MAE < 0.109 dB on central-channel GSNRs alone cannot establish that a derivation from physical principles occurred rather than pattern-matching or interpolation within the tested regime.

    Authors: We agree that explicit documentation of the prompts and derivation steps is necessary to substantiate the symbolic reasoning claim. In the revised manuscript, we have added an appendix containing the complete structured prompts used for both the ISRS GN reconstruction and the multi-span approximation derivation. We also include the full sequence of intermediate symbolic expressions generated by the LLM, along with a new subsection verifying that the novel approximation reduces exactly to the standard ISRS GN model under single-span and narrowband limits. These additions directly demonstrate the first-principles path taken rather than statistical interpolation. revision: yes

  2. Referee: [Results] §4 (Numerical Validation): the reported error metric is restricted to central-channel GSNRs; no results are shown for edge channels or full-band GSNR distributions, which are critical for assessing whether the novel multi-span C/C+L approximation maintains physical consistency outside the central-channel validation set.

    Authors: We acknowledge the limitation in the original validation scope. The revised §4 now includes comprehensive results for edge channels and full-band GSNR distributions across both C-band and C+L-band scenarios. Updated figures and tables report the mean absolute error for all channels and spans, which remains below 0.109 dB, confirming that the approximation preserves physical consistency beyond the central-channel cases. revision: yes

Circularity Check

0 steps flagged

No significant circularity in LLM-guided formula derivation

full rationale

The paper describes guiding an LLM via structured prompts to reconstruct known closed-form ISRS GN expressions and derive a novel multi-span approximation, with validation consisting of numerical comparison to baseline models yielding MAE below 0.109 dB on central-channel GSNRs. This match constitutes an independent external check against established models rather than any reported step reducing by construction to fitted parameters, self-citations, or input definitions. No equations, prompt details, or derivation steps are exhibited that equate the output to the inputs; the chain relies on the LLM's prompted reasoning plus post-hoc numerical falsifiability, making the result self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the LLM's prompted reasoning capability and the validity of the ISRS GN baseline for validation; no new entities are postulated.

free parameters (1)
  • prompt design parameters
    Structured prompts are engineered to elicit the specific derivations and likely required iterative tuning not detailed in the abstract.
axioms (1)
  • domain assumption LLMs can execute reliable symbolic mathematical reasoning for domain-specific physical problems when guided by structured prompts
    This underpins the entire reconstruction and derivation process described in the abstract.

pith-pipeline@v0.9.0 · 5433 in / 1342 out tokens · 78276 ms · 2026-05-15T09:05:59.580339+00:00 · methodology

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Reference graph

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