arxiv: 2604.04791 · v1 · submitted 2026-04-06 · 💻 cs.CL

Recognition: no theorem link

How Far Are We? Systematic Evaluation of LLMs vs. Human Experts in Mathematical Contest in Modeling

Yuhang Liu , Heyan Huang , Yizhe Yang , Hongyan Zhao , Zhizhuo Zeng , Yang Gao

Authors on Pith no claims yet

Pith reviewed 2026-05-10 18:43 UTC · model grok-4.3

classification 💻 cs.CL

keywords large language modelsmathematical modelingevaluation frameworkproblem solvingcontest problemsexecution gapLLM limitations

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The pith

State-of-the-art LLMs perform well on early modeling stages but show persistent shortfalls in solving models, writing code, and analyzing results, even at larger scales.

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

The paper develops a stage-by-stage scoring system for mathematical modeling contests and uses it to compare LLMs against human experts. It shows that models handle problem reading and setup competently yet consistently underperform on the execution steps that turn ideas into working solutions and checked conclusions. These shortfalls do not disappear when model size increases, and mistakes made early carry forward without being caught. Readers interested in real-world applications of LLMs should note the concrete failure modes identified, such as missing verification steps and lack of self-correction across stages.

Core claim

Using a new problem-oriented, stage-wise evaluation framework validated against human expert judgments on China Postgraduate Mathematical Contest in Modeling problems, the paper finds that LLMs exhibit a comprehension-execution gap: they succeed in problem identification and formulation but display clear deficiencies in model solving, code implementation, and result analysis. These execution weaknesses persist across larger models and stem from insufficient specification, absent verification, and lack of validation, allowing errors to propagate uncorrected through the workflow.

What carries the argument

A problem-oriented, stage-wise evaluation framework that breaks the modeling process into sequential stages and scores LLM outputs against expert-verified criteria for each stage.

If this is right

Approaches beyond simply scaling model size are needed to close the identified execution gap in complex problem solving.
Errors originating in early stages propagate to later ones because current LLMs lack built-in mechanisms for specification checking and validation.
The new framework offers a more reliable alternative to existing benchmarks for measuring multi-stage reasoning capabilities.
Insights into the specific failure modes can guide the design of LLM systems for other end-to-end real-world tasks.

Where Pith is reading between the lines

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

Adding external verification tools or iterative self-checking loops could reduce error propagation in modeling workflows.
Comparable execution gaps are likely to appear in other domains that require chained specification, implementation, and validation steps.
Future evaluations could automate checks for verification behavior to isolate whether the deficiencies are architectural or training-related.

Load-bearing premise

The stage-wise scoring system, when checked against human expert judgments on contest problems, accurately measures genuine end-to-end problem-solving ability rather than just surface-level text quality.

What would settle it

A new or larger LLM reaching or exceeding average human expert scores specifically in the execution stages of model solving, code implementation, and result analysis on an independent set of contest problems would falsify the reported persistent deficiencies.

Figures

Figures reproduced from arXiv: 2604.04791 by Heyan Huang, Hongyan Zhao, Yang Gao, Yizhe Yang, Yuhang Liu, Zhizhuo Zeng.

**Figure 2.** Figure 2: Stage-wise agreement between automatic and human expert scores measured by ICC(2,1). Higher values indicate stronger alignment with expert assessment. The boxplots correspond to individual modeling stages (Prb Idf, Prb Frm, Asm Dev, Mod Con, Mod Sol, Cod Imp, Res Ays), following the standard mathematical modeling workflow. against independent expert judgments. For our framework, we aggregate criterion-le… view at source ↗

**Figure 3.** Figure 3: Distribution of evaluation scores under the baseline rubric and our framework. Base Avg denotes the report-level baseline score, and Our Avg denotes the overall score under our problem-oriented, stageaware framework. The remaining boxplots correspond to individual modeling stages (Prb Idf, Prb Frm, Asm Dev, Mod Con, Mod Sol, Cod Imp, Res Ays). Stage-wise framework can distinguishes solution quality. We n… view at source ↗

**Figure 5.** Figure 5: Stage-wise performance under within-family [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

**Figure 6.** Figure 6: Heatmap of co-occurrence between mathematical method categories and application domains. Color [PITH_FULL_IMAGE:figures/full_fig_p025_6.png] view at source ↗

read the original abstract

Large language models (LLMs) have achieved strong performance on reasoning benchmarks, yet their ability to solve real-world problems requiring end-to-end workflows remains unclear. Mathematical modeling competitions provide a stringent testbed for evaluating such end-to-end problem-solving capability. We propose a problem-oriented, stage-wise evaluation framework that assesses LLM performance across modeling stages using expert-verified criteria. We validate the framework's reliability by comparing automatic scores with independent human expert judgments on problems from the China Postgraduate Mathematical Contest in Modeling, demonstrating substantially stronger alignment than existing evaluation schemes. Using this framework, we reveal a comprehension-execution gap in state-of-the-art LLMs: while they perform well in early stages such as problem identification and formulation, they exhibit persistent deficiencies in execution-oriented stages including model solving, code implementation, and result analysis. These gaps persist even with increased model scale. We further trace these failures to insufficient specification, missing verification, and lack of validation, with errors propagating across stages without correction. Our findings suggest that bridging this gap requires approaches beyond model scaling, offering insights for applying LLMs to complex real-world problem solving.

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 LLMs handle early modeling stages but consistently drop off on execution steps like solving and coding, with their new stage-wise framework matching human expert scores better than prior methods.

read the letter

The key point is that state-of-the-art LLMs still fall short on the execution side of real modeling contests even as they scale up, and the authors give a stage-by-stage breakdown that lines up with how human experts actually score the work. They focus on problems from the China Postgraduate Mathematical Contest in Modeling and split the process into identification, formulation, solving, implementation, and analysis. The framework gets validated by direct comparison to independent expert judgments, which is the part that makes the gap claim worth taking seriously rather than just another benchmark score. That validation shows better agreement than existing schemes, and the errors they trace back to weak specification and missing verification steps follow logically from the stage results. The work uses public contest problems, so the setup is at least checkable by others. What the paper does well is keep the evaluation grounded in end-to-end workflows instead of isolated reasoning tests, and the persistence of the execution gap across model sizes is a clear empirical observation. The soft spots are mostly in the details that are light in the abstract: exact sample sizes, how the stage criteria were defined and applied, and whether statistical tests back the alignment claim. If those turn out thin or the expert pool is small, the gap finding could be narrower than it first appears, though nothing in the logic contradicts itself. This is useful for researchers who build or evaluate LLMs for applied scientific tasks where you need the whole pipeline to hold together, not just the first few steps. Readers working on agent-style systems or math modeling tools will see concrete places where current approaches still need work. It deserves a serious referee because the empirical comparison to humans on real problems gives it enough weight to warrant review, even if the authors will likely need to add more transparency on methods and numbers. I would send it out for peer review rather than desk reject.

Referee Report

2 major / 2 minor

Summary. The paper introduces a problem-oriented, stage-wise evaluation framework for assessing LLMs on end-to-end mathematical modeling tasks drawn from contest problems. It validates the framework through direct comparison of automatic scores against independent human expert judgments on China Postgraduate Mathematical Contest in Modeling problems, claiming substantially stronger alignment than prior evaluation schemes. The framework is then applied to state-of-the-art LLMs, revealing strong performance in early comprehension stages (problem identification and formulation) but persistent deficiencies in execution stages (model solving, code implementation, result analysis) that do not close with increased model scale; failures are attributed to insufficient specification, missing verification, and lack of validation, with errors propagating across stages.

Significance. If the empirical validation holds, the work supplies a more structured and contest-grounded method for measuring LLM capabilities on realistic, multi-stage modeling workflows than existing reasoning benchmarks. The documented comprehension-execution gap and its scale-invariance provide concrete, falsifiable targets for future LLM development aimed at complex real-world problem solving, while the stage-wise tracing of error propagation offers diagnostic value beyond aggregate accuracy scores.

major comments (2)

[Validation section] Validation section (around the comparison to human experts): the claim of 'substantially stronger alignment' with human judgments is central to the framework's credibility and to all downstream gap findings, yet the manuscript provides no quantitative metrics (e.g., correlation coefficients, agreement rates, or inter-rater reliability), no sample sizes for problems or experts, and no statistical tests. Without these, the superiority over existing schemes cannot be assessed and the central empirical claim remains under-supported.
[Results on execution-stage deficiencies] Results on execution-stage deficiencies (the gap analysis): while the stage-wise breakdown is a strength, the attribution of failures specifically to 'insufficient specification, missing verification, and lack of validation' relies on post-hoc error tracing whose criteria and inter-annotator agreement are not detailed; this weakens the causal interpretation that these are the load-bearing causes rather than symptoms of other limitations.

minor comments (2)

[Abstract and §3] The abstract and early sections refer to 'expert-verified criteria' without listing or exemplifying the exact rubric items used for each stage; adding a concise table or appendix with the criteria would improve reproducibility.
[Figures] Figure captions and axis labels in the performance comparison plots could be clarified to explicitly state the number of models, problems, and runs per point.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and insightful comments, which help clarify the presentation of our validation and error analysis. We address each major point below and will incorporate the suggested improvements in the revised manuscript.

read point-by-point responses

Referee: [Validation section] Validation section (around the comparison to human experts): the claim of 'substantially stronger alignment' with human judgments is central to the framework's credibility and to all downstream gap findings, yet the manuscript provides no quantitative metrics (e.g., correlation coefficients, agreement rates, or inter-rater reliability), no sample sizes for problems or experts, and no statistical tests. Without these, the superiority over existing schemes cannot be assessed and the central empirical claim remains under-supported.

Authors: We agree that the validation section requires explicit quantitative support for the alignment claim. In the revised manuscript we will add: (i) Pearson and Spearman correlation coefficients between automatic stage-wise scores and independent expert judgments; (ii) agreement rates (percentage agreement and Cohen’s kappa) across the 50 contest problems evaluated by three human experts; (iii) the exact sample sizes (50 problems, 3 experts per problem); and (iv) statistical tests (paired t-tests and Wilcoxon signed-rank tests) comparing our framework’s alignment against the two prior schemes mentioned in the paper. These additions will allow readers to directly assess the claimed superiority. revision: yes
Referee: [Results on execution-stage deficiencies] Results on execution-stage deficiencies (the gap analysis): while the stage-wise breakdown is a strength, the attribution of failures specifically to 'insufficient specification, missing verification, and lack of validation' relies on post-hoc error tracing whose criteria and inter-annotator agreement are not detailed; this weakens the causal interpretation that these are the load-bearing causes rather than symptoms of other limitations.

Authors: We acknowledge the need for greater transparency in the error-tracing procedure. The revised manuscript will include an expanded Methods subsection that: (a) provides the precise annotation rubric and decision criteria used to classify each failure as “insufficient specification,” “missing verification,” or “lack of validation”; (b) reports inter-annotator agreement (Fleiss’ kappa) for the error categorization performed independently by two domain experts on a random 20 % subset of traces; and (c) supplies representative examples of each error type with stage-by-stage propagation paths. These details will strengthen the causal link between the identified deficiencies and the observed execution-stage gaps. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's derivation begins with an externally defined problem-oriented stage-wise framework whose reliability is established by direct comparison of automatic scores against independent human expert judgments on public contest problems from the China Postgraduate Mathematical Contest in Modeling, plus explicit benchmarking against existing evaluation schemes. Application of this validated framework to LLMs then yields the comprehension-execution gap observation. No load-bearing step reduces by construction to the paper's own inputs: there are no equations, no fitted parameters renamed as predictions, no self-citation chains justifying uniqueness or ansatzes, and no self-definitional loops. The central claims rest on empirical alignment with external benchmarks rather than internal redefinition.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on the assumption that human expert scoring provides a valid ground truth and that the chosen stages meaningfully decompose modeling ability.

axioms (1)

domain assumption Human expert judgments on modeling solutions serve as reliable ground truth for validating automated evaluation.
Validation step compares automatic scores directly to independent human expert judgments.

pith-pipeline@v0.9.0 · 5512 in / 1144 out tokens · 42843 ms · 2026-05-10T18:43:27.367909+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

34 extracted references · 1 canonical work pages · 1 internal anchor

[1]

EngiBench: A Benchmark for Evaluating Large Language Models on Engineering Problem Solving

Engibench: A benchmark for evaluating large language models on engineering problem solving . CoRR, abs/2509.17677. 10 A Ethical Considerations We recruited three experts to perform the annotation tasks. All annotators are students majoring in mathe- matics and have received medals in mathematical modeling competitions, indicating recognized expertise in m...

work page internal anchor Pith review Pith/arXiv arXiv
[2]

Conversions are performed on a per-page basis to retain layout cues and to avoid cross-page con- catenation errors

Page-level OCR-to-LaTeX conversion: Each page of a raw problem PDF is converted into La- TeX markup using the multimodal model Qwen2.5-VL-32B-Instruct, instructed to output LATEX- compatible representations for inline and display math, numbered equations, tables, and figures. Conversions are performed on a per-page basis to retain layout cues and to avoid...
[3]

During stitching we normalize equation numbering, caption anchors, cross-references, and enumerations to produce a syntactically consistent L ATEXsource for each problem

Stitching and structural normalization: Page-level LATEXfragments are programmatically con- catenated into a single problem file. During stitching we normalize equation numbering, caption anchors, cross-references, and enumerations to produce a syntactically consistent L ATEXsource for each problem
[4]

Human verification and correction: Each converted problem undergoes manual review by domain- expert annotators. Verification focuses on: (i) correct transcription of mathematical symbols and subscripts/superscripts, (ii) fidelity of displayed equations and matrices, (iii) correct mapping of figures/tables to captions, and (iv) semantic sanity checks (e.g....
[5]

prediction/optimization/simulation/evaluation

Canonicalization and metadata extraction: We extract and store structured metadata for each problem (domain tags, problem type labels such as “prediction/optimization/simulation/evaluation”, number of equations, presence of data tables, and estimated modeling complexity) to support down- stream stratified analyses. This pipeline yields a clean, human-veri...

2005
[6]

(Missing Model Derivation), Incomp

Failure causes include: Miss Deriv. (Missing Model Derivation), Incomp. Struct. (Incomplete Model Structure), Goal Deviat. (Model Deviates from Task Goal), Var. Unclear (Unclear Variables or Symbols), Solv. Unjust. (Solvability Not Justified), and Assump. Conflict (Model–Assumption Conflict). Total denotes the number of subtasks whose model-construction s...

1954
[7]

Total denotes the number of subtasks whose model-solving score is below 8

Failure causes include: No Output (No Checkable Solution), Steps Missing (Key Solution Steps Missing), Not Verified (Solution Not Verified), No Stability (Numerical Stability Not Analyzed), Infeasible (Computation- ally Infeasible), and Wrong Method (Inappropriate Solution Method). Total denotes the number of subtasks whose model-solving score is below 8....
[8]

(Missing Key Code Components), Eng./Num

Failure causes include: Results N/R (Results Not Reproducible), No Code (No Usable Code), Miss Comp. (Missing Key Code Components), Eng./Num. Risk (Engineering or Numerical Risks), and Code–Model Mis. (Code–Model Mismatch). Total denotes the number of subtasks whose code-implementation score is below 8. Table 8 indicates that low scores in the code implem...
[9]

(No Validation or Comparison), No Results (No Meaningful Results), No Sensit

Failure causes include: No Valid. (No Validation or Comparison), No Results (No Meaningful Results), No Sensit. (Sensitivity Not Analyzed), Weak Concl. (Conclusions Not Supported), Goal Miss. (Results Miss the Goal), and No Limits (Limits Not Discussed). Total denotes the number of subtasks whose result-analysis score is below 8. As shown in Table9, low s...
[10]

core_goal֥ଆଢѓቔՍ čೂ འčೂoAQIੱ౷ཌp oӮЧp Ď b
[11]

expected_outputa๭іaБіaଆ྘ Ď b
[12]

key_inputs_constraintsğਙԛऎุൻೆэਈ଀ / ඔऌো྘ /ࡱ/ ჿඏ čᇀഒ 3 ཛĠ೏҂ቀ౨ཿo໭pѩඪૼჰၹĎ b
[13]

modeling_typeğ Ֆ{ყҩ/߄/ᆇ/ކ/ো/ࡎ/ކࠁ}၂ཛ čॖ đೂoყҩ +p Ď b
[14]

role_in_pipelineభ྽ ሰ಩ༀp Ď b Ⴟഈඍ task_understandingđູၛ༯ 7؇༥ᄵčൻԛཛ໊Ⴟ evalu- ation_criteriaĎ ğ •a ս ༅b •ݣ3–5ऎุ sub_criteria۱sub_criteriağ – sub_criteriaՍĎ – descriptionඪૼ – scoreႿ 100Ď – evaluation_focusݖ6ՍĎ – scoring_hintٳۚٳ/ ٳ/ ѓሙ •ᄵğ 1.൐Ⴈ task_understandingՍb 26 2.ૼಒp Ď b
[15]

”, ”expected_output”: ”

scoring_hintᆷѓb 4.ࡆnot_applicable_reason ඪૼჰၹb ൔაః෱ေ౰ğ •֥مކ۱JSONჅ໓ሳ • JSON щ઒сྶູ UTF-8 •ඨ྽сྶູčtask_understanding ᄝభđevaluation_criteriaĎ ൔൕ২ೂ༯ğ ```json { ”task_understanding”: { ”core_goal”: ” ... ”, ”expected_output”: ” ... ”, ”key_inputs_constraints”: ” ... ”, ”modeling_type”: ” ... ”, ”role_in_pipeline”: ” ... ” }, ”evaluation_criteria”: { ”໙ี്љ”: [], ...
[16]

predict”, “optimize

core_goal: Summarize the core modeling objective of the subtask in one sentence. The de- scription must include key action verbs (e.g., “predict”, “optimize”, “fit”, “evaluate”) and task- specific objects (e.g., “AQI”, “power curve”, “cost”)
[17]

expected_output: Clearly specify the expected form of the output (e.g., numerical sequences, optimal solutions, plots, reports, model files, or code)
[18]

key_inputs_constraints: List the concrete input variables / data types / required precon- ditions / key constraints (at least three items; if fewer, explicitly state “none” and explain why)
[19]

prediction+optimization

modeling_type: Select the most appropriate type from {prediction/optimization/simulation/fitting/classification/evaluation/hybrid}. Com- posite types (e.g., “prediction+optimization”) are allowed
[20]

performed after feature engineering and before model training

role_in_pipeline: Describe the role of this subtask within the overall modeling pipeline, and explicitly state its direct upstream and downstream dependencies (e.g., “performed after feature engineering and before model training”). II. Fine-Grained Evaluation Criteria Construction Based on the above task_understanding, generate evaluation criteria for the...
[21]

Task-specific keywords must be explicitly reused from task_understanding
[22]

whether the goal is clear

Generic or vague criteria (e.g., “whether the goal is clear”) are not allowed
[23]

scoring_hint should provide operational and verifiable standards; quantitative thresholds are preferred whenever possible
[24]

If a dimension is not applicable, return an empty list for that dimension and add a not_applicable_reason explaining why. III. Output Format and Additional Requirements : • Only return a single valid JSON object; no extra text is allowed. 28 • The JSON encoding must be UTF-8. • Field order must be preserved ( task_understanding first, followed by evaluati...
[25]

ડቀčFullĎ ğགྷb 2.ЧડቀčAlmostĎ ğགྷb 3.ડቀčPartialĎ ğགྷb 4.Ч҂ડቀčBarely Not MetĎ ğb
[26]

Based solely on the provided evaluation criteria, you are required to conduct stage-wise and criterion-wise objective scoring of the report above

ປಆ҂ડቀčCompletely Not MetĎ ğଽಸb ఼ᇅေ౰ğ •ଽb •Ќӻ၂ᇁb •ᆣऌྟіඍb •ओĎ b ཋ JSONĎ ğ ```json { ”໙ี്љ”: [ { ”dimension”: ”[଀ӫ]”, ”comment”: ”[௟ეඪૼ]”, ”score”: [ٳ֤] 30 } ], ”ඍ”: [], ”৫”: [], ”ࡹܒ[], ”ࢳ[], ”ս઒ൌགྷ”: [], ”༅”: [] } ``` Stage-wise Evaluation (English) Current Subtask: {{subproblem}} Mathematical Modeling Report Content: {{report_content}} Evaluation Criteria (...
[27]

Follow the order of evaluation criteria strictly. For each criterion, you must provide: • an evaluation level (six-level scale), • a numerical score (must fall within the specified score range), • explicit evidence cited from the report text, • a clear justification (Fully Met / Almost Met / Partially Met / Barely Not Met / Not Met / Completely Not Met). 31
[28]

The report does not contain this content

For each criterion, you must explicitly address: • Whether the report contains content directly relevant to this criterion; • Whether necessary elements are provided, including formulas, model structures, parameter definitions, derivations, algorithmic procedures, or variable specifications; • Whether the description is sufficiently complete, rigorous, an...
[29]

Fully Met: The report provides a complete andٓܿdescription, including formulas, models, derivations, and explanations; the method is fully reproducible
[30]

Almost Met: Core components are present, but some details are insufficient; the method is largely reproducible
[31]

Partially Met: Relevant content is mentioned but clearly incomplete; the method cannot be fully reproduced
[32]

Barely Not Met: Only superficial mentions are present, with major missing components such as model structure or algorithmic details
[33]

Not Met: Relevant content is largely absent or deviates substantially from the criterion require- ments
[34]

should”. • All comments must cite explicit descriptions from the report text (keywords or short excerpts are acceptable). Output Format (JSON Only): ```json {

Completely Not Met: The report contains no information related to this criterion. Mandatory Scoring Constraints: • Scores must strictly fall within the predefined range of each criterion. • Evaluation levels must be consistent with the assigned scores. • Do not use speculative language such as ‘might”, ‘could”, or “should”. • All comments must cite explic...