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arxiv: 2605.28700 · v2 · pith:TYL5VBDLnew · submitted 2026-05-27 · 💻 cs.AI · cs.CL

The Importance of Being Statistically Earnest: A Critical Re-evaluation of GSM-Symbolic

Dominika Agnieszka D{\l}ugosz , Arlindo Oliveira , Natalia D\'iaz-Rodr\'iguez This is my paper

Pith reviewed 2026-06-29 12:14 UTC · model grok-4.3

classification 💻 cs.AI cs.CL
keywords GSM-SymbolicLLM evaluationstatistical analysisreasoning benchmarksinteger distributionGLMMperformance dropsbenchmark criticism
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The pith

Re-evaluation finds only half of LLMs show statistically significant drops on GSM-Symbolic after accounting for larger integers in the data.

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

The paper challenges the GSM-Symbolic benchmark's conclusion that large language models lack genuine reasoning because they drop in performance on template variants. Using generalized linear mixed models with per-question random effects on 20 open-weight models, it finds that only half show statistically significant changes under the original prompt format. The authors also report that the main GSM-Symbolic dataset contains a systematically shifted distribution of larger integers relative to the base set, with a Kolmogorov-Smirnov statistic of 0.12 and p less than 0.001. Controlling for this large-number effect removes statistical significance in roughly half the remaining cases. The paper concludes that blanket claims of reasoning failure are statistically premature and that models instead show distinct, model-specific failure patterns.

Core claim

Re-evaluating 20 open-weight models with Generalised Linear Mixed Models that include per-question random effects shows that only half exhibit statistically significant performance changes on the original GSM-Symbolic prompt format. The main dataset contains a shifted distribution of larger integers compared with GSM-Base, contradicting prior claims that the variants were equivalent. Controlling for this integer-size shift accounts for significance in roughly half the remaining cases, and the models that retain significance display distinct failure profiles such as variable-binding fragility, arithmetic limits, and dual-task interference.

What carries the argument

Generalised Linear Mixed Models with per-question random effects, paired with Kolmogorov-Smirnov testing of integer-value distributions between datasets.

If this is right

  • Only half the tested models exhibit statistically significant performance changes under the original prompt format.
  • The large-integer distribution shift accounts for significance in roughly half the remaining cases after GLMM analysis.
  • Models with retained significance display distinct, model-specific failure profiles rather than a uniform reasoning deficit.
  • Original GSM-Symbolic claims of consistent reasoning failure rest on incomplete statistical controls.

Where Pith is reading between the lines

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

  • Benchmark creators should match numerical magnitude distributions when generating symbolic variants to avoid confounding size effects with reasoning demands.
  • GLMM-style per-item random effects may be required to separate question difficulty from model capability in future LLM evaluations.
  • Model-specific failure profiles identified here could guide targeted diagnostic tests rather than relying on aggregate accuracy scores.

Load-bearing premise

That controlling for the observed shift in larger integers fully isolates its causal contribution to performance drops rather than capturing other correlated but unmeasured factors such as problem complexity.

What would settle it

Re-generate the GSM-Symbolic problems with integer sizes matched exactly to the GSM-Base distribution and re-run the same 20 models to test whether the performance deltas lose statistical significance.

Figures

Figures reproduced from arXiv: 2605.28700 by Arlindo Oliveira, Dominika Agnieszka D{\l}ugosz, Natalia D\'iaz-Rodr\'iguez.

Figure 1
Figure 1. Figure 1: Reproduction of the GSM-Symbolic benchmark. Top: odds ratios and confidence intervals obtained using [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Accuracies and and accuracy changes (variant performance delta ( [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Values and significance of variant performance deltas for the [PITH_FULL_IMAGE:figures/full_fig_p024_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Values and significance of variant performance deltas for the structured natural language prompt. Top: [PITH_FULL_IMAGE:figures/full_fig_p025_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Values and significance of variant performance deltas for the [PITH_FULL_IMAGE:figures/full_fig_p027_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Values and significance of variant performance deltas for the [PITH_FULL_IMAGE:figures/full_fig_p028_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Distribution of integers extracted from problem texts in [PITH_FULL_IMAGE:figures/full_fig_p031_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Variant effect and large number effect - a combined case study of six LLMs. Top: log-odds ratio for [PITH_FULL_IMAGE:figures/full_fig_p034_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Total counts of error types in the three NL prompts: the original [PITH_FULL_IMAGE:figures/full_fig_p036_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Total per-model error counts on the GSM-Variants dataset for the two code prompts: [PITH_FULL_IMAGE:figures/full_fig_p037_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Proportions of per-model errors other than [PITH_FULL_IMAGE:figures/full_fig_p038_11.png] view at source ↗
read the original abstract

The GSM-Symbolic benchmark (Mirzadeh et al., 2025) reported consistent performance drops across 25 Large Language Models (LLMs) when tested on template-generated variants of GSM8K problems, concluding that the models lack genuine reasoning capabilities. We argue that this conclusion rests on shaky statistical ground. Re-evaluating 20 open-weight models using Generalised Linear Mixed Models with per-question random effects, we find that only half exhibit statistically significant performance changes under the original prompt format. Moreover, we identify a previously unacknowledged factor: the main GSM-Symbolic dataset contains a systematically shifted distribution of larger integers in problem texts relative to GSM-Base (K-S statistic = 0.12, p < 0.001), contradicting the original authors' claims. Controlling for this large number effect accounts for significance in roughly half the remaining cases. Among models with statistically significant performance deltas, we identify distinct, model-specific failure profiles - including fragility of variable binding, arithmetic limitations, and dual-task interference - underscoring that blanket claims about LLM reasoning are both statistically premature and mechanistically misleading.

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 re-evaluates the GSM-Symbolic benchmark (Mirzadeh et al., 2025) by applying Generalised Linear Mixed Models (GLMM) with per-question random effects to performance data from 20 open-weight LLMs. It reports that only half of these models exhibit statistically significant performance changes under the original prompt format. The paper further identifies a previously unacknowledged distributional shift toward larger integers in the main GSM-Symbolic dataset relative to GSM-Base (Kolmogorov-Smirnov statistic = 0.12, p < 0.001) and claims that controlling for this shift via the GLMM accounts for statistical significance in roughly half of the remaining cases. It concludes that blanket claims about LLM reasoning deficits are statistically premature and identifies distinct, model-specific failure profiles such as variable-binding fragility and arithmetic limitations.

Significance. If the GLMM specifications and controls prove robust upon detailed reporting, the work would usefully demonstrate the value of mixed-effects modeling and distributional diagnostics in LLM benchmark analysis. It would strengthen the case for moving beyond aggregate accuracy deltas to account for problem-feature shifts and model heterogeneity, thereby supporting more precise, falsifiable claims about reasoning capabilities.

major comments (1)
  1. [Abstract] Abstract: the central claim that 'controlling for this large number effect accounts for significance in roughly half the remaining cases' is load-bearing for the paper's re-evaluation but rests on an unspecified GLMM. No equation, covariate definition (e.g., max operand, mean log-value, or binned threshold), interaction structure, or sensitivity analysis is provided; the text mentions only per-question random effects. This directly prevents verification of whether the control isolates the integer-size factor or proxies for correlated unmeasured variables such as template complexity, undermining the contradiction with the original authors' claims.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful review and constructive comment. We agree that the GLMM requires fuller specification to support verification of our claims and will revise the manuscript to address this.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that 'controlling for this large number effect accounts for significance in roughly half the remaining cases' is load-bearing for the paper's re-evaluation but rests on an unspecified GLMM. No equation, covariate definition (e.g., max operand, mean log-value, or binned threshold), interaction structure, or sensitivity analysis is provided; the text mentions only per-question random effects. This directly prevents verification of whether the control isolates the integer-size factor or proxies for correlated unmeasured variables such as template complexity, undermining the contradiction with the original authors' claims.

    Authors: We accept the referee's point that the current manuscript provides insufficient detail on the GLMM. The abstract and main text mention only per-question random effects and do not include the model equation, explicit covariate definitions for the large-number effect, interaction terms, or sensitivity checks. In the revised manuscript we will add the full specification (e.g., performance ~ prompt_format + log(max_operand) + (1|question), with max_operand defined as the largest integer appearing in the problem statement), report the precise covariate construction, test alternative operationalizations (mean log-value, binned thresholds), and include a sensitivity analysis. These additions will allow readers to assess whether the covariate isolates the documented distributional shift rather than serving as a proxy for template complexity or other factors. We view this as a necessary clarification that strengthens rather than alters the paper's conclusions. revision: yes

Circularity Check

0 steps flagged

No significant circularity; analysis applies external statistical methods to public benchmark data.

full rationale

The paper re-evaluates 20 models on GSM-Symbolic using GLMM with per-question random effects and K-S tests for integer distribution shifts. These are standard, pre-existing statistical tools applied to publicly described datasets. No self-citations are load-bearing, no parameters are fitted to target deltas and then renamed as predictions, and no derivation reduces by construction to its inputs. The claim that the shift accounts for significance in half the cases is an empirical statistical outcome, not a definitional equivalence. The paper is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on the validity of standard statistical assumptions for GLMMs and the K-S test; no new free parameters, invented entities, or ad-hoc axioms are introduced in the abstract.

axioms (2)
  • domain assumption Generalized linear mixed models with per-question random effects are an appropriate model for binary LLM correctness data across template variants.
    Invoked to test statistical significance of performance changes.
  • standard math The Kolmogorov-Smirnov test correctly identifies a meaningful distributional difference in integer magnitudes between datasets.
    Used to support the claim of a systematic shift (K-S statistic = 0.12, p < 0.001).

pith-pipeline@v0.9.1-grok · 5742 in / 1539 out tokens · 36450 ms · 2026-06-29T12:14:14.951424+00:00 · methodology

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Reference graph

Works this paper leans on

5 extracted references · 4 canonical work pages · 2 internal anchors

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