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REVIEW 3 major objections 6 minor 2 cited by

The paper introduces RIMO, a benchmark of IMO problems rewritten to admit one unique integer answer, and reports that the top of ten frontier LLMs scores 62.96% while smaller models fall below 25%, a large drop from their scores on GSM8K an

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2026-08-04 21:47 UTC pith:DYGKZEVH

load-bearing objection A useful integer-answer IMO benchmark whose 'profound reasoning gap' claim outruns the evidence, because difficulty preservation is asserted rather than shown. the 3 major comments →

arxiv 2509.07711 v1 pith:DYGKZEVH submitted 2025-09-09 cs.AI

RIMO: An Easy-to-Evaluate, Hard-to-Solve Olympiad Benchmark for Advanced Mathematical Reasoning

Ziye Chen , Chengwei Qin , Yao Shu This is my paper
classification cs.AI
keywords mathematical reasoning benchmarkInternational Mathematical OlympiadLLM evaluationexact-match gradingproof decompositionanswer sparsityRIMO-NRIMO-P
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

RIMO is a two-track benchmark built from International Mathematical Olympiad problems published between 1959 and 2023. The paper's central claim is that once IMO problems are rewritten so each admits a single unique integer answer—enabling exact string-match grading—frontier LLMs show a large performance drop relative to their near-saturated scores on GSM8K and MATH. The best model evaluated, DeepSeek-R1-671B, reaches 62.96% on the numeric track, while several 7–8B models score below 25%. The proof track, RIMO-P, decomposes 456 problems into guided subproblems and reports even lower performance, which the paper interprets as evidence that answer-finding and rigorous proof-writing are distinct capabilities. If the difficulty-preserving rewrite is sound, RIMO supplies a reproducible, high-resolution yardstick for tracking progress toward Olympiad-level reasoning.

Core claim

The discovery is stated as an empirical gap: on RIMO-N, all ten evaluated models drop sharply compared with GSM8K and MATH, with scores ranging from 15.82% to 62.96%. The gap is not uniform: when the answer is restricted to 0 or 1, every model's score rises by 8 to 30 percentage points, indicating that part of the difficulty is locating an exact integer on a wide numerical spectrum. Reasoning-optimized models consistently outperform size-matched vanilla models, by up to 19.4 points, so the paper argues that explicit reasoning training, rather than scale or recency, is what moves the needle at this level. On RIMO-P, models solve only a small proportion of consecutive proof subproblems, leavin

What carries the argument

The load-bearing mechanisms are (1) the integer-remake: IMO statements are rewritten—tightening hypotheses, renaming variables, reframing objectives—so the answer is a unique integer, making grading a constant-time string comparison with no LLM judge; and (2) the proof decomposition: each RIMO-P problem is split into one to four guided subproblems derived from an expert-verified solution, and a model is credited only for consecutive correct steps according to a strict judge prompt. The integer-remake is what gives RIMO-N its zero-noise claim, and the binary-answer subset is used as a probe to show how answer-space size contributes to measured hardness.

Load-bearing premise

The load-bearing premise is that rewriting an IMO problem to produce a unique integer answer does not reduce its logical difficulty; if the rewrites systematically simplify the problems, RIMO-N's sharp drop measures reformatting rather than Olympiad reasoning.

What would settle it

For a random sample of RIMO-N items, have expert solvers attempt both the original IMO statement and the rewritten integer version and compare solve rates and rated difficulty; if the rewritten forms are solved substantially more often, the difficulty-preservation claim fails. A model-level version: run the same ten models on both forms and check whether original-form accuracy is materially lower than rewritten-form accuracy.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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If this is right

  • A model that clears the current best RIMO-N score of 62.96% under the same greedy-decoding protocol would demonstrate a substantive advance over frontier models on IMO-level numeric reasoning, not just on saturated benchmarks.
  • RIMO-P extends the same material into a process-oriented measurement: because scores are low and answer-finding does not guarantee proof success, it can separate models that retrieve answers from models that can sustain deductive chains.
  • The finding that binary-answer items inflate accuracy by 8 to 30 points implies that answer-space restriction is itself a difficulty dial for future benchmark design.
  • The 0.21 Spearman correlation between release date and accuracy suggests that incremental model releases should not be expected to improve Olympiad reasoning; progress has to be checked specifically on this kind of benchmark.
  • The RIMO-P results point to step verification, external tools, and explicit proof planning as likely levers for closing the proof gap, since sheer scale or recency did not produce it.

Where Pith is reading between the lines

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

  • The authors implicitly assume that their rewrite preserves difficulty; a straightforward control—running the same models on original statements under an exact or normalized grader—would quantify any reformatting effect and is not reported.
  • The binary-answer boost suggests the measured gap is partly a search-space effect: models may know the truth of a claim yet fail to name the integer. That distinction could be tested by giving models narrowed ranges or scaffolding.
  • RIMO-P's step grading is performed by deepseek-r1, so despite RIMO-N's exact-match design, the proof track still carries LLM-judge noise; cross-checking a sample with independent judges or formal proof checking would establish how much.
  • If the difficulty-preservation assumption holds, the integer-remake technique could turn other hard problem sets, such as shortlist problems, into exact-match evaluation tasks.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper introduces RIMO, a two-track benchmark built from IMO problems (1959–2023). RIMO-N contains 335 problems rewritten to have a single unique integer answer, graded by exact string match; RIMO-P contains 456 proof problems decomposed into guided sub-problems, graded by a sequential protocol in which a deepseek-r1 LLM judge decides correctness of each sub-solution. The authors evaluate ten LLMs on RIMO-N and three on RIMO-P, reporting large accuracy drops relative to GSM8K and MATH, and derive claims about scale, recency, reasoning optimization, and a persistent 'proof gap.' The central contribution is a deterministic, reproducible integer-answer track that appears to be substantially harder than existing benchmarks.

Significance. If the difficulty-preservation claim for RIMO-N is substantiated, this benchmark would be a valuable, low-noise yardstick for Olympiad-level mathematical reasoning. The exact-match integer scoring is robust, the multi-source verification of ground-truth answers is a strength, and the analysis of the binary-answer subset is an insightful diagnostic. However, the strong conclusion of a 'profound reasoning gap' rests on an unvalidated assumption that rewriting preserves problem difficulty, and the RIMO-P track reintroduces an LLM judge, contradicting the paper's stated goal of eliminating evaluation noise. With additional validation, the benchmark could become a useful community resource; in its current form, the claims outrun the evidence.

major comments (3)
  1. [§3.1, Figure 3] The central claim that rewriting IMO problems into single-integer form preserves 'the logical core and difficulty' is asserted without evidence. The examples are not merely cosmetic: a concurrency proof becomes a counting question, and a classification of triples becomes a single numerical computation. These transformations can change the nature of the task (from proof construction to finite search/computation) and impose all-or-nothing exact-match grading. The paper's own §4.1.1 (Figure 9) shows that restricting to binary answers improves accuracy by 8–30 points across models, demonstrating that output-space size materially affects measured performance. Without a difficulty-equivalence check—e.g., human solvers on original vs. rewritten problems, or an independent expert rating of the rewritten items—the observed drop from MATH/GSM8K cannot be cleanly attributed to 'Olympiad-level reaso
  2. [§4.1.2, Eq. (1), Figure 11] RIMO-P grading is performed by deepseek-r1, which is itself one of the ten benchmarked models and the strongest on RIMO-N. This reintroduces exactly the type of model-based evaluation noise the paper promises to eliminate. No validation of the judge is provided (e.g., agreement with human expert graders on a sample), and the sequential rubric is prompt-based, so the reported 'step-by-step reasoning' scores are not noise-free. The claim that current models have a 'profound deficit in deductive ability' is therefore only as strong as the unvalidated judge. The authors should either validate the judge, use a judge that is not among the evaluated models, or present RIMO-P as a preliminary model-judged track rather than as part of a noise-free benchmark.
  3. [§4.1.2, §5] Only three models (Qwen3-8B, InternLM3-8B-instruct, Mathstral-7B) are evaluated on RIMO-P. The conclusions about domain-specific fine-tuning, recency versus training type, and the 'proof gap' relative to 'advanced human students' are drawn from this very small sample, and no human data are actually reported. The statement in §5 that 'advanced human students, all of whom used the same rubric' exhibit better performance is unsupported because no human-baseline results are given. The authors should either include human baseline scores or soften the corresponding claims to reflect the lack of direct comparison.
minor comments (6)
  1. [Abstract] The abstract says the benchmark 'eliminates evaluation noise' but RIMO-P uses an LLM judge; the wording should be qualified to refer only to RIMO-N, or the RIMO-P grading should be described as 'reduced-noise' rather than noise-free.
  2. [Table 2] For RIMO-P, the '# Unif.' column is marked with a dash; it would be helpful to clarify that the sub-problem outputs are not uniform in format, and that the 'Noise' value 'LLM' indicates the intended contrast with RIMO-N.
  3. [A.1] The prompt header says 'eavluate' (typo). Also, the Omni-MATH judge prompt is excessively long for an appendix example; consider trimming.
  4. [§4.1.1] The phrase 'Scores jump by 8 to 30 percentage points across in every baseline' has a grammatical issue ('across in'). Also, the Spearman correlation of 0.21 is reported without a p-value or confidence interval; given only ten data points, its interpretation is limited.
  5. [§3.1] The sentence 'Each shortlist problem retains the jury’s official integer' is unclear: if a shortlist problem is rewritten, it is not the original official integer but a new derived integer. Clarify the relationship between the rewriting and the official answer.
  6. [§3.2] The phrase 'expert-verified proofs' is not operationalized; specify the expertise of the verifiers and whether inter-rater agreement was measured.

Circularity Check

1 steps flagged

RIMO-N is independent and non-circular; RIMO-P's proof-gap conclusion is partially self-referential because the judge (deepseek-r1) is one of the evaluated models and the human-level comparison is asserted, not measured.

specific steps
  1. self definitional [Section 4.1.2, Equation (1); Section 5, 'A Persistent Proof Gap']
    "A proof attempt is graded based on the number of consecutive sub-problems solved correctly, judged by deepseek-r1 (the top RIMO-N model). ... The low scores on RIMO-P highlight a profound deficit in deductive ability. This represents a large gap in the performance of advanced human students, all of whom used the same rubric."

    Equation (1) defines the RIMO-P score P as the average share of sub-problems that deepseek-r1—itself one of the ten LLMs being benchmarked—marks 'correct'. The paper then interprets low P as a 'profound deficit in deductive ability' and a gap versus 'advanced human students', but no human scores are reported and deepseek-r1's reliability as an expert proof verifier is not validated. The measured quantity is, by construction, an LLM-judge acceptance rate; the conclusion about human-level proof ability is a renaming of that rate into a broader construct, making the 'proof gap' partly a restatement of the definition of P rather than an independent, externally anchored measurement.

full rationale

RIMO-N, which carries the paper's headline claim, is not circular: the 335 integer answers are grounded in official IMO jury keys or in agreement among three independent community sources (Section 3.1), and grading is deterministic string-match, so the observed accuracy drop relative to GSM8K/MATH is an external, reproducible fact, not a by-construction consequence of the benchmark's definition. The paper's own binary-subset analysis (96 problems with answers 0/1, accuracy rising 8–30 points) provides an honest internal control showing that answer-space size materially affects measured performance; this means the Section 3.1 assertion that 'the logical core and difficulty of the source problem remain intact' is an unvalidated construct-validity assumption—a real weakness, but not a circular reduction. The only meaningful circularity is in RIMO-P: the score P (Eq. 1) is the proportion of steps accepted by deepseek-r1, an LLM from the same evaluated model population; the paper then presents low P as evidence of a 'profound deficit in deductive ability' relative to 'advanced human students', without human control scores or any verification that deepseek-r1's judgments coincide with human expert judgments. The official reference solution is an external anchor, so the circularity is partial, but the human-level 'gap' is asserted rather than derived, and the 'proof gap' conclusion is in part a restatement of the choice of an LLM judge. The OlymMATH self-citation (a co-author of this paper is also an author of OlymMATH) is merely motivational comparison in Section 2.2 and is not load-bearing for RIMO's results. Overall, the core RIMO-N result stands independently; only the RIMO-P proof-gap inference is partially self-referential, yielding a moderate circularity score of 3.

Axiom & Free-Parameter Ledger

0 free parameters · 4 axioms · 0 invented entities

The paper's central measurements rest on the dataset construction being faithful to IMO difficulty and on the reliability of the grading protocols. No mathematical derivations or fitted parameters are introduced; the ledger therefore consists entirely of domain assumptions about benchmark validity and the trustworthiness of community sources and the LLM judge.

axioms (4)
  • ad hoc to paper Rewriting IMO problems into single-integer form preserves original difficulty
    Section 3.1 asserts 'the logical core and difficulty of the source problem remain intact' without a check such as human-baseline comparisons.
  • domain assumption Community sources (AoPS Wiki, YouTube, ParSe) provide trustworthy ground truth for contest problems
    Section 3.1 accepts a problem when at least two of three community sources agree, assuming these sources are reliable and not contaminated by errors.
  • ad hoc to paper deepseek-r1 is a reliable strict judge for RIMO-P sub-problems
    Section 4.1.2 uses 'deepseek-r1 (the top RIMO-N model)' to judge correctness of candidate sub-solutions; no validation of judge accuracy or bias is reported.
  • domain assumption The 1959-2023 IMO corpus is representative of olympiad-level reasoning
    The benchmark is assembled entirely from IMO materials; the paper assumes this corpus is a suitable proxy for peak mathematical reasoning without further justification.

reviewed 2026-08-04 · how reviews work

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Cite this review

Pith. "Pith review of RIMO: An Easy-to-Evaluate, Hard-to-Solve Olympiad Benchmark for Advanced Mathematical Reasoning." pith.science (2026). https://pith.science/paper/DYGKZEVH

@misc{pith2026250907711,
  author       = {Pith},
  title        = {Pith review of: RIMO: An Easy-to-Evaluate, Hard-to-Solve Olympiad Benchmark for Advanced Mathematical Reasoning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DYGKZEVH}},
  note         = {Machine review of arXiv:2509.07711}
}
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read the original abstract

As large language models (LLMs) reach high scores on established mathematical benchmarks, such as GSM8K and MATH, the research community has turned to International Mathematical Olympiad (IMO) problems to push the evaluation frontier. However, existing Olympiad-level benchmarks suffer from practical constraints that introduce grading noise and potential bias, such as heterogeneous answer formats requiring model-based judges and a reliance on potentially flawed solutions. We introduce RIMO, a two-track benchmark designed to preserve peak Olympiad difficulty while eliminating this evaluation noise. The first track, RIMO-N, rewrites 335 IMO problems to admit a single, unique integer answer, allowing for deterministic correctness checking. The second track, RIMO-P, features 456 proof problems with expert-checked solutions, which are decomposed into a sequence of sub-problems to evaluate the step-by-step reasoning process via an automated grading system. Our benchmarking of ten frontier LLMs, including GPT-4o and Gemini 2.5 Flash, reveals that while these systems excel on older benchmarks, their performance drops sharply on RIMO. These results highlight a substantial gap between current LLM capabilities and actual Olympiad-level reasoning. By providing a challenging yet easy-to-evaluate suite, RIMO offers a high-resolution yardstick for future research, presenting a clear target for closing the profound reasoning gap our findings expose.

Figures

Figures reproduced from arXiv: 2509.07711 by Chengwei Qin, Yao Shu, Ziye Chen.

Figure 1
Figure 1. Figure 1: Comparisons among different models on GSM8K, MATH, and RIMO-N, where the models are ranked based on [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: End-to-end construction pipeline of RIMO-N and RIMO-P [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Vanilla vs. Remade questions. Grey text is copied verbatim from the original statement; the coloured line is rewritten so the answer becomes a unique integer. proportions, covering algebra (96 items), geometry (95), number theory (86), and combinatorics (58). Each shortlist problem retains the jury’s official integer. A contest problem, lacking an authorised key, is accepted only when at least two of three… view at source ↗
Figure 5
Figure 5. Figure 5: Example of the Problems in RIMO-P. GSM8K and MATH. All generations use a single greedy decode with zero temperature (T = 0) under the same prompt template and context window; this reproduces the protocol used by the two earlier benchmarks and removes prompt engineering confounding. 4.1.1. RIMO-N RESULTS On RIMO-N, all models exhibit a drastic performance drop compared to their scores on MATH and GSM8K ( [… view at source ↗
Figure 7
Figure 7. Figure 7: RIMO-N accuracy versus first-release date. [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: Pass@1 on the full RIMO-N (dark bars) versus [PITH_FULL_IMAGE:figures/full_fig_p006_9.png] view at source ↗
Figure 8
Figure 8. Figure 8: RIMO-N accuracy versus parameter size. Does Answer Sparsity Change the Game? Binary￾valued items (in Olympiad terms, many of these are true-or￾false statements whose proof reduces to deciding whether the claim is correct) substantially relax the search space for an LLM. RIMO-N contains 96 such problems whose ground-truth integer happens to be 0 or 1. Roughly two￾thirds of them are genuine T/F formulations … view at source ↗
Figure 11
Figure 11. Figure 11: The performance scores of Qwen3-8B, InternLM3-8B-instruct and Mathstral-7B in RIMO-P. Newer instruction corpora alone are insufficient for better proofs. While the recent InternLM3-8B beats Qwen, it still trails the specialized Mathstral, indicating training type is more critical than recency. • A Persistent “Proof Gap”: All models remain far from human-level performance, leaving a large “proof gap” compa… view at source ↗

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This paper was first reviewed by deepseek-v4-flash on August 4, 2026.