{"id":"17750faa-7c09-4826-83f0-04d39f554d25","arxiv_id":"2506.00309","paper_version":3,"verdict":"REJECT","confidence":"HIGH","novelty_score":3.0,"correctness_risk":"high","formal_verification":"none","parameter_count":3,"one_line_summary":"A three-model, three-dataset LLM math evaluation using a multi-dimensional reasoning rubric, undermined by contradictory accuracy tables.","lead":"This paper compares three chatbots on elementary, intermediate, and university-level math problems, scoring reasoning steps in addition to final answers. The reported results are internally contradictory, with the summary praising GPT-4o while the accuracy tables show Gemini-2.0 ahead on every dataset.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Central claim contradicts paper's own accuracy tables: GPT-4o is last, not first, on all three datasets, so 'most stable and consistent' is unsupported.","rationale":"The reader's strongest claim directly identifies the load-bearing flaw. I considered the alternative that 'stable and consistent' might refer to SCoT quality scores or average subject scores (Table 16) rather than accuracy; if so, the paper should say so and should not place the claim in the accuracy summary section. Moreover, Table 16 shows GPT-4o stable only within the University dataset; it does not support 'across all the datasets.' The other candidate concern, the unvalidated DeepSeek-V3 automated grader for GPT-4o in §4.3, would invalidate University rankings if real, but it is not necessary to reject the central claim: GSM8K and MATH500 tables already contradict the abstract. Thus the concern is internal inconsistency, not a disagreement with external consensus. The verdict should remain REJECT, with no change from the reader's assessment.","tokens_in":28944,"tokens_out":6690,"duration_ms":61099,"concrete_test":"Run the released repository evaluation on GSM8K with the paper's stated settings and compare the reproduced GPT-4o accuracy to Table 5 (50.0%) and the §4.5 prose (54.7%); then, from the reproduced Tables 5/7/10, compute each model's mean accuracy across the three datasets and its cross-dataset standard deviation. If GPT-4o's reproduced value matches 50.0% and Gemini ranks first on mean accuracy with the smallest standard deviation while GPT-4o is last on both, the abstract's 'most stable and consistent' claim is false under the paper's own accuracy criterion.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's headline result—'GPT-4o is the most stable and consistent in performance across all the datasets' (Abstract, repeated in §4.5)—is contradicted by its own quantitative summary. Table 17 (with source Tables 5, 7, 10) reports GPT-4o accuracy of 50.0%, 36.8%, 35.6% on GSM8K, MATH500, and University; DeepSeek-V3 of 42.6%, 51.1%, 42.8%; and Gemini-2.0 of 53.9%, 54.7%, 54.4%. Gemini is therefore the highest-accuracy model on every dataset, and GPT-4o is the lowest-accuracy model on every dataset. If 'stable across datasets' is read literally as low variance of these accuracy numbers, GPT-4o is again the worst: sample standard deviation across the three datasets is about 8.0 percentage points for GPT-4o, 4.9 for DeepSeek, and 0.4 for Gemini. The §4.5 prose adds a further inconsistency: it lists GSM8K accuracy for 'GPT-4o, DeepSeek, Gemini' as '54.7%, 54.4%, 53.9%', which matches neither Table 5 nor Table 17 (the 54.7% value belongs to Gemini on MATH500), so the authors' intended measured values are unclear. No run-to-run consistency metric or SCoT aggregation that would place GPT-4o first across all datasets is reported. A possible rescue via Table 16 average subject scores would make GPT-4o stable only on the University dataset, and that is not the claim made in the abstract. The automated DeepSeek-V3 grader issue noted in §4.3 is secondary: even if University grading were perfect, Tables 5 and 7 alone contradict the cross-dataset conclusion.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper compares GPT-4o, DeepSeek-V3, and Gemini-2.0 on three mathematics datasets (GSM8K, MATH500, and a University/MIT OCW dataset) using a Structured Chain-of-Thought (SCoT) framework with five evaluation dimensions. It reports accuracy and qualitative error analyses and concludes that GPT-4o is the most stable and consistent model across all datasets, with Gemini strong in structured problems, DeepSeek strong in computation but weak in inference, and GPT-4o lacking explanation precision. The paper also introduces an automated grading component and reports accuracy tables for each dataset.","tokens_in":29409,"tokens_out":3293,"duration_ms":30560,"significance":"If the evaluation were sound, the cross-model comparison on datasets of varying difficulty, including a university-level dataset, would provide useful evidence for educators selecting LLMs for mathematics tutoring and assessment. The authors make code and data publicly available and apply a multi-dimensional evaluation framework, which are positive features. However, the central claim of the paper is directly contradicted by its own accuracy tables, and the University-dataset grading procedure uses one of the compared models as the automated grader without validation. These issues undermine the reliability of the reported rankings and the paper's headline conclusion.","major_comments":[{"comment":"The claim that \"GPT-4o is the most stable and consistent in performance across all the datasets\" is contradicted by the paper's own accuracy tables. Table 5 shows GPT-4o at 50.0% vs Gemini 53.9% on GSM8K; Table 7 shows GPT-4o at 36.8% vs Gemini 54.7% on MATH500; Table 10 shows GPT-4o at 35.6% vs Gemini 54.4% on the University dataset; and Table 17 repeats these values. GPT-4o has the lowest accuracy of the three models on every dataset, and Gemini has the highest. No run-to-run consistency metric or alternative aggregation is reported that would support placing GPT-4o first on stability.","section":"Abstract and §4.5"},{"comment":"The summary section contains numerical inconsistencies that further undermine the central claim. It states that \"the accuracy of GPT-4o, DeepSeek, and Gemini for the GSM8K dataset is 54.7%, 54.4%, and 53.9%\", which matches neither Table 5 (50.0%, 42.6%, 53.9%) nor Table 17. It also states that \"The overall accuracy for University problems is 29%\", while Table 17 reports 35.6% for GPT-4o, 42.8% for DeepSeek, and 54.4% for Gemini. Later in the same section, GPT-4o is said to have \"an average correctness rate of 82%\" on University questions, which is inconsistent with the 35.6% in Table 10. These contradictions make the reported results and the headline conclusion unreliable.","section":"§4.5"},{"comment":"The evaluation of GPT-4o on the University dataset uses \"an automated grading model based on Deepseek-V3 that evaluates each solution step.\" This means one of the models under comparison acts as the grader for another model's outputs. No validation of this grader against human judgments, no inter-rater reliability, and no agreement statistics are reported. Since the University dataset is the only source for the GPT-4o stability claim, the rankings on that dataset rest on an unverified and potentially biased grading process. This is a load-bearing methodological flaw, not a minor concern.","section":"§4.3"},{"comment":"The paper lists \"Consistency\" as a core evaluation dimension and uses it in the headline claim, but it never reports a quantitative consistency metric. No variance across repeated runs, no standard deviation, and no agreement measure is given for any model or dataset. The only support for \"stable and consistent\" appears to be the qualitative statements in §4.5. Without an operationalized consistency measure, the central claim is not empirically supported.","section":"§3.4 and §4"}],"minor_comments":[{"comment":"There are numerous typos and inconsistencies, including \"DeekSeek\" (§4.3), \"vaggue\" (Table 18), \"Univesrity\" (Table 19 title), and inconsistent use of \"MATH 500\" vs \"MATH500.\" The manuscript would benefit from a careful proofreading pass.","section":"Throughout"},{"comment":"The introduction refers to the \"University of New South Sales\" dataset, while Table 1 and Table 2 describe \"MIT Open Courseware\" as the source. This naming inconsistency should be resolved, and the relationship between the UNSW and MIT OCW datasets should be clarified.","section":"Introduction and Table 2"},{"comment":"The MATH500 subject-level and difficulty-level accuracy numbers for DeepSeek and GPT-4o in Table 9 are internally inconsistent: for example, DeepSeek's listed subject accuracies (e.g., Prealgebra 52%, Algebra 40%) are difficult to reconcile with its overall accuracy of 51.1% given the reported difficulty distribution. The authors should provide per-cell counts or clarifying details.","section":"Table 9"},{"comment":"The sentence \"29% accuracy is not much surprising due to the rigorous criterion. Only a full mark answer can be considered correct for proof problems\" is unclear, as the paper reports accuracy values far above 29% in Table 10 and does not explain how the 29% figure was derived. This should be rewritten or removed.","section":"§4.3"}],"recommendation":"reject","confidential_remarks":"The paper's central claim is contradicted by its own data tables, and the University-dataset grading is compromised by using one compared model as the grader. These are not cosmetic issues; they affect the validity of the main conclusion. The paper also shows signs of insufficient internal consistency checking (e.g., the mismatched numbers in §4.5). I would advise against publication in its current form. If the authors were to substantially revise the analysis and claims, a resubmission might be considered, but the current version does not meet the standard for acceptance."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the paper has a sensible evaluation design—three LLMs, three difficulty tiers, and a multi-dimensional scoring rubric based on SCoT—and the 140-question MIT/UNSW university dataset is a genuinely useful addition to the benchmark pool. But the paper's central claim, repeated in the abstract and Section 4.5, is that GPT-4o is 'the most stable and consistent' across datasets. The paper's own Tables 5, 7, and 10 show GPT-4o with the lowest accuracy on all three datasets (50.0% vs 53.9% on GSM8K; 36.8% vs 54.7% on MATH500; 35.6% vs 54.4% on University). If 'stable' means low cross-dataset variance, GPT-4o is again the worst: its accuracy swings about 8 points, while Gemini's swings 0.4 points. The prose in §4.5 lists GSM8K values (54.7%, 54.4%, 53.9%) that match neither Table 5 nor Table 17, so the authors' intended numbers are unclear.\n\nThat contradiction is load-bearing. The paper's main takeaway for educators is unsupported by its own measurements.\n\nWhat is worth keeping: the SCoT-based rubric (accuracy, reasoning, completeness, consistency, intermediate calculations) is a reasonable way to go beyond final-answer accuracy, and the error taxonomy in Table 14 is informative. The university dataset, if provenance is clarified, addresses a gap—most evaluations stop at MATH. The code/data link is a plus.\n\nThe soft spots beyond the headline: Section 4.3 says an automated grader based on DeepSeek-V3 evaluates GPT-4o's step-by-step solutions. Since DeepSeek is one of the models being compared, this is a conflict of interest unless the grader is validated against human ratings. No inter-rater reliability or grader-accuracy numbers are reported, so the University rankings rest on an unverified process. Also, the dataset description is inconsistent: the introduction mentions a 'University of New South Sales' problem set, while Table 1 and the abstract refer to MIT Open Courseware. That is exactly the kind of detail that matters for reproducibility.\n\nBottom line: this is a competent evaluative framework but a flawed execution. The central claim contradicts the data, the automated grader is unvalidated, and the dataset origin is muddled. A serious editor should not send this to peer review as-is. I would desk-reject with an invitation to resubmit after the authors correct the headline claim (or redefine 'stability' to match a metric they actually report), validate the grader, and reconcile the dataset description. If those fixes land, it could be a modest, citable evaluation study. As it stands, I would not cite it.","headline":"The multi-dimensional evaluation idea and MIT dataset are useful, but the paper's central claim that GPT-4o is most stable is contradicted by its own tables; the work needs major corrections before peer review.","tokens_in":29905,"tokens_out":3244,"would_cite":false,"duration_ms":29749,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper compares GPT-4o, DeepSeek-V3, and Gemini-2.0 on three mathematics datasets and claims GPT-4o is the most stable model, even though its own accuracy tables place Gemini-2.0 first on every dataset.","keywords":["large language models","mathematical problem solving","GPT-4o","DeepSeek-V3","Gemini-2.0","SCoT","chain-of-thought","benchmark evaluation"],"falsifier":"Re-evaluate the three datasets across repeated runs with fixed prompts, record accuracy and score distributions per model, and have human graders independently score a random subset of the university problems; if GPT-4o's accuracy remains the lowest on all three datasets and its run-to-run variance is no smaller than Gemini-2.0's, the 'most stable and consistent' claim is falsified.","tokens_in":28803,"feed_emoji":"🧮","tokens_out":9755,"duration_ms":86403,"temperature":0.7,"pith_summary":"This paper compares GPT-4o, DeepSeek-V3, and Gemini-2.0 on mathematics problems at three difficulty levels, using a Structured Chain-of-Thought (SCoT) rubric that scores final-answer accuracy, step completeness, step validity, intermediate calculation accuracy, and problem comprehension. The intended conclusion is that GPT-4o is the most stable and consistent of the three models overall, and especially strong on high-level university questions, while DeepSeek-V3 excels in well-structured optimisation tasks and Gemini-2.0 reads problems fluently but struggles with multi-step reasoning. The paper's own accuracy tables, however, place GPT-4o last on all three datasets: 50.0% versus 53.9% on GSM8K, 36.8% versus 54.7% on MATH500, and 35.6% versus 54.4% on the university problems, with Gemini-2.0 first each time. The paper does not reconcile this contradiction explicitly.","feed_headline":"Benchmark tables rank Gemini first, not GPT-4o","feed_subtitle":"On GSM8K, MATH500, and the university dataset, Gemini-2.0 posts the highest reported accuracy on every one.","key_machinery":"The Structured Chain-of-Thought (SCoT) framework is the central instrument: it decomposes each model's solution into steps and scores five dimensions—final-answer accuracy, step completeness, step validity, intermediate calculation accuracy, and problem comprehension. The framework also includes an automated grading model built on DeepSeek-V3 for the university-level dataset, a 1-to-5 scoring rubric for non-perfect solutions, and a ten-category manual error taxonomy. This machinery converts raw LLM outputs into comparable quality scores and produces the per-subject and per-difficulty comparisons that the paper's conclusions rest on.","core_discovery":"The paper's central assertion, stated in the abstract and in Section 4.5, is that GPT-4o is the most stable and consistent performer across GSM8K, MATH500, and the University dataset, with especially strong results on high-level open-courseware problems. It also claims DeepSeek-V3 is competitive in well-structured computational and optimisation domains but loses accuracy in statistical inference, and that Gemini-2.0 has strong linguistic understanding but weak multi-step reasoning and symbolic logic. The intended discovery is thus a differentiated capability profile per model, produced by the SCoT evaluation rather than by final-answer accuracy alone. The reported accuracy figures in the same paper tell a different rank order on the accuracy dimension: GPT-4o scores lower than the other two on every dataset, and Gemini-2.0 has the highest accuracy on all three. In the paper's own terms, the evidence supports a model-specific strengths-and-weaknesses profile, but the 'most stable' label is not what the accuracy tables show.","pith_inferences":["The paper leaves implicit that 'stability' and 'accuracy' are different quantities; if stability means low variance across repeated runs, the claim and the tables could both be true, but the paper never reports the repeated-run variance that would verify it.","Because the automated grader for the university dataset is itself DeepSeek-V3, one of the models under comparison, the SCoT scores for that dataset could carry an undetected grader bias; a fairer design would use a hold-out grader or human marking.","A testable extension: rerun the same three datasets with several temperatures and seeds, record score distributions rather than point accuracies, and compare variance across models—this would turn 'stable and consistent' into a measured quantity.","The roughly 50-percent accuracies on GSM8K echo a broader pattern that LLM arithmetic reasoning degrades sharply on multi-step word problems, so the practical educational lesson may be that these models need verification layers rather than raw generation in tutoring tools."],"forward_implications":["If the stability claim were taken at face value, educators choosing a general-purpose model for mixed mathematics courses would prefer GPT-4o despite its lower reported accuracy.","If DeepSeek-V3's optimisation strengths are real, its best classroom use is computational and optimisation problem sets rather than statistical inference.","If Gemini-2.0's documented weakness in multi-step reasoning and symbolic logic is real, it needs structured step-by-step prompts or verification before use on proof-heavy material.","Prompt scaffolding changes outcomes for all three models, so any single-prompt evaluation understates what the models can do when guided.","The discrepancy between the abstract and the accuracy tables means that an evaluation summary built on the SCoT dimensions must report per-dimension scores explicitly before a reader can judge a stability claim."],"supporting_citations":[{"why":"Supplies the GSM8K word-problem set used as the elementary benchmark and accuracy baseline.","marker":"[113]"},{"why":"Supplies the MATH500 subset used as the intermediate benchmark and difficulty-level breakdown.","marker":"[114]"},{"why":"Provides the SCoT automatic-scoring method on which the five evaluation dimensions are built.","marker":"[115]"},{"why":"Prior work on LLM mathematical-reasoning limitations that the paper says its results match.","marker":"[138]"},{"why":"Prior analysis of chain-of-thought and reasoning that frames the paper's prompting discussion.","marker":"[139]"},{"why":"Background reference for the GPT-4o model family under evaluation.","marker":"[41]"},{"why":"Background reference for the Gemini-2.0 model under evaluation.","marker":"[42]"},{"why":"Background reference for the DeepSeek-V3 model under evaluation.","marker":"[43]"}],"fun_headline_variants":["Gemini tops every math benchmark, GPT-4o claims stability","Accuracy tables contradict GPT-4o's 'most stable' label","Math rankings: Gemini-2.0 first, GPT-4o elsewhere","SCoT error analysis exposes distinct gaps per model"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the SCoT scores, including those produced by an automated DeepSeek-V3 grader for the university dataset, are fair and consistent enough to rank the models, because the reported accuracy tables alone do not support calling GPT-4o the most stable performer.","fun_headline_variants_meta":{"raw":{"variants":["Gemini tops every math benchmark, GPT-4o claims stability","Accuracy tables contradict GPT-4o's 'most stable' label","Math rankings: Gemini-2.0 first, GPT-4o elsewhere","SCoT error analysis exposes distinct gaps per model"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000322,"raw_usage":{"total_tokens":1830,"prompt_tokens":987,"completion_tokens":843,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":603,"completion_tokens_details":{"reasoning_tokens":770}},"tokens_in":603,"tokens_out":843,"duration_ms":8316,"temperature":1.0,"reasoning_tokens":770,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T12:07:08.934274+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-evaluate the three datasets across repeated runs with fixed prompts, record accuracy and score distributions per model, and have human graders independently score a random subset of the university problems; if GPT-4o's accuracy remains the lowest on all three datasets and its run-to-run variance is no smaller than Gemini-2.0's, the 'most stable and consistent' claim is falsified.","supporting_citations":[],"review_version":1}