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arxiv: 2504.11456 · v2 · submitted 2025-04-15 · 💻 cs.CL · cs.AI

Recognition: 1 theorem link

DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning

Zhiwei He , Tian Liang , Jiahao Xu , Qiuzhi Liu , Xingyu Chen , Yue Wang , Linfeng Song , Dian Yu
show 7 more authors
Zhenwen Liang Wenxuan Wang Zhuosheng Zhang Rui Wang Zhaopeng Tu Haitao Mi Dong Yu
Authors on Pith no claims yet

Pith reviewed 2026-05-16 10:27 UTC · model grok-4.3

classification 💻 cs.CL cs.AI
keywords mathematical reasoningreinforcement learninglarge language modelsdatasetdecontaminationverifiable answersgeneralizationmathematical benchmarks
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The pith

DeepMath-103K supplies 103K hard, clean math problems that let reinforcement learning reach state-of-the-art reasoning performance.

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

The paper presents DeepMath-103K as a large collection of difficult mathematical problems intended for training language models with reinforcement learning. Its key features are high difficulty, thorough removal of overlaps with known test sets, and answers that can be checked automatically. Training on this data produces models that set new records on tough math tests while also improving on tasks in biology, physics, and chemistry. Readers should care because better data of this kind can unlock more reliable advances in AI systems that handle complex problems.

Core claim

DeepMath-103K is a dataset of 103,000 mathematical problems at high difficulty levels, decontaminated against many existing benchmarks and equipped with verifiable answers for reward signals in reinforcement learning. It comes with three R1 solutions suitable for supervised fine-tuning and other methods. Models trained using this dataset attain state-of-the-art results on challenging mathematical benchmarks and exhibit generalization to non-mathematical domains including biology, physics, and chemistry.

What carries the argument

The DeepMath-103K dataset itself, which supplies scale, difficulty, decontamination, and verifiability to support rule-based rewards in RL training.

Load-bearing premise

The decontamination step completely eliminates any test-set overlap and the selected problems are hard enough to produce real reasoning gains instead of overfitting.

What would settle it

Train a model on the dataset and measure whether its performance on standard math benchmarks fails to exceed previous methods or if hidden overlap with benchmarks is later discovered.

read the original abstract

Reinforcement learning (RL) with large language models shows promise in complex reasoning. However, its progress is hindered by the lack of large-scale training data that is sufficiently challenging, contamination-free and verifiable. To this end, we introduce DeepMath-103K, a large-scale mathematical dataset designed with high difficulty (primarily levels 5-9), rigorous decontamination against numerous benchmarks, and verifiable answers for rule-based RL reward. It further includes three distinct R1 solutions adaptable for diverse training paradigms such as supervised fine-tuning (SFT). Spanning a wide range of mathematical topics, DeepMath-103K fosters the development of generalizable and advancing reasoning. Notably, models trained on DeepMath-103K achieve state-of-the-art results on challenging mathematical benchmarks and demonstrate generalization beyond math such as biology, physics and chemistry, underscoring its broad efficacy. Data: https://huggingface.co/datasets/zwhe99/DeepMath-103K.

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

3 major / 2 minor

Summary. The manuscript introduces DeepMath-103K, a dataset of 103K high-difficulty (primarily levels 5-9) mathematical problems that has undergone rigorous decontamination against numerous benchmarks and includes verifiable answers suitable for rule-based RL rewards. It also supplies three distinct R1 solutions to support diverse training paradigms such as SFT. The central claims are that models trained on this dataset achieve state-of-the-art results on challenging mathematical benchmarks and demonstrate generalization to non-mathematical domains including biology, physics, and chemistry.

Significance. If the decontamination procedure is shown to be effective and the reported gains are reproducible with proper baselines, the dataset would constitute a useful resource for RL-based reasoning research by supplying large-scale, challenging, and verifiable training data. The provision of multiple solution formats is a practical strength that could facilitate varied training setups. Cross-domain generalization, if substantiated, would further indicate utility for scientific reasoning tasks beyond mathematics.

major comments (3)
  1. [Decontamination subsection] Decontamination subsection: The abstract states 'rigorous decontamination against numerous benchmarks' but provides no explicit list of those benchmarks, no similarity metric (exact string, n-gram, or embedding cosine), and no overlap threshold. This information is load-bearing for the claim that SOTA results reflect genuine reasoning improvements rather than train-test leakage.
  2. [Experimental Results section] Experimental Results section: No details are given on training protocols (e.g., RL hyperparameters, model sizes), baseline models, or the precise benchmarks and metrics where SOTA is claimed. Without these, the central empirical assertions cannot be evaluated.
  3. [Generalization paragraph] Generalization paragraph: The claim of generalization to biology, physics, and chemistry lacks any description of the evaluation tasks, quantitative results, or controls showing that gains arise from improved reasoning rather than domain-specific artifacts.
minor comments (2)
  1. [Abstract] Abstract: Consider adding one or two key quantitative performance numbers to make the SOTA claim more concrete for readers.
  2. [Dataset description] Dataset description: Clarify the exact number of problems per difficulty level and topic distribution to allow better assessment of coverage.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive feedback on our manuscript. We agree that additional details are needed to support the claims regarding decontamination, experimental results, and cross-domain generalization. We will revise the manuscript to address these points and provide the requested information.

read point-by-point responses

  1. Referee: [Decontamination subsection] Decontamination subsection: The abstract states 'rigorous decontamination against numerous benchmarks' but provides no explicit list of those benchmarks, no similarity metric (exact string, n-gram, or embedding cosine), and no overlap threshold. This information is load-bearing for the claim that SOTA results reflect genuine reasoning improvements rather than train-test leakage.

    Authors: We agree that the decontamination procedure must be documented with greater specificity. In the revised manuscript, we will expand the Decontamination subsection to provide an explicit list of all benchmarks used, detail the similarity metrics applied (exact string matching, n-gram overlap, and embedding cosine similarity), and state the overlap thresholds employed for removal of contaminated items. This will allow readers to evaluate the effectiveness of the procedure and confirm the absence of train-test leakage. revision: yes

  2. Referee: [Experimental Results section] Experimental Results section: No details are given on training protocols (e.g., RL hyperparameters, model sizes), baseline models, or the precise benchmarks and metrics where SOTA is claimed. Without these, the central empirical assertions cannot be evaluated.

    Authors: We acknowledge that the Experimental Results section requires more comprehensive documentation. The revised version will include full details on the RL training protocols (hyperparameters and model sizes), the baseline models used for comparison, and the exact benchmarks and metrics on which state-of-the-art performance is reported. These additions will make the empirical claims fully evaluable. revision: yes

  3. Referee: [Generalization paragraph] Generalization paragraph: The claim of generalization to biology, physics, and chemistry lacks any description of the evaluation tasks, quantitative results, or controls showing that gains arise from improved reasoning rather than domain-specific artifacts.

    Authors: We agree that the generalization claims need supporting details. In the revised manuscript, we will expand the Generalization paragraph to describe the specific evaluation tasks in biology, physics, and chemistry, report the quantitative results, and include controls or analyses showing that the observed gains derive from improved reasoning rather than domain-specific artifacts. revision: yes

Circularity Check

0 steps flagged

No circularity: dataset release relies on external benchmarks and independent verification

full rationale

The paper presents a new dataset DeepMath-103K constructed via collection, decontamination, and verification steps, then evaluates models trained on it against external mathematical and cross-domain benchmarks. No derivation chain, equations, parameter fitting, or self-citation load-bearing steps exist that reduce claims to inputs by construction. The SOTA and generalization results are empirical outcomes from training and testing on held-out data, with decontamination presented as a procedural safeguard rather than a self-referential proof. This is a standard dataset contribution whose validity rests on reproducibility of the data pipeline and independent benchmark performance, not internal redefinition.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This is a dataset release paper rather than a theoretical derivation, so no free parameters, axioms, or invented entities are required for the central claim.

pith-pipeline@v0.9.0 · 5520 in / 1020 out tokens · 41808 ms · 2026-05-16T10:27:45.145056+00:00 · methodology

discussion (0)

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