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arxiv: 2402.03300 · v3 · submitted 2024-02-05 · 💻 cs.CL · cs.AI· cs.LG

DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models

Zhihong Shao , Peiyi Wang , Qihao Zhu , Runxin Xu , Junxiao Song , Xiao Bi , Haowei Zhang , Mingchuan Zhang
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Y.K. Li Y. Wu Daya Guo
This is my paper

Pith reviewed 2026-05-24 03:20 UTC · model grok-4.3

classification 💻 cs.CL cs.AIcs.LG
keywords mathematical reasoninglanguage modelscontinued pre-trainingreinforcement learningMATH benchmarkpolicy optimizationopen source modelsweb data curation
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The pith

DeepSeekMath 7B reaches 51.7% on the MATH benchmark by continuing pre-training on 120B curated web math tokens and applying Group Relative Policy Optimization.

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

The paper introduces DeepSeekMath 7B, created by taking DeepSeek-Coder-Base-v1.5 7B and continuing its pre-training on 120 billion math-related tokens extracted from Common Crawl along with natural language and code data. It reports 51.7 percent accuracy on the competition-level MATH benchmark without external toolkits or voting, and 60.9 percent when applying self-consistency over 64 samples. The authors present this result as evidence that the combination of a careful web-data selection pipeline and the new Group Relative Policy Optimization method can produce strong mathematical reasoning in an open 7B model.

Core claim

DeepSeekMath 7B shows that continued pre-training on a large volume of curated math tokens from public web data, followed by reinforcement learning with Group Relative Policy Optimization, enables a 7B open model to reach 51.7 percent on the MATH benchmark and approach the level of closed frontier systems without relying on external tools or ensembles.

What carries the argument

Group Relative Policy Optimization (GRPO), a memory-efficient variant of Proximal Policy Optimization that scores groups of responses relative to one another, combined with a data selection pipeline that extracts and filters 120B math-related tokens from Common Crawl.

If this is right

  • Self-consistency sampling over 64 responses raises MATH accuracy from 51.7 percent to 60.9 percent.
  • Open 7B models can reach performance close to closed models on competition math without tool use or voting.
  • GRPO reduces the memory footprint of PPO while still improving reasoning performance.
  • Public web data contains enough high-quality math content to support large-scale continued pre-training when filtered carefully.

Where Pith is reading between the lines

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

  • The same data-curation approach could be tested on other structured reasoning domains such as code or physics problem solving.
  • GRPO might transfer to reinforcement learning settings outside mathematics where relative scoring within batches is feasible.
  • Further increases in the volume of filtered math tokens or model size could narrow the remaining gap to closed frontier systems.

Load-bearing premise

The performance on MATH is driven primarily by the data selection pipeline and the GRPO algorithm rather than by other details of the base model or training setup.

What would settle it

Train an otherwise identical 7B model on the same base checkpoint but without the math-data selection step or without GRPO and measure whether accuracy on MATH stays well below 51.7 percent.

read the original abstract

Mathematical reasoning poses a significant challenge for language models due to its complex and structured nature. In this paper, we introduce DeepSeekMath 7B, which continues pre-training DeepSeek-Coder-Base-v1.5 7B with 120B math-related tokens sourced from Common Crawl, together with natural language and code data. DeepSeekMath 7B has achieved an impressive score of 51.7% on the competition-level MATH benchmark without relying on external toolkits and voting techniques, approaching the performance level of Gemini-Ultra and GPT-4. Self-consistency over 64 samples from DeepSeekMath 7B achieves 60.9% on MATH. The mathematical reasoning capability of DeepSeekMath is attributed to two key factors: First, we harness the significant potential of publicly available web data through a meticulously engineered data selection pipeline. Second, we introduce Group Relative Policy Optimization (GRPO), a variant of Proximal Policy Optimization (PPO), that enhances mathematical reasoning abilities while concurrently optimizing the memory usage of PPO.

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

2 major / 2 minor

Summary. The paper introduces DeepSeekMath 7B, obtained by continued pre-training of DeepSeek-Coder-Base-v1.5 7B on 120B math-related tokens from Common Crawl plus natural language and code data. It reports 51.7% accuracy on the MATH benchmark (60.9% with 64-sample self-consistency) without external toolkits or voting, approaching Gemini-Ultra and GPT-4. The authors attribute the gains to a meticulously engineered data selection pipeline from web data and the introduction of Group Relative Policy Optimization (GRPO), a PPO variant that improves mathematical reasoning while reducing memory usage.

Significance. If the attribution to the data pipeline and GRPO is substantiated by controls, the result would demonstrate that open 7B models can reach near-closed-model performance on competition math through public-data curation and a memory-efficient RL variant, offering a reproducible route for advancing reasoning capabilities.

major comments (2)
  1. [Experiments section (results and attribution paragraphs)] The central claim attributes the jump to 51.7% MATH primarily to the data selection pipeline and GRPO, yet no ablation results are supplied for (a) the base DeepSeek-Coder-Base-v1.5 7B on MATH, (b) the same 120B tokens with standard SFT or PPO instead of GRPO, or (c) the identical pipeline without the “meticulous” filtering step. This absence leaves the causal contribution of the two listed factors unsecured.
  2. [Results tables] Table reporting MATH scores (and any comparison tables) does not include the base model score or the continued-pretraining-only condition, making it impossible to quantify how much of the reported gain is due to the claimed factors versus scale of math tokens or the code-strong base model.
minor comments (2)
  1. [Abstract] The abstract states “120B math-related tokens” but does not clarify the total token count, the exact mix of math/NL/code, or the filtering criteria used in the pipeline.
  2. [Method section on GRPO] Notation for GRPO (reward formulation, group size, KL coefficient) should be defined with explicit equations in the method section to allow direct comparison with standard PPO.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive comments and the recommendation for major revision. We address the concerns about missing ablations and table information below, and will make appropriate revisions to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Experiments section (results and attribution paragraphs)] The central claim attributes the jump to 51.7% MATH primarily to the data selection pipeline and GRPO, yet no ablation results are supplied for (a) the base DeepSeek-Coder-Base-v1.5 7B on MATH, (b) the same 120B tokens with standard SFT or PPO instead of GRPO, or (c) the identical pipeline without the “meticulous” filtering step. This absence leaves the causal contribution of the two listed factors unsecured.

    Authors: We acknowledge the importance of ablations to substantiate the claims. In the revised manuscript, we will add the performance of the base model DeepSeek-Coder-Base-v1.5 7B on the MATH benchmark. For comparisons involving standard SFT or PPO, and the pipeline without filtering, these experiments were not conducted due to computational constraints. We will provide additional discussion on the rationale behind GRPO and the data curation process to better support the attribution. revision: partial

  2. Referee: [Results tables] Table reporting MATH scores (and any comparison tables) does not include the base model score or the continued-pretraining-only condition, making it impossible to quantify how much of the reported gain is due to the claimed factors versus scale of math tokens or the code-strong base model.

    Authors: We agree that including these baselines will improve clarity. We will update the tables in the results section to include the base model score and clarify the contributions from continued pre-training. revision: yes

standing simulated objections not resolved
  • Full ablation studies on the effects of the data filtering pipeline and direct comparisons between GRPO and standard PPO, as these require new experiments not present in the original work.

Circularity Check

0 steps flagged

No circularity; empirical training results with no self-referential derivation.

full rationale

The paper reports benchmark scores from continued pretraining of an existing base model (DeepSeek-Coder-Base-v1.5 7B) on 120B tokens followed by GRPO fine-tuning. The central claims are measured outcomes (51.7% MATH) and an attribution to two engineering choices (data pipeline + GRPO). No equations, uniqueness theorems, fitted parameters renamed as predictions, or self-citations that close a logical loop appear in the abstract or stated claims. Attribution without ablations is a weakness of evidence, not circularity by construction. The work is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides insufficient detail to identify specific free parameters, axioms, or invented entities beyond the high-level description of GRPO as a variant of PPO.

pith-pipeline@v0.9.0 · 5753 in / 1176 out tokens · 60175 ms · 2026-05-24T03:20:21.561498+00:00 · methodology

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