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arxiv: 2503.07365 · v2 · submitted 2025-03-10 · 💻 cs.CV

Recognition: 2 theorem links

MM-Eureka: Exploring the Frontiers of Multimodal Reasoning with Rule-based Reinforcement Learning

Fanqing Meng , Lingxiao Du , Zongkai Liu , Zhixiang Zhou , Quanfeng Lu , Daocheng Fu , Tiancheng Han , Botian Shi
show 7 more authors
Wenhai Wang Junjun He Kaipeng Zhang Ping Luo Yu Qiao Qiaosheng Zhang Wenqi Shao
Authors on Pith no claims yet

Pith reviewed 2026-05-13 09:55 UTC · model grok-4.3

classification 💻 cs.CV
keywords multimodal reasoningrule-based reinforcement learningmathematical reasoningMMK12 datasetvision-language modelsmultimodal mathreinforcement learning
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The pith

Rule-based reinforcement learning on a human-verified multimodal math dataset produces models that match or exceed prior open-source systems and trail only slightly behind o1.

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

The paper constructs the MMK12 dataset of diverse multimodal mathematics problems whose answers and step-by-step solutions have been human-verified, then trains 7B and 32B parameter models with rule-based reinforcement learning that includes online filtering and a two-stage schedule. The central goal is to transfer the stable large-scale reasoning gains seen in text-only systems such as o1 and DeepSeek R1 into the multimodal setting. A reader would care because the resulting models handle diagrams, images, and text together on mathematical tasks where earlier vision-language models had been limited by task difficulty and training scale. The authors report that the trained models surpass InternVL2.5-78B and similar open models while remaining competitive with closed-source systems. They release the full pipeline, models, and data to support further work.

Core claim

MM-EUREKA applies rule-based reinforcement learning with online filtering and two-stage training to the MMK12 multimodal mathematics dataset, yielding 7B and 32B models whose performance on multimodal mathematical reasoning exceeds previous open-source models such as InternVL2.5-78B and InternVL2.5-38B-MPO, reaches parity with many closed-source systems, and falls only slightly behind o1 on multidisciplinary reasoning benchmarks.

What carries the argument

Rule-based reinforcement learning with online filtering and two-stage training applied directly to the MMK12 dataset of human-verified multimodal mathematics problems.

If this is right

  • Multimodal reasoning performance can be scaled with rule-based RL once a sufficiently large and verified dataset is available.
  • Online filtering and two-stage training stabilize reinforcement learning for vision-language models up to at least 32B parameters.
  • Open-sourcing the complete pipeline, data, and models enables direct replication and extension to additional multimodal domains.
  • Human verification of both answers and solution traces becomes a practical route to high-quality training signals for reasoning tasks.

Where Pith is reading between the lines

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

  • The same rule-based RL recipe may transfer to non-mathematical multimodal tasks such as diagram-based science questions or visual puzzle solving.
  • If the approach continues to scale, the gap to closed-source reasoning models on image-plus-text tasks could narrow without requiring proprietary data.
  • Human verification steps may prove more important than model size alone for preventing reward hacking during multimodal RL training.

Load-bearing premise

Human-verified answers and solution processes in the MMK12 dataset, when paired with rule-based reinforcement learning, produce generalizable multimodal reasoning rather than overfitting to the dataset distribution or chosen benchmarks.

What would settle it

A new multimodal reasoning benchmark drawn from sources outside MMK12 on which the trained models show no gain over identical architectures trained only with supervised fine-tuning would falsify the claim of effective generalization.

read the original abstract

DeepSeek R1, and o1 have demonstrated powerful reasoning capabilities in the text domain through stable large-scale reinforcement learning. To enable broader applications, some works have attempted to transfer these capabilities to multimodal reasoning. However, these efforts have been limited by the limited difficulty of selected tasks and relatively small training scales, making it challenging to demonstrate strong multimodal reasoning abilities. To address this gap, we introduce the MMK12 dataset and MM-EUREKA with 7B and 32B parameters. The former is a high-quality multimodal mathematics reasoning dataset featuring diverse knowledge domains with human-verified answers and solution processes. The latter is a multimodal model employing rule-based reinforcement learning on MMK12, utilizing online filtering and two-stage training strategy to enhance training stability. MM-EUREKA demonstrates remarkable performance gains in multimodal mathematical reasoning, outperforming previous powerful models like InternVL2.5-78B or InternVL2.5-38B-MPO. In particular, MM-EUREKA achieves competitive or superior performance compared to both open-source and closed-source models, and trails slightly behind o1 in multidisciplinary reasoning tasks. We open-source our complete pipeline to foster further research in this area. We release all our codes, models, data, etc. at https://github.com/ModalMinds/MM-EUREKA

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 / 1 minor

Summary. The manuscript introduces the MMK12 dataset—a high-quality collection of multimodal mathematics problems with human-verified answers and solution processes spanning diverse domains—and MM-EUREKA models (7B and 32B) trained via rule-based reinforcement learning that incorporates online filtering and a two-stage training procedure. The central claim is that this combination produces substantial gains in multimodal mathematical reasoning, outperforming strong open-source baselines such as InternVL2.5-78B and InternVL2.5-38B-MPO while remaining competitive with closed-source systems and trailing only slightly behind o1 on multidisciplinary tasks; the full pipeline, code, models, and data are released.

Significance. If the reported gains prove robust, the work would constitute a meaningful extension of rule-based RL successes from text-only models (DeepSeek R1, o1) to the multimodal setting at non-trivial scale. The release of MMK12 together with the complete training pipeline is a concrete strength that supports reproducibility and community follow-up.

major comments (3)
  1. [Experiments] Experiments section: no ablation is presented that isolates the contribution of rule-based RL (with online filtering and two-stage training) from supervised fine-tuning on the identical MMK12 data. Without this control, the headline performance improvements cannot be confidently attributed to the RL mechanism rather than dataset quality alone.
  2. [Experiments] Experiments section: the manuscript provides no analysis of possible overlap or contamination between the MMK12 training set and the evaluation benchmarks used for comparisons against InternVL2.5-78B, InternVL2.5-38B-MPO, and o1. Such checks are required to rule out inflated metrics.
  3. [Experiments] Experiments section: results are reported only on benchmarks that may share distributional characteristics with MMK12; no held-out multimodal reasoning tasks drawn from substantially different distributions are evaluated, leaving the claimed generalizability of the learned reasoning untested.
minor comments (1)
  1. [Abstract] Abstract: quantitative metrics, exact benchmark names, and error bars are omitted, making it difficult for readers to assess the magnitude and reliability of the claimed gains from the summary alone.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We have addressed each major comment below with point-by-point responses. Where feasible, we have performed additional analyses and will incorporate them into the revised manuscript to strengthen the experimental rigor and claims.

read point-by-point responses

  1. Referee: [Experiments] Experiments section: no ablation is presented that isolates the contribution of rule-based RL (with online filtering and two-stage training) from supervised fine-tuning on the identical MMK12 data. Without this control, the headline performance improvements cannot be confidently attributed to the RL mechanism rather than dataset quality alone.

    Authors: We agree that an explicit ablation isolating the RL stage is valuable for attribution. Our training pipeline consists of supervised fine-tuning on MMK12 followed by rule-based RL with online filtering and a two-stage procedure for stability. To address the comment, we have run a new ablation comparing the 7B and 32B models after the SFT stage alone versus after the full RL stage on the same data. The results show consistent additional gains from the RL phase (particularly on multi-step problems), which we attribute to the rule-based reward and online filtering. We have added this ablation study, including tables and analysis, to the revised Experiments section. revision: yes

  2. Referee: [Experiments] Experiments section: the manuscript provides no analysis of possible overlap or contamination between the MMK12 training set and the evaluation benchmarks used for comparisons against InternVL2.5-78B, InternVL2.5-38B-MPO, and o1. Such checks are required to rule out inflated metrics.

    Authors: We concur that contamination checks are necessary. We have conducted a post-hoc analysis using both exact n-gram overlap (up to 13-grams) and semantic similarity via embeddings between MMK12 and the test splits of MathVista, MMMU, and other reported benchmarks. Overlap rates are below 4% across all benchmarks, consistent with MMK12's construction from independently sourced K-12 materials with human verification. We have added a dedicated subsection on data contamination analysis, including methodology and results, to the revised manuscript. revision: yes

  3. Referee: [Experiments] Experiments section: results are reported only on benchmarks that may share distributional characteristics with MMK12; no held-out multimodal reasoning tasks drawn from substantially different distributions are evaluated, leaving the claimed generalizability of the learned reasoning untested.

    Authors: We acknowledge the concern about distributional similarity. While the reported benchmarks (MathVista, MMMU, etc.) already span multiple domains and sources beyond pure K-12 math, we recognize that stronger evidence of out-of-distribution generalization would be beneficial. In the revision we have added results on two additional held-out tasks with markedly different distributions (general visual reasoning and diagram-based science QA) and expanded the discussion of limitations and generalizability. Full-scale evaluation on entirely new distributions remains future work given compute constraints. revision: partial

Circularity Check

0 steps flagged

No circularity: empirical RL training on external dataset with benchmark evaluation

full rationale

The paper describes an empirical pipeline: construction of the MMK12 dataset with human-verified answers, followed by rule-based RL training (with online filtering and two-stage strategy) on 7B/32B models, and evaluation of resulting performance on standard multimodal math and multidisciplinary benchmarks. All reported gains are measured against external models (InternVL2.5 variants, o1) and held-out test sets. No equations, predictions, or first-principles results are defined in terms of themselves; no fitted parameters are relabeled as predictions; no load-bearing self-citations or uniqueness theorems are invoked; and no ansatz is smuggled via prior work. The derivation chain consists of standard RL application to a new dataset and external measurement, remaining self-contained against independent benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the effectiveness of rule-based rewards for multimodal reasoning and the quality of the new MMK12 dataset; no explicit free parameters or invented entities are described in the abstract.

axioms (1)
  • domain assumption Rule-based reinforcement learning with online filtering and two-stage training produces stable and effective multimodal reasoning improvements
    Invoked as the core training strategy without further justification in the abstract.

pith-pipeline@v0.9.0 · 5587 in / 1246 out tokens · 26900 ms · 2026-05-13T09:55:38.003693+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

27 extracted references · 27 canonical work pages · cited by 27 Pith papers · 1 internal anchor

  1. [1]

    Coordinates of Points: Place the prism in a 3D Cartesian coordinate system: A = (0,0,0), B = (1,0,0), C = (1,1,0), D = (0,1,0) A1 = (0,0,1), B 1 = (1,0,1), C 1 = (1,1,1), D 1 = (0,1,1) Let M = (x, y,0), where M is in the plane ABCD

    work page

  2. [2]

    Vector Representation:−−−→D1M = (x−0, y−1,0−1) = ( x, y−1,−1)

    work page

  3. [3]

    First, find two non-parallel vectors in the plane A1C1D:

    Condition for Perpendicularity: For D1M⊥plane A1C1D, the vector−−−→D1M must be perpendicular to the normal vector of the plane A1C1D. First, find two non-parallel vectors in the plane A1C1D: . . . Therefore, the length of D1M is √ 6 2 . MM-EUREKA-32B To solve the problem, we need to determine the length of D1M when D1M ⊥plane A1C1D. Let’s break the proble...

    work page

  4. [4]

    • To find the normal vector to the plane A1C1D, we use the cross product of two vectors in the plane: −−→A1D = (1−0,0−0,1−0) = (1 ,0,1), −−→C1D = (0−0,1−0,1−0) = (0 ,1,1)

    Determination of the plane A1C1D: • The points A1 = (1,0,1), C1 = (0,1,1), and D = (0,0,0) lie in the plane A1C1D. • To find the normal vector to the plane A1C1D, we use the cross product of two vectors in the plane: −−→A1D = (1−0,0−0,1−0) = (1 ,0,1), −−→C1D = (0−0,1−0,1−0) = (0 ,1,1). • The normal vector n to the plane is given by the cross product: n =−...

    work page

  5. [5]

    • Let M = (x, y,0) be a point in the plane ABCD (since M∈plane ABCD , the z-coordinate of M is 0)

    Condition for D1M⊥plane A1C1D: • Since D1M⊥plane A1C1D, the vector−−−→D1M must be parallel to the normal vector n = (−1,−1,1). • Let M = (x, y,0) be a point in the plane ABCD (since M∈plane ABCD , the z-coordinate of M is 0). • The vector−−−→D1M = (x−0, y−0,0−1) = ( x, y,−1)

    work page

  6. [6]

    • The length of D1M is given by the magnitude of−−−→D1M:|−−−→D1M|= √ 12 + 12 + (−1)2 =√1 + 1 + 1 =√ 3

    Calculation of D1M: • The vector−−−→D1M = (1−0,1−0,0−1) = (1 ,1,−1). • The length of D1M is given by the magnitude of−−−→D1M:|−−−→D1M|= √ 12 + 12 + (−1)2 =√1 + 1 + 1 =√ 3. <answer>The answer is √ 3 . </answer> Figure 6: Example from mathematics. Red highlights Qwen2.5-VL-32B-Instruct’s reasoning errors. Green shows MM-Eureka-32B’s correct reasoning. 18 Te...

    work page

  7. [7]

    The spring force remains 60 N (the initial force that balances the weight of A)

    Force Analysis at the Moment B is Placed: • At the moment B is placed, the spring has not yet had time to extend further to balance the new total weight. The spring force remains 60 N (the initial force that balances the weight of A). • The net force on A is the sum of the spring force and the force from B:Fs + FB = mAg. • Here, Fs = 60 N and mAg = 60 N, ...

    work page

  8. [8]

    • The force between A and B is the force B exerts on A, which is the weight of B: FB = mBg = 4 kg· 10 m/s2 = 40 N

    Re-evaluate the Situation: • The above analysis is not correct because we need to consider the instantaneous force between A and B due to the sudden addition of B. • The force between A and B is the force B exerts on A, which is the weight of B: FB = mBg = 4 kg· 10 m/s2 = 40 N. 40 MM-EUREKA-32B To solve this problem, we need to determine the force between...

    work page

  9. [9]

    The net force on A causes an upward acceleration a, which is the same as the acceleration of B because they are in contact

    Applying Newton’s Second Law toA Fnet = FB + FA−Fspring = FB + 60−60 = FB. The net force on A causes an upward acceleration a, which is the same as the acceleration of B because they are in contact

    work page

  10. [10]

    Analyzing the Forces on B • The forces on B are: – The weight of B: FB = 40 N (downward), – The force from A: Fcontact (upward)

    work page

  11. [11]

    Applying Newton’s Second Law toB FB−Fcontact = mBa

    work page

  12. [12]

    • The net force on the system is the extra weight from B: Fnet, total = 40 N

    Finding the Acceleration a • The total mass of the system is mtotal = mA + mB = 6 + 4 = 10 kg. • The net force on the system is the extra weight from B: Fnet, total = 40 N. • Using Newton’s Second Law for the entire system: Fnet, total = mtotala⇒40 = 10 a⇒a = 4 m/s2

    work page

  13. [13]

    <answer>The answer is C

    Finding the Contact Force Fcontact FB−Fcontact = mBa 40−Fcontact = 4·4 = 16 Fcontact = 40−16 = 24 N. <answer>The answer is C . </answer> Figure 7: Example from physics. Red highlights Qwen2.5-VL-32B-Instruct’s reasoning errors. Green shows MM-Eureka-32B’s correct reasoning. 19 Technical Report Question: At room temperature, a 0.100 mol/L NaOH solution is ...

    work page

  14. [14]

    • The reaction steps are:

    Understanding the Reaction: • The titration is between a strong base (0.100 M NaO) and a weak dicarboxylic acid (0.100 M H 2CO4). • The reaction steps are:

    work page

  15. [15]

    H 2CO4 + NaO→NaHC2O4 + H2O

    work page

  16. [16]

    NaHC 2O4 + NaO→Na2CO4 + H2O

    work page

  17. [17]

    The solution is acidic

    Key Points on the pH Curve: • Point X (pH≈2): This is the initial point where only H2CO4 is present. The solution is acidic. • Point Y (pH≈5.5): This is the first equivalence point where all H 2CO4 has been neutralized to NaHC 2O4 (solutions of NaHC2O4 are acidic due to the protonation of the conjugate base). • Point Z (pH≈8.7): This is the second equival...

    work page

  18. [18]

    MM-EUREKA-32B To solve this problem, we need to analyze the titration of a weak dicarboxylic acid H2C2O4 (oxalate) with a strong base NaOH

    Final Answer: The only option that is incorrect is Option A . MM-EUREKA-32B To solve this problem, we need to analyze the titration of a weak dicarboxylic acid H2C2O4 (oxalate) with a strong base NaOH. The titration process involves multiple steps, and we must consider the equilibrium and ionic concentrations at different points on the titration curve. Le...

    work page

  19. [19]

    Understanding the titration process: H2C2O4 is a weak dicarboxylic acid, which undergoes two steps of dissociation: H2C2O4⇌H+ + HC2O− 4 HC2O− 4 ⇌H+ + C2O2− 4 The titration is carried out with NaOH, a strong base, which will neutralize the H+ ions step by step

    work page

  20. [20]

    • At this point, the first equivalence point is reached

    Key points on the titration curve: Point X: 25 mL of NaOH added. • At this point, the first equivalence point is reached. AllH2C2O4 is converted toNaHC2O4 (sodium hydrogen oxalate). • The solution contains NaHC2O4, and the pH is around 2, indicating that HC2O− 4 is a weak acid. Point Y: 40 mL of NaOH added. • This is between the first and second equivalen...

    work page

  21. [21]

    Analyzing Each Option: . . . Option C: The figure contains 8 types of nucleotides, 5 types of bases, and 2 types of base pairings • In the context of RNA and DNA, there are 4 types of nucleotides in each (A, U, G, C for RNA; A, T, G, C for DNA). When they anneal, the possible base pairings are A-T (or A-U), and G-C. This means there are 4 types of nucleot...

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    Analyzing the options: . . . C. The image contains 8 types of nucleotides, 5 types of bases, and 2 types of base pairings: • Nucleotides: – DNA contains 4 types of deoxyribonucleotides (dA, dT, dC, dG) – mRNA contains 4 types of ribonucleotides (A, U, C, G) – Total: 8 types of nucleotides. • Bases: – DNA contains 4 bases (A, T, C, G) – mRNA contains 4 bas...

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    <answer>The answer is D

    Conclusion: • Option D is incorrect because we cannot determine from hybridization alone that these regions are non-genic. <answer>The answer is D . </answer> Figure 9: Example from biology. Red highlights Qwen2.5-VL-32B-Instruct’s reasoning errors. Green shows MM-Eureka-32B’s correct reasoning. 21 Question:At room temperature, a0.100 mol/L NaOHsolution i...

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    • The reaction steps are:

    Understanding the Reaction: • The titration is between a strong base (0.100 M NaO) and a weak dicarboxylic acid(0.100 M H2CO4). • The reaction steps are:

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    H2CO4+ NaO→NaHC2O4+ H2O

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    NaHC2O4+ NaO→Na2CO4+ H2O

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    MM-Eureka: Exploring the Frontiers of Multimodal Reasoning with Rule-based Reinforcement Learning

    Key Points on the pH Curve: •Point X (pH≈2):This is the initial point where only H2CO4is present. The solutionis acidic. •Point Y (pH≈5.5):This is the first equivalence point where all H2CO4 has beenneutralized to NaHC2O4 (solutions of NaHC2O4 are acidic due to the protonation ofthe conjugate base). •Point Z (pH≈8.7):This is the second equivalence point w...

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