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RMath: A Logic Reasoning-Focused Datasets Toward Mathematical Multistep Reasoning Tasks
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Builds RMath, a 200-problem logic-focused math reasoning dataset with propositional annotations, and a proposition-based problem-solving framework used for prompt tuning of LLMs evaluated on RMath.
Problem
Existing math datasets emphasize commonsense knowledge or fixed-format arithmetic rather than pure multistep logical reasoning from given conditions, so LLM logical reasoning ability is not well measured.
Approach
A dataset of 200 knowledge-free multistep logic problems (direct, hypothetical, nested) annotated with atomic propositions, truth values, and proposition relations, plus a nine-step propositional-logic solving framework used to create prompt-tuning training data.
Key results
- DeepSeekMath 7B scores 45.0% on RMath while ToRA 70B scores only 31.0% despite >80% on GSM8K, SVAMP and ASDIV.
- Prompt tuning on RMath-train raises RMath accuracy by about 5.3% on average across models, with Llama3 70B gaining the most (up to 31%, from 33.0% to 64.0%).
- Llama2 7B and 13B score 0% on RMath before tuning.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Prompt tune Llama2 7b on RMath using the problem-solving framework (ablation) | Llama2 7b · RMath | accuracy: 0 -> 18.5 | Helped |
| Prompt tune WizardMath 7b on RMath using the problem-solving framework (ablation) | WizardMath 7b · RMath | accuracy: 19.5 -> 24.0 | Helped |
| Prompt tune MetaMath 7b on RMath using the problem-solving framework (ablation) | MetaMath 7b · RMath | accuracy: 17.0 -> 20.0 | Helped |
| Prompt tune ToRA 7b on RMath using the problem-solving framework (ablation) | ToRA 7b · RMath | accuracy: 15.5 -> 21.0 | Helped |
| Prompt tune Llama2 13b on RMath using the problem-solving framework (ablation) | Llama2 13b · RMath | accuracy: 0 -> 23.0 | Helped |
| Prompt tune WizardMath 13b on RMath using the problem-solving framework (ablation) | WizardMath 13b · RMath | accuracy: 47.5 -> 31.0 | Hurt |
| Prompt tune MetaMath 13b on RMath using the problem-solving framework (ablation) | MetaMath 13b · RMath | accuracy: 32.0 -> 54.0 | Helped |
| Prompt tune ToRA 13b on RMath using the problem-solving framework (ablation) | ToRA 13b · RMath | accuracy: 26.0 -> 30.5 | Helped |
| Prompt tune Llama2 70b on RMath using the problem-solving framework (ablation) | Llama2 70b · RMath | accuracy: 39.5 -> 43.5 | Helped |
| Prompt tune Llama3 8b on RMath using the problem-solving framework (ablation) | Llama3 8b · RMath | accuracy: 23.0 -> 41.0 | Helped |
| Prompt tune Llama3 70b on RMath using the problem-solving framework (ablation) | Llama3 70b · RMath | accuracy: 33.0 -> 64.0 | Helped |
| Prompt tune WizardMath 70b on RMath using the problem-solving framework (ablation) | WizardMath 70b · RMath | accuracy: 54.5 -> 28.5 | Hurt |
Surprising findings
- Some models (WizardMath 13B, MetaMath 70B) perform worse on RMath after prompt tuning than before.
- ToRA 70B, which exceeds 80% on several standard math benchmarks, reaches only 31% on RMath.
Limitations
- Dataset is small, with only 200 problems.
- Problems were filtered to exclude commonsense and very hard problems, and multi-answer problems were reduced to single answers.
- Prompt-tuning gains are inconsistent, with some models degrading after tuning, and the explanation is only speculative.
Experimental setup
Datasets: RMath GSM8K MATH SVAMP ASDIV MAWPS TabMWP
Benchmarks: RMath GSM8K MATH SVAMP ASDIV MAWPS TabMWP
Metrics: accuracy
Baselines: Llama2 Llama3 WizardMath MetaMath ToRA DeepSeekMath
Builds on: MATH GSM8K ToRA MetaMath WizardMath
Closest papers by meaning
- Advancing Mathematical Reasoning in Language Models: The Impact of Problem-Solving Data, Data Synthesis Methods, and Training Stages (ICLR 2025 · similarity 0.91)
- MathFimer: Enhancing Mathematical Reasoning by Expanding Reasoning Steps through Fill-in-the-Middle Task (ICLR 2026 · similarity 0.90)
- UGMathBench: A Diverse and Dynamic Benchmark for Undergraduate-Level Mathematical Reasoning with Large Language Models (ICLR 2025 · similarity 0.90)
- Premise-Augmented Reasoning Chains Improve Error Identification in Math reasoning with LLMs (ICML 2025 · similarity 0.89)
- Evaluating Mathematical Reasoning Beyond Accuracy (AAAI 2025 · similarity 0.89)
- OMEGA: Can LLMs Reason Outside the Box in Math? Evaluating Exploratory, Compositional, and Transformative Generalization (NeurIPS 2025 · similarity 0.89)
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