Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning

• URL: http://arxiv.org/abs/2506.06877v2
• Date: Tue, 24 Jun 2025 13:55:38 GMT
• Title: Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning
• Authors: Jiaxing Guo, Wenjie Yang, Shengzhong Zhang, Tongshan Xu, Lun Du, Da Zheng, Zengfeng Huang,
• Abstract summary: We introduce MathOlympiadEval, a new dataset with fine-grained annotations, which reveals a significant gap between LLMs' answer correctness and their low process correctness.<n>Existing automated methods like LLM-as-a-judge struggle to reliably detect these reasoning flaws.<n>We propose ParaStepVerifier, a novel methodology for meticulous, step-by-step verification of mathematical solutions.
• Score: 35.142294794883455
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Outcome-rewarded Large Language Models (LLMs) have demonstrated remarkable success in mathematical problem-solving. However, this success often masks a critical issue: models frequently achieve correct answers through fundamentally unsound reasoning processes, a phenomenon indicative of reward hacking. We introduce MathOlympiadEval, a new dataset with fine-grained annotations, which reveals a significant gap between LLMs' answer correctness and their low process correctness. Existing automated methods like LLM-as-a-judge struggle to reliably detect these reasoning flaws. To address this, we propose ParaStepVerifier, a novel methodology for meticulous, step-by-step verification of mathematical solutions. ParaStepVerifier identifies incorrect reasoning steps. Empirical results demonstrate that ParaStepVerifier substantially improves the accuracy of identifying flawed solutions compared to baselines, especially for complex, multi-step problems. This offers a more robust path towards evaluating and training LLMs with genuine mathematical reasoning.

Related papers

• FINEREASON: Evaluating and Improving LLMs' Deliberate Reasoning through Reflective Puzzle Solving [90.88021670297664]
  FINEREASON is a logic-puzzle benchmark for evaluation of large language models' reasoning capabilities.<n>We introduce two tasks: state checking, and state transition, for a comprehensive evaluation of how models assess the current situation and plan the next move.<n>We show that models trained on our state checking and transition data demonstrate gains in math reasoning by up to 5.1% on GSM8K.
  arXiv  Detail & Related papers  (2025-02-27T16:23:25Z)
• Step-KTO: Optimizing Mathematical Reasoning through Stepwise Binary Feedback [94.25162866972077]
  Step-KTO is a training framework that combines process-level and outcome-level binary feedback.<n>Our experiments show that Step-KTO significantly improves both final answer accuracy and the quality of intermediate reasoning steps.
  arXiv  Detail & Related papers  (2025-01-18T15:38:03Z)
• BoostStep: Boosting mathematical capability of Large Language Models via improved single-step reasoning [83.03531832811386]
  BoostStep is a method that enhances reasoning accuracy through step-aligned ICL examples.<n>It integrates seamlessly with chain-of-thought (CoT) and tree search algorithms.<n>It improves DeepSeek-R1-671B's performance on AIME by 2.2%, leveraging simple examples only from the MATH dataset.
  arXiv  Detail & Related papers  (2025-01-06T18:59:13Z)
• Subtle Errors in Reasoning: Preference Learning via Error-injected Self-editing [59.405145971637204]
  We propose a novel preference learning framework called eRror-Injected Self-Editing (RISE)<n>RISE injects predefined subtle errors into pivotal tokens in reasoning or steps to construct hard pairs for error mitigation.<n>Experiments validate the effectiveness of RISE, with preference learning on Qwen2-7B-Instruct yielding notable improvements of 3.0% on GSM8K and 7.9% on MATH with only 4.5K training samples.
  arXiv  Detail & Related papers  (2024-10-09T07:43:38Z)
• Improving LLM Reasoning through Scaling Inference Computation with Collaborative Verification [52.095460362197336]
  Large language models (LLMs) struggle with consistent and accurate reasoning. LLMs are trained primarily on correct solutions, reducing their ability to detect and learn from errors. We propose a novel collaborative method integrating Chain-of-Thought (CoT) and Program-of-Thought (PoT) solutions for verification.
  arXiv  Detail & Related papers  (2024-10-05T05:21:48Z)
• S^3cMath: Spontaneous Step-level Self-correction Makes Large Language Models Better Mathematical Reasoners [23.713779973116733]
  Self-correction is a method that can stimulate the potential reasoning abilities of large language models (LLMs)<n>We propose S$3$c-Math, which are able to perform Spontaneous Step-level Self-correction for Mathematical reasoning.
  arXiv  Detail & Related papers  (2024-09-03T01:40:21Z)
• DOP: Diagnostic-Oriented Prompting for Large Language Models in Mathematical Correction [21.511831985975473]
  Math world problems correction(MWPC) is a novel task dedicated to rectifying reasoning errors in the process of solving mathematical problems. We address two key objectives: Distinguishing between mathematical reasoning and error correction. We propose a novel method called diagnostic-oriented promping(DOP) aimed at facilitating LLMs to excel in error correction.
  arXiv  Detail & Related papers  (2024-05-20T15:13:22Z)
• AlphaMath Almost Zero: Process Supervision without Process [6.318873143509028]
  We propose an innovative framework, AlphaMath, that bypasses the need for process annotations by leveraging Monte Carlo Tree Search (MCTS) This framework focuses on unleashing the potential of a well-pretrained LLM to autonomously enhance its mathematical reasoning. The experimental results on both in-domain and out-of-domain datasets demonstrate that even without GPT-4 or human-annotated process supervision, our AlphaMath framework achieves comparable or superior results to previous state-of-the-art methods.
  arXiv  Detail & Related papers  (2024-05-06T15:20:30Z)
• Distilling Algorithmic Reasoning from LLMs via Explaining Solution Programs [2.3020018305241337]
  Distilling explicit chain-of-thought reasoning paths has emerged as an effective method for improving the reasoning abilities of large language models. We propose a novel approach to distill reasoning abilities from LLMs by leveraging their capacity to explain solutions. Our experiments demonstrate that learning from explanations enables the Reasoner to more effectively guide program implementation by a Coder.
  arXiv  Detail & Related papers  (2024-04-11T22:19:50Z)
• SelfCheck: Using LLMs to Zero-Shot Check Their Own Step-by-Step Reasoning [55.76083560152823]
  SelfCheck is a general-purpose zero-shot verification schema for recognizing errors in step-by-step reasoning. We test SelfCheck on three datasets (GSM8K, MathQA, and MATH) and find that it successfully recognizes errors and, in turn, increases final answer accuracies.
  arXiv  Detail & Related papers  (2023-08-01T10:31:36Z)
• SatLM: Satisfiability-Aided Language Models Using Declarative Prompting [68.40726892904286]
  We propose a new satisfiability-aided language modeling (SatLM) approach for improving the reasoning capabilities of large language models (LLMs) We use an LLM to generate a declarative task specification rather than an imperative program and leverage an off-the-shelf automated theorem prover to derive the final answer. We evaluate SATLM on 8 different datasets and show that it consistently outperforms program-aided LMs in the imperative paradigm.
  arXiv  Detail & Related papers  (2023-05-16T17:55:51Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.