Making Mathematical Reasoning Adaptive

• URL: http://arxiv.org/abs/2510.04617v2
• Date: Mon, 13 Oct 2025 03:08:12 GMT
• Title: Making Mathematical Reasoning Adaptive
• Authors: Zhejian Lai, Xiang Geng, Zhijun Wang, Yang Bai, Jiahuan Li, Rongxiang Weng, Jingang Wang, Xuezhi Cao, Xunliang Cai, Shujian Huang,
• Abstract summary: We propose the AdaR framework to enable adaptive reasoning in large language models (LLMs)<n>AdaR synthesizes logically equivalent queries by varying variable values, and trains models with RLVR on these data to penalize spurious logic.<n> Experimental results demonstrate that AdaR improves robustness and generalization, achieving substantial improvement in mathematical reasoning.
• Score: 61.45161826629692
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Mathematical reasoning is a primary indicator of large language models (LLMs) intelligence. However, existing LLMs exhibit failures of robustness and generalization. This paper attributes these deficiencies to spurious reasoning, i.e., producing answers from superficial features. To address this challenge, we propose the AdaR framework to enable adaptive reasoning, wherein models rely on problem-solving logic to produce answers. AdaR synthesizes logically equivalent queries by varying variable values, and trains models with RLVR on these data to penalize spurious logic while encouraging adaptive logic. To improve data quality, we extract the problem-solving logic from the original query and generate the corresponding answer by code execution, then apply a sanity check. Experimental results demonstrate that AdaR improves robustness and generalization, achieving substantial improvement in mathematical reasoning while maintaining high data efficiency. Analysis indicates that data synthesis and RLVR function in a coordinated manner to enable adaptive reasoning in LLMs. Subsequent analyses derive key design insights into the effect of critical factors and the applicability to instruct LLMs. Our project is available at https://github.com/NJUNLP/AdaR.

Related papers

• Are More Tokens Rational? Inference-Time Scaling in Language Models as Adaptive Resource Rationality [1.5994376682356057]
  We introduce a Variable Attribution Task in which models infer which variables determine outcomes given candidate variables, input-output trials, and predefined logical functions.<n>Both models exhibit a transition from brute-force to analytic strategies as complexity increases.<n>These findings suggest that models can adjust their reasoning behavior in response to task complexity, even without explicit cost-based reward.
  arXiv  Detail & Related papers  (2026-02-10T22:07:05Z)
• Training LLMs with LogicReward for Faithful and Rigorous Reasoning [75.30425553246177]
  We propose LogicReward, a reward system that guides model training by enforcing step-level logical correctness with a theorem prover.<n>An 8B model trained on data constructed with LogicReward surpasses GPT-4o and o4-mini by 11.6% and 2% on natural language inference and logical reasoning tasks.
  arXiv  Detail & Related papers  (2025-12-20T03:43:02Z)
• Reasoning Pattern Matters: Learning to Reason without Human Rationales [27.684703630371043]
  Large Language Models (LLMs) have demonstrated remarkable reasoning capabilities under the widely adopted SFT+RLVR paradigm.<n>This paper investigates when and how rationale annotation costs can be substantially reduced without compromising reasoning performance.
  arXiv  Detail & Related papers  (2025-10-14T15:34:38Z)
• Pushing LLMs to Their Logical Reasoning Bound: The Role of Data Reasoning Intensity [59.27594125465172]
  We introduce Data Reasoning Intensity (DRI), a novel metric that quantifies the latent logical reasoning complexity of samples.<n>We then introduce a re-cognizing optimization strategy that systematically enhances the logical reasoning intensity of training data.
  arXiv  Detail & Related papers  (2025-09-29T14:20:04Z)
• Synthesis by Design: Controlled Data Generation via Structural Guidance [7.938713951512933]
  We propose to extract structural information with generated problem-solving code from mathematical reasoning.<n>Our approach produces 39K problems with labeled intermediate steps and a 6.1K-problem benchmark of higher difficulty.<n>Results on our benchmark show that model performance declines as reasoning length increases.
  arXiv  Detail & Related papers  (2025-06-09T11:38:23Z)
• Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models [49.61246073215651]
  Large Language Models (LLMs) have demonstrated remarkable capabilities in complex tasks.<n>Recent advancements in OpenAI o1 and DeepSeek-R1 have further improved performance in System-2 reasoning domains.<n>However, they also introduce significant computational overhead due to verbose and redundant outputs.
  arXiv  Detail & Related papers  (2025-03-20T17:59:38Z)
• JustLogic: A Comprehensive Benchmark for Evaluating Deductive Reasoning in Large Language Models [51.99046112135311]
  We introduce JustLogic, a synthetically generated deductive reasoning benchmark for rigorous evaluation of Large Language Models (LLMs)<n>JustLogic is highly complex, capable of generating a diverse range of linguistic patterns, vocabulary, and argument structures.<n>Our experimental results reveal that (i) state-of-the-art (SOTA) reasoning LLMs perform on par or better than the human average but significantly worse than the human ceiling.
  arXiv  Detail & Related papers  (2025-01-24T15:49:10Z)
• Critical-Questions-of-Thought: Steering LLM reasoning with Argumentative Querying [0.3659498819753633]
  State-of-the-art Large Language models (LLMs) continue to struggle when performing logical and mathematical reasoning.<n>This paper makes use of the notion of critical questions from the literature on argumentation theory, focusing in particular on Toulmin's model of argumentation.<n>We show that employing these critical questions can improve the reasoning capabilities of LLMs.
  arXiv  Detail & Related papers  (2024-12-19T18:51:30Z)
• LogicAsker: Evaluating and Improving the Logical Reasoning Ability of Large Language Models [63.14196038655506]
  We introduce LogicAsker, a novel approach for evaluating and enhancing the logical reasoning capabilities of large language models (LLMs) Our methodology reveals significant gaps in LLMs' learning of logical rules, with identified reasoning failures ranging from 29% to 90% across different models. We leverage these findings to construct targeted demonstration examples and fine-tune data, notably enhancing logical reasoning in models like GPT-4o by up to 5%.
  arXiv  Detail & Related papers  (2024-01-01T13:53:53Z)
• Abstract Meaning Representation-Based Logic-Driven Data Augmentation for Logical Reasoning [27.224364543134094]
  We introduce a novel logic-driven data augmentation approach, AMR-LDA.<n> AMR-LDA converts the original text into an Abstract Meaning Representation (AMR) graph.<n>The modified AMR graphs are subsequently converted back into text to create augmented data.
  arXiv  Detail & Related papers  (2023-05-21T23:16:26Z)

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.