# AdaR: A Framework for Equipping LLMs with Adaptive Reasoning

arXiv: https://arxiv.org/abs/2510.04617 · HTML: https://mlsanity.com/paper/2510.04617/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 25 of its 36 references that are in the map.
- First posted on arXiv 6 Oct 2025.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 25 of 25)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [TheoremQA: A Theorem-driven Question Answering dataset](https://mlsanity.com/paper/2305.12524/) (2023)
- [Orca-Math: Unlocking the potential of SLMs in Grade School Math](https://mlsanity.com/paper/2402.14830/) (2024)
- [MathScale: Scaling Instruction Tuning for Mathematical Reasoning](https://mlsanity.com/paper/2403.02884/) (2024)
- [DART-Math: Difficulty-Aware Rejection Tuning for Mathematical Problem-Solving](https://mlsanity.com/paper/2407.13690/) (2024)
- [Atom of Thoughts for Markov LLM Test-Time Scaling](https://mlsanity.com/paper/2502.12018/) (2025)
- [Beyond Pass@1: Self-Play with Variational Problem Synthesis Sustains RLVR](https://mlsanity.com/paper/2508.14029/) (2025)
- [MuggleMath: Assessing the Impact of Query and Response Augmentation on Math Reasoning](https://mlsanity.com/paper/2310.05506/) (2023)
- [A Comprehensive Survey on Data Augmentation](https://mlsanity.com/paper/2405.09591/) (2024)
- [Quagmires in SFT-RL Post-Training: When High SFT Scores Mislead and What to Use Instead](https://mlsanity.com/paper/2510.01624/) (2025)
- [Evaluating Mathematical Reasoning Across Large Language Models: A Fine-Grained Approach](https://mlsanity.com/paper/2503.10573/) (2025)

## Abstract (arXiv)

Mathematical reasoning is a primary indicator of large language models (LLMs) intelligence. However, existing LLMs exhibit failures in robustness and generalization. This paper attributes these deficiencies to spurious reasoning, wherein generated reasoning traces are driven by superficial correlations, leading models to blindly reproduce memorized patterns from the training data. To address this challenge, we propose the AdaR framework to equip LLMs with adaptive reasoning, wherein models establish correct correlations between query templates and reasoning processes. AdaR automatically synthesizes logically equivalent queries by varying variable values and trains models using Reinforcement Learning with Verifiable Rewards (RLVR) to penalize spurious logic while encouraging adaptive logic. To ensure data quality, we extract the problem-solving logic from the original query, generate the corresponding answer through code execution, and then apply a sanity check. Experimental results demonstrate that AdaR achieves substantial improvements in mathematical reasoning while maintaining high data efficiency. Furthermore, even advanced LLMs still exhibit deficiencies in robustness and generalization, which our work effectively mitigates. Our project is available at https://github.com/NJUNLP/AdaR.