# AbstRaL: Augmenting LLMs' Reasoning by Reinforcing Abstract Thinking

arXiv: https://arxiv.org/abs/2506.07751 · HTML: https://mlsanity.com/paper/2506.07751/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 55 of its 74 references that are in the map.
- First posted on arXiv 9 Jun 2025.

## Placed in

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

## Builds on (most cited first, 30 of 55)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [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)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [AGIEval: A Human-Centric Benchmark for Evaluating Foundation Models](https://mlsanity.com/paper/2304.06364/) (2023)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [Dynamic Prompt Learning via Policy Gradient for Semi-structured Mathematical Reasoning](https://mlsanity.com/paper/2209.14610/) (2022)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [Data Contamination: From Memorization to Exploitation](https://mlsanity.com/paper/2203.08242/) (2022)
- [Fixing Data Augmentation to Improve Adversarial Robustness](https://mlsanity.com/paper/2103.01946/) (2021)

## Built on by (most cited first, 4 of 4)

- [RL for Reasoning by Adaptively Revealing Rationales](https://mlsanity.com/paper/2506.18110/) (2025)
- [Goldilocks RL: Tuning Task Difficulty to Escape Sparse Rewards for Reasoning](https://mlsanity.com/paper/2602.14868/) (2026)
- [Decoupling Understanding from Reasoning via Problem Space Mapping for Small-Scale Model Reasoning](https://mlsanity.com/paper/2508.10019/) (2025)
- [Reasoning over Video: Evaluating How MLLMs Extract, Integrate, and Reconstruct Spatiotemporal Evidence](https://mlsanity.com/paper/2603.13091/) (2026)

## Abstract (arXiv)

Recent studies have shown that large language models (LLMs), especially smaller ones, often lack robustness in grade school math (GSM) reasoning. In particular, they tend to experience performance drops when faced with distribution shifts, such as changes to numerical or nominal variables, or insertions of distracting clauses. A possible strategy to address this involves generating synthetic data to further "instantiate" reasoning problems on potential variations. In this work, we instead focus on the strategy of "abstracting" reasoning problems. This not only helps counteract distribution shifts but also facilitates the connection to symbolic tools for deriving solutions. Focusing on GSM, we find that this abstraction process is better acquired through reinforcement learning (RL) than just supervised fine-tuning, which often fails to produce faithful abstractions. Our method, AbstRaL -- which promotes abstract reasoning in LLMs using RL on granular abstraction data -- significantly mitigates performance degradation on recent GSM perturbation benchmarks. Besides, improving GSM robustness via AbstRaL is shown to also implicitly benefit LLMs' capabilities on OOD mathematical and general reasoning tasks, indicating that abstract thinking broadly enables better generalizability.