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AbstRaL: Augmenting LLMs' Reasoning by Reinforcing Abstract Thinking

ICLR 2026 · Large language models › Reasoning and chain of thought · approach: Routing, pruning and distillation for reasoning

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Proposes AbstRaL, which teaches LLMs to abstract GSM math problems into symbolic variables and derivations via SFT followed by GRPO with model-free symbolic-distance and answer rewards, improving robustness to numeric/name perturbations and distractors.

Problem

LLMs, especially small ones, are brittle on grade-school math under distribution shifts such as changed numbers/names or added distracting clauses.

Approach

Train LLMs to produce abstract answers using symbolic placeholders (in0, out0) over granular, socratic sub-question decomposition, then retrieve the abstraction via regex and solve with SymPy; RL uses model-free rewards (answer correctness plus edit-distance-based symbolic similarity to gold abstraction) rather than a learned reward model.

Key results

• On Qwen2.5-0.5B-Instruct, AbstRaL reaches 44.6% on GSM-Symbolic Vary Both versus 34.0% for CoT-8S, with Delta of -1.27% versus 10.6%.
• On Qwen2.5-Math-7B-Instruct, AbstRaL scores 89.1% on GSM-Plus numerical perturbations and 82.3% on Distract, versus 84.1% and 76.3% for CoT-8S.
• AbstRaL improves zero-shot OOD results, e.g., Qwen2.5-0.5B-Instruct on SAT-Math rises to 62.5 from 46.9 for Ori-SFT and BBH to 26.3 from 21.0.

Surprising findings

• Removing the oracle-based condition recognition (using the LLM itself) causes only minor performance loss, suggesting gains come from abstraction learning rather than tool use.
• SFT-only abstraction methods (CoA, AoT) often underperform plain CoT on robustness, and CoT-RL can fall below the original checkpoints on OOD math tasks.

Limitations

• Evaluated only on GSM-style math; generality to other domains is inferred from zero-shot results rather than tested with abstraction training.
• Relies on a 70B oracle LLM and few-shot prompting to rewrite training data, with a 13% filtering loss.
• Some results on large models are not consistently superior (e.g., Origin 100 accuracy lower than CoT for some 7B/8B models).

Experimental setup

Datasets: GSM8K socratic GSM-Symbolic GSM-Plus

Benchmarks: GSM-Symbolic GSM-Plus MATH Minerva MATH SAT-Math AIME24 SVAMP ASDiv MAWPS Gaokao-2023 TABMWP College-Math

Metrics: accuracy relative drop (Delta) standard deviation over rounds

Baselines: CoT-8S PoT-8S CoT-RL CoA AoT SyReLM

Builds on: GRPO socratic CoT program-of-thought chain-of-abstraction

Closest papers by meaning

• GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models (ICLR 2025 · similarity 0.91)
• Meaningful Learning: Enhancing Abstract Reasoning in Large Language Models via Generic Fact Guidance (NeurIPS 2024 · similarity 0.90)
• Beyond Accuracy: Dissecting Mathematical Reasoning for LLMs Under Reinforcement Learning (NeurIPS 2025 · similarity 0.90)
• Frugal LMs Trained to Invoke Symbolic Solvers Achieve Parameter-Efficient Arithmetic Reasoning (AAAI 2024 · similarity 0.90)
• MathSmith: Towards Extremely Hard Mathematical Reasoning by Forging Synthetic Problems with a Reinforced Policy (AAAI 2026 · similarity 0.90)
• General-Reasoner: Advancing LLM Reasoning Across All Domains (NeurIPS 2025 · similarity 0.90)