8/N More qualitatively, in the solution, we see (in cyan) references (“cheatsheet”) and keywords from the abstraction being used meaningfully in the reasoning trace of the solution generator model, showcasing that strategies can be elicited through abstractions.

7/N We additionally perform analysis of the abstractions and solutions that RLAD generates. Here, RLAD produces solutions with greater semantic diversity across different abstractions (left) and higher adherence of the solution to the abstraction (right) compared to baselines.

6/N Furthermore, the abstraction generator shows weak-to-strong generalization, where if we swap out the solution generator with o4-mini (with a 24K token budget), conditioning on abstractions consistently yields higher pass@k accuracy compared to question-only conditioning.

5/N On AIME 2025, as inference compute grows, efficiency improves when more budget is devoted to abstraction over solution generation—robust across all normalization offsets 𝑘₀. Local errors can be corrected with retries, but fresh abstractions help once retries are exhausted!

4/N We evaluate RLAD on Math Reasoning on benchmarks such as AIME 2025, DeepScaleR Hard, AMC 2023, achieving consistent accuracy gains over the base Qwen 3-1.7B model and DAPO. Performance is measured without (w/o), with (w/), and with the best abstraction among 4 samples.

3/N We instantiate a two-player RL framework:
1. An Abstraction Generator proposes reasoning strategies.
2. A Solution Generator uses that strategy to produce an answer.
The reward corresponds to the average success rate, leading the first player to find useful abstractions.

2/N Reasoning requires going beyond pattern-matching and recall to the execution of algorithmic procedures. RLVR aims to induce this, but models often underthink—switching logic midstream. Instead, can we optimize “breadth", training models to explore a wider array of strategies?

🚨🚨New Paper: Training LLMs to Discover Abstractions for Solving Reasoning Problems

Introducing RLAD, a two-player RL framework for LLMs to discover 'reasoning abstractions'—natural language hints that encode procedural knowledge for structured exploration in reasoning.🧵⬇️