# Compositional Reasoning in Language Models under Reinforcement Learning Post-Training

arXiv: https://arxiv.org/abs/2609.19465 · HTML: https://mlsanity.com/paper/2609.19465/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 12 of its 29 references that are in the map.
- First posted on arXiv 16 Sep 2026.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 12 of 12)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [Olmo 3](https://mlsanity.com/paper/2512.13961/) (2025)
- [From f(x) and g(x) to f(g(x)): LLMs Learn New Skills in RL by Composing Old Ones](https://mlsanity.com/paper/2509.25123/) (2025)
- [On Provable Length and Compositional Generalization](https://mlsanity.com/paper/2402.04875/) (2024)
- [Composition-RL: Compose Your Verifiable Prompts for Reinforcement Learning of Large Language Models](https://mlsanity.com/paper/2602.12036/) (2026)
- [Can LLMs Reason Structurally? Benchmarking via the Lens of Data Structures](https://mlsanity.com/paper/2505.24069/) (2025)
- [Learning Composable Chains-of-Thought](https://mlsanity.com/paper/2505.22635/) (2025)

## Abstract (arXiv)

Compositional reasoning is critical for real-world problem solving: since training data is necessarily limited, models must generalize by composing learned skills in new ways. While post-training methods such as reinforcement learning (RL) have substantially improved the reasoning abilities of language models (LMs), their effects on compositional reasoning remain less well understood. We propose a dependency-graph framework to formalize compositional reasoning, yielding three levels of compositionality with increasing complexity. Empirically, we instantiate this framework with data-structure tasks, which provide deterministic reward computation and clear compositional structure. We find a consistent decomposed-to-composed asymmetry: decomposed-skill training does not reliably transfer to composed tasks, whereas composed-task training transfers more readily back to decomposed tasks. We provide theoretical explanation for this asymmetry, and further evaluate compositional generalization under length extrapolation, structural distribution shift, and transfer to tasks requiring unseen skills. Finally, we present a pilot study on real-world tool-calling benchmarks, showing preliminary evidence that the decomposed-to-composed asymmetry can extend to practical settings.