# Learning Composable Chains-of-Thought

arXiv: https://arxiv.org/abs/2505.22635 · HTML: https://mlsanity.com/paper/2505.22635/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 46 of its 72 references that are in the map.
- First posted on arXiv 28 May 2025.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 30 of 46)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [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)
- [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)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [Merging Models with Fisher-Weighted Averaging](https://mlsanity.com/paper/2111.09832/) (2021)
- [Decomposed Prompting: A Modular Approach for Solving Complex Tasks](https://mlsanity.com/paper/2210.02406/) (2022)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [COGS: A Compositional Generalization Challenge Based on Semantic Interpretation](https://mlsanity.com/paper/2010.05465/) (2020)
- [To CoT or not to CoT? Chain-of-thought helps mainly on math and symbolic reasoning](https://mlsanity.com/paper/2409.12183/) (2024)
- [Chain of Thought Empowers Transformers to Solve Inherently Serial Problems](https://mlsanity.com/paper/2402.12875/) (2024)
- [From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step](https://mlsanity.com/paper/2405.14838/) (2024)
- [The Unreliability of Explanations in Few-shot Prompting for Textual Reasoning](https://mlsanity.com/paper/2205.03401/) (2022)
- [CoT-Valve: Length-Compressible Chain-of-Thought Tuning](https://mlsanity.com/paper/2502.09601/) (2025)
- [Diverse Demonstrations Improve In-context Compositional Generalization](https://mlsanity.com/paper/2212.06800/) (2022)
- [Easy-to-Hard Generalization: Scalable Alignment Beyond Human Supervision](https://mlsanity.com/paper/2403.09472/) (2024)
- [Compositional Semantic Parsing with Large Language Models](https://mlsanity.com/paper/2209.15003/) (2022)
- [Complementary Explanations for Effective In-Context Learning](https://mlsanity.com/paper/2211.13892/) (2022)

## Built on by (most cited first, 3 of 3)

- [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)
- [From Implicit to Explicit: Token-Efficient Logical Supervision for Mathematical Reasoning in LLMs](https://mlsanity.com/paper/2601.03682/) (2026)
- [Compositional Reasoning in Language Models under Reinforcement Learning Post-Training](https://mlsanity.com/paper/2609.19465/) (2026)

## Abstract (arXiv)

A common approach for teaching large language models (LLMs) to reason is to train on chain-of-thought (CoT) traces of in-distribution reasoning problems, but such annotated data is costly to obtain for every problem of interest. We want reasoning models to generalize beyond their training distribution, and ideally to generalize compositionally: combine atomic reasoning skills to solve harder, unseen reasoning tasks. We take a step towards compositional generalization of reasoning skills when addressing a target compositional task that has no labeled CoT data. We find that simply training models on CoT data of atomic tasks leads to limited generalization, but minimally modifying CoT formats of constituent atomic tasks to be composable can lead to improvements. We can train "atomic CoT" models on the atomic tasks with Composable CoT data and combine them with multitask learning or model merging for better zero-shot performance on the target compositional task. Such a combined model can be further bootstrapped on a small amount of compositional data using rejection sampling fine-tuning (RFT). Results on string operations and natural language skill compositions show that training LLMs on Composable CoT outperforms multitask learning and continued fine-tuning baselines within a given training data budget.