# Complexity Agnostic Recursive Decomposition of Thoughts

arXiv: https://arxiv.org/abs/2601.04210 · HTML: https://mlsanity.com/paper/2601.04210/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 13 of its 14 references that are in the map.
- First posted on arXiv 10 Dec 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 13 of 13)

- [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)
- [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)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Decomposed Prompting: A Modular Approach for Solving Complex Tasks](https://mlsanity.com/paper/2210.02406/) (2022)
- [Token-Budget-Aware LLM Reasoning](https://mlsanity.com/paper/2412.18547/) (2024)
- [ADaPT: As-Needed Decomposition and Planning with Language Models](https://mlsanity.com/paper/2311.05772/) (2023)
- [Estimating Knowledge in Large Language Models Without Generating a Single Token](https://mlsanity.com/paper/2406.12673/) (2024)
- [On the Empirical Complexity of Reasoning and Planning in LLMs](https://mlsanity.com/paper/2404.11041/) (2024)
- [Accelerating Training Speed of Tiny Recursive Models with Curriculum Guided Adaptive Recursion](https://mlsanity.com/paper/2511.08653/) (2025)
- [ComplexityNet: Increasing LLM Inference Efficiency by Learning Task Complexity](https://mlsanity.com/paper/2312.11511/) (2023)

## Built on by (most cited first, 1 of 1)

- [VERIFY-RL: Verifiable Recursive Decomposition for Reinforcement Learning in Mathematical Reasoning](https://mlsanity.com/paper/2602.07559/) (2026)

## Abstract (arXiv)

Large language models often fail on multi-step reasoning due to fixed reasoning strategies that ignore problem specific difficulty. We introduce CARD (Complexity Agnostic Recursive Decomposition), a framework that predicts problem complexity before generation and adapts decomposition accordingly. Our system comprises MRCE (Multi-dimensional Reasoning Complexity Estimator), a 0.6B Qwen model predicting 30 fine-grained features from question text and a two-stage recursive solver: (1) hierarchical decomposition into K steps based on task profile and (2) per-step thought budget allocation (1, 5-9, or 10 thoughts) via recursive MRCE profiling. Evaluated on three reasoning models (Qwen3-0.6B, DeepSeek-R1-Distill-Qwen-1.5B, Qwen3-1.7B), CARD achieves 81.4% to 89.2% accuracy on GSM8K while reducing token cost by 1.88x to 2.40x compared to fixed decomposition baselines. On MATH-500, CARD reaches 75.1 to 86.8% accuracy using 1.71x to 5.74x fewer tokens. Our results demonstrate that preemptive complexity estimation enables both higher accuracy and significant efficiency gains.