Complexity Agnostic Recursive Decomposition of Thoughts

TL;DR

This paper introduces CARD, a framework that predicts problem complexity to adaptively decompose reasoning tasks, improving accuracy and efficiency in large language models' multi-step reasoning.

Contribution

CARD is the first system to predict problem complexity and adapt decomposition strategies accordingly, enhancing reasoning performance and reducing token costs.

Findings

Achieves 81.4% to 89.2% accuracy on GSM8K

Reduces token cost by 1.88x to 2.40x compared to fixed methods

Reaches 75.1% to 86.8% accuracy on MATH-500 with fewer tokens

Abstract

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.