Complexity Agnostic Recursive Decomposition of Thoughts

TL;DR

CARD tackles the inefficiency of fixed recursive decompositions in multi-step reasoning by introducing a preemptive, complexity-aware framework. It combines MRCE, a 0.6B Qwen-based estimator predicting 30 features to compute a complexity score $ ho$, with a two-stage adaptive solver that allocates step depth and per-step thought budgets based on sub-problem difficulty. The approach yields higher GSM8K and MATH-500 accuracy while substantially reducing token usage across several small models, outperforming fixed-decomposition baselines and reactive methods. This complexity-driven paradigm offers practical efficiency gains and lays groundwork for domain-adaptive, resource-aware reasoning in LLM systems.

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.

Figures (2)

• Figure 1: CARD framework architecture and execution flow.
• Figure 2: MRCE training convergence and feature prediction accuracy.