Think or Not? Exploring Thinking Efficiency in Large Reasoning Models via an Information-Theoretic Lens

TL;DR

Think or Not investigates thinking efficiency in large reasoning models through an information-theoretic lens. It defines $InfoBias$ and $InfoGain$ to quantify trajectory divergence from ideal reasoning and stepwise information contribution, and demonstrates that longer reasoning chains often incur semantic drift with diminishing gains. The work introduces an entropy-based Adaptive Think that halts reasoning when average entropy over the answer space falls below a tunable threshold $\alpha$, yielding both accuracy improvements and substantial token reductions across diverse benchmarks. Through extensive experiments with multiple models and tasks, the approach shows a practical path to balance reasoning depth and computational cost, improving cost-efficiency without sacrificing reliability. These contributions provide a framework for adaptive, confidence-aware reasoning in large language models.

Abstract

The recent rise of Large Reasoning Models (LRMs) has significantly improved multi-step reasoning performance, but often at the cost of generating excessively long reasoning chains. This paper revisits the efficiency of such reasoning processes through an information-theoretic lens, revealing a fundamental trade-off between reasoning length and semantic efficiency. We propose two metrics, InfoBias and InfoGain, to quantify divergence from ideal reasoning paths and stepwise information contribution, respectively. Empirical analyses show that longer reasoning chains tend to exhibit higher information bias and diminishing information gain, especially for incorrect answers. Motivated by these findings, we introduce an entropy-based Adaptive Think strategy that dynamically halts reasoning once confidence is sufficiently high, improving efficiency while maintaining competitive accuracy. Compared to the Vanilla Think approach (default mode), our strategy yields a 1.10% improvement in average accuracy and a 50.80% reduction in token usage on QwQ-32B across six benchmark tasks spanning diverse reasoning types and difficulty levels, demonstrating superior efficiency and reasoning performance. These results underscore the promise of entropy-based methods for enhancing both accuracy and cost-effiiciency in large language model deployment.

Figures (8)

• Figure 1: Understanding thinking inefficiency via Shannon & Weaver’s Communication Model. (a) Technical Level: On the GSM8K dataset, incorrect answers exhibit higher InfoBias and longer token lengths, suggesting that longer reasoning does not necessarily lead to better outcomes. (b) Semantic Level: The InfoGain rate shows a nonlinear decline as the thinking progresses, indicating diminishing contribution to entropy reduction over the final answer space. (c) Pragmatic Level: Results across various models and benchmarks show longer reasoning yields diminishing returns and may even reduce final accuracy. Detailed calculation methods and analysis are provided in \ref{['sec.quantifying']}.
• Figure 2: Normalized InfoBias per token as a function of average reasoning length for different models on the GSM8K dataset. Blue and red points represent instances with correct and incorrect answers, respectively, with density estimates of tokens and InfoBias shown on the top and right.
• Figure 3: Uncertainty dynamics across different reasoning benchmarks for QwQ-32B. Each set includes two subplots: (1) entropy of the answer distribution vs. normalized reasoning steps, and (2) model-predicted probability of the correct answer over the same steps. Blue/orange lines denote correct/incorrect predictions; solid/dashed lines correspond to Vanilla Think and No-Think. Shaded areas mark the average token proportion used in No-Think mode. Step-wise analysis shows that models often exhibit early intuitive confidence in correct answers, even before reasoning starts. As reasoning unfolds, uncertainty decreases and confidence grows in task-specific ways.
• Figure 4: An illustration of four thinking modes on a sample question from the GSM8K dataset.
• Figure 5: Proportion of think vs. no-think samples in Gate Think mode and corresponding token usage under Adaptive Think.