Think Twice Before You Write -- an Entropy-based Decoding Strategy to Enhance LLM Reasoning

Chain-of-thought (CoT) reasoning can improve LLM performance, but its benefits vary across tasks, models, and individual queries. On some tasks, CoT provides marginal or negative accuracy gains while substantially increasing token consumption. We investigate whether early decoding dynamics can help identify when explicit reasoning is useful. Our analysis shows that tasks with larger CoT gains tend to exhibit decreasing early-stage entropy, while low-gain tasks more often show oscillatory or increasing trajectories. These patterns motivate an empirical regime interpretation of decoding behavior. We propose EDRM (Entropy Dynamics-based Reasoning Manifold), a lightweight routing framework whose default heuristic requires no router training. EDRM summarizes early entropy trajectories with a compact, interpretable representation and selects among Direct, Standard, and CoT decoding. Across 15 benchmarks and 7 LLMs, its global and instance-level variants offer 16--55% token savings at comparable accuracy. The Full instance-level configuration combines routing with a short Direct fallback branch; our heuristic-router ablation reports up to 4.9 percentage points of additional accuracy from oracle answer selection over routing without fallback. These results support selective reasoning based on early decoding signals and demonstrate the potential of entropy-based control for efficient LLM inference.

Large language models (LLMs) achieve remarkable generative performance, yet their output quality is dependent on the decoding strategy. While sampling-based methods (e.g., top-k, nucleus) and search-and-select based methods (e.g., beam search, best-of-n, majority voting) can improve upon greedy decoding, both approaches suffer from limitations: sampling generally commits to a single path, while search often expends excessive computation regardless of task complexity. To address these, we introduce Entropy-informed decoding (EDEN), a plug-and-play, model-agnostic decoding framework that adaptively allocates computation based on the model's own uncertainty, approximating higher-width beam search with fewer expansions. At each generation step, EDEN estimates the entropy of the output token distribution and adjusts the branching factor monotonically with the entropy, expanding more candidates in high-entropy regions and following a greedier path in low-entropy regions, improving token efficiency. Experiments across complex tasks, including mathematical reasoning, code generation, and scientific questions, demonstrate that EDEN consistently improves output quality over existing decoding strategies, achieving better accuracy-expansion trade-offs than fixed-width beam search. By treating next-token selection as a noisy maximisation problem, we prove that branching factors monotone in entropy are guaranteed to find better (i.e. more probable) continuations than any fixed branching factor within the same total expansion budget, and derive explicit regret rates characterising the benefit of the adaptive allocation.

Speculative decoding (SD) accelerates large language model (LLM) inference by using a lightweight draft model to propose tokens and a stronger target model to verify them. However, standard SD is mainly designed for acceleration, and its output quality is typically constrained by the target model. In this work, we propose Entropy-Aware Speculative Decoding (EASD), a lightweight and training-free extension of SD that improves reasoning quality through token-level entropy-guided rejection. EASD detects cases where both draft and target models exhibit high uncertainty while strongly overlapping in their top predictions. In such uncertain-agreement cases, EASD rejects the aligned token and resamples from the target distribution, preventing low-confidence errors from propagating. Experiments on challenging reasoning benchmarks show that EASD consistently improves accuracy over standard SD and reward-guided variants while maintaining comparable inference efficiency. Notably, EASD can surpass the standalone performance of the target model, suggesting that speculative decoding can serve not only as an acceleration method but also as an effective mechanism for improving reasoning quality. The code is available at https://github.com/ECNU-Text-Computing/EASD.