Selective Regenerative Decoding: Trajectory-Level Intervention for Inference-Time Reasoning

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.

Scaling inference-time compute for Large Language Models (LLMs) has unlocked unprecedented reasoning capabilities. However, existing inference-time scaling methods typically rely on inefficient and suboptimal discrete search algorithms or trial-and-error prompting to improve the online policy. In this paper, we propose $\nabla$-Reasoner, an iterative generation framework that integrates differentiable optimization over token logits into the decoding loop to refine the policy on the fly. Our core component, Differentiable Textual Optimization (DTO), leverages gradient signals from both the LLM's likelihood and a reward model to refine textual representations. $\nabla$-Reasoner further incorporates rejection sampling and acceleration design to robustify and speed up decoding. Theoretically, we show that performing inference-time gradient descent in the sample space to maximize reward is dual to aligning an LLM policy via KL-regularized reinforcement learning. Empirically, $\nabla$-Reasoner achieves over 20% accuracy improvement on a challenging mathematical reasoning benchmark, while reducing number of model calls by approximately 10-40% compared to strong baselines. Overall, our work introduces a paradigm shift from zeroth-order search to first-order optimization at test time, offering a cost-effective path to amplify LLM reasoning.

Speculative decoding accelerates autoregressive generation by letting draft tokens bypass full verification, but conventional frameworks suffer from frequent false rejections, particularly when draft models produce semantically correct but lexically divergent outputs. In this paper, we present Calibrated Speculative Decoding (CSD), a training-free framework that recovers valid tokens discarded by standard verification. Guided by the principle of "Frequency-Guided Candidate Selection and Probability-Guarded Acceptance," CSD incorporates two lightweight modules: Online Correction Memory, which aggregates historical rejections to propose recurring divergence patterns as rescue candidates, and Semantic Consistency Gating, which verifies candidate admissibility using probability ratios instead of exact token matching. Our evaluation across diverse large language models demonstrates that CSD outperforms existing methods, achieving a peak throughput speedup of 2.33x. CSD preserves model accuracy across all tasks while further boosting performance on complex reasoning datasets. These results establish CSD as a highly effective, lightweight solution for practical LLM deployments.