arXiv cs.CL· Erfan Baghaei Potraghloo, Milad Heidari Sorkhehdizaj, Shahab Rahimirad, Aliasghar Pourghani, Seyedarmin Azizi, Souvik Kundu, Abolfazl Hashemi, Joseph Campbell, Vijay Gupta·· 10 小时前AI 评分31
粒子解码的序列级 Rényi 熵：为 LLM 自适应推理提供零成本不确定性信号
Free Lunch Uncertainty: Sequence-Level R\'enyi Entropy from Particle Decoding for Adaptive LLM Reasoning
AI 导读
研究者证明，用于 power sampling 的 Sequential Monte Carlo（SMC）解码在估计幂分布归一化常数时，可零边际成本读出模型补全分布的序列级 Rényi 熵（SRE），且在任意粒子预算下都有保证。
正文 · 原文
Abstract:Quantifying uncertainty over an entire LLM completion is critical for selective prediction and adaptive compute. Zero-cost signals such as mean token entropy and log-probability are local to tokens or to one completion, and self-consistency needs many extra completions. We show that Sequential Monte Carlo (SMC) decoding for power sampling already estimates the normalizing constant of the power distribution, which gives the sequence-level R'enyi entropy (SRE) of the model's completion distribution at zero marginal cost, with a guarantee at every particle budget. A R'enyi chain rule extends this readout to a family of stepwise entropies of any order. We prove that orders above one are tied to the most likely token of each step, which explains why they track log-probability, while the order-1/2 member accumulates the log of per-step search effort. This member is the best zero-cost selective-prediction signal in 10 of 13 settings. On MATH500 its AUROC is 0.022 to 0.044 above log-probability with all four models and within length quartiles, and the same order is selected when each setting is held out. An 8-particle probe identifies the problems that benefit from more particles, and a two-pass policy matches 64-particle accuracy on MATH500 with 34.2% fewer particles over three seeds.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computation and Language (cs.CL) |
| Cite as: | arXiv:2611.13414 [cs.LG] |
| (or arXiv:2611.13414v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2611.13414 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Shahab Rahimirad [view email]
[v1]
Tue, 10 Nov 2026 00:49:36 UTC (679 KB)
来源：arXiv cs.CL · arxiv.org