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Large Language Models (LLMs) are increasingly applied to complex tasks that require extended reasoning. In such settings, models often benefit from diverse chains-of-thought to arrive at multiple candidate solutions. This requires two…

Machine Learning · Computer Science 2025-10-08 Xueyan Li , Guinan Su , Mrinmaya Sachan , Jonas Geiping

In this work, we introduce Entropy Area Score (EAS), a simple yet effective metric to quantify uncertainty in the answer generation process of reasoning large language models (LLMs). EAS requires neither external models nor repeated…

Artificial Intelligence · Computer Science 2025-08-29 Yongfu Zhu , Lin Sun , Guangxiang Zhao , Weihong Lin , Xiangzheng Zhang

Entropy-based deep reasoning has emerged as a promising direction for improving the reasoning capabilities of Large Language Models (LLMs), but existing methods often either increase response length indiscriminately or shorten responses at…

Computation and Language · Computer Science 2026-05-20 Shuyu Wei , Jian Sun , Delai Qiu , Yining Wang , Shengping Liu , Jiaen Liang , Ying Fu , Wei Huang , Jitao Sang

Recently, Large Language Models (LLMs) have demonstrated outstanding performance across a wide range of downstream language tasks. Temperature sampling is a commonly used decoding strategy for LLMs' generation process. However, a fixed…

Computation and Language · Computer Science 2024-04-04 Shimao Zhang , Yu Bao , Shujian Huang

In large language models (LLMs), each block operates on the residual stream to map input token sequences to output token distributions. However, most of the interpretability literature focuses on internal latent representations, leaving…

Machine Learning · Computer Science 2026-02-03 Riccardo Ali , Francesco Caso , Christopher Irwin , Pietro Liò

Entropy minimization (EM) trains the model to concentrate even more probability mass on its most confident outputs. We show that this simple objective alone, without any labeled data, can substantially improve large language models' (LLMs)…

Machine Learning · Computer Science 2025-05-22 Shivam Agarwal , Zimin Zhang , Lifan Yuan , Jiawei Han , Hao Peng

Large language models (LLMs) have shown remarkable reasoning capabilities when trained with chain-of-thought (CoT) supervision. However, the long and verbose CoT traces, especially those distilled from large reasoning models (LRMs) such as…

Machine Learning · Computer Science 2025-06-05 Jinghan Jia , Hadi Reisizadeh , Chongyu Fan , Nathalie Baracaldo , Mingyi Hong , Sijia Liu

In this study, the output of large language models (LLM) is considered an information source generating an unlimited sequence of symbols drawn from a finite alphabet. Given the probabilistic nature of modern LLMs, we assume a probabilistic…

Computation and Language · Computer Science 2026-02-24 Marco Scharringhausen

This paper investigates a novel lossy compression framework operating under logarithmic loss, designed to handle situations where the reconstruction distribution diverges from the source distribution. This framework is especially relevant…

Machine Learning · Computer Science 2024-10-30 M. Reza Ebrahimi , Jun Chen , Ashish Khisti

LLM text decoding is key component for perceived LLM quality. We demonstrate two experiments showing that decoding methods could be improved by manipulation of token probabilities. First, we test few LLM on SummEval summary scoring dataset,…

Computation and Language · Computer Science 2024-09-27 Krystian Zawistowski

We study the problem of entropy calibration, which asks whether a language model's entropy over generations matches its log loss on human text. Past work found that models are miscalibrated, with entropy per step increasing as generations…

Computation and Language · Computer Science 2026-01-14 Steven Cao , Gregory Valiant , Percy Liang

Probabilistic next-token prediction trained using cross-entropy loss is the basis of most large language models. Given a sequence of previous values, next-token prediction assigns a probability to each possible next value in the vocabulary.…

Machine Learning · Statistics 2025-05-19 Jacob Trauger , Ambuj Tewari

Maximum entropy models provide the least constrained probability distributions that reproduce statistical properties of experimental datasets. In this work we characterize the learning dynamics that maximizes the log-likelihood in the case…

Disordered Systems and Neural Networks · Physics 2016-09-21 Ulisse Ferrari

Chain-of-thought (CoT) reasoning improves large language model performance on complex tasks, but often produces excessively long and inefficient reasoning traces. Existing methods shorten CoTs using length penalties or global entropy…

Artificial Intelligence · Computer Science 2026-04-08 Xuan Xiong , Huan Liu , Li Gu , Zhixiang Chi , Yue Qiu , Yuanhao Yu , Yang Wang

The translation of written language has been known since the 3rd century BC; however, its necessity has become increasingly common in the information age. Today, many translators exist, based on encoder-decoder deep architectures,…

Computation and Language · Computer Science 2025-11-18 Ronit D. Gross , Yanir Harel , Ido Kanter

Uncertainty decomposition refers to the task of decomposing the total uncertainty of a predictive model into aleatoric (data) uncertainty, resulting from inherent randomness in the data-generating process, and epistemic (model) uncertainty,…

Computation and Language · Computer Science 2024-06-12 Bairu Hou , Yujian Liu , Kaizhi Qian , Jacob Andreas , Shiyu Chang , Yang Zhang

Dynamic retrieval-augmented generation (RAG) allows large language models (LLMs) to fetch external knowledge on demand, offering greater adaptability than static RAG. A central challenge in this setting lies in determining the optimal…

Computation and Language · Computer Science 2025-11-14 Bo Li , Tian Tian , Zhenghua Xu , Hao Cheng , Shikun Zhang , Wei Ye

Large Language Models (LLMs) that can express interpretable and calibrated uncertainty are crucial in high-stakes domains. While methods to compute uncertainty post-hoc exist, they are often sampling-based and therefore computationally…

Machine Learning · Computer Science 2026-03-09 Azza Jenane , Nassim Walha , Lukas Kuhn , Florian Buettner

Large Language Models (LLMs) exhibit strong performance across various natural language processing (NLP) tasks but remain vulnerable to hallucinations, generating factually incorrect or misleading outputs. Uncertainty estimation, often…

Machine Learning · Computer Science 2025-11-12 Manh Nguyen , Sunil Gupta , Hung Le

Data is the cornerstone of large language models (LLMs), but not all data is useful for model learning. Carefully selected data can better elicit the capabilities of LLMs with much less computational overhead. Most methods concentrate on…

Machine Learning · Computer Science 2024-07-12 Mingjia Yin , Chuhan Wu , Yufei Wang , Hao Wang , Wei Guo , Yasheng Wang , Yong Liu , Ruiming Tang , Defu Lian , Enhong Chen