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Learning complex functions that involve multi-step reasoning poses a significant challenge for standard supervised learning from input-output examples. Chain-of-thought (CoT) supervision, which provides intermediate reasoning steps together…

Machine Learning · Statistics 2025-05-23 Awni Altabaa , Omar Montasser , John Lafferty

Chain-of-thought (CoT) supervision can substantially improve transformer performance, yet the mechanisms by which models learn to follow and benefit from CoT remain poorly understood. We investigate these learning dynamics through the lens…

Machine Learning · Computer Science 2025-10-31 Zihan Pengmei , Costas Mavromatis , Zhengyuan Shen , Yunyi Zhang , Vassilis N. Ioannidis , Huzefa Rangwala

Chain-of-thought (CoT) is a method that enables language models to handle complex reasoning tasks by decomposing them into simpler steps. Despite its success, the underlying mechanics of CoT are not yet fully understood. In an attempt to…

Machine Learning · Computer Science 2023-11-09 Yingcong Li , Kartik Sreenivasan , Angeliki Giannou , Dimitris Papailiopoulos , Samet Oymak

Chain-of-Thought (CoT) reasoning has emerged as a powerful tool for enhancing the problem-solving capabilities of large language models (LLMs). However, the theoretical foundations of learning from CoT data remain underdeveloped, and…

Artificial Intelligence · Computer Science 2025-07-29 Shai Shalev-Shwartz , Amnon Shashua

Chain-of-Thought (CoT) holds a significant place in augmenting the reasoning performance for large language models (LLMs). While some studies focus on improving CoT accuracy through methods like retrieval enhancement, yet a rigorous…

Computation and Language · Computer Science 2024-06-19 Lijie Hu , Liang Liu , Shu Yang , Xin Chen , Hongru Xiao , Mengdi Li , Pan Zhou , Muhammad Asif Ali , Di Wang

Chain of Thought (CoT) reasoning enhances language models' performance but often leads to inefficient "overthinking" on simple problems. We identify that existing approaches directly penalizing reasoning length fail to account for varying…

Computation and Language · Computer Science 2025-05-22 Junjie Yang , Ke Lin , Xing Yu

Chain of Thought (CoT) of multi-step benefits from the logical structure of the reasoning steps and task-specific actions, significantly enhancing the mathematical reasoning capabilities of large language models. As the prevalence of long…

Artificial Intelligence · Computer Science 2025-03-07 Wen Yang , Minpeng Liao , Kai Fan

Chain-of-Thought (CoT) is an efficient prompting method that enables the reasoning ability of large language models by augmenting the query using multiple examples with multiple intermediate steps. Despite the empirical success, the…

Machine Learning · Computer Science 2025-05-27 Hongkang Li , Songtao Lu , Pin-Yu Chen , Xiaodong Cui , Meng Wang

Chain-of-thought (CoT) reasoning has emerged as an effective approach for activating latent capabilities in LLMs. Interestingly, we observe that both CoT reasoning and self-training share the core objective: iteratively leveraging…

Computation and Language · Computer Science 2025-05-27 Zongqian Wu , Baoduo Xu , Ruochen Cui , Mengmeng Zhan , Xiaofeng Zhu , Lei Feng

Large Language Models (LLMs) have revolutionized natural language processing and hold immense potential for advancing Artificial Intelligence. However, the core architecture of most mainstream LLMs -- the Transformer -- has inherent…

Computation and Language · Computer Science 2024-10-21 Xiang Zhang , Dujian Ding

This is the second in a series of short reports that seek to help business, education, and policy leaders understand the technical details of working with AI through rigorous testing. In this report, we investigate Chain-of-Thought (CoT)…

Computation and Language · Computer Science 2025-06-10 Lennart Meincke , Ethan Mollick , Lilach Mollick , Dan Shapiro

Reasoning with a chain-of-thought (CoT) enables Large Language Models (LLMs) to solve complex tasks but incurs significant inference costs due to the generation of long rationales. We propose Thinking States, a method that performs…

Computation and Language · Computer Science 2026-02-10 Ido Amos , Avi Caciularu , Mor Geva , Amir Globerson , Jonathan Herzig , Lior Shani , Idan Szpektor

Chain-of-Thought (CoT) prompting is a widely used inference-time technique for improving reasoning, yet its gains are uneven across tasks. We analyze when and why CoT helps by modeling the step-wise reasoning trajectory as a Markov chain.…

Machine Learning · Computer Science 2026-03-03 Zihan Wang , Yijun Dong , Qi Lei

Chain-of-Thought (CoT) reasoning is known to improve Large Language Models both empirically and in terms of theoretical approximation power. However, our understanding of the inner workings and conditions of apparition of CoT capabilities…

Machine Learning · Computer Science 2024-10-29 Vivien Cabannes , Charles Arnal , Wassim Bouaziz , Alice Yang , Francois Charton , Julia Kempe

Latent Chain-of-Thought (Latent-CoT) aims to enable step-by-step computation without emitting long rationales, yet its mechanisms remain unclear. We study CODI, a continuous-thought teacher-student distillation model, on strictly sequential…

Artificial Intelligence · Computer Science 2026-02-03 Jia Liang , Liangming Pan

Recently, inference-time scaling of chain-of-thought (CoT) has been demonstrated as a promising approach for addressing multi-modal reasoning tasks. While existing studies have predominantly centered on text-based thinking, the integration…

Computation and Language · Computer Science 2025-05-27 Yujie Lin , Ante Wang , Moye Chen , Jingyao Liu , Hao Liu , Jinsong Su , Xinyan Xiao

Chain-of-Thought (CoT) is a technique that guides Large Language Models (LLMs) to decompose complex tasks into multi-step reasoning through intermediate steps in natural language form. Briefly, CoT enables LLMs to think step by step.…

Computation and Language · Computer Science 2023-10-19 Caoyun Fan , Jidong Tian , Yitian Li , Wenqing Chen , Hao He , Yaohui Jin

Chain-of-Thought (CoT) prompting substantially improves the sample efficiency of transformers, reducing the complexity of tasks like parity learning from exponential to polynomial in the input length. However, generating explicit reasoning…

Machine Learning · Computer Science 2026-05-28 Yixiao Huang , Hanlin Zhu , Zixuan Wang , Jiantao Jiao , Stuart Russell , Somayeh Sojoudi , Song Mei

Large reasoning models (LRMs) increasingly rely on step-by-step Chain-of-Thought (CoT) reasoning to improve task performance, particularly in high-resource languages such as English. While recent work has examined final-answer accuracy in…

Computation and Language · Computer Science 2025-10-13 Raoyuan Zhao , Yihong Liu , Hinrich Schütze , Michael A. Hedderich

Recently, Large Language Models (LLMs) have demonstrated remarkable capabilities. Chain-of-Thought (CoT) has been proposed as a way of assisting LLMs in performing complex reasoning. However, developing effective prompts can be a…

Machine Learning · Computer Science 2023-06-02 Yuxin Tang
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