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Modern language models generate chain-of-thought traces by autoregressively sampling tokens from a finite vocabulary. While this discrete sampling has achieved remarkable success, conducting chain-of-thought with continuously-valued tokens…

Machine Learning · Computer Science 2026-03-06 Halil Alperen Gozeten , M. Emrullah Ildiz , Xuechen Zhang , Hrayr Harutyunyan , Ankit Singh Rawat , Samet Oymak

Test-time scaling, which leverages additional computation during inference to improve model accuracy, has enabled a new class of Large Language Models (LLMs) that are able to reason through complex problems by understanding the goal,…

Computation and Language · Computer Science 2025-11-25 Shaltiel Shmidman , Asher Fredman , Oleg Sudakov , Meriem Bendris

Large language models (LLMs) now exhibit strong multi-step reasoning abilities, but existing inference-time scaling methods remain computationally expensive, often relying on extensive sampling or external evaluators. We propose a…

Artificial Intelligence · Computer Science 2026-03-10 Nicolas Legrand , Kenneth Enevoldsen , Márton Kardos , Kristoffer Nielbo

Reinforcement learning substantially improves reasoning in large language models, but it also tends to lengthen chain of thought outputs and increase computational cost during both training and inference. Though length control methods have…

Computation and Language · Computer Science 2026-02-12 Daisuke Nohara , Taishi Nakamura , Rio Yokota

Recent studies have shown that making a model spend more time thinking through longer Chain of Thoughts (CoTs) enables it to gain significant improvements in complex reasoning tasks. While current researches continue to explore the benefits…

Computation and Language · Computer Science 2025-10-14 Wenkai Yang , Shuming Ma , Yankai Lin , Furu Wei

Large reasoning models (LRMs) like OpenAI o1 and DeepSeek-R1 achieve high accuracy on complex tasks by adopting long chain-of-thought (CoT) reasoning paths. However, the inherent verbosity of these processes frequently results in redundancy…

Computation and Language · Computer Science 2026-03-10 Chenzhi Hu , Qinzhe Hu , Yuhang Xu , Junyi Chen , Ruijie Wang , Shengzhong Liu , Jianxin Li , Fan Wu , Guihai Chen

Reasoning Large Language Models (LLMs) enable test-time scaling, with dataset-level accuracy improving as the token budget increases, motivating adaptive reasoning -- spending tokens when they improve reliability and stopping early when…

Artificial Intelligence · Computer Science 2026-05-15 Xi Wang , Anushri Suresh , Alvin Zhang , Rishi More , William Jurayj , Benjamin Van Durme , Mehrdad Farajtabar , Daniel Khashabi , Eric Nalisnick

Recent advances leverage post-training to enhance model reasoning performance, which typically requires costly training pipelines and still suffers from inefficient, overly lengthy outputs. We introduce Speculative Thinking, a training-free…

Computation and Language · Computer Science 2025-04-18 Wang Yang , Xiang Yue , Vipin Chaudhary , Xiaotian Han

Thinking Tokens (TT) have been proposed as an unsupervised method to facilitate reasoning in language models. However, despite their conceptual appeal, our findings show that TTs marginally improves performance and consistently…

Computation and Language · Computer Science 2024-11-19 Sreeram Vennam , David Valente , David Herel , Ponnurangam Kumaraguru

To enhance reasoning capabilities, previous works have explored incorporating special-purpose tokens into the training process. These strategies strengthen the learning mechanism of transformer-based large language models (LLMs). Building…

Computation and Language · Computer Science 2025-08-12 Eunki Kim , Sangryul Kim , James Thorne

Reasoning-oriented Large Language Models (LLMs) often rely on generating explicit tokens step by step, and their effectiveness typically hinges on large-scale supervised fine-tuning or reinforcement learning. While Chain-of-Thought (CoT)…

Computation and Language · Computer Science 2025-09-30 Haoyu Zheng , Zhuonan Wang , Yuqian Yuan , Tianwei Lin , Wenqiao Zhang , Zheqi Lv , Juncheng Li , Siliang Tang , Yueting Zhuang , Hongyang He

When writing and talking, people sometimes pause to think. Although reasoning-focused works have often framed reasoning as a method of answering questions or completing agentic tasks, reasoning is implicit in almost all written text. For…

Computation and Language · Computer Science 2024-03-19 Eric Zelikman , Georges Harik , Yijia Shao , Varuna Jayasiri , Nick Haber , Noah D. Goodman

Chain-of-thought responses from language models improve performance across most benchmarks. However, it remains unclear to what extent these performance gains can be attributed to human-like task decomposition or simply the greater…

Computation and Language · Computer Science 2024-04-25 Jacob Pfau , William Merrill , Samuel R. Bowman

Chain-of-thought and more broadly test-time compute are known to augment the expressive capabilities of language models and have led to major innovations in reasoning. Motivated by this success, this paper explores latent chain-of-thought…

Machine Learning · Computer Science 2026-05-20 Carson Dudley , Samet Oymak

Test-Time Scaling (TTS) refers to approaches that improve reasoning performance by allocating extra computation during inference, without altering the model's parameters. While existing TTS methods operate in a discrete token space by…

Computation and Language · Computer Science 2025-05-28 Yige Xu , Xu Guo , Zhiwei Zeng , Chunyan Miao

Recent advances in large language models (LLMs) have shown that test-time scaling can substantially improve model performance on complex tasks, particularly in the coding domain. Under this paradigm, models use a larger token budget during…

Artificial Intelligence · Computer Science 2026-04-21 Jiaxin Fang , Runyuan He , Sahil Bhatia , Neel Gajare , Alvin Cheung

This paper introduces a simple and scalable approach to improve the data efficiency of large language model (LLM) training by augmenting existing text data with thinking trajectories. The compute for pre-training LLMs has been growing at an…

Computation and Language · Computer Science 2025-10-20 Liang Wang , Nan Yang , Shaohan Huang , Li Dong , Furu Wei

Verification is crucial for effective mathematical reasoning. We present a new temporal consistency method where verifiers iteratively refine their judgments based on the previous assessment. Unlike one-round verification or multi-model…

Computation and Language · Computer Science 2025-12-01 Jiacheng Guo , Yue Wu , Jiahao Qiu , Kaixuan Huang , Xinzhe Juan , Ling Yang , Mengdi Wang

Although LLMs have demonstrated improved performance by scaling parallel test-time compute, doing so relies on generating reasoning paths that are both diverse and accurate. For challenging problems, the forking tokens that trigger diverse…

Computation and Language · Computer Science 2026-03-03 Sheng Jia , Xiao Wang , Shiva Prasad Kasiviswanathan

Chain-of-thought (CoT) decoding enables language models to improve reasoning performance at the cost of high generation latency in decoding. Recent proposals have explored variants of contemplation tokens, a term we introduce that refers to…

Computation and Language · Computer Science 2024-12-18 Jeffrey Cheng , Benjamin Van Durme