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Uncertainty estimation is critical for deploying reasoning language models, yet remains poorly understood under extended chain-of-thought reasoning. We study parallel sampling as a fully black-box approach using verbalized confidence and…

Artificial Intelligence · Computer Science 2026-03-20 Maksym Del , Markus Kängsepp , Marharyta Domnich , Ardi Tampuu , Lisa Yankovskaya , Meelis Kull , Mark Fishel

Self-consistency boosts inference-time performance by sampling multiple reasoning traces in parallel and voting. However, in constrained domains like math and code, this strategy is compute-inefficient because it samples with replacement,…

Machine Learning · Computer Science 2026-04-23 Xueyan Li , Johannes Zenn , Ekaterina Fadeeva , Guinan Su , Mrinmaya Sachan , Jonas Geiping

One of the most striking findings in modern research on large language models (LLMs) is that scaling up compute during training leads to better results. However, less attention has been given to the benefits of scaling compute during…

Computation and Language · Computer Science 2024-11-21 Sean Welleck , Amanda Bertsch , Matthew Finlayson , Hailey Schoelkopf , Alex Xie , Graham Neubig , Ilia Kulikov , Zaid Harchaoui

Reasoning is a key component of language understanding in Large Language Models. While Chain-of-Thought prompting enhances performance via explicit intermediate steps, it suffers from sufficient token overhead and a fixed reasoning…

Computation and Language · Computer Science 2025-11-18 Xinyuan Wang , Dongjie Wang , Wangyang Ying , Haoyue Bai , Nanxu Gong , Sixun Dong , Kunpeng Liu , Yanjie Fu

Scaling test-time compute via parallel sampling can substantially improve LLM reasoning, but is often limited by Best-of-N selection quality. Generative selection methods, such as GenSelect, address this bottleneck, yet strong selection…

Chain-of-Thought (CoT) and Looped Transformers have been shown to empirically improve performance on reasoning tasks and to theoretically enhance expressivity by recursively increasing the number of computational steps. However, their…

Machine Learning · Computer Science 2025-10-27 Kevin Xu , Issei Sato

As language model (LM) outputs get more and more natural, it is becoming more difficult than ever to evaluate their quality. Simultaneously, increasing LMs' "thinking" time through scaling test-time compute has proven an effective technique…

Recent research has highlighted that Large Language Models (LLMs), even when trained to generate extended long reasoning steps, still face significant challenges on hard reasoning problems. However, much of the existing literature relies on…

Artificial Intelligence · Computer Science 2025-05-29 Fanzeng Xia , Yidong Luo , Tinko Sebastian Bartels , Yaqi Xu , Tongxin Li

We study self-rewarding reasoning large language models (LLMs), which can simultaneously generate step-by-step reasoning and evaluate the correctness of their outputs during the inference time-without external feedback. This integrated…

Artificial Intelligence · Computer Science 2025-02-28 Wei Xiong , Hanning Zhang , Chenlu Ye , Lichang Chen , Nan Jiang , Tong Zhang

Most efforts to improve the reasoning capabilities of large language models (LLMs) involve either scaling the number of parameters and the size of training data, or scaling inference computation by letting models generate complex chains of…

Machine Learning · Computer Science 2025-10-10 Yeskendir Koishekenov , Aldo Lipani , Nicola Cancedda

Supervised fine-tuning (SFT) on chain-of-thought data is an essential post-training step for reasoning language models. Standard machine learning intuition suggests that training with more unique training samples yields better…

Computation and Language · Computer Science 2026-02-12 Dawid J. Kopiczko , Sagar Vaze , Tijmen Blankevoort , Yuki M. Asano

Scaling test-time compute is a promising axis for improving LLM capabilities. However, test-time compute can be scaled in a variety of ways, and effectively combining different approaches remains an active area of research. Here, we explore…

Machine Learning · Computer Science 2025-02-04 Ryan Ehrlich , Bradley Brown , Jordan Juravsky , Ronald Clark , Christopher Ré , Azalia Mirhoseini

We propose new sequential sorting operations by adapting techniques and methods used for designing parallel sorting algorithms. Although the norm is to parallelize a sequential algorithm to improve performance, we adapt a contrarian…

Data Structures and Algorithms · Computer Science 2016-09-01 Alexandros V Gerbessiotis

Self-consistency (SC), a widely used decoding strategy for chain-of-thought reasoning, shows significant gains across various multi-step reasoning tasks but comes with a high cost due to multiple sampling with the preset size. Its variants,…

Computation and Language · Computer Science 2025-02-13 Xinglin Wang , Shaoxiong Feng , Yiwei Li , Peiwen Yuan , Yueqi Zhang , Chuyi Tan , Boyuan Pan , Yao Hu , Kan Li

Inference-time methods that aggregate and prune multiple samples have emerged as a powerful paradigm for steering large language models, yet we lack any principled understanding of their accuracy-cost tradeoffs. In this paper, we introduce…

Scaling test-time compute with multi-path chain-of-thought improves reasoning accuracy, but its effectiveness depends critically on the exploration-exploitation trade-off. Existing approaches address this trade-off in rigid ways:…

Artificial Intelligence · Computer Science 2026-05-12 Shengxuan Qiu , Haochen Huang , Shuzhang Zhong , Pengfei Zuo , Meng Li

The recent rise of Large Reasoning Models (LRMs) has significantly improved multi-step reasoning performance, but often at the cost of generating excessively long reasoning chains. This paper revisits the efficiency of such reasoning…

Computation and Language · Computer Science 2025-05-27 Xixian Yong , Xiao Zhou , Yingying Zhang , Jinlin Li , Yefeng Zheng , Xian Wu

Reasoning models represent a significant advance in LLM capabilities, particularly for complex reasoning tasks such as mathematics and coding. Previous studies confirm that parallel test-time compute-sampling multiple solutions and…

Machine Learning · Computer Science 2025-10-27 Raul Cavalcante Dinardi , Bruno Yamamoto , Anna Helena Reali Costa , Artur Jordao

Structured reasoning can improve the inference performance of large language models (LLMs), but it also introduces computational cost and control constraints. When additional reasoning structure helps, and when it instead reduces efficiency…

Machine Learning · Computer Science 2026-04-14 Junyu Guo , Shangding Gu , Ming Jin , Costas Spanos , Javad Lavaei

Test-time scaling is a promising new approach to language modeling that uses extra test-time compute to improve performance. Recently, OpenAI's o1 model showed this capability but did not publicly share its methodology, leading to many…