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Verification bias is a well-known problem that may occur in the evaluation of predictive ability of diagnostic tests. When a binary disease status is considered, various solutions can be found in the literature to correct inference based on…

Methodology · Statistics 2023-04-10 Khanh To Duc , Monica Chiogna , Gianfranco Adimari

Prevalent reinforcement learning~(RL) methods for fine-tuning LLM reasoners, such as GRPO or Leave-one-out PPO, abandon the learned value function in favor of empirically estimated returns. This hinders test-time compute scaling that relies…

Machine Learning · Computer Science 2026-04-14 Kusha Sareen , Morgane M Moss , Alessandro Sordoni , Rishabh Agarwal , Arian Hosseini

Reinforcement Learning with Verifiable Rewards (RLVR) has become a prominent method for post-training Large Language Models (LLMs). However, verifiers are rarely error-free; even deterministic checks can be inaccurate, and the growing…

Machine Learning · Computer Science 2026-04-10 Andreas Plesner , Francisco Guzmán , Anish Athalye

Recent research has generated hope that inference scaling, such as resampling solutions until they pass verifiers like unit tests, could allow weaker models to match stronger ones. Beyond inference, this approach also enables training…

Machine Learning · Computer Science 2026-03-27 Benedikt Stroebl , Sayash Kapoor , Arvind Narayanan

Verifiers or reward models are often used to enhance the reasoning performance of large language models (LLMs). A common approach is the Best-of-N method, where N candidate solutions generated by the LLM are ranked by a verifier, and the…

Machine Learning · Computer Science 2025-02-25 Lunjun Zhang , Arian Hosseini , Hritik Bansal , Mehran Kazemi , Aviral Kumar , Rishabh Agarwal

The long-standing vision of general-purpose robots hinges on their ability to understand and act upon natural language instructions. Vision-Language-Action (VLA) models have made remarkable progress toward this goal, yet their generated…

Robotics · Computer Science 2026-02-19 Jacky Kwok , Xilun Zhang , Mengdi Xu , Yuejiang Liu , Azalia Mirhoseini , Chelsea Finn , Marco Pavone

Sampling-based search, a simple paradigm for utilizing test-time compute, involves generating multiple candidate responses and selecting the best one -- typically by having models self-verify each response for correctness. In this paper, we…

Machine Learning · Computer Science 2025-02-21 Eric Zhao , Pranjal Awasthi , Sreenivas Gollapudi

Test-time scaling paradigms have significantly advanced the capabilities of large language models (LLMs) on complex tasks. Despite their empirical success, theoretical understanding of the sample efficiency of various test-time strategies…

Machine Learning · Computer Science 2025-06-13 Baihe Huang , Shanda Li , Tianhao Wu , Yiming Yang , Ameet Talwalkar , Kannan Ramchandran , Michael I. Jordan , Jiantao Jiao

Large Reasoning Models (LRMs) achieve strong performance on mathematical reasoning tasks but remain unreliable on challenging instances. Existing test-time scaling methods, such as repeated sampling, self-correction, and tree search,…

Artificial Intelligence · Computer Science 2026-04-30 Zhimin Lin , Yixin Ji , Jinpeng Li , Yu Luo , Dong Li , Junhua Fang , Juntao Li , Min Zhang

A simple yet effective method for inference-time alignment of generative models is Best-of-$N$ (BoN), where $N$ outcomes are sampled from a reference policy, evaluated using a proxy reward model, and the highest-scoring one is selected.…

Machine Learning · Statistics 2025-07-09 Gholamali Aminian , Idan Shenfeld , Amir R. Asadi , Ahmad Beirami , Youssef Mroueh

Trustworthy verifiers are essential for the success of reinforcement learning with verifiable reward (RLVR), which is the core methodology behind various large reasoning models such as DeepSeek-R1. In complex domains like mathematical…

Machine Learning · Computer Science 2025-10-08 Yuzhen Huang , Weihao Zeng , Xingshan Zeng , Qi Zhu , Junxian He

To evaluate a classification algorithm, it is common practice to plot the ROC curve using test data. However, the inherent randomness in the test data can undermine our confidence in the conclusions drawn from the ROC curve, necessitating…

Methodology · Statistics 2024-05-22 Zheshi Zheng , Bo Yang , Peter Song

The newly released OpenAI-o1 and DeepSeek-R1 have demonstrated that test-time scaling can significantly improve model performance, especially in complex tasks such as logical reasoning. Common test-time scaling methods involve generating…

Computation and Language · Computer Science 2025-10-01 Zhendong Tan , Xingjun Zhang , Chaoyi Hu , Yancheng Pan , Shaoxun Wang

Inference-time computation offers a powerful axis for scaling the performance of language models. However, naively increasing computation in techniques like Best-of-N sampling can lead to performance degradation due to reward hacking.…

Artificial Intelligence · Computer Science 2025-04-09 Audrey Huang , Adam Block , Qinghua Liu , Nan Jiang , Akshay Krishnamurthy , Dylan J. Foster

Best-of-N (BoN) sampling is a widely used inference-time alignment method for language models, whereby N candidate responses are sampled from a reference model and the one with the highest predicted reward according to a learned reward…

Machine Learning · Computer Science 2026-03-09 Ved Sriraman , Adam Block

Recent progress in large language models (LLMs) highlights the power of scaling test-time compute to achieve strong performance on complex tasks, such as mathematical reasoning and code generation. This raises a critical question: how…

Machine Learning · Computer Science 2025-11-26 Feng Chen , Allan Raventos , Nan Cheng , Surya Ganguli , Shaul Druckmann

Large language models for code generation increasingly rely on synthetic data, where both problem solutions and verification tests are generated by models. While this enables scalable data creation, it introduces a previously unexplored…

Software Engineering · Computer Science 2025-09-26 Srishti Gureja , Elena Tommasone , Jingyi He , Sara Hooker , Matthias Gallé , Marzieh Fadaee

LLM inference often generates a batch of candidates for a prompt and selects one via strategies like majority voting or Best-of- N (BoN). For difficult tasks, this single-shot selection often underperforms. Consequently, evaluations…

Machine Learning · Computer Science 2025-10-06 Qiwei Di , Kaixuan Ji , Xuheng Li , Heyang Zhao , Quanquan Gu

Model checking plays an important role in linear regression as model misspecification seriously affects the validity and efficiency of regression analysis. In practice, model checking is often performed by subjectively evaluating the plot…

Statistics Theory · Mathematics 2019-11-19 Rok Blagus , Jakob Peterlin , Janez Stare

The application of Reinforcement Learning with Verifiable Rewards (RLVR) to mathematical and coding domains has demonstrated significant improvements in the reasoning and problem-solving abilities of Large Language Models. Despite its…

Machine Learning · Computer Science 2025-10-28 Farid Bagirov , Mikhail Arkhipov , Ksenia Sycheva , Evgeniy Glukhov , Egor Bogomolov