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Process reward models (PRMs) provide more nuanced supervision compared to outcome reward models (ORMs) for optimizing policy models, positioning them as a promising approach to enhancing the capabilities of LLMs in complex reasoning tasks.…

Computation and Language · Computer Science 2025-05-30 Hongzhan Chen , Tao Yang , Shiping Gao , Ruijun Chen , Xiaojun Quan , Hongtao Tian , Ting Yao

Scaling laws have been used to describe how large language model (LLM) performance scales with model size, training data size, or amount of computational resources. Motivated by the fact that neural quantum states (NQS) has increasingly…

Machine Learning · Computer Science 2025-09-17 Oliver Knitter , Dan Zhao , Stefan Leichenauer , Shravan Veerapaneni

Neural scaling laws characterize how model performance improves as the model size scales up. Inspired by empirical observations, we introduce a resource model of neural scaling. A task is usually composite hence can be decomposed into many…

Machine Learning · Computer Science 2024-05-16 Jinyeop Song , Ziming Liu , Max Tegmark , Jeff Gore

The scientific scale-up of large language models (LLMs) necessitates a comprehensive understanding of their scaling properties. However, the existing literature on the scaling properties only yields an incomplete answer: optimization loss…

Computation and Language · Computer Science 2024-04-18 Shengding Hu , Xin Liu , Xu Han , Xinrong Zhang , Chaoqun He , Weilin Zhao , Yankai Lin , Ning Ding , Zebin Ou , Guoyang Zeng , Zhiyuan Liu , Maosong Sun

Widely observed neural scaling laws, in which error falls off as a power of the training set size, model size, or both, have driven substantial performance improvements in deep learning. However, these improvements through scaling alone…

Machine Learning · Computer Science 2023-04-25 Ben Sorscher , Robert Geirhos , Shashank Shekhar , Surya Ganguli , Ari S. Morcos

In this work, we provide a large-scale empirical study of the scaling properties of multilingual neural machine translation models. We examine how increases in the model size affect the model performance and investigate the role of the…

Computation and Language · Computer Science 2023-02-21 Patrick Fernandes , Behrooz Ghorbani , Xavier Garcia , Markus Freitag , Orhan Firat

Recently, Large Language Models (LLMs) have been widely adopted in a wide range of tasks, leading to increasing attention towards the research on how scaling LLMs affects their performance. Existing works, termed Scaling Laws, have…

Computation and Language · Computer Science 2025-09-23 Yizhe Xiong , Xiansheng Chen , Xin Ye , Hui Chen , Zijia Lin , Haoran Lian , Zhenpeng Su , Wei Huang , Jianwei Niu , Jungong Han , Guiguang Ding

The use of machine learning models in system identification has increased due to their ability to approximate complex nonlinear dynamics with high accuracy. However, often it is not clear how the performance of trained models scales with…

Optimization and Control · Mathematics 2026-03-26 Marco Roschkowski , Karim Cherifi , Hannes Gernandt

Because large language models are expensive to pretrain on different datasets, using smaller-scale experiments to decide on data is crucial for reducing costs. Which benchmarks and methods of making decisions from observed performance at…

Pruning eliminates unnecessary parameters in neural networks; it offers a promising solution to the growing computational demands of large language models (LLMs). While many focus on post-training pruning, sparse pre-training--which…

Since compute grows much faster than web text available for language model pre-training, we ask how one should approach pre-training under fixed data and no compute constraints. We first show that existing data-constrained approaches of…

Machine Learning · Computer Science 2025-09-19 Konwoo Kim , Suhas Kotha , Percy Liang , Tatsunori Hashimoto

Neural generative models can be used to learn complex probability distributions from data, to sample from them, and to produce probability density estimates. We propose a computational framework for developing neural generative models…

Machine Learning · Computer Science 2022-01-06 Alexander Ororbia , Daniel Kifer

Language models achieve impressive performance on a variety of knowledge, language, and reasoning tasks due to the scale and diversity of pretraining data available. The standard training recipe is a two-stage paradigm: pretraining first on…

Computation and Language · Computer Science 2026-03-20 Skyler Seto , Pierre Ablin , Anastasiia Filippova , Jiayuan Ye , Louis Bethune , Angelos Katharopoulos , David Grangier

Continual Pre-training (CPT) serves as a fundamental approach for adapting foundation models to domain-specific applications. Scaling laws for pre-training define a power-law relationship between dataset size and the test loss of an LLM.…

Machine Learning · Computer Science 2025-12-29 Lei Liu , Hao Zhu , Yue Shen , Zhixuan Chu , Jian Wang , Jinjie Gu , Kui Ren

Scaling laws enable the optimal selection of data amount and language model size, yet the impact of the data unit, the token, on this relationship remains underexplored. In this work, we systematically investigate how the information…

Computation and Language · Computer Science 2026-05-27 Tomasz Limisiewicz , Artidoro Pagnoni , Srini Iyer , Mike Lewis , Sachin Mehta , Alisa Liu , Margaret Li , Gargi Ghosh , Luke Zettlemoyer

Scaling the number of parameters and the size of training data has proven to be an effective strategy for improving large language model (LLM) performance. Yet, as these models grow increasingly powerful and widely deployed, the cost of…

Machine Learning · Computer Science 2026-05-14 Song Bian , Tao Yu , Shivaram Venkataraman , Youngsuk Park

Synthetic-to-real transfer learning is a framework in which a synthetically generated dataset is used to pre-train a model to improve its performance on real vision tasks. The most significant advantage of using synthetic images is that the…

Machine Learning · Computer Science 2021-10-12 Hiroaki Mikami , Kenji Fukumizu , Shogo Murai , Shuji Suzuki , Yuta Kikuchi , Taiji Suzuki , Shin-ichi Maeda , Kohei Hayashi

The prediction of learning curves for Natural Language Processing (NLP) models enables informed decision-making to meet specific performance objectives, while reducing computational overhead and lowering the costs associated with dataset…

Machine Learning · Computer Science 2025-10-21 Viktoria Schram , Markus Hiller , Daniel Beck , Trevor Cohn

Recent work has shown that, in generative modeling, cross-entropy loss improves smoothly with model size and training compute, following a power law plus constant scaling law. One challenge in extending these results to reinforcement…

Machine Learning · Computer Science 2023-02-21 Jacob Hilton , Jie Tang , John Schulman

Researchers build scaling laws to forecast the training performance of expensive large-scale runs with larger model size N and data size D. These laws assume that other training hyperparameters are optimally chosen, which can require…

Machine Learning · Computer Science 2026-02-12 Huaqing Zhang , Kaiyue Wen , Tengyu Ma