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The cross-entropy scaling law has long served as a key tool for guiding the development of large language models. It shows that cross-entropy loss decreases in a predictable power-law rate as the model size increases. However, recent…

Machine Learning · Computer Science 2026-03-03 Junxi Yan , Zixi Wei , Qingyao Ai , Yiqun Liu , Jingtao Zhan

For deploying foundation models, practitioners increasingly need prescriptive scaling laws: given a pre training compute budget, what downstream accuracy is attainable with contemporary post training practice, and how stable is that mapping…

Machine Learning · Computer Science 2026-02-18 Hanlin Zhang , Jikai Jin , Vasilis Syrgkanis , Sham Kakade

The remarkable progress in deep learning in recent years is largely driven by improvements in scale, where bigger models are trained on larger datasets for longer schedules. To predict the benefit of scale empirically, we argue for a more…

Machine Learning · Computer Science 2022-11-02 Ibrahim Alabdulmohsin , Behnam Neyshabur , Xiaohua Zhai

While large language models (LLMs) have demonstrated remarkable capabilities in language modeling, recent studies reveal that they often fail on out-of-distribution (OOD) samples due to spurious correlations acquired during pre-training.…

Machine Learning · Computer Science 2025-06-12 Shurui Gui , Shuiwang Ji

Neural scaling laws have revolutionized the design and optimization of large-scale AI models by revealing predictable relationships between model size, dataset volume, and computational resources. Early research established power-law…

Computation and Language · Computer Science 2025-05-28 Ayan Sengupta , Yash Goel , Tanmoy Chakraborty

Domain adaptation for large neural language models (NLMs) is coupled with massive amounts of unstructured data in the pretraining phase. In this study, however, we show that pretrained NLMs learn in-domain information more effectively and…

Computation and Language · Computer Science 2022-08-30 Shahriar Golchin , Mihai Surdeanu , Nazgol Tavabi , Ata Kiapour

Scaling laws are a critical component of the LLM development pipeline, most famously as a way to forecast training decisions such as 'compute-optimally' trading-off parameter count and dataset size, alongside a more recent growing list of…

Machine Learning · Computer Science 2025-06-17 Nicholas Roberts , Niladri Chatterji , Sharan Narang , Mike Lewis , Dieuwke Hupkes

Process reward models (PRMs) have demonstrated significant efficacy in enhancing the mathematical reasoning capabilities of large language models (LLMs) by leveraging test-time scaling (TTS). However, while most PRMs exhibit substantial…

Artificial Intelligence · Computer Science 2025-09-30 Haotian Zhang , Liu Liu , Baosheng Yu , Jiayan Qiu , Likang Xiao , Yanwei Ren , Quan Chen , Xianglong Liu

We identify empirical scaling laws for the cross-entropy loss in four domains: generative image modeling, video modeling, multimodal image$\leftrightarrow$text models, and mathematical problem solving. In all cases autoregressive…

When using supervised fine-tuning (SFT) to adapt large language models (LLMs) to specific domains, a significant challenge arises: should we use the entire SFT dataset for fine-tuning? Common practice often involves fine-tuning directly on…

Computation and Language · Computer Science 2025-05-26 Xiang Liu , Zhaoxiang Liu , Peng Wang , Kohou Wang , Huan Hu , Kai Wang , Shiguo Lian

The prevailing paradigm for enhancing the reasoning abilities of LLMs revolves around post-training on high-quality, reasoning-intensive data. While emerging literature suggests that reasoning data is increasingly incorporated also during…

Hyperparameter optimization is an important subfield of machine learning that focuses on tuning the hyperparameters of a chosen algorithm to achieve peak performance. Recently, there has been a stream of methods that tackle the issue of…

Machine Learning · Computer Science 2023-10-26 Arlind Kadra , Maciej Janowski , Martin Wistuba , Josif Grabocka

Large language model (LLM) post-training enhances latent skills, unlocks value alignment, improves performance, and enables domain adaptation. Unfortunately, post-training is known to induce forgetting, especially in the ubiquitous use-case…

Machine Learning · Computer Science 2026-05-25 Lukas Thede , Stefan Winzeck , Zeynep Akata , Jonathan Richard Schwarz

Many deep architectures and self-supervised pre-training techniques have been proposed for human activity recognition (HAR) from wearable multimodal sensors. Scaling laws have the potential to help move towards more principled design by…

Machine Learning · Computer Science 2025-05-22 Tom Hoddes , Alex Bijamov , Saket Joshi , Daniel Roggen , Ali Etemad , Robert Harle , David Racz

Personalizing diffusion models using limited data presents significant challenges, including overfitting, loss of prior knowledge, and degradation of text alignment. Overfitting leads to shifts in the noise prediction distribution,…

Computer Vision and Pattern Recognition · Computer Science 2025-07-04 JungWoo Chae , Jiyoon Kim , JaeWoong Choi , Kyungyul Kim , Sangheum Hwang

Power-law scaling indicates that large-scale training with uniform sampling is prohibitively slow. Active learning methods aim to increase data efficiency by prioritizing learning on the most relevant examples. Despite their appeal, these…

Artificial Intelligence · Computer Science 2024-10-17 Talfan Evans , Shreya Pathak , Hamza Merzic , Jonathan Schwarz , Ryutaro Tanno , Olivier J. Henaff

Large Language Models have driven significant AI advancements, yet their training is resource-intensive and highly sensitive to hyper-parameter selection. While scaling laws provide valuable guidance on model size and data requirements,…

Machine Learning · Computer Science 2026-05-21 Xingyu Xie , Kuangyu Ding , Shuicheng Yan , Kim-Chuan Toh , Tianwen Wei

Continual learning necessitates the continual adaptation of models to newly emerging tasks while minimizing the catastrophic forgetting of old ones. This is extremely challenging for large language models (LLMs) with vanilla full-parameter…

Computation and Language · Computer Science 2024-10-28 Chenyang Song , Xu Han , Zheni Zeng , Kuai Li , Chen Chen , Zhiyuan Liu , Maosong Sun , Tao Yang

Pre-training large language models is dominated by the memory cost of storing full-rank weights, gradients, and optimizer states. Low-rank pre-training has emerged to address this, and the space of methods has grown rapidly. A central…

Machine Learning · Computer Science 2026-05-20 Namrata Shivagunde , Vijeta Deshpande , Sherin Muckatira , Anna Rumshisky

Language models (LMs) trained on vast quantities of unlabelled data have greatly advanced the field of natural language processing (NLP). In this study, we re-visit the widely accepted notion in NLP that continued pre-training LMs on…

Computation and Language · Computer Science 2023-10-09 Zhengxiang Shi , Aldo Lipani