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We propose a statistical framework built on latent variable modeling for scaling laws of large language models (LLMs). Our work is motivated by the rapid emergence of numerous new LLM families with distinct architectures and training…

Token-level reweighting is a simple yet effective mechanism for controlling supervised fine-tuning, but common indicators are largely one-dimensional: the ground-truth probability reflects downstream alignment, while token entropy reflects…

Machine Learning · Computer Science 2026-05-28 Wenhao Yu , Shaohang Wei , Jiahong Liu , Yifan Li , Minda Hu , Aiwei Liu , Hao Zhang , Irwin King

We present an adaptation of RNN sequence models to the problem of multi-label classification for text, where the target is a set of labels, not a sequence. Previous such RNN models define probabilities for sequences but not for sets;…

Computation and Language · Computer Science 2019-04-12 Kechen Qin , Cheng Li , Virgil Pavlu , Javed A. Aslam

Recently a number of empirical "universal" scaling law papers have been published, most notably by OpenAI. `Scaling laws' refers to power-law decreases of training or test error w.r.t. more data, larger neural networks, and/or more compute.…

Machine Learning · Computer Science 2021-02-15 Marcus Hutter

Relevance labels, which indicate whether a search result is valuable to a searcher, are key to evaluating and optimising search systems. The best way to capture the true preferences of users is to ask them for their careful feedback on…

Information Retrieval · Computer Science 2024-05-20 Paul Thomas , Seth Spielman , Nick Craswell , Bhaskar Mitra

Increasing model size has unlocked a dazzling array of capabilities in modern language models. At the same time, even frontier models remain vulnerable to jailbreaks and prompt injections, despite concerted efforts to make them robust. As…

Machine Learning · Computer Science 2025-06-06 Nikolaus Howe , Ian McKenzie , Oskar Hollinsworth , Michał Zajac , Tom Tseng , Aaron Tucker , Pierre-Luc Bacon , Adam Gleave

Robustness and Effectiveness are critical aspects of developing dense retrieval models for real-world applications. It is known that there is a trade-off between the two. Recent work has addressed scaling laws of effectiveness in dense…

Information Retrieval · Computer Science 2025-06-02 Yu-An Liu , Ruqing Zhang , Jiafeng Guo , Maarten de Rijke , Yixing Fan , Xueqi Cheng

The growing disparity between the exponential scaling of computational resources and the finite growth of high-quality text data now constrains conventional scaling approaches for large language models (LLMs). To address this challenge, we…

Large Language Models (LLMs) can achieve inflated scores on multiple-choice tasks by exploiting inherent biases in option positions or labels, rather than demonstrating genuine understanding. This study introduces SCOPE, an evaluation…

Computation and Language · Computer Science 2025-08-05 Wonjun Jeong , Dongseok Kim , Taegkeun Whangbo

Work on scaling laws has found that large language models (LMs) show predictable improvements to overall loss with increased scale (model size, training data, and compute). Here, we present evidence for the claim that LMs may show inverse…

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

Natural languages are full of rules and exceptions. One of the most famous quantitative rules is Zipf's law which states that the frequency of occurrence of a word is approximately inversely proportional to its rank. Though this `law' of…

Computation and Language · Computer Science 2015-05-27 Jake Ryland Williams , James P. Bagrow , Christopher M. Danforth , Peter Sheridan Dodds

Language prediction is constrained by informational entropy intrinsic to language, such that there exists a limit to how accurate any language model can become and equivalently a lower bound to language compression. The most efficient…

Computation and Language · Computer Science 2025-11-14 Benjamin L. Badger , Matthew Neligeorge

Many multilingual NLP applications need to translate words between different languages, but cannot afford the computational expense of inducing or applying a full translation model. For these applications, we have designed a fast algorithm…

cmp-lg · Computer Science 2008-02-03 I. Dan Melamed

As the vocabulary size of modern word-based language models becomes ever larger, many sampling-based training criteria are proposed and investigated. The essence of these sampling methods is that the softmax-related traversal over the…

Computation and Language · Computer Science 2021-06-18 Yingbo Gao , David Thulke , Alexander Gerstenberger , Khoa Viet Tran , Ralf Schlüter , Hermann Ney

According to the Probability Ranking Principle (PRP), ranking documents in decreasing order of their probability of relevance leads to an optimal document ranking for ad-hoc retrieval. The PRP holds when two conditions are met: [C1] the…

Information Retrieval · Computer Science 2021-01-13 Gustavo Penha , Claudia Hauff

In multiclass classification, the goal is to learn how to predict a random label $Y$, valued in $\mathcal{Y}=\{1,\; \ldots,\; K \}$ with $K\geq 3$, based upon observing a r.v. $X$, taking its values in $\mathbb{R}^q$ with $q\geq 1$ say, by…

Machine Learning · Statistics 2020-02-24 Stephan Clémençon , Robin Vogel

Scaling laws in deep learning -- empirical power-law relationships linking model performance to resource growth -- have emerged as simple yet striking regularities across architectures, datasets, and tasks. These laws are particularly…

Machine Learning · Computer Science 2026-05-01 Francesco D'Amico , Dario Bocchi , Matteo Negri

In this paper we combine statistical analysis of large text databases and simple stochastic models to explain the appearance of scaling laws in the statistics of word frequencies. Besides the sublinear scaling of the vocabulary size with…

Physics and Society · Physics 2014-11-05 Martin Gerlach , Eduardo G. Altmann

In recent years, the expansion of neural network models and training data has driven remarkable progress in deep learning, particularly in computer vision and natural language processing. This advancement is underpinned by the concept of…

Machine Learning · Computer Science 2025-08-06 Yi Ma , Hongyao Tang , Chenjun Xiao , Yaodong Yang , Wei Wei , Jianye Hao , Jiye Liang