A Latent Variable Framework for Scaling Laws in Large Language Models

Fuente: arXiv
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Main Authors: Cai, Peiyao, Cui, Chengyu, Polo, Felipe Maia, Somerstep, Seamus, Choshen, Leshem, Yurochkin, Mikhail, Banerjee, Moulinath, Sun, Yuekai, Tan, Kean Ming, Xu, Gongjun
Format: Preprint
Published: 2025
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author Cai, Peiyao
Cui, Chengyu
Polo, Felipe Maia
Somerstep, Seamus
Choshen, Leshem
Yurochkin, Mikhail
Banerjee, Moulinath
Sun, Yuekai
Tan, Kean Ming
Xu, Gongjun
author_facet Cai, Peiyao
Cui, Chengyu
Polo, Felipe Maia
Somerstep, Seamus
Choshen, Leshem
Yurochkin, Mikhail
Banerjee, Moulinath
Sun, Yuekai
Tan, Kean Ming
Xu, Gongjun
contents 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 strategies, evaluated on an increasing number of benchmarks. This heterogeneity makes a single global scaling curve inadequate for capturing how performance varies across families and benchmarks. To address this, we propose a latent variable modeling framework in which each LLM family is associated with a latent variable that captures the common underlying features in that family. An LLM's performance on different benchmarks is then driven by its latent skills, which are jointly determined by the latent variable and the model's own observable features. We develop an estimation procedure for this latent variable model and establish its statistical properties. We also design efficient numerical algorithms that support estimation and various downstream tasks. Empirically, we evaluate the approach on 12 widely used benchmarks from the Open LLM Leaderboard (v1/v2).
format Preprint
id arxiv_https___arxiv_org_abs_2512_06553
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A Latent Variable Framework for Scaling Laws in Large Language Models
Cai, Peiyao
Cui, Chengyu
Polo, Felipe Maia
Somerstep, Seamus
Choshen, Leshem
Yurochkin, Mikhail
Banerjee, Moulinath
Sun, Yuekai
Tan, Kean Ming
Xu, Gongjun
Applications
Machine Learning
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 strategies, evaluated on an increasing number of benchmarks. This heterogeneity makes a single global scaling curve inadequate for capturing how performance varies across families and benchmarks. To address this, we propose a latent variable modeling framework in which each LLM family is associated with a latent variable that captures the common underlying features in that family. An LLM's performance on different benchmarks is then driven by its latent skills, which are jointly determined by the latent variable and the model's own observable features. We develop an estimation procedure for this latent variable model and establish its statistical properties. We also design efficient numerical algorithms that support estimation and various downstream tasks. Empirically, we evaluate the approach on 12 widely used benchmarks from the Open LLM Leaderboard (v1/v2).
title A Latent Variable Framework for Scaling Laws in Large Language Models
topic Applications
Machine Learning
url https://arxiv.org/abs/2512.06553