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This research introduces a latent variable modeling framework to address the inadequacy of single global scaling curves amidst the growing heterogeneity of LLM architectures and training strategies. By associating latent variables with specific model families, the approach isolates underlying skill drivers that jointly determine performance across diverse benchmarks. The study provides a statistically rigorous estimation procedure and efficient algorithms validated on 12 Open LLM Leaderboard benchmarks, offering a more nuanced tool for analyzing model capabilities.
A Latent Variable Framework for Scaling Laws in Large Language Models
arXiv:2512.06553v2 Announce Type: replace-cross Abstract: 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).
Abstract: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).
Applications (stat.AP); Machine Learning (cs.LG)
arXiv:2512.06553 [stat.AP]
(or arXiv:2512.06553v2 [stat.AP] for this version)
https://doi.org/10.48550/arXiv.2512.06553 Focus to learn more arXiv-issued DOI via DataCite
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