A Latent Variable Framework for Scaling Laws in Large Language Models

TL;DR

This paper introduces a latent variable modeling framework to better understand and predict the performance scaling laws of diverse large language models across multiple benchmarks, addressing heterogeneity issues.

Contribution

It presents a novel latent variable approach that captures common features within LLM families and models their benchmark performance, with an estimation procedure and empirical validation.

Findings

Effective modeling of performance across diverse LLMs

Supports estimation and downstream tasks

Validated on 12 benchmarks from Open LLM Leaderboard

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).