Unified Scaling Laws for Compressed Representations

TL;DR

This paper develops a unified scaling law framework that predicts model performance across various compressed representations, such as sparse and quantized formats, facilitating better understanding and optimization of compressed models.

Contribution

It validates a general scaling law applicable to multiple compression types and introduces a capacity metric to predict efficiency and accuracy across compressed formats.

Findings

A simple capacity metric predicts parameter efficiency across compression formats.

The scaling law framework is validated both theoretically and empirically.

Extensions enable comparison of compressed formats and improved training algorithms.

Abstract

Scaling laws have shaped recent advances in machine learning by enabling predictable scaling of model performance based on model size, computation, and data volume. Concurrently, the rise in computational cost for AI has motivated model compression techniques, notably quantization and sparsification, which have emerged to mitigate the steep computational demands associated with large-scale training and inference. This paper investigates the interplay between scaling laws and compression formats, exploring whether a unified scaling framework can accurately predict model performance when training occurs over various compressed representations, such as sparse, scalar-quantized, sparse-quantized or even vector-quantized formats. Our key contributions include validating a general scaling law formulation and showing that it is applicable both individually but also composably across compression types. Based on this, our main finding is demonstrating both theoretically and empirically that there exists a simple "capacity" metric -- based on the representation's ability to fit random Gaussian data -- which can robustly predict parameter efficiency across multiple compressed representations. On the practical side, we extend our formulation to directly compare the accuracy potential of different compressed formats, and to derive better algorithms for training over sparse-quantized formats.