Quantization of Large Language Models with an Overdetermined Basis

TL;DR

This paper presents Kashin Quantization, a novel data compression method for large language models that decomposes data into factors with constrained norms, enabling efficient quantization without significant performance loss.

Contribution

The paper introduces a new quantization algorithm based on Kashin representation, providing theoretical insights and demonstrating competitive compression performance in language modeling tasks.

Findings

Achieves competitive or superior model performance after quantization

Effectively compresses data with minimal impact on downstream tasks

Provides theoretical analysis of the quantization method

Abstract

In this paper, we introduce an algorithm for data quantization based on the principles of Kashin representation. This approach hinges on decomposing any given vector, matrix, or tensor into two factors. The first factor maintains a small infinity norm, while the second exhibits a similarly constrained norm when multiplied by an orthogonal matrix. Surprisingly, the entries of factors after decomposition are well-concentrated around several peaks, which allows us to efficiently replace them with corresponding centroids for quantization purposes. We study the theoretical properties of the proposed approach and rigorously evaluate our compression algorithm in the context of next-word prediction tasks and on a set of downstream tasks for text classification. Our findings demonstrate that Kashin Quantization achieves competitive or superior quality in model performance while ensuring data compression, marking a significant advancement in the field of data quantization.