Quantization of Large Language Models with an Overdetermined Basis
This work addresses the challenge of data compression for large language models, offering a novel method that could reduce storage and computational costs, though it appears incremental as it builds on existing quantization principles.
The paper tackles the problem of compressing large language models by introducing a quantization algorithm based on Kashin representation, which decomposes data into factors with constrained norms and uses centroids for efficient quantization, achieving competitive or superior performance in next-word prediction and text classification tasks.
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.