Geometry is All You Need: A Unified Taxonomy of Matrix and Tensor Factorization for Compression of Generative Language Models

TL;DR

This paper introduces a unified geometric algebra-based taxonomy for matrix and tensor factorizations, linking them to NLP model compression techniques to improve understanding and algorithm design.

Contribution

It proposes a formal subspace-based framework that unifies matrix and tensor decompositions with NLP model concepts, facilitating better algorithm development.

Findings

Reformulates matrix/tensor decompositions as geometric transformations.

Bridges algebraic structures with NLP model components.

Identifies research gaps and suggests potential solutions.

Abstract

Matrix and tensor-guided parametrization for Natural Language Processing (NLP) models is fundamentally useful for the improvement of the model's systematic efficiency. However, the internal links between these two algebra structures and language model parametrization are poorly understood. Also, the existing matrix and tensor research is math-heavy and far away from machine learning (ML) and NLP research concepts. These two issues result in the recent progress on matrices and tensors for model parametrization being more like a loose collection of separate components from matrix/tensor and NLP studies, rather than a well-structured unified approach, further hindering algorithm design. To this end, we propose a unified taxonomy, which bridges the matrix/tensor compression approaches and model compression concepts in ML and NLP research. Namely, we adopt an elementary concept in linear algebra, that of a subspace, which is also the core concept in geometric algebra, to reformulate the matrix/tensor and ML/NLP concepts (e.g. attention mechanism) under one umbrella. In this way, based on our subspace formalization, typical matrix and tensor decomposition algorithms can be interpreted as geometric transformations. Finally, we revisit recent literature on matrix- or tensor-guided language model compression, rephrase and compare their core ideas, and then point out the current research gap and potential solutions.