DoTA: Weight-Decomposed Tensor Adaptation for Large Language Models

TL;DR

This paper introduces DoTA, a tensor decomposition-based method for efficient fine-tuning of large language models, which outperforms random initialization and supports quantization for reduced memory usage.

Contribution

It proposes Weight-Decomposed Tensor Adaptation (DoTA) using MPO decomposition for better initialization in LLM fine-tuning, and introduces QDoTA for quantized, memory-efficient adaptation.

Findings

DoTA outperforms random initialization in fine-tuning accuracy.

QDoTA achieves comparable performance with lower memory consumption.

Experiments demonstrate effectiveness on reasoning tasks.

Abstract

Low-rank adaptation (LoRA) reduces the computational and memory demands of fine-tuning large language models (LLMs) by approximating updates with low-rank matrices. However, low-rank approximation in two-dimensional space fails to capture high-dimensional structures within the target matrix. Recently, tensor decomposition methods have been explored for fine-tuning LLMs, leveraging their ability to extract structured information. Yet, these approaches primarily rely on random initialization, and the impact of initialization on tensor adaptation remains underexplored. In this paper, we reveal that random initialization significantly diverges from the validation loss achieved by full fine-tuning. To address this, we propose Weight-Decomposed Tensor Adaptation (DoTA), which leverages the Matrix Product Operator (MPO) decomposition of pre-trained weights for effective initialization in fine-tuning LLMs. Additionally, we introduce QDoTA, a quantized version of DoTA designed for 4-bit quantization. Experiments on commonsense and arithmetic reasoning tasks show that DoTA outperforms random initialization methods with fewer parameters. QDoTA further reduces memory consumption and achieves comparable performance to DoTA on commonsense reasoning tasks. We will release our code to support future research.