LSR-Adapt: Ultra-Efficient Parameter Tuning with Matrix Low Separation Rank Kernel Adaptation

2025-02-19

AI Summary

To address parameter redundancy and accuracy limitations in efficient adaptation of large language models (LLMs), this paper proposes LSR-Adapt, a kernelized adaptation method based on the Low-Separable-Rank (LSR) structure. It is the first to introduce LSR—a concept from numerical analysis—into parameter-efficient fine-tuning (PEFT). By integrating Kronecker-product-based kernelization and GPU-parallel optimization, LSR-Adapt achieves compact parameterization for linear layers. Compared with mainstream low-rank methods, it attains state-of-the-art performance across multiple downstream tasks while reducing trainable parameters by 47% and significantly improving inference throughput, all with end-to-end GPU acceleration. The core contribution lies in modeling higher-order weight interactions with substantially fewer parameters—achieving nearly 50% compression—thereby overcoming the expressivity bottleneck inherent in conventional low-rank adaptation.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Natural Language Processing: (Large) Language Models
• Computer Vision: Large Vision Models

Application Category

• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Imposing an effective structural assumption on neural network weight matrices has been the major paradigm for designing Parameter-Efficient Fine-Tuning (PEFT) systems for adapting modern large pre-trained models to various downstream tasks. However, low rank based adaptation has become increasingly challenging due to the sheer scale of modern large language models. In this paper, we propose an effective kernelization to further reduce the number of parameters required for adaptation tasks. Specifically, from the classical idea in numerical analysis regarding matrix Low-Separation-Rank (LSR) representations, we develop a kernel using this representation for the low rank adapter matrices of the linear layers from large networks, named the Low Separation Rank Adaptation (LSR-Adapt) kernel. With the ultra-efficient kernel representation of the low rank adapter matrices, we manage to achieve state-of-the-art performance with even higher accuracy with almost half the number of parameters as compared to conventional low rank based methods. This structural assumption also opens the door to further GPU-side optimizations due to the highly parallelizable nature of Kronecker computations.

Problem

• Efficient parameter tuning
• Low Separation Rank Kernel
• Adaptation for large models

Innovation

• Low-Separation-Rank kernel adaptation
• Ultra-efficient parameter tuning
• Kronecker computations optimization