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TriAdaptLoRA: Brain-Inspired Triangular Adaptive Low-Rank Adaptation for Parameter-Efficient Fine-Tuning

Yao Liang, Yuwei Wang, Yi Zeng

TL;DR

TriAdaptLoRA tackles the challenge of efficient yet effective fine-tuning of large language models by introducing a brain-inspired PEFT framework that dynamically reallocates trainable parameters. It achieves this with a triangular split of transformation matrices, an efficient normalized-Frobenius-norm based importance metric, and adaptive rank-growth governed by dynamic thresholds, enabling scalable parameter growth without excessive computation. Empirical results on GLUE and SQuAD 2.0 show that TriAdaptLoRA outperforms fixed-rank LoRA variants and competitive adaptive baselines while reducing overhead and maintaining stability. The approach holds promise for resource-constrained settings, offering a practical, interpretable path toward robust, low-cost fine-tuning of large models.

Abstract

The fine-tuning of Large Language Models (LLMs) is pivotal for achieving optimal performance across diverse downstream tasks. However, while full fine-tuning delivers superior results, it entails significant computational and resource costs. Parameter-Efficient Fine-Tuning (PEFT) methods, such as LoRA, address these challenges by reducing the number of trainable parameters, but they often struggle with rank adjustment efficiency and task-specific adaptability. We propose Triangular Adaptive Low-Rank Adaptation (TriAdaptLoRA), a novel PEFT framework inspired by neuroscience principles, which dynamically optimizes the allocation of trainable parameters. TriAdaptLoRA introduces three key innovations: 1) a triangular split of transformation matrices into lower and upper triangular components to maximize parameter utilization, 2) a parameter importance metric based on normalized Frobenius norms for efficient adaptation, and 3) an adaptive rank-growth strategy governed by dynamic thresholds, allowing flexible parameter allocation across training steps. Experiments conducted on a variety of natural language understanding and generation tasks demonstrate that TriAdaptLoRA consistently outperforms existing PEFT methods. It achieves superior performance, enhanced stability, and reduced computational overhead, particularly under linear threshold-driven rank growth. These results highlight its efficacy as a scalable and resource-efficient solution for fine-tuning LLMs.

TriAdaptLoRA: Brain-Inspired Triangular Adaptive Low-Rank Adaptation for Parameter-Efficient Fine-Tuning

TL;DR

TriAdaptLoRA tackles the challenge of efficient yet effective fine-tuning of large language models by introducing a brain-inspired PEFT framework that dynamically reallocates trainable parameters. It achieves this with a triangular split of transformation matrices, an efficient normalized-Frobenius-norm based importance metric, and adaptive rank-growth governed by dynamic thresholds, enabling scalable parameter growth without excessive computation. Empirical results on GLUE and SQuAD 2.0 show that TriAdaptLoRA outperforms fixed-rank LoRA variants and competitive adaptive baselines while reducing overhead and maintaining stability. The approach holds promise for resource-constrained settings, offering a practical, interpretable path toward robust, low-cost fine-tuning of large models.

Abstract

The fine-tuning of Large Language Models (LLMs) is pivotal for achieving optimal performance across diverse downstream tasks. However, while full fine-tuning delivers superior results, it entails significant computational and resource costs. Parameter-Efficient Fine-Tuning (PEFT) methods, such as LoRA, address these challenges by reducing the number of trainable parameters, but they often struggle with rank adjustment efficiency and task-specific adaptability. We propose Triangular Adaptive Low-Rank Adaptation (TriAdaptLoRA), a novel PEFT framework inspired by neuroscience principles, which dynamically optimizes the allocation of trainable parameters. TriAdaptLoRA introduces three key innovations: 1) a triangular split of transformation matrices into lower and upper triangular components to maximize parameter utilization, 2) a parameter importance metric based on normalized Frobenius norms for efficient adaptation, and 3) an adaptive rank-growth strategy governed by dynamic thresholds, allowing flexible parameter allocation across training steps. Experiments conducted on a variety of natural language understanding and generation tasks demonstrate that TriAdaptLoRA consistently outperforms existing PEFT methods. It achieves superior performance, enhanced stability, and reduced computational overhead, particularly under linear threshold-driven rank growth. These results highlight its efficacy as a scalable and resource-efficient solution for fine-tuning LLMs.
Paper Structure (31 sections, 17 equations, 5 figures, 7 tables, 1 algorithm)

This paper contains 31 sections, 17 equations, 5 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related work
  3. The Proposed Method
  4. Neuroscience Inspiration
  5. Parameter Expansion via Triangular Split
  6. Efficient Parameter Importance Evaluation
  7. Adaptive Rank Growth with Dynamic Thresholds
  8. Linear Threshold
  9. Nonlinear Threshold
  10. Rank Growth
  11. Analysis of the Role of the Transformation Matrix
  12. Experiments
  13. Baseline
  14. Natural Language Understanding Tasks
  15. Base Model and Tasks
  16. ...and 16 more sections

Figures (5)

  • Figure 1: Schematic diagram of TriAdaptLoRA's overall structure.
  • Figure 2: Heatmaps illustrate the final rank distributions. These distributions are shown for each layer and weight matrix of the TriAdaptLoRA, AdaLoRA, and IncreLoRA methods on the MNLI task.
  • Figure 3: Experimental results on the RTE task with different initial warm-up steps for TriAdaptLoRA and IncreLoRA methods based on the DeBERTaV3-base model.
  • Figure 4: Experimental results on the RTE task with different rank update intervals for TriAdaptLoRA and IncreLoRA methods based on the DeBERTaV3-base model.
  • Figure 5: Experimental results on the RTE task with different reference rank sizes for TriAdaptLoRA and IncreLoRA methods based on the DeBERTaV3-base model.