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Adaptive Principal Components Allocation with the $\ell_{2,g}$-regularized Gaussian Graphical Model for Efficient Fine-Tuning Large Models

Jingjing Zheng, Yankai Cao

TL;DR

This paper tackles the challenge of parameter-efficient fine-tuning for very large models by modeling inter-parameter interactions with a Gaussian Graphical Model. It introduces a novel $\ell_{2,g}$-regularized GGM and an SVD-based node construction to selectively train principal components per layer, capturing global dependencies that local low-rank methods miss. A BCD optimization framework solves the non-convex $\ell_{2,g}$ objective via a coupled $(\Omega,\Delta)$ formulation, enabling effective node selection through structural sparsity and important-node metrics. Empirical results on the GLUE benchmark with RoBERTa-Base demonstrate competitive performance with significantly fewer trainable parameters, and ablations show the value of including an important-nodes mechanism. Overall, the work advances PEFT by integrating global dependency modeling and non-convex sparsity to achieve both efficiency and effectiveness in fine-tuning.

Abstract

In this work, we propose a novel Parameter-Efficient Fine-Tuning (PEFT) approach based on Gaussian Graphical Models (GGMs), marking the first application of GGMs to PEFT tasks, to the best of our knowledge. The proposed method utilizes the $\ell_{2,g}$-norm to effectively select critical parameters and capture global dependencies. The resulting non-convex optimization problem is efficiently solved using a Block Coordinate Descent (BCD) algorithm. Experimental results on the GLUE benchmark [24] for fine-tuning RoBERTa-Base [18] demonstrate the effectiveness of the proposed approach, achieving competitive performance with significantly fewer trainable parameters. The code for this work is available at: https://github.com/jzheng20/Course projects.git.

Adaptive Principal Components Allocation with the $\ell_{2,g}$-regularized Gaussian Graphical Model for Efficient Fine-Tuning Large Models

TL;DR

This paper tackles the challenge of parameter-efficient fine-tuning for very large models by modeling inter-parameter interactions with a Gaussian Graphical Model. It introduces a novel -regularized GGM and an SVD-based node construction to selectively train principal components per layer, capturing global dependencies that local low-rank methods miss. A BCD optimization framework solves the non-convex objective via a coupled formulation, enabling effective node selection through structural sparsity and important-node metrics. Empirical results on the GLUE benchmark with RoBERTa-Base demonstrate competitive performance with significantly fewer trainable parameters, and ablations show the value of including an important-nodes mechanism. Overall, the work advances PEFT by integrating global dependency modeling and non-convex sparsity to achieve both efficiency and effectiveness in fine-tuning.

Abstract

In this work, we propose a novel Parameter-Efficient Fine-Tuning (PEFT) approach based on Gaussian Graphical Models (GGMs), marking the first application of GGMs to PEFT tasks, to the best of our knowledge. The proposed method utilizes the -norm to effectively select critical parameters and capture global dependencies. The resulting non-convex optimization problem is efficiently solved using a Block Coordinate Descent (BCD) algorithm. Experimental results on the GLUE benchmark [24] for fine-tuning RoBERTa-Base [18] demonstrate the effectiveness of the proposed approach, achieving competitive performance with significantly fewer trainable parameters. The code for this work is available at: https://github.com/jzheng20/Course projects.git.

Paper Structure

This paper contains 15 sections, 18 equations, 2 figures, 4 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Conventions
  3. The Proposed Methodology
  4. How to define the nodes and their values?
  5. Node Definition
  6. Node Value Calculation
  7. The Proposed Gaussian Graphical Model
  8. The $\ell_{2,1}$-regularized Gaussian Graphical Model
  9. The $\ell_{2,1}$-regularized Gaussian Graphical Model with "Important Nodes"
  10. The $\ell_{2,g}$-regularized Gaussian Graphical Model
  11. Optimization by Block Coordinate Descent (BCD) for the Proposed $\ell_{2,g}$-regularized Model
  12. The Updating of the Precision Matrix
  13. The Updating of the Auxiliary Variable
  14. Experiments
  15. Conclusion

Figures (2)

  • Figure 1: Growth of Large Model Parameters (2018–2022).
  • Figure 2: Illustration of the low-rank property in the learned over-parametrized models for (a) Roberta-base (Query) and (b) Roberta-large (Query).