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Optimizing Soft Prompt Tuning via Structural Evolution

Zhenzhen Huang, Chaoning Zhang, Haoyu Bian, Songbo Zhang, Chi-lok Andy Tai, Jiaquan Zhang, Caiyan Qin, Jingjing Qu, Yalan Ye, Yang Yang, Heng Tao Shen

TL;DR

This work employs persistent homology from topological data analysis (TDA) to quantify the structural representations of soft prompts in continuous parameter space and their training process evolution, and constructs a loss function for optimizing soft prompt tuning, termed Topological Soft Prompt Loss (TSLoss).

Abstract

Soft prompt tuning leverages continuous embeddings to capture task-specific information in large pre-trained language models (LLMs), achieving competitive performance in few-shot settings. However, soft prompts rely on high-dimensional, implicit representations and lack explicit semantics and traceable training behaviors, which limits their interpretability. To address this limitation, we propose a soft prompt tuning optimization method based on topological morphological evolution. Specifically, we employ persistent homology from topological data analysis (TDA) to quantify the structural representations of soft prompts in continuous parameter space and their training process evolution. Quantitative analysis shows that topologically stable and compact soft prompts achieve better downstream performance. Based on this empirical observation, we construct a loss function for optimizing soft prompt tuning, termed Topological Soft Prompt Loss (TSLoss). TSLoss guides the model to learn structurally stable adaptations by quantifying inter-parameter connectivity and redundancy. Extensive experiments show that training with TSLoss accelerates convergence and improves tuning performance, providing an interpretable method to understand and optimize soft prompt tuning from structural and topological perspectives.

Optimizing Soft Prompt Tuning via Structural Evolution

TL;DR

This work employs persistent homology from topological data analysis (TDA) to quantify the structural representations of soft prompts in continuous parameter space and their training process evolution, and constructs a loss function for optimizing soft prompt tuning, termed Topological Soft Prompt Loss (TSLoss).

Abstract

Soft prompt tuning leverages continuous embeddings to capture task-specific information in large pre-trained language models (LLMs), achieving competitive performance in few-shot settings. However, soft prompts rely on high-dimensional, implicit representations and lack explicit semantics and traceable training behaviors, which limits their interpretability. To address this limitation, we propose a soft prompt tuning optimization method based on topological morphological evolution. Specifically, we employ persistent homology from topological data analysis (TDA) to quantify the structural representations of soft prompts in continuous parameter space and their training process evolution. Quantitative analysis shows that topologically stable and compact soft prompts achieve better downstream performance. Based on this empirical observation, we construct a loss function for optimizing soft prompt tuning, termed Topological Soft Prompt Loss (TSLoss). TSLoss guides the model to learn structurally stable adaptations by quantifying inter-parameter connectivity and redundancy. Extensive experiments show that training with TSLoss accelerates convergence and improves tuning performance, providing an interpretable method to understand and optimize soft prompt tuning from structural and topological perspectives.
Paper Structure (24 sections, 12 equations, 19 figures, 6 tables)

This paper contains 24 sections, 12 equations, 19 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Soft Prompt Tuning
  4. TDA for Natural Language Process (NLP) Analysis
  5. Structural Analysis of Soft Prompt Tuning
  6. Structural Quantification
  7. Empirical Observations
  8. Topological Soft Prompt Loss
  9. Experiments
  10. Datasets, Models, and Baselines
  11. Implementation Details
  12. Main Result
  13. Convergence Analysis
  14. Parameter Sensitivity Analysis
  15. Generalization Analysis
  16. ...and 9 more sections

Figures (19)

  • Figure 1: Topological evolution of soft prompts parameter space during training process.
  • Figure 2: Changes in density and topological complexity of soft prompts during the training process.
  • Figure 3: Overview of the structural analysis and optimization framework for soft prompts. Persistent homology is used to characterize the structural evolution of soft prompt representations during training, which motivates the design of the proposed TSLoss.
  • Figure 4: Comparison of convergence behavior of overall loss functions with and without TSLoss across different datasets and models.
  • Figure 5: Convergence of overall loss under different TSLoss weight values.
  • ...and 14 more figures