# Optimizing Soft Prompt Tuning via Structural Evolution

arXiv: https://arxiv.org/abs/2602.16500 · HTML: https://mlsanity.com/paper/2602.16500/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 48 references that are in the map.
- First posted on arXiv 18 Feb 2026.

## Builds on (most cited first, 30 of 34)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding](https://mlsanity.com/paper/2308.14508/) (2023)
- [Parameter-Efficient Fine-Tuning for Large Models: A Comprehensive Survey](https://mlsanity.com/paper/2403.14608/) (2024)
- [DeepSeek LLM: Scaling Open-Source Language Models with Longtermism](https://mlsanity.com/paper/2401.02954/) (2024)
- [SPoT: Better Frozen Model Adaptation through Soft Prompt Transfer](https://mlsanity.com/paper/2110.07904/) (2021)
- [Cross-Entropy Loss Functions: Theoretical Analysis and Applications](https://mlsanity.com/paper/2304.07288/) (2023)
- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [The Prompt Report: A Systematic Survey of Prompt Engineering Techniques](https://mlsanity.com/paper/2406.06608/) (2024)
- [Unveiling and Harnessing Hidden Attention Sinks: Enhancing Large Language Models without Training through Attention Calibration](https://mlsanity.com/paper/2406.15765/) (2024)
- [Artificial Text Detection via Examining the Topology of Attention Maps](https://mlsanity.com/paper/2109.04825/) (2021)
- [Efficient Prompting Methods for Large Language Models: A Survey](https://mlsanity.com/paper/2404.01077/) (2024)
- [MMLU-CF: A Contamination-free Multi-task Language Understanding Benchmark](https://mlsanity.com/paper/2412.15194/) (2024)
- [Universality and Limitations of Prompt Tuning](https://mlsanity.com/paper/2305.18787/) (2023)
- [Soft Prompt Generation for Domain Generalization](https://mlsanity.com/paper/2404.19286/) (2024)
- [The Geometry of Prompting: Unveiling Distinct Mechanisms of Task Adaptation in Language Models](https://mlsanity.com/paper/2502.08009/) (2025)
- [Persistent Topological Features in Large Language Models](https://mlsanity.com/paper/2410.11042/) (2024)
- [Promptomatix: An Automatic Prompt Optimization Framework for Large Language Models](https://mlsanity.com/paper/2507.14241/) (2025)
- [TOPFORMER: Topology-Aware Authorship Attribution of Deepfake Texts with Diverse Writing Styles](https://mlsanity.com/paper/2309.12934/) (2023)
- [Topological Analysis of Syntactic Structures](https://mlsanity.com/paper/1903.05181/) (2019)
- [Improving Complex Reasoning with Dynamic Prompt Corruption: A soft prompt Optimization Approach](https://mlsanity.com/paper/2503.13208/) (2025)
- [Enhancing Cross-lingual Natural Language Inference by Soft Prompting with Multilingual Verbalizer](https://mlsanity.com/paper/2305.12761/) (2023)
- [Soft-Prompting with Graph-of-Thought for Multi-modal Representation Learning](https://mlsanity.com/paper/2404.04538/) (2024)
- [Does the Geometry of Word Embeddings Help Document Classification? A Case Study on Persistent Homology Based Representations](https://mlsanity.com/paper/1705.10900/) (2017)
- [Soft Language Prompts for Language Transfer](https://mlsanity.com/paper/2407.02317/) (2024)

## Abstract (arXiv)

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.