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

cs.CLFeb 18, 2026

Optimizing Soft Prompt Tuning via Structural Evolution

Authors: Zhenzhen Huang, Chaoning Zhang, Haoyu Bian, Songbo Zhang, Chi-lok Andy Tai, Jiaquan Zhang, Caiyan Qin, Jingjing Qu,

Organizations: School of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu, China · School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China · College of Professional and Continuing Education, The Hong Kong Polytechnic University, Hong Kong, China · School of Robotics and Advanced Manufacture, Harbin Institute of Technology, Shenzhen, China ·

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.

Figures & tables

Fig. 1: Topological evolution of soft prompts parameter space during training process.

Topological Data Analysis Notation
Symbol	Description
$H_{0}$	Zero-dimensional homology group
$H_{1}$	First-dimensional homology group
$(b_{i},d_{i})$	Birth-death pair of $i$ -th topological feature
$l_{i}$	Lifespan of topological feature ( $l_{i}=d_{i}-b_{i}$ )
$L$	Total lifespan ( $L=\sum_{i}l_{i}$ )

TABLE I: Notation summary for topological analysis of soft prompts

Fig. 2: Changes in density and topological complexity of soft prompts during the training process.

Metric	Spearman Correlation		Mann-Whitney U Test
Metric	$\rho$	p-value	$U$	p-value
$\|H_{0}\|$	N/A	N/A	$2664.5$	$1.000$
$\|H_{1}\|$	$-0.324$	$6.60\times 10^{-5}$	$3600.5$	$9.7\times 10^{-5}$
Avg. $l_{i}$ ( $H_{0}$ )	$0.866$	$3.40\times 10^{-45}$	$0.0$	$1.9\times 10^{-25}$
Avg. $l_{i}$ ( $H_{1}$ )	$0.018$	$0.826$	$2608.0$	$0.827$
PE	$-0.809$	$5.10\times 10^{-35}$	$5153.0$	$2.1\times 10^{-22}$

TABLE II: Correlation and significance of topological features and accuracy

Fig. 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.

Model	Dataset	Soft Prompt	+ L2-Reg	+ PDLoss	ACT	Prefix-Tuning	DPC	Ours
Gemma-2B-IT	GSM8K	14.2	14.8	16.5	16.0	17.8	19.8	20.5
	MMLU	26.5	27.0	28.8	28.2	29.5	31.8	32.4
	LongBench	15.1	15.5	17.2	16.8	18.0	20.0	20.8
Open-LLaMA-7B	GSM8K	32.5	33.1	35.8	34.2	36.5	37.9	38.2
	MMLU	40.2	40.8	42.5	41.5	43.1	45.2	44.8
	LongBench	21.5	21.8	23.2	22.5	23.8	24.8	25.1

TABLE III: Accuracy (%) of different soft prompt tuning methods across models and datasets.

Model	Method	Single-sample			Multi-sample
Model	Method	GSM8K	MMLU-CF	LongBench	GSM8K	MMLU-CF	LongBench
Gemma 2B-IT	Standard	154	8	12	118	16	104
	Prefix-Tuning	128	7	10	96	15	88
	P-Tuning v2	96	6	9	74	14	65
	Ours	88	6	8	62	14	58
Open-LLaMA 7B	Standard	12	4	6	10	8	38

TABLE IV: Number of iterations for soft prompts to achieve complete task accuracy.

Fig. 4: Comparison of convergence behavior of overall loss functions with and without TSLoss across different datasets and models.

Weight ( $\lambda$ )		Temperature ( $\alpha$ )
Value	Iter.	Value	Iter.
0	154	5	112
0.1	130	10	88
0.5	112	20	135
1	88	–	–
10	–	–	–

TABLE V: Impact of weight (

\lambda

) and temperature (

\alpha

) on training iterations.

Fig. 5: Convergence of overall loss under different TSLoss weight values.

Model	Configuration	Iterations to Converge	Improvement
Gemma-2B-IT	CE Baseline	154	–
	CE + $H_{0}$ only	132	14.30%
	CE + $H_{1}$ only	115	25.30%
	CE + TSLoss	88	42.90%
Open-LLaMA-7B	CE Baseline	12	–
	CE + $H_{0}$ only	11	8.30%

TABLE VI: Convergence iterations and relative improvement of different loss components on GSM8K under the single-sample setting.

Fig. 6: Evolution of topological features of soft prompts under different training strategies.

Fig. 7: Heatmaps of the pairwise Euclidean distance matrix among soft prompt vectors.

Fig. 8: Evolution of soft prompt point clouds in PCA space.

Fig. 9: Evolution of soft prompt point clouds in t-SNE space.

Fig. 10: Averaged results of persistent homology in single-sample and multi-sample training on all datasets.

Fig. 11: Averaged results of persistent homology barcodes and lifetime distributions across all datasets. Left panel: single-sample training; right panel: multi-sample training.

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Fig. 12: Single-sample results on GSM8K dataset.

Fig. 13: Multi-sample results on GSM8K dataset.

Fig. 14: Single-sample results on MATH dataset.

Fig. 15: Multi-sample results on MATH dataset.

Fig. 16: Single-sample results on BBH dataset.

Fig. 17: Single-sample results on MMLU-CF dataset.

Fig. 18: Single-sample results on HotpotQA dataset.

Fig. 19: Single-sample results on LongBench dataset.

Prompt Tuning

Prompt tuning adapts pretrained models by learning compact prompts or prefixes instead of updating all model parameters.

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Benchmark scores often misrepresent a large language model's (LLM's) knowledge, because they rely, e.g., on the model's ability to follow specific formatting requirements. This especially penalizes base models that may know the correct answers but lack the ability -- typically introduced in post-training -- to structure them as instructed. To overcome this, we propose an efficient, automated, and architecture-agnostic method for model evaluation based on soft-prompt tuning. By optimizing only 10 soft-prompt vectors (~0.0006% parameters for a 7B model) over a short tuning period, we adapt models to specific benchmark formats, closing gaps in format-following and ensuring that underlying knowledge is accurately reflected in benchmark scores. We evaluate soft-prompt tuning across 7 models and 11 datasets. Our results show that (a) soft-prompt tuning saturates format-following within 150 steps (~1200 samples) while preserving knowledge accuracy, (b) it closely matches strong evaluation-harness baselines on well-studied benchmarks while requiring no manual benchmark-specific prompt or parser design, (c) it improves evaluation signal in settings where baselines are harder to transfer, including long-context datasets and instruction-tuned variants with different output styles, and (d) it produces cleaner outputs that improve agreement between exact match scoring and independent LLM judges. Overall, we propose a lightweight, automated, and flexible protocol based on limited-budget soft-prompt tuning for evaluating LLM knowledge.

Abstract

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