Caiyan Qin

Zhenzhen Huang, Chaoning Zhang, Haoyu Bian et al.

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.

Jiaquan Zhang, Qigan Sun, Chaoning Zhang et al.

Enhancing the reasoning capability of large language models (LLMs) remains a core challenge in natural language processing. The Chain-of-Thought (CoT) paradigm dominates practical applications for its single-round efficiency, yet its reasoning chains often exhibit logical gaps. While multi-round paradigms like Graph-of-Thoughts (GoT), Tree-of-Thoughts (ToT), and Atom of Thought (AoT) achieve strong performance and reveal effective reasoning structures, their high cost limits practical use. To address this problem, this paper proposes a topology-based method for optimizing reasoning chains. The framework embeds essential topological patterns of effective reasoning into the lightweight CoT paradigm. Using persistent homology, we map CoT, ToT, and GoT into a unified topological space to quantify their structural features. On this basis, we design a unified optimization system: a Topological Optimization Agent diagnoses deviations in CoT chains from desirable topological characteristics and simultaneously generates targeted strategies to repair these structural deficiencies. Compared with multi-round reasoning methods like ToT and GoT, experiments on multiple datasets show that our approach offers a superior balance between reasoning accuracy and efficiency, showcasing a practical solution to ``single-round generation with multi-round intelligence''.

Zhenzhen Huang, Haoyu Bian, Jiaquan Zhang et al.

Several complex physical systems are governed by multi-scale partial differential equations (PDEs) that exhibit both smooth low-frequency components and localized high-frequency structures. Existing physics-informed neural network (PINN) methods typically train with fixed coordinate system inputs, where geometric misalignment with these structures induces gradient stiffness and ill-conditioning that hinder convergence. To address this issue, we introduce a mapping paradigm that reshapes the input coordinates through differentiable geometric compactification mappings and couples the geometric structure of PDEs with the spectral properties of residual operators. Based on this paradigm, we propose Geometric Compactification (GC)-PINN, a framework that introduces three mapping strategies for periodic boundaries, far-field scale expansion, and localized singular structures in the input domain without modifying the underlying PINN architecture. Extensive empirical evaluation demonstrates that this approach yields more uniform residual distributions and higher solution accuracy on representative 1D and 2D PDEs, while improving training stability and convergence speed.