Optimizing Soft Prompt Tuning via Structural Evolution

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.

Rethinking Input Domains in Physics-Informed Neural Networks via Geometric Compactification Mappings

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.

Geometric Neural Operators via Lie Group-Constrained Latent Dynamics

Neural operators offer an effective framework for learning solutions of partial differential equations for many physical systems in a resolution-invariant and data-driven manner. Existing neural operators, however, often suffer from instability in multi-layer iteration and long-horizon rollout, which stems from the unconstrained Euclidean latent space updates that violate the geometric and conservation laws. To address this challenge, we propose to constrain manifolds with low-rank Lie algebra parameterization that performs group action updates on the latent representation. Our method, termed Manifold Constraining based on Lie group (MCL), acts as an efficient \emph{plug-and-play} module that enforces geometric inductive bias to existing neural operators. Extensive experiments on various partial differential equations, such as 1-D Burgers and 2-D Navier-Stokes, over a wide range of parameters and steps demonstrate that our method effectively lowers the relative prediction error by 30-50\% at the cost of 2.26\% of parameter increase. The results show that our approach provides a scalable solution for improving long-term prediction fidelity by addressing the principled geometric constraints absent in the neural operator updates.

On Robustness and Chain-of-Thought Consistency of RL-Finetuned VLMs

Reinforcement learning (RL) fine-tuning has become a key technique for enhancing large language models (LLMs) on reasoning-intensive tasks, motivating its extension to vision language models (VLMs). While RL-tuned VLMs improve on visual reasoning benchmarks, they remain vulnerable to weak visual grounding, hallucinations, and over-reliance on textual cues. We show that simple, controlled textual perturbations--misleading captions or incorrect chain-of-thought (CoT) traces--cause substantial drops in robustness and confidence, and that these effects are more pronounced when CoT consistency is taken into account across open-source multimodal reasoning models. Entropy-based metrics further show that these perturbations reshape model uncertainty and probability mass on the correct option, exposing model-specific trends in miscalibration. To better understand these vulnerabilities, we further analyze RL fine-tuning dynamics and uncover an accuracy-faithfulness trade-off: fine-tuning raises benchmark accuracy, but can simultaneously erode the reliability of the accompanying CoT and its robustness to contextual shifts. Although adversarial augmentation improves robustness, it does not by itself prevent faithfulness drift. Incorporating a faithfulness-aware reward can restore alignment between answers and reasoning, but when paired with augmentation, training risks collapsing onto shortcut strategies and robustness remains elusive. Together, these findings highlight the limitations of accuracy-only evaluations and motivate training and assessment protocols that jointly emphasize correctness, robustness, and the faithfulness of visually grounded reasoning.

Multimodal Classification via Total Correlation Maximization

Multimodal learning integrates data from diverse sensors to effectively harness information from different modalities. However, recent studies reveal that joint learning often overfits certain modalities while neglecting others, leading to performance inferior to that of unimodal learning. Although previous efforts have sought to balance modal contributions or combine joint and unimodal learning, thereby mitigating the degradation of weaker modalities with promising outcomes, few have examined the relationship between joint and unimodal learning from an information-theoretic perspective. In this paper, we theoretically analyze modality competition and propose a method for multimodal classification by maximizing the total correlation between multimodal features and labels. By maximizing this objective, our approach alleviates modality competition while capturing inter-modal interactions via feature alignment. Building on Mutual Information Neural Estimation (MINE), we introduce Total Correlation Neural Estimation (TCNE) to derive a lower bound for total correlation. Subsequently, we present TCMax, a hyperparameter-free loss function that maximizes total correlation through variational bound optimization. Extensive experiments demonstrate that TCMax outperforms state-of-the-art joint and unimodal learning approaches. Our code is available at https://github.com/hubaak/TCMax.

UMAP Is Spectral Clustering on the Fuzzy Nearest-Neighbor Graph

UMAP (Uniform Manifold Approximation and Projection) is among the most widely used algorithms for non linear dimensionality reduction and data visualisation. Despite its popularity, and despite being presented through the lens of algebraic topology, the exact relationship between UMAP and classical spectral methods has remained informal. In this work, we prove that UMAP performs spectral clustering on the fuzzy k nearest neighbour graph. Our proof proceeds in three steps: (1) we show that UMAP's stochastic optimisation with negative sampling is a contrastive learning objective on the similarity graph; (2) we invoke the result of HaoChen et al. [8], establishing that contrastive learning on a similarity graph is equivalent to spectral clustering; and (3) we verify that UMAP's spectral initialisation computes the exact linear solution to this spectral problem. The equivalence is exact for Gaussian kernels, and holds as a first order approximation for UMAP's default Cauchy type kernel. Our result unifies UMAP, contrastive learning, and spectral clustering under a single framework, and provides theoretical grounding for several empirical observations about UMAP's behaviour.

Brain4FMs: A Benchmark of Foundation Models for Electrical Brain Signal

Brain Foundation Models (BFMs) are transforming neuroscience by enabling scalable and transferable learning from neural signals, advancing both clinical diagnostics and cutting-edge neuroscience exploration. Their emergence is powered by large-scale clinical recordings, particularly electroencephalography (EEG) and intracranial EEG, which provide rich temporal and spatial representations of brain dynamics. However, despite their rapid proliferation, the field lacks a unified understanding of existing methodologies and a standardized evaluation framework. To fill this gap, we map the benchmark design space along two axes: (i) from the model perspective, we organize BFMs under a self-supervised learning (SSL) taxonomy; and (ii) from the dataset perspective, we summarize common downstream tasks and curate representative public datasets across clinical and human-centric neurotechnology applications. Building on this consolidation, we introduce Brain4FMs, an open evaluation platform with plug-and-play interfaces that integrates 15 representative BFMs and 18 public datasets. It enables standardized comparisons and analysis of how pretraining data, SSL strategies, and architectures affect generalization and downstream performance, guiding more accurate and transferable BFMs. The code is available at https://anonymous.4open.science/r/Brain4FMs-85B8.

Adaptive Debiasing Tsallis Entropy for Test-Time Adaptation

Mainstream Test-Time Adaptation (TTA) methods for adapting vision-language models, e.g., CLIP, typically rely on Shannon Entropy (SE) at test time to measure prediction uncertainty and inconsistency. However, since CLIP has a built-in bias from pretraining on highly imbalanced web-crawled data, SE inevitably results in producing biased estimates of uncertainty entropy. To address this issue, we notably find and demonstrate that Tsallis Entropy (TE), a generalized form of SE, is naturally suited for characterizing biased distributions by introducing a non-extensive parameter q, with the performance of SE serving as a lower bound for TE. Building upon this, we generalize TE into Adaptive Debiasing Tsallis Entropy (ADTE) for TTA, customizing a class-specific parameter q^l derived by normalizing the estimated label bias from continuously incoming test instances, for each category. This adaptive approach allows ADTE to accurately select high-confidence views and seamlessly integrate with a label adjustment strategy to enhance adaptation, without introducing distribution-specific hyperparameter tuning. Besides, our investigation reveals that both TE and ADTE can serve as direct, advanced alternatives to SE in TTA, without any other modifications. Experimental results show that ADTE outperforms state-of-the-art methods on ImageNet and its five variants, and achieves the highest average performance on 10 cross-domain benchmarks, regardless of the model architecture or text prompts used. Our code is available at https://github.com/Jinx630/ADTE.

Text summarization via global structure awareness

Text summarization is a fundamental task in natural language processing (NLP), and the information explosion has made long-document processing increasingly demanding, making summarization essential. Existing research mainly focuses on model improvements and sentence-level pruning, but often overlooks global structure, leading to disrupted coherence and weakened downstream performance. Some studies employ large language models (LLMs), which achieve higher accuracy but incur substantial resource and time costs. To address these issues, we introduce GloSA-sum, the first summarization approach that achieves global structure awareness via topological data analysis (TDA). GloSA-sum summarizes text efficiently while preserving semantic cores and logical dependencies. Specifically, we construct a semantic-weighted graph from sentence embeddings, where persistent homology identifies core semantics and logical structures, preserved in a ``protection pool'' as the backbone for summarization. We design a topology-guided iterative strategy, where lightweight proxy metrics approximate sentence importance to avoid repeated high-cost computations, thus preserving structural integrity while improving efficiency. To further enhance long-text processing, we propose a hierarchical strategy that integrates segment-level and global summarization. Experiments on multiple datasets demonstrate that GloSA-sum reduces redundancy while preserving semantic and logical integrity, striking a balance between accuracy and efficiency, and further benefits LLM downstream tasks by shortening contexts while retaining essential reasoning chains.

LLM-Grounded Dynamic Task Planning with Hierarchical Temporal Logic for Human-Aware Multi-Robot Collaboration

While Large Language Models (LLM) enable non-experts to specify open-world multi-robot tasks, the generated plans often lack kinematic feasibility and are not efficient, especially in long-horizon scenarios. Formal methods like Linear Temporal Logic (LTL) offer correctness and optimal guarantees, but are typically confined to static, offline settings and struggle with computational scalability. To bridge this gap, we propose a neuro-symbolic framework that grounds LLM reasoning into hierarchical LTL specifications and solves the corresponding Simultaneous Task Allocation and Planning (STAP) problem. Unlike static approaches, our system resolves stochastic environmental changes, such as moving users or updated instructions via a receding horizon planning (RHP) loop with real-time perception, which dynamically refines plans through a hierarchical state space. Extensive real-world experiments demonstrate that our approach significantly outperforms baseline methods in success rate and interaction fluency while minimizing planning latency.