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.

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.

GHS-TDA: A Synergistic Reasoning Framework Integrating Global Hypothesis Space with Topological Data Analysis

Chain-of-Thought (CoT) has been shown to significantly improve the reasoning accuracy of large language models (LLMs) on complex tasks. However, due to the autoregressive, step-by-step generation paradigm, existing CoT methods suffer from two fundamental limitations. First, the reasoning process is highly sensitive to early decisions: once an initial error is introduced, it tends to propagate and amplify through subsequent steps, while the lack of a global coordination and revision mechanism makes such errors difficult to correct, ultimately leading to distorted reasoning chains. Second, current CoT approaches lack structured analysis techniques for filtering redundant reasoning and extracting key reasoning features, resulting in unstable reasoning processes and limited interpretability. To address these issues, we propose GHS-TDA. GHS-TDA first constructs a semantically enriched global hypothesis graph to aggregate, align, and coordinate multiple candidate reasoning paths, thereby providing alternative global correction routes when local reasoning fails. It then applies topological data analysis based on persistent homology to capture stable multi-scale structures, remove redundancy and inconsistencies, and extract a more reliable reasoning skeleton. By jointly leveraging reasoning diversity and topological stability, GHS-TDA achieves self-adaptive convergence, produces high-confidence and interpretable reasoning paths, and consistently outperforms strong baselines in terms of both accuracy and robustness across multiple reasoning benchmarks.

Fat-Cat: Document-Driven Metacognitive Multi-Agent System for Complex Reasoning

The effectiveness of LLM-based agents is often limited not by model capacity alone, but by how efficiently contextual information is utilized at runtime. Existing agent frameworks rely on rigid, syntax-heavy state representations such as nested JSON, which require models to devote a substantial portion of their limited attention to syntactic processing rather than semantic reasoning. In this paper, we propose Fat-Cat, a document-driven agent architecture that improves the signal-to-noise ratio of state management. By integrating three key components: (1) a Semantic File System that represents agent state as Markdown documents aligned with common pre-training corpora, (2) a Textual Strategy Evolution module that accumulates task-solving knowledge without parameter updates, and (3) a Closed-Loop Watcher that monitors reasoning trajectories to reduce hallucinations. Extensive reasoning, retrieval, and coding benchmarks, Fat-Cat consistently improves agent performance. It enables the Kimi-k2 model to outperform the proprietary GPT-4o baseline on HotPotQA. Replacing the document-based state with JSON leads to performance drop, while empirically validating the critical necessity of document-driven state modeling over rigid syntax. The code is available at https://github.com/answeryt/Fat-Cat.

LLaVA-FA: Learning Fourier Approximation for Compressing Large Multimodal Models

Large multimodal models (LMMs) have achieved impressive performance on various vision-language tasks, but their substantial computational and memory costs hinder their practical deployment. Existing compression methods often decouple low-rank decomposition and quantization, leading to compounded reconstruction errors, especially in multimodal architectures with cross-modal redundancy. To address this issue, we propose LLaVA-FA, a novel efficient LMM that performs joint low-rank plus quantization approximation in the frequency domain. By leveraging the de-correlation and conjugate symmetry properties of Fourier transform, LLaVA-FA achieves more compact and accurate weight representations. Furthermore, we introduce PolarQuant, a polar-coordinate quantization method tailored for complex matrices, and an optional diagonal calibration (ODC) scheme that eliminates the need for large-scale calibration data. Extensive experimental results demonstrate that our proposed LLaVA-FA outperforms existing efficient multimodal models across multiple benchmarks while maintaining minimal activated parameters and low computational costs, validating its effectiveness as a powerful solution for compressing LMMs.

GRASP: Guided Region-Aware Sparse Prompting for Adapting MLLMs to Remote Sensing

In recent years, Multimodal Large Language Models (MLLMs) have made significant progress in visual question answering tasks. However, directly applying existing fine-tuning methods to remote sensing (RS) images often leads to issues such as overfitting on background noise or neglecting target details. This is primarily due to the large-scale variations, sparse target distributions, and complex regional semantic features inherent in RS images. These challenges limit the effectiveness of MLLMs in RS tasks. To address these challenges, we propose a parameter-efficient fine-tuning (PEFT) strategy called Guided Region-Aware Sparse Prompting (GRASP). GRASP introduces spatially structured soft prompts associated with spatial blocks extracted from a frozen visual token grid. Through a question-guided sparse fusion mechanism, GRASP dynamically aggregates task-specific context into a compact global prompt, enabling the model to focus on relevant regions while filtering out background noise. Extensive experiments on multiple RSVQA benchmarks show that GRASP achieves competitive performance compared to existing fine-tuning and prompt-based methods while maintaining high parameter efficiency.

Code Evolution for Control: Synthesizing Policies via LLM-Driven Evolutionary Search

Designing effective control policies for autonomous systems remains a fundamental challenge, traditionally addressed through reinforcement learning or manual engineering. While reinforcement learning has achieved remarkable success, it often suffers from high sample complexity, reward shaping difficulties, and produces opaque neural network policies that are hard to interpret or verify. Manual design, on the other hand, requires substantial domain expertise and struggles to scale across diverse tasks. In this work, we demonstrate that LLM-driven evolutionary search can effectively synthesize interpretable control policies in the form of executable code. By treating policy synthesis as a code evolution problem, we harness the LLM's prior knowledge of programming patterns and control heuristics while employing evolutionary search to explore the solution space systematically. We implement our approach using EvoToolkit, a framework that seamlessly integrates LLM-driven evolution with customizable fitness evaluation. Our method iteratively evolves populations of candidate policy programs, evaluating them against task-specific objectives and selecting superior individuals for reproduction. This process yields compact, human-readable control policies that can be directly inspected, modified, and formally verified. This work highlights the potential of combining foundation models with evolutionary computation for synthesizing trustworthy control policies in autonomous systems. Code is available at https://github.com/pgg3/EvoControl.

Fast SAM2 with Text-Driven Token Pruning

Segment Anything Model 2 (SAM2), a vision foundation model has significantly advanced in prompt-driven video object segmentation, yet their practical deployment remains limited by the high computational and memory cost of processing dense visual tokens across time. The SAM2 pipelines typically propagate all visual tokens produced by the image encoder through downstream temporal reasoning modules, regardless of their relevance to the target object, resulting in reduced scalability due to quadratic memory attention overhead. In this work, we introduce a text-guided token pruning framework that improves inference efficiency by selectively reducing token density prior to temporal propagation, without modifying the underlying segmentation architecture. Operating after visual encoding and before memory based propagation, our method ranks tokens using a lightweight routing mechanism that integrates local visual context, semantic relevance derived from object-centric textual descriptions (either user-provided or automatically generated), and uncertainty cues that help preserve ambiguous or boundary critical regions. By retaining only the most informative tokens for downstream processing, the proposed approach reduces redundant computation while maintaining segmentation fidelity. Extensive experiments across multiple challenging video segmentation benchmarks demonstrate that post-encoder token pruning provides a practical and effective pathway to efficient, prompt-aware video segmentation, achieving up to 42.50 percent faster inference and 37.41 percent lower GPU memory usage compared to the unpruned baseline SAM2, while preserving competitive J and F performance. These results highlight the potential of early token selection to improve the scalability of transformer-based video segmentation systems for real-time and resource-constrained applications.