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.

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.

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.

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.

LiteFusion: Taming 3D Object Detectors from Vision-Based to Multi-Modal with Minimal Adaptation

3D object detection is fundamental for safe and robust intelligent transportation systems. Current multi-modal 3D object detectors often rely on complex architectures and training strategies to achieve higher detection accuracy. However, these methods heavily rely on the LiDAR sensor so that they suffer from large performance drops when LiDAR is absent, which compromises the robustness and safety of autonomous systems in practical scenarios. Moreover, existing multi-modal detectors face difficulties in deployment on diverse hardware platforms, such as NPUs and FPGAs, due to their reliance on 3D sparse convolution operators, which are primarily optimized for NVIDIA GPUs. To address these challenges, we reconsider the role of LiDAR in the camera-LiDAR fusion paradigm and introduce a novel multi-modal 3D detector, LiteFusion. Instead of treating LiDAR point clouds as an independent modality with a separate feature extraction backbone, LiteFusion utilizes LiDAR data as a complementary source of geometric information to enhance camera-based detection. This straightforward approach completely eliminates the reliance on a 3D backbone, making the method highly deployment-friendly. Specifically, LiteFusion integrates complementary features from LiDAR points into image features within a quaternion space, where the orthogonal constraints are well-preserved during network training. This helps model domain-specific relations across modalities, yielding a compact cross-modal embedding. Experiments on the nuScenes dataset show that LiteFusion improves the baseline vision-based detector by +20.4% mAP and +19.7% NDS with a minimal increase in parameters (1.1%) without using dedicated LiDAR encoders. Notably, even in the absence of LiDAR input, LiteFusion maintains strong results , highlighting its favorable robustness and effectiveness across diverse fusion paradigms and deployment scenarios.

Understanding Chain-of-Thought in Large Language Models via Topological Data Analysis

With the development of large language models (LLMs), particularly with the introduction of the long reasoning chain technique, the reasoning ability of LLMs in complex problem-solving has been significantly enhanced. While acknowledging the power of long reasoning chains, we cannot help but wonder: Why do different reasoning chains perform differently in reasoning? What components of the reasoning chains play a key role? Existing studies mainly focus on evaluating reasoning chains from a functional perspective, with little attention paid to their structural mechanisms. To address this gap, this work is the first to analyze and evaluate the quality of the reasoning chain from a structural perspective. We apply persistent homology from Topological Data Analysis (TDA) to map reasoning steps into semantic space, extract topological features, and analyze structural changes. These changes reveal semantic coherence, logical redundancy, and identify logical breaks and gaps. By calculating homology groups, we assess connectivity and redundancy at various scales, using barcode and persistence diagrams to quantify stability and consistency. Our results show that the topological structural complexity of reasoning chains correlates positively with accuracy. More complex chains identify correct answers sooner, while successful reasoning exhibits simpler topologies, reducing redundancy and cycles, enhancing efficiency and interpretability. This work provides a new perspective on reasoning chain quality assessment and offers guidance for future optimization.

Grounding Everything in Tokens for Multimodal Large Language Models

Multimodal large language models (MLLMs) have made significant advancements in vision understanding and reasoning. However, the autoregressive Transformer architecture used by MLLMs requries tokenization on input images, which limits their ability to accurately ground objects within the 2D image space. This raises an important question: how can sequential language tokens be improved to better ground objects in 2D spatial space for MLLMs? To address this, we present a spatial representation method for grounding objects, namely GETok, that integrates a specialized vocabulary of learnable tokens into MLLMs. GETok first uses grid tokens to partition the image plane into structured spatial anchors, and then exploits offset tokens to enable precise and iterative refinement of localization predictions. By embedding spatial relationships directly into tokens, GETok significantly advances MLLMs in native 2D space reasoning without modifying the autoregressive architecture. Extensive experiments demonstrate that GETok achieves superior performance over the state-of-the-art methods across various referring tasks in both supervised fine-tuning and reinforcement learning settings.

Information Gain-based Policy Optimization: A Simple and Effective Approach for Multi-Turn LLM Agents

Large language model (LLM)-based agents are increasingly trained with reinforcement learning (RL) to enhance their ability to interact with external environments through tool use, particularly in search-based settings that require multi-turn reasoning and knowledge acquisition. However, existing approaches typically rely on outcome-based rewards that are only provided at the final answer. This reward sparsity becomes particularly problematic in multi-turn settings, where long trajectories exacerbate two critical issues: (i) advantage collapse, where all rollouts receive identical rewards and provide no useful learning signals, and (ii) lack of fine-grained credit assignment, where dependencies between turns are obscured, especially in long-horizon tasks. In this paper, we propose Information Gain-based Policy Optimization (IGPO), a simple yet effective RL framework that provides dense and intrinsic supervision for multi-turn agent training. IGPO models each interaction turn as an incremental process of acquiring information about the ground truth, and defines turn-level rewards as the marginal increase in the policy's probability of producing the correct answer. Unlike prior process-level reward approaches that depend on external reward models or costly Monte Carlo estimation, IGPO derives intrinsic rewards directly from the model's own belief updates. These intrinsic turn-level rewards are combined with outcome-level supervision to form dense reward trajectories. Extensive experiments on both in-domain and out-of-domain benchmarks demonstrate that IGPO consistently outperforms strong baselines in multi-turn scenarios, achieving higher accuracy and improved sample efficiency.

GeoPurify: A Data-Efficient Geometric Distillation Framework for Open-Vocabulary 3D Segmentation

Recent attempts to transfer features from 2D Vision-Language Models (VLMs) to 3D semantic segmentation expose a persistent trade-off. Directly projecting 2D features into 3D yields noisy and fragmented predictions, whereas enforcing geometric coherence necessitates costly training pipelines and large-scale annotated 3D data. We argue that this limitation stems from the dominant segmentation-and-matching paradigm, which fails to reconcile 2D semantics with 3D geometric structure. The geometric cues are not eliminated during the 2D-to-3D transfer but remain latent within the noisy and view-aggregated features. To exploit this property, we propose GeoPurify that applies a small Student Affinity Network to purify 2D VLM-generated 3D point features using geometric priors distilled from a 3D self-supervised teacher model. During inference, we devise a Geometry-Guided Pooling module to further denoise the point cloud and ensure the semantic and structural consistency. Benefiting from latent geometric information and the learned affinity network, GeoPurify effectively mitigates the trade-off and achieves superior data efficiency. Extensive experiments on major 3D benchmarks demonstrate that GeoPurify achieves or surpasses state-of-the-art performance while utilizing only about 1.5% of the training data. Our codes and checkpoints are available at [https://github.com/tj12323/GeoPurify](https://github.com/tj12323/GeoPurify).

Careful Queries, Credible Results: Teaching RAG Models Advanced Web Search Tools with Reinforcement Learning

Retrieval-Augmented Generation (RAG) enhances large language models (LLMs) by integrating up-to-date external knowledge, yet real-world web environments present unique challenges. These limitations manifest as two key challenges: pervasive misinformation in the web environment, which introduces unreliable or misleading content that can degrade retrieval accuracy, and the underutilization of web tools, which, if effectively employed, could enhance query precision and help mitigate this noise, ultimately improving the retrieval results in RAG systems. To address these issues, we propose WebFilter, a novel RAG framework that generates source-restricted queries and filters out unreliable content. This approach combines a retrieval filtering mechanism with a behavior- and outcome-driven reward strategy, optimizing both query formulation and retrieval outcomes. Extensive experiments demonstrate that WebFilter improves answer quality and retrieval precision, outperforming existing RAG methods on both in-domain and out-of-domain benchmarks.