Mapper-GIN: Lightweight Structural Graph Abstraction for Corrupted 3D Point Cloud Classification

Robust 3D point cloud classification is often pursued by scaling up backbones or relying on specialized data augmentation. We instead ask whether structural abstraction alone can improve robustness, and study a simple topology-inspired decomposition based on the Mapper algorithm. We propose Mapper-GIN, a lightweight pipeline that partitions a point cloud into overlapping regions using Mapper (PCA lens, cubical cover, and followed by density-based clustering), constructs a region graph from their overlaps, and performs graph classification with a Graph Isomorphism Network. On the corruption benchmark ModelNet40-C, Mapper-GIN achieves competitive and stable accuracy under Noise and Transformation corruptions with only 0.5M parameters. In contrast to prior approaches that require heavier architectures or additional mechanisms to gain robustness, Mapper-GIN attains strong corruption robustness through simple region-level graph abstraction and GIN message passing. Overall, our results suggest that region-graph structure offers an efficient and interpretable source of robustness for 3D visual recognition.

Training A Foundation Model to Represent Graphs as Vectors

This paper aims to train a graph foundation model that is able to represent any graph as a vector preserving structural and semantic information useful for downstream graph-level tasks such as graph classification and graph clustering. To learn the features of graphs from diverse domains while maintaining strong generalization ability to new domains, we propose a multi-graph-based feature alignment method, which constructs weighted graphs using the attributes of all nodes in each dataset and then generates consistent node embeddings. To enhance the consistency of the features from different datasets, we propose a density maximization mean alignment algorithm with guaranteed convergence. The original graphs and generated node embeddings are fed into a graph neural network to achieve discriminative graph representations in contrastive learning. More importantly, to enhance the information preservation from node-level representations to the graph-level representation, we construct a multi-layer reference distribution module without using any pooling operation. We also provide a theoretical generalization bound to support the effectiveness of the proposed model. The experimental results of few-shot graph classification and graph clustering show that our model outperforms strong baselines.

Horizon-LM: A RAM-Centric Architecture for LLM Training

The rapid growth of large language models (LLMs) has outpaced the evolution of single-GPU hardware, making model scale increasingly constrained by memory capacity rather than computation. While modern training systems extend GPU memory through distributed parallelism and offloading across CPU and storage tiers, they fundamentally retain a GPU-centric execution paradigm in which GPUs host persistent model replicas and full autograd graphs. As a result, scaling large models remains tightly coupled to multi-GPU clusters, complex distributed runtimes, and unpredictable host memory consumption, creating substantial barriers for node-scale post-training workloads such as instruction tuning, alignment, and domain adaptation. We present Horizon-LM, a memory-centric training system that redefines the roles of CPU and GPU for large-model optimization. Horizon-LM treats host memory as the authoritative parameter store and uses GPUs solely as transient compute engines through a CPU-master, GPU-template execution model. By eliminating persistent GPU-resident modules and autograd graphs, employing explicit recomputation with manual gradient propagation, and introducing a pipelined double-buffered execution engine, Horizon-LM decouples model scale from GPU count and bounds memory usage to the theoretical parameter footprint. On a single H200 GPU with 1.5\,TB host RAM, Horizon-LM reliably trains models up to 120B parameters. On a standard single A100 machine, Horizon-LM achieves up to 12.2$\times$ higher training throughput than DeepSpeed ZeRO-3 with CPU offloading while preserving numerical correctness. Across platforms and scales, Horizon-LM sustains high device utilization and predictable memory growth, demonstrating that host memory, not GPU memory, defines the true feasibility boundary for node-scale large-model training.

USS-Nav: Unified Spatio-Semantic Scene Graph for Lightweight UAV Zero-Shot Object Navigation

Zero-Shot Object Navigation in unknown environments poses significant challenges for Unmanned Aerial Vehicles (UAVs) due to the conflict between high-level semantic reasoning requirements and limited onboard computational resources. To address this, we present USS-Nav, a lightweight framework that incrementally constructs a Unified Spatio-Semantic scene graph and enables efficient Large Language Model (LLM)-augmented Zero-Shot Object Navigation in unknown environments. Specifically, we introduce an incremental Spatial Connectivity Graph generation method utilizing polyhedral expansion to capture global geometric topology, which is dynamically partitioned into semantic regions via graph clustering. Concurrently, open-vocabulary object semantics are instantiated and anchored to this topology to form a hierarchical environmental representation. Leveraging this hierarchical structure, we present a coarse-to-fine exploration strategy: LLM grounded in the scene graph's semantics to determine global target regions, while a local planner optimizes frontier coverage based on information gain. Experimental results demonstrate that our framework outperforms state-of-the-art methods in terms of computational efficiency and real-time update frequency (15 Hz) on a resource-constrained platform. Furthermore, ablation studies confirm the effectiveness of our framework, showing substantial improvements in Success weighted by Path Length (SPL). The source code will be made publicly available to foster further research.

OD-DEAL: Dynamic Expert-Guided Adversarial Learning with Online Decomposition for Scalable Capacitated Vehicle Routing

Solving large-scale capacitated vehicle routing problems (CVRP) is hindered by the high complexity of heuristics and the limited generalization of neural solvers on massive graphs. We propose OD-DEAL, an adversarial learning framework that tightly integrates hybrid genetic search (HGS) and online barycenter clustering (BCC) decomposition, and leverages high-fidelity knowledge distillation to transfer expert heuristic behavior. OD-DEAL trains a graph attention network (GAT)-based generative policy through a minimax game, in which divide-and-conquer strategies from a hybrid expert are distilled into dense surrogate rewards. This enables high-quality, clustering-free inference on large-scale instances. Empirical results demonstrate that OD-DEAL achieves state-of-the-art (SOTA) real-time CVRP performance, solving 10000-node instances with near-constant neural scaling. This uniquely enables the sub-second, heuristic-quality inference required for dynamic large-scale deployment.

hSNMF: Hybrid Spatially Regularized NMF for Image-Derived Spatial Transcriptomics

High-resolution spatial transcriptomics platforms, such as Xenium, generate single-cell images that capture both molecular and spatial context, but their extremely high dimensionality poses major challenges for representation learning and clustering. In this study, we analyze data from the Xenium platform, which captures high-resolution images of tumor microarray (TMA) tissues and converts them into cell-by-gene matrices suitable for computational analysis. We benchmark and extend nonnegative matrix factorization (NMF) for spatial transcriptomics by introducing two spatially regularized variants. First, we propose Spatial NMF (SNMF), a lightweight baseline that enforces local spatial smoothness by diffusing each cell's NMF factor vector over its spatial neighborhood. Second, we introduce Hybrid Spatial NMF (hSNMF), which performs spatially regularized NMF followed by Leiden clustering on a hybrid adjacency that integrates spatial proximity (via a contact-radius graph) and transcriptomic similarity through a tunable mixing parameter alpha. Evaluated on a cholangiocarcinoma dataset, SNMF and hSNMF achieve markedly improved spatial compactness (CHAOS < 0.004, Moran's I > 0.96), greater cluster separability (Silhouette > 0.12, DBI < 1.8), and higher biological coherence (CMC and enrichment) compared to other spatial baselines. Availability and implementation: https://github.com/ishtyaqmahmud/hSNMF

Community-Level Modeling of Gyral Folding Patterns for Robust and Anatomically Informed Individualized Brain Mapping

Cortical folding exhibits substantial inter-individual variability while preserving stable anatomical landmarks that enable fine-scale characterization of cortical organization. Among these, the three-hinge gyrus (3HG) serves as a key folding primitive, showing consistent topology yet meaningful variations in morphology, connectivity, and function. Existing landmark-based methods typically model each 3HG independently, ignoring that 3HGs form higher-order folding communities that capture mesoscale structure. This simplification weakens anatomical representation and makes one-to-one matching sensitive to positional variability and noise. We propose a spectral graph representation learning framework that models community-level folding units rather than isolated landmarks. Each 3HG is encoded using a dual-profile representation combining surface topology and structural connectivity. Subject-specific spectral clustering identifies coherent folding communities, followed by topological refinement to preserve anatomical continuity. For cross-subject correspondence, we introduce Joint Morphological-Geometric Matching, jointly optimizing geometric and morphometric similarity. Across over 1000 Human Connectome Project subjects, the resulting communities show reduced morphometric variance, stronger modular organization, improved hemispheric consistency, and superior alignment compared with atlas-based and landmark-based or embedding-based baselines. These findings demonstrate that community-level modeling provides a robust and anatomically grounded framework for individualized cortical characterization and reliable cross-subject correspondence.

MK-SGC-SC: Multiple Kernel Guided Sparse Graph Construction in Spectral Clustering for Unsupervised Speaker Diarization

Speaker diarization aims to segment audio recordings into regions corresponding to individual speakers. Although unsupervised speaker diarization is inherently challenging, the prospect of identifying speaker regions without pretraining or weak supervision motivates research on clustering techniques. In this work, we share the notable observation that measuring multiple kernel similarities of speaker embeddings to thereafter craft a sparse graph for spectral clustering in a principled manner is sufficient to achieve state-of-the-art performances in a fully unsupervised setting. Specifically, we consider four polynomial kernels and a degree one arccosine kernel to measure similarities in speaker embeddings, using which sparse graphs are constructed in a principled manner to emphasize local similarities. Experiments show the proposed approach excels in unsupervised speaker diarization over a variety of challenging environments in the DIHARD-III, AMI, and VoxConverse corpora. To encourage further research, our implementations are available at https://github.com/nikhilraghav29/MK-SGC-SC.

Word-Centered Semantic Graphs for Interpretable Diachronic Sense Tracking

We propose an interpretable, graph-based framework for analyzing semantic shift in diachronic corpora. For each target word and time slice, we induce a word-centered semantic network that integrates distributional similarity from diachronic Skip-gram embeddings with lexical substitutability from time-specific masked language models. We identify sense-related structure by clustering the peripheral graph, align clusters across time via node overlap, and track change through cluster composition and normalized cluster mass. In an application study on a corpus of New York Times Magazine articles (1980 - 2017), we show that graph connectivity reflects polysemy dynamics and that the induced communities capture contrasting trajectories: event-driven sense replacement (trump), semantic stability with cluster over-segmentation effects (god), and gradual association shifts tied to digital communication (post). Overall, word-centered semantic graphs offer a compact and transparent representation for exploring sense evolution without relying on predefined sense inventories.

SPARK: Stochastic Propagation via Affinity-guided Random walK for training-free unsupervised segmentation

We argue that existing training-free segmentation methods rely on an implicit and limiting assumption, that segmentation is a spectral graph partitioning problem over diffusion-derived affinities. Such approaches, based on global graph partitioning and eigenvector-based formulations of affinity matrices, suffer from several fundamental drawbacks, they require pre-selecting the number of clusters, induce boundary oversmoothing due to spectral relaxation, and remain highly sensitive to noisy or multi-modal affinity distributions. Moreover, many prior works neglect the importance of local neighborhood structure, which plays a crucial role in stabilizing affinity propagation and preserving fine-grained contours. To address these limitations, we reformulate training-free segmentation as a stochastic flow equilibrium problem over diffusion-induced affinity graphs, where segmentation emerges from a stochastic propagation process that integrates global diffusion attention with local neighborhoods extracted from stable diffusion, yielding a sparse yet expressive affinity structure. Building on this formulation, we introduce a Markov propagation scheme that performs random-walk-based label diffusion with an adaptive pruning strategy that suppresses unreliable transitions while reinforcing confident affinity paths. Experiments across seven widely used semantic segmentation benchmarks demonstrate that our method achieves state-of-the-art zero-shot performance, producing sharper boundaries, more coherent regions, and significantly more stable masks compared to prior spectral-clustering-based approaches.