相关论文: Geometry-Aware Simplicial Message Passing

Random walk kernels have been introduced in seminal work on graph learning and were later largely superseded by kernels based on the Weisfeiler-Leman test for graph isomorphism. We give a unified view on both classes of graph kernels. We…

An increasing number of machine learning tasks deal with learning representations from set-structured data. Solutions to these problems involve the composition of permutation-equivariant modules (e.g., self-attention, or individual…

Many scientific problems require to process data in the form of geometric graphs. Unlike generic graph data, geometric graphs exhibit symmetries of translations, rotations, and/or reflections. Researchers have leveraged such inductive bias…

The combinatorial refinement techniques have proven to be an efficient approach to isomorphism testing for particular classes of graphs. If the number of refinement rounds is small, this puts the corresponding isomorphism problem in a…

Propagation modeling is a crucial tool for successful wireless deployments and spectrum planning with the demand for high modeling accuracy continuing to grow. Recognizing that detailed knowledge of the physical environment (terrain and…

Geometric Problem Solving (GPS) poses a unique challenge for Multimodal Large Language Models (MLLMs), requiring not only the joint interpretation of text and diagrams but also iterative visuospatial reasoning. While existing approaches…

Numerous subgraph-enhanced graph neural networks (GNNs) have emerged recently, provably boosting the expressive power of standard (message-passing) GNNs. However, there is a limited understanding of how these approaches relate to each other…

A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links,…

We develop a unified framework for distributed inference, semantic communication, and exploration in spatial networks by integrating stochastic geometry with information geometry - a direction that has not been explored in prior literature.…

Despite their proficiency in general tasks, Multi-modal Large Language Models (MLLMs) struggle with automatic Geometry Problem Solving (GPS), which demands understanding diagrams, interpreting symbols, and performing complex reasoning. This…

Capitalizing on the intuitive premise that shape characteristics are more robust to perturbations, we bridge adversarial graph learning with the emerging tools from computational topology, namely, persistent homology representations of…

Geometric ability is a significant challenge for large language models (LLMs) due to the need for advanced spatial comprehension and abstract thinking. Existing datasets primarily evaluate LLMs on their final answers, but they cannot truly…

Graph Self-Supervised Learning (GSSL) provides a robust pathway for acquiring embeddings without expert labelling, a capability that carries profound implications for molecular graphs due to the staggering number of potential molecules and…

The coherent configuration $\mathsf{WL}(X)$ of a graph $X$ is the smallest coherent configuration on the vertices of $X$ that contains the edge set of $X$ as a relation. The aim of the paper is to study $\mathsf{WL}(X)$ when $X$ is a…

Understanding geometry relies heavily on vision. In this work, we evaluate whether state-of-the-art vision language models (VLMs) can understand simple geometric concepts. We use a paradigm from cognitive science that isolates visual…

Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks, yet have been shown to be oblivious to eminent substructures such as cycles. We present TOGL, a novel layer that incorporates global topological…

We present a neighborhood similarity layer (NSL) which induces appearance invariance in a network when used in conjunction with convolutional layers. We are motivated by the observation that, even though convolutional networks have low…

Graph Neural Networks (GNNs) have achieved remarkable success across diverse applications, yet they remain limited by oversmoothing and poor performance on heterophilic graphs. To address these challenges, we introduce a novel framework…

We extend the framework of K\"ahler information manifolds for complex-valued signal processing filters by introducing weighted Hardy spaces and smooth transformations of transfer functions. We demonstrate that the Riemannian geometry…

Large language models (LLMs) are pretrained by minimizing the cross-entropy loss for next-token prediction. In this paper, we study whether this optimization strategy can induce geometric structure in the learned model weights and context…