Related papers: Positional Encoding meets Persistent Homology on G…

We propose a fast methodology for encoding graphs with information-theoretically minimum numbers of bits. Specifically, a graph with property pi is called a pi-graph. If pi satisfies certain properties, then an n-node m-edge pi-graph G can…

Persistent Homology is a powerful tool in Topological Data Analysis (TDA) to capture topological properties of data succinctly at different spatial resolutions. For graphical data, shape, and structure of the neighborhood of individual data…

The flexibility and effectiveness of message passing based graph neural networks (GNNs) induced considerable advances in deep learning on graph-structured data. In such approaches, GNNs recursively update node representations based on their…

Graph neural networks (GNNs) learn to represent nodes by aggregating information from their neighbors. As GNNs increase in depth, their receptive field grows exponentially, leading to high memory costs. Several existing methods address this…

Neuronal morphology encodes critical information about circuit function, development, and disease, yet current methods analyze topology or graph structure in isolation. We introduce GraPHFormer, a multimodal architecture that unifies these…

Graph neural networks (GNNs), which capture graph structures via a feature aggregation mechanism following the graph embedding framework, have demonstrated a powerful ability to support various tasks. According to the topology properties…

Solving partial differential equations (PDEs) serves as a cornerstone for modeling complex dynamical systems. Recent progresses have demonstrated grand benefits of data-driven neural-based models for predicting spatiotemporal dynamics…

The goal of representation learning of knowledge graph is to encode both entities and relations into a low-dimensional embedding spaces. Many recent works have demonstrated the benefits of knowledge graph embedding on knowledge graph…

Graph Nerual Networks (GNNs) are effective models in graph embedding. It extracts shallow features and neighborhood information by aggregating neighbor information to learn the embedding representation of different nodes. However, the local…

Graph pooling compresses graph information into a compact representation. State-of-the-art graph pooling methods follow a hierarchical approach, which reduces the graph size step-by-step. These methods must balance memory efficiency with…

While music remains a challenging domain for generative models like Transformers, recent progress has been made by exploiting suitable musically-informed priors. One technique to leverage information about musical structure in Transformers…

Graph Transformers are popular neural networks that extend the well-known Transformer architecture to the graph domain. These architectures operate by applying self-attention on graph nodes and incorporating graph structure through the use…

Hypergraphs, with their capacity to depict high-order relationships, have emerged as a significant extension of traditional graphs. Although Graph Neural Networks (GNNs) have remarkable performance in graph representation learning, their…

Graph coarsening reduces the size of a graph while preserving certain properties. Most existing methods preserve either spectral or spatial characteristics. Recent research has shown that preserving topological features helps maintain the…

Graph Neural Networks (GNNs) have demonstrated remarkable success in learning from graph-structured data. However, the influence of the input graph's topology on GNN behavior remains poorly understood. In this work, we explore whether GNNs…

We propose a conditional positional encoding (CPE) scheme for vision Transformers. Unlike previous fixed or learnable positional encodings, which are pre-defined and independent of input tokens, CPE is dynamically generated and conditioned…

We conducted empirical experiments to assess the transferability of a light curve transformer to datasets with different cadences and magnitude distributions using various positional encodings (PEs). We proposed a new approach to…

Rotary Positional Embeddings (RoPE) have become the standard for Large Language Models (LLMs) due to their ability to encode relative positions through geometric rotation. However, we identify a significant limitation we term ''Spectral…

Graph Neural Networks (GNNs) have achieved significant success across various domains by leveraging graph structures in data. Existing spectral GNNs, which use low-degree polynomial filters to capture graph spectral properties, may not…

Transformers are increasingly employed for graph data, demonstrating competitive performance in diverse tasks. To incorporate graph information into these models, it is essential to enhance node and edge features with positional encodings.…