Graph neural networks have recently achieved remarkable success in representing graph-structured data, with rapid progress in both the node embedding and graph pooling methods. Yet, they mostly focus on capturing information from the nodes considering their connectivity, and not much work has been done in representing the edges, which are essential components of a graph. However, for tasks such as graph reconstruction and generation, as well as graph classification tasks for which the edges are important for discrimination, accurately representing edges of a given graph is crucial to the success of the graph representation learning. To this end, we propose a novel edge representation learning framework based on Dual Hypergraph Transformation (DHT), which transforms the edges of a graph into the nodes of a hypergraph. This dual hypergraph construction allows us to apply message-passing techniques for node representations to edges. After obtaining edge representations from the hypergraphs, we then cluster or drop edges to obtain holistic graph-level edge representations. We validate our edge representation learning method with hypergraphs on diverse graph datasets for graph representation and generation performance, on which our method largely outperforms existing graph representation learning methods. Moreover, our edge representation learning and pooling method also largely outperforms state-of-theart graph pooling methods on graph classification, not only because of its accurate edge representation learning, but also due to its lossless compression of the nodes and removal of irrelevant edges for effective message-passing.1

This paper pertains to an emerging machine learning paradigm: learning higher-order functions, i.e. functions whose inputs are functions themselves, particularly

Observation-Graph Interaction and Key-Detail Guidance for Vision and Language Navigation Yifan Xie 1, 2, Binkai Ou 3, Fei Ma 4, and Y aohua Liu 2 Abstract -- Vision and Language Navigation (VLN) requires an agent to navigate through environments following natural language instructions. In this paper, we propose OIKG (Observation-graph Interaction and Key-detail Guidance), a novel framework that addresses these limitations through two key components: (1) an observation-graph interaction module that decouples angular and visual information while strengthening edge representations in the navigation space, and (2) a key-detail guidance module that dynamically extracts and utilizes fine-grained location and object information from instructions. By enabling more precise cross-modal alignment and dynamic instruction interpretation, our approach significantly improves the agent's ability to follow complex navigation instructions. Extensive experiments on the R2R and RxR datasets demonstrate that OIKG achieves state-of-the-art performance across multiple evaluation metrics, validating the effectiveness of our method in enhancing navigation precision through better observation-instruction alignment. I. INTRODUCTION Vision and Language Navigation (VLN) [1] is a challenging task that requires an AI agent to navigate through complex 3D environments [2], [3] by following natural language instructions. In this task, agents must process visual information from their surroundings while interpreting detailed navigation instructions to reach specified target locations. This involves understanding spatial relationships, recognizing objects and landmarks, and making sequential navigation decisions based on the cross-modal alignment between visual observations and linguistic guidance.

Dynamic Text-Attributed Graphs (DyTAGs) have numerous real-world applications, e.g. social, collaboration, citation, communication, and review networks. In these networks, nodes and edges often contain text descriptions, and the graph structure can evolve over time. Future link prediction, edge classification, relation generation, and other downstream tasks on DyTAGs require powerful representations that encode structural, temporal, and textual information. Although graph neural networks (GNNs) excel at handling structured data, encoding temporal information within dynamic graphs remains a significant challenge. In this work, we propose LLM-driven Knowledge Distillation for Dynamic Text Attributed Graph (LKD4DyTAG) with temporal encoding to address these challenges. We use a simple, yet effective approach to encode temporal information in edges so that graph convolution can simultaneously capture both temporal and structural information in the hidden representations. To leverage LLM's text processing capabilities for learning richer representations on DyTAGs, we distill knowledge from LLM-driven edge representations (based on a neighborhood's text attributes) into saptio-temporal representations using a lightweight GNN model that encodes temporal and structural information. The objective of knowledge distillation enables the GNN to learn representations that more effectively encode the available structural, temporal, and textual information in DyTAG. We conducted extensive experimentation on six real-world DyTAG datasets to verify the effectiveness of our approach LKD4DyTAG for future link prediction and edge classification task. The results show that our approach significantly improves the performance of downstream tasks compared to the baseline models.

Graph neural networks have recently achieved remarkable success in representing graph-structured data, with rapid progress in both the node embedding and graph pooling methods. Yet, they mostly focus on capturing information from the nodes considering their connectivity, and not much work has been done in representing the edges, which are essential components of a graph. However, for tasks such as graph reconstruction and generation, as well as graph classification tasks for which the edges are important for discrimination, accurately representing edges of a given graph is crucial to the success of the graph representation learning. To this end, we propose a novel edge representation learning framework based on Dual Hypergraph Transformation (DHT), which transforms the edges of a graph into the nodes of a hypergraph. This dual hypergraph construction allows us to apply message-passing techniques for node representations to edges.

Graph representation learning (GRL) is to encode graph elements into informative vector representations, which can be used in downstream tasks for analyzing graph-structured data and has seen extensive applications in various domains. However, the majority of extant studies on GRL are geared towards generating node representations, which cannot be readily employed to perform edge-based analytics tasks in edge-attributed bipartite graphs (EABGs) that pervade the real world, e.g., spam review detection in customer-product reviews and identifying fraudulent transactions in user-merchant networks. Compared to node-wise GRL, learning edge representations (ERL) on such graphs is challenging due to the need to incorporate the structure and attribute semantics from the perspective of edges while considering the separate influence of two heterogeneous node sets U and V in bipartite graphs. To our knowledge, despite its importance, limited research has been devoted to this frontier, and existing workarounds all suffer from sub-par results. Motivated by this, this paper designs EAGLE, an effective ERL method for EABGs. Building on an in-depth and rigorous theoretical analysis, we propose the factorized feature propagation (FFP) scheme for edge representations with adequate incorporation of long-range dependencies of edges/features without incurring tremendous computation overheads. We further ameliorate FFP as a dual-view FFP by taking into account the influences from nodes in U and V severally in ERL. Extensive experiments on 5 real datasets showcase the effectiveness of the proposed EAGLE models in semi-supervised edge classification tasks. In particular, EAGLE can attain a considerable gain of at most 38.11% in AP and 1.86% in AUC when compared to the best baselines.

This paper pertains to an emerging machine learning paradigm: learning higher-order functions, i.e. functions whose inputs are functions themselves, $\textit{particularly when these inputs are Neural Networks (NNs)}$. With the growing interest in architectures that process NNs, a recurring design principle has permeated the field: adhering to the permutation symmetries arising from the connectionist structure of NNs. $\textit{However, are these the sole symmetries present in NN parameterizations}$? Zooming into most practical activation functions (e.g. sine, ReLU, tanh) answers this question negatively and gives rise to intriguing new symmetries, which we collectively refer to as $\textit{scaling symmetries}$, that is, non-zero scalar multiplications and divisions of weights and biases. In this work, we propose $\textit{Scale Equivariant Graph MetaNetworks - ScaleGMNs}$, a framework that adapts the Graph Metanetwork (message-passing) paradigm by incorporating scaling symmetries and thus rendering neuron and edge representations equivariant to valid scalings. We introduce novel building blocks, of independent technical interest, that allow for equivariance or invariance with respect to individual scalar multipliers or their product and use them in all components of ScaleGMN. Furthermore, we prove that, under certain expressivity conditions, ScaleGMN can simulate the forward and backward pass of any input feedforward neural network. Experimental results demonstrate that our method advances the state-of-the-art performance for several datasets and activation functions, highlighting the power of scaling symmetries as an inductive bias for NN processing.