The importance of higher-order relations is widely recognized in numerous real-world systems. However, annotating them is a tedious and sometimes even impossible task. Consequently, current approaches for data modelling either ignore the higher-order interactions altogether or simplify them into pairwise connections. To facilitate higher-order processing, even when a hypergraph structure is not available, we introduce SPHINX, a model that learns to infer a latent hypergraph structure in an unsupervised way, solely from the final task-dependent signal. To ensure broad applicability, we design the model to be end-to-end differentiable, capable of generating a discrete hypergraph structure compatible with any modern hypergraph networks, and easily optimizable without requiring additional regularization losses. Through extensive ablation studies and experiments conducted on four challenging datasets, we demonstrate that our model is capable of inferring suitable latent hypergraphs in both transductive and inductive tasks. Moreover, the inferred latent hypergraphs are interpretable and contribute to enhancing the final performance, outperforming existing methods for hypergraph prediction.

Higher-order relations are widespread in nature, with numerous phenomena involving complex interactions that extend beyond simple pairwise connections. As a result, advancements in higher-order processing can accelerate the growth of various fields requiring structured data. Current approaches typically represent these interactions using hypergraphs. We enhance this representation by introducing cellular sheaves for hypergraphs, a mathematical construction that adds extra structure to the conventional hypergraph while maintaining their local, higher-order connectivity. Drawing inspiration from existing Laplacians in the literature, we develop two unique formulations of sheaf hypergraph Laplacians: linear and non-linear. Our theoretical analysis demonstrates that incorporating sheaves into the hypergraph Laplacian provides a more expressive inductive bias than standard hypergraph diffusion, creating a powerful instrument for effectively modelling complex data structures. We employ these sheaf hypergraph Laplacians to design two categories of models: Sheaf Hypergraph Neural Networks and Sheaf Hypergraph Convolutional Networks. These models generalize classical Hypergraph Networks often found in the literature. Through extensive experimentation, we show that this generalization significantly improves performance, achieving top results on multiple benchmark datasets for hypergraph node classification.

Graph Neural Networks are perfectly suited to capture latent interactions between various entities in the spatio-temporal domain (e.g. videos). However, when an explicit structure is not available, it is not obvious what atomic elements should be represented as nodes. Current works generally use pre-trained object detectors or fixed, predefined regions to extract graph nodes. Improving upon this, our proposed model learns nodes that dynamically attach to well-delimited salient regions, which are relevant for a higher-level task, without using any object-level supervision. Constructing these localized, adaptive nodes gives our model inductive bias towards object-centric representations and we show that it discovers regions that are well correlated with objects in the video. In extensive ablation studies and experiments on two challenging datasets, we show superior performance to previous graph neural networks models for video classification.

Learning in the space-time domain remains a very challenging problem in machine learning and computer vision. Current computational models for understanding spatio-temporal visual data are heavily rooted in the classical single-image based paradigm. It is not yet well understood how to integrate information in space and time into a single, general model. We propose a neural graph model, recurrent in space and time, suitable for capturing both the local appearance and the complex higher-level interactions of different entities and objects within the changing world scene. Nodes and edges in our graph have dedicated neural networks for processing information. Nodes operate over features extracted from local parts in space and time and over previous memory states. Edges process messages between connected nodes at different locations and spatial scales or between past and present time. Messages are passed iteratively in order to transmit information globally and establish long range interactions. Our model is general and could learn to recognize a variety of high level spatio-temporal concepts and be applied to different learning tasks. We demonstrate, through extensive experiments and ablation studies, that our model outperforms strong baselines and top published methods on recognizing complex activities in video. Moreover, we obtain state-of-the-art performance on the challenging Something-Something human-object interaction dataset.