Sheaf Hypergraph Networks

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, higherorder 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.

Dynamic Regions Graph Neural Networks for Spatio-Temporal Reasoning

Graph Neural Networks are perfectly suited to capture latent interactions occurring in the spatio-temporal domain. But when an explicit structure is not available, as in the visual domain, it is not obvious what atomic elements should be represented as nodes. They should depend on the context and the kinds of relations that we are interested in. We are focusing on modeling relations between instances by proposing a method that takes advantage of the locality assumption to create nodes that are clearly localised in space. Current works are using external object detectors or fixed regions to extract features corresponding to graph nodes, while we propose a module for generating the regions associated with each node dynamically, without explicit object-level supervision. Conditioned on the input, for each node we predict the location and size of a region and use them to pool node features using a differentiable mechanism. Constructing these localised, adaptive nodes makes our model biased towards object-centric representations and we show that it improves the modeling of visual interactions. By relying on a few localized nodes, our method learns to focus on salient regions leading to a more explainable model. Our model achieves superior results on video classification tasks involving instance interactions.

Recurrent Space-time Graphs for Video Understanding

Visual learning in the space-time domain remains a very challenging problem in artificial intelligence. Current computational models for understanding video data are heavily rooted in the classical single-image based paradigm. It is not yet well understood how to integrate visual information from space and time into a single, general model. We propose a neural graph model, recurrent in space and time, suitable for capturing both the appearance and the complex interactions of different entities and objects within the changing world scene. Nodes and links in our graph have dedicated neural networks for processing information. Edges process messages between connected nodes at different locations and scales or between past and present time. Nodes compute over features extracted from local parts in space and time and over messages received from their neighbours and previous memory states. 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, a competitive performance over strong baselines on the tasks of recognizing complex patterns of movement in video.

Mining for meaning: from vision to language through multiple networks consensus

Describing visual data into natural language is a very challenging task, at the intersection of computer vision, natural language processing and machine learning. Language goes well beyond the description of physical objects and their interactions and can convey the same abstract idea in many ways. It is both about content at the highest semantic level as well as about fluent form. Here we propose an approach to describe videos in natural language by reaching a consensus among multiple encoder-decoder networks. Finding such a consensual linguistic description, which shares common properties with a larger group, has a better chance to convey the correct meaning. We propose and train several network architectures and use different types of image, audio and video features. Each model produces its own description of the input video and the best one is chosen through an efficient, two-phase consensus process. We demonstrate the strength of our approach by obtaining state of the art results on the challenging MSR-VTT dataset.