Related papers: Simplicial 2-Complex Convolutional Neural Nets
Motivated by the relevance of higher-order interactions in quantum physics and materials science at the nanoscale, recently a model has been introduced for new classes of networks that grow by the geometrically constrained aggregation of…
Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the…
In this article we show the duality between tensor networks and undirected graphical models with discrete variables. We study tensor networks on hypergraphs, which we call tensor hypernetworks. We show that the tensor hypernetwork on a…
Network Science provides a universal formalism for modelling and studying complex systems based on pairwise interactions between agents. However, many real networks in the social, biological or computer sciences involve interactions among…
Simplicial complexes are gaining increasing scientific attention as they are generalized network structures that can represent the many-body interactions existing in complex systems raging from the brain to high-order social networks.…
The fields of neural computation and artificial neural networks have developed much in the last decades. Most of the works in these fields focus on implementing and/or learning discrete functions or behavior. However, technical, physical,…
We explore a novel method to generate and characterize complex networks by means of their embedding on hyperbolic surfaces. Evolution through local elementary moves allows the exploration of the ensemble of networks which share common…
Optimization for deep networks is currently a very active area of research. As neural networks become deeper, the ability in manually optimizing the network becomes harder. Mini-batch normalization, identification of effective respective…
This paper introduces a generalization of Convolutional Neural Networks (CNNs) from low-dimensional grid data, such as images, to graph-structured data. We propose a novel spatial convolution utilizing a random walk to uncover the relations…
Group convolutional layers with respect to some group $G$ are modeled by convolutions or cross-correlations with a filter, and they provide the fundamental building block for group convolutional neural networks. For entirely unconstrained…
In this paper, we present a hypergraph neural networks (HGNN) framework for data representation learning, which can encode high-order data correlation in a hypergraph structure. Confronting the challenges of learning representation for…
In order to choose a neural network architecture that will be effective for a particular modeling problem, one must understand the limitations imposed by each of the potential options. These limitations are typically described in terms of…
In this paper, we present SIMAP, a novel layer integrated into deep learning models, aimed at enhancing the interpretability of the output. The SIMAP layer is an enhanced version of Simplicial-Map Neural Networks (SMNNs), an explainable…
Graph neural networks have been shown to be very effective in utilizing pairwise relationships across samples. Recently, there have been several successful proposals to generalize graph neural networks to hypergraph neural networks to…
Building on previous work, this paper extends the modeling of political structures from simplicial complexes to hypergraphs. This allows the analysis of more complex political dynamics where agents who are willing to form coalitions contain…
Graph Convolutional Networks (GCNs) have recently become the primary choice for learning from graph-structured data, superseding hash fingerprints in representing chemical compounds. However, GCNs lack the ability to take into account the…
Recent 2D-to-3D human pose estimation works tend to utilize the graph structure formed by the topology of the human skeleton. However, we argue that this skeletal topology is too sparse to reflect the body structure and suffer from serious…
Hypernetworks are neural networks that generate weights for another neural network. We formulate the hypernetwork training objective as a compromise between accuracy and diversity, where the diversity takes into account trivial symmetry…
Complex networks can be used to analyze structures and systems in the embryo. Not only can we characterize growth and the emergence of form, but also differentiation. The process of differentiation from precursor cell populations to…
Convolutional neural networks are witnessing wide adoption in computer vision systems with numerous applications across a range of visual recognition tasks. Much of this progress is fueled through advances in convolutional neural network…