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Knowledge hypergraphs generalize knowledge graphs using hyperedges to connect multiple entities and depict complicated relations. Existing methods either transform hyperedges into an easier-to-handle set of binary relations or view…

The Strong Platonic Representation Hypothesis suggests that representational convergence in artificial neural networks can be harnessed constructively: embeddings can be translated across models through a universal latent space without…

In a graph convolutional network, we assume that the graph $G$ is generated wrt some observation noise. During learning, we make small random perturbations $\Delta{}G$ of the graph and try to improve generalization. Based on quantum…

One of the pillars of the geometric approach to networks has been the development of model-based mapping tools that embed real networks in its latent geometry. In particular, the tool Mercator embeds networks into the hyperbolic plane.…

We present HARP, a novel method for learning low dimensional embeddings of a graph's nodes which preserves higher-order structural features. Our proposed method achieves this by compressing the input graph prior to embedding it, effectively…

Emerging brain network studies suggest that interactions between various distributed neuronal populations may be characterized by an organized complex topological structure. Many brain diseases are associated with altered topological…

In network data analysis, it is becoming common to work with a collection of graphs that exhibit \emph{heterogeneity}. For example, neuroimaging data from patient cohorts are increasingly available. A critical analytical task is to identify…

Hyperbolic representations are effective in modeling knowledge graph data which is prevalently used to facilitate multi-hop reasoning. However, a rigorous and detailed comparison of the two spaces for this task is lacking. In this paper,…

The high computational complexity and increasing parameter counts of deep neural networks pose significant challenges for deployment in resource-constrained environments, such as edge devices or real-time systems. To address this, we…

Graphical models have been used extensively for modeling brain connectivity networks. However, unmeasured confounders and correlations among measurements are often overlooked during model fitting, which may lead to spurious scientific…

Graph Neural Networks (GNN) can capture the geometric properties of neural representations in EEG data. Here we utilise those to study how reinforcement-based motor learning affects neural activity patterns during motor planning, leveraging…

The observation, design and analysis of mesh-like networks in bionics, polymer physics and biological systems has brought forward an extensive catalog of fascinating structures of which a subgroup share a particular, yet critically under…

With the recent advance of geometric deep learning, neural networks have been extensively used for data in non-Euclidean domains. In particular, hyperbolic neural networks have proved successful in processing hierarchical information of…

Network embedding is an effective technique to learn the low-dimensional representations of nodes in networks. Real-world networks are usually with multiplex or having multi-view representations from different relations. Recently, there has…

Nickel and Kiela (2017) present a new method for embedding tree nodes in the Poincare ball, and suggest that these hyperbolic embeddings are far more effective than Euclidean embeddings at embedding nodes in large, hierarchically structured…

The correlation matrix is a central representation of functional brain networks in neuroimaging. Traditional analyses often treat pairwise interactions independently in a Euclidean setting, overlooking the intrinsic geometry of correlation…

Forecasting chaotic dynamics beyond a few Lyapunov times is difficult because infinitesimal errors grow exponentially. Existing Echo State Networks (ESNs) mitigate this growth but employ reservoirs whose Euclidean geometry is mismatched to…

Several problems such as network intrusion, community detection, and disease outbreak can be described by observations attributed to nodes or edges of a graph. In these applications presence of intrusion, community or disease outbreak is…

Functional brain graphs are often characterized with separate graph-theoretic or spectral descriptors, overlooking how these properties covary and partially overlap across brains and conditions. We anticipate that dense, weighted functional…

Graph embedding is becoming an important method with applications in various areas, including social networks and knowledge graph completion. In particular, Poincar\'e embedding has been proposed to capture the hierarchical structure of…