Related papers: Neural Feature Geometry Evolves as Discrete Ricci …

Modern artificial neural networks, including convolutional neural networks and vision transformers, have mastered several computer vision tasks, including object recognition. However, there are many significant differences between the…

The human brain forms functional networks on all spatial scales. Modern fMRI scanners allow to resolve functional brain data in high resolutions, allowing to study large-scale networks that relate to cognitive processes. The analysis of…

The majority of descriptor-based methods for geometric processing of non-rigid shape rely on hand-crafted descriptors. Recently, learning-based techniques have been shown effective, achieving state-of-the-art results in a variety of tasks.…

Deep Neural Networks have shown tremendous success in the area of object recognition, image classification and natural language processing. However, designing optimal Neural Network architectures that can learn and output arbitrary graphs…

The human brain is a complex inter-wired system that emerges spontaneous functional fluctuations. In spite of tremendous success in the experimental neuroscience field, a system-level understanding of how brain anatomy supports various…

The visual system is hierarchically organized to process visual information in successive stages. Neural representations vary drastically across the first stages of visual processing: at the output of the retina, ganglion cell receptive…

This study addresses the limitations of the traditional analysis of message-passing, central to graph learning, by defining {\em \textbf{generalized propagation}} with directed and weighted graphs. The significance manifest in two ways.…

Geometric trees are characterized by their tree-structured layout and spatially constrained nodes and edges, which significantly impacts their topological attributes. This inherent hierarchical structure plays a crucial role in domains such…

A goal in network science is the geometrical characterization of complex networks. In this direction, we have recently introduced Forman's discretization of Ricci curvature to the realm of undirected networks. Investigation of this…

Neural networks with a large number of parameters often do not overfit, owing to implicit regularization that favors \lq good\rq{} networks. Other related and puzzling phenomena include properties of flat minima, saddle-to-saddle dynamics,…

Humans effortlessly navigate the dynamic visual world, yet deep neural networks (DNNs), despite excelling at many visual tasks, are surprisingly vulnerable to minor image perturbations. Past theories suggest that human visual robustness…

Deep neural networks come in many sizes and architectures. The choice of architecture, in conjunction with the dataset and learning algorithm, is commonly understood to affect the learned neural representations. Yet, recent results have…

Graph representation learning aim at integrating node contents with graph structure to learn nodes/graph representations. Nevertheless, it is found that many existing graph learning methods do not work well on data with high heterophily…

Time series forecasting is an extensively studied subject in statistics, economics, and computer science. Exploration of the correlation and causation among the variables in a multivariate time series shows promise in enhancing the…

The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of the success of convolutional neural networks (ConvNets) in image data analysis and other tasks. Inspired by recent interest…

Learning graph representations is a fundamental task aimed at capturing various properties of graphs in vector space. The most recent methods learn such representations for static networks. However, real world networks evolve over time and…

The topological (or graph) structures of real-world networks are known to be predictive of multiple dynamic properties of the networks. Conventionally, a graph structure is represented using an adjacency matrix or a set of hand-crafted…

Euclidean deep learning is often inadequate for addressing real-world signals where the representation space is irregular and curved with complex topologies. Interpreting the geometric properties of such feature spaces has become paramount…

The manifold hypothesis is a core mechanism behind the success of deep learning, so understanding the intrinsic manifold structure of image data is central to studying how neural networks learn from the data. Intrinsic dataset manifolds and…

Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…