Related papers: Scalable Geometric Learning with Correlation-Based…

Modeling non-Euclidean data is drawing extensive attention along with the unprecedented successes of deep neural networks in diverse fields. Particularly, a symmetric positive definite matrix is being actively studied in computer vision,…

The recent reconstruction of the Drosophila brain provides a neural network of unprecedented size and level of details. In this work, we study the geometrical properties of this system by applying network embedding techniques to the graph…

Graph Neural Networks (GNNs) have demonstrated impressive capabilities in modeling graph-structured data, while Spiking Neural Networks (SNNs) offer high energy efficiency through sparse, event-driven computation. However, existing spiking…

Manifold learning has been proven to be an effective method for capturing the implicitly intrinsic structure of non-Euclidean data, in which one of the primary challenges is how to maintain the distortion-free (isometry) of the data…

The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of convolutional neural networks. Inspired by recent interest in geometric deep learning, which aims to generalize convolutional…

Deep neural networks can approximate functions on different types of data, from images to graphs, with varied underlying structure. This underlying structure can be viewed as the geometry of the data manifold. By extending recent advances…

Collision detection is essential to virtually all robotics applications. However, traditional geometric collision detection methods generally require pre-existing workspace geometry representations; thus, they are unable to infer the…

Non-invasive electrophysiology lacks methods that accurately reconstruct whole-brain spatiotemporal dynamics while incorporating individual cortical geometry, leaving current electroencephalography and magnetoencephalography source imaging…

The problem of linking functional connectomics to behavior is extremely challenging due to the complex interactions between the two distinct, but related, data domains. We propose a coupled manifold optimization framework which projects…

In geosciences, the use of classical Euclidean methods is unsuitable for treating and analyzing some types of data, as this may not belong to a vector space. This is the case for correlation matrices, belonging to a subfamily of symmetric…

Machine learning problems have an intrinsic geometric structure as central objects including a neural network's weight space and the loss function associated with a particular task can be viewed as encoding the intrinsic geometry of a given…

Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic…

Data produced by resting-state functional Magnetic Resonance Imaging are widely used to infer brain functional connectivity networks. Such networks correlate neural signals to connect brain regions, which consist in groups of dependent…

Graphs are ubiquitous, and learning on graphs has become a cornerstone in artificial intelligence and data mining communities. Unlike pixel grids in images or sequential structures in language, graphs exhibit a typical non-Euclidean…

This paper introduces GeoMorph, a novel geometric deep-learning framework designed for image registration of cortical surfaces. The registration process consists of two main steps. First, independent feature extraction is performed on each…

Graph representation learning has been widely studied and demonstrated effectiveness in various graph tasks. Most existing works embed graph data in the Euclidean space, while recent works extend the embedding models to hyperbolic or…

Geometric Deep Learning (GDL) unifies a broad class of machine learning techniques from the perspectives of symmetries, offering a framework for introducing problem-specific inductive biases like Graph Neural Networks (GNNs). However, the…

Hyperbolic geometry has emerged as an effective latent space for representing complex networks, owing to its ability to capture hierarchical organization and heterogeneous connectivity patterns using low-dimensional embeddings. As a result,…

State-space models (SSMs) have become a cornerstone for unraveling brain dynamics, revealing how latent neural states evolve over time and give rise to observed signals. By combining the flexibility of deep learning with the principled…

In recent years, functional magnetic resonance imaging has emerged as a powerful tool for investigating the human brain's functional connectivity networks. Related studies demonstrate that functional connectivity networks in the human brain…