Related papers: Scalable Geometric Learning with Correlation-Based…

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…

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…

Embedding graphs in continous spaces is a key factor in designing and developing algorithms for automatic information extraction to be applied in diverse tasks (e.g., learning, inferring, predicting). The reliability of graph embeddings…

A large number of surface-based analyses on brain imaging data adopt some specific brain atlases to better assess structural and functional changes in one or more brain regions. In these analyses, it is necessary to obtain an anatomically…

Graph neural networks face two fundamental challenges rooted in the linear structure of Euclidean vector spaces: (1) Current architectures represent geometry through vectors (directions, gradients), yet many tasks require matrix-valued…

In this paper, we present a method of embedding physics data manifolds with metric structure into lower dimensional spaces with simpler metrics, such as Euclidean and Hyperbolic spaces. We then demonstrate that it can be a powerful step in…

Neural computation in biological and artificial networks relies on the nonlinear summation of many inputs. The structural connectivity matrix of synaptic weights between neurons is a critical determinant of overall network function, but…

Neural models learn representations of high-dimensional data on low-dimensional manifolds. Multiple factors, including stochasticities in the training process, model architectures, and additional inductive biases, may induce different…

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…

Geometric Machine Learning (GML) has shown that respecting non-Euclidean geometry in data spaces can significantly improve performance over naive Euclidean assumptions. In parallel, Quantum Machine Learning (QML) has emerged as a promising…

Euclidean representation learning methods have achieved promising results in image fusion tasks, which can be attributed to their clear advantages in handling with linear space. However, data collected from a realistic scene usually has a…

Riemannian geometry has been applied to Brain Computer Interface (BCI) for brain signals classification yielding promising results. Studying electroencephalographic (EEG) signals from their associated covariance matrices allows a mitigation…

We survey the mathematical foundations of geometric deep learning, focusing on group equivariant and gauge equivariant neural networks. We develop gauge equivariant convolutional neural networks on arbitrary manifolds $\mathcal{M}$ using…

Diffusion geometry is a manifold learning framework that uses random walks defined by Markov transition matrices to characterize the geometry of a dataset at multiple scales. We use diffusion geometry for neural representations,…

In this work, we develop new generalization bounds for neural networks trained on data supported on Riemannian manifolds. Existing generalization theories often rely on complexity measures derived from Euclidean geometry, which fail to…

This article presents a neural network approach for estimating the covariance function of spatial Gaussian random fields defined in a portion of the Euclidean plane. Our proposal builds upon recent contributions, expanding from the purely…

Learning representations on Grassmann manifolds is popular in quite a few visual recognition tasks. In order to enable deep learning on Grassmann manifolds, this paper proposes a deep network architecture by generalizing the Euclidean…

Grassmannian manifold offers a powerful carrier for geometric representation learning by modelling high-dimensional data as low-dimensional subspaces. However, existing approaches predominantly rely on static single-subspace…

This paper introduces the Neural Differential Manifold (NDM), a novel neural network architecture that explicitly incorporates geometric structure into its fundamental design. Departing from conventional Euclidean parameter spaces, the NDM…

Graph representation learning in Euclidean space, despite its widespread adoption and proven utility in many domains, often struggles to effectively capture the inherent hierarchical and complex relational structures prevalent in real-world…