Related papers: Embed Me If You Can: A Geometric Perceptron

Modern deep learning architectures increasingly contend with sophisticated signals that are natively infinite-dimensional, such as time series, probability distributions, or operators, and are defined over irregular domains. Yet, a unified…

Recent works in geometric deep learning have introduced neural networks that allow performing inference tasks on three-dimensional geometric data by defining convolution, and sometimes pooling, operations on triangle meshes. These methods,…

Superposition -- when a neural network represents more ``features'' than it has dimensions -- seems to pose a serious challenge to mechanistically interpreting current AI systems. Existing theory work studies \emph{representational}…

Existing deep learning algorithms for point cloud analysis mainly concern discovering semantic patterns from global configuration of local geometries in a supervised learning manner. However, very few explore geometric properties revealing…

In high-energy physics, the increasing luminosity and detector granularity at the Large Hadron Collider are driving the need for more efficient data processing solutions. Machine Learning has emerged as a promising tool for reconstructing…

Matrix manifolds, such as manifolds of Symmetric Positive Definite (SPD) matrices and Grassmann manifolds, appear in many applications. Recently, by applying the theory of gyrogroups and gyrovector spaces that is a powerful framework for…

Neural implicit surface representations have recently emerged as popular alternative to explicit 3D object encodings, such as polygonal meshes, tabulated points, or voxels. While significant work has improved the geometric fidelity of these…

We present a new technique that enables manifold learning to accurately embed data manifolds that contain holes, without discarding any topological information. Manifold learning aims to embed high dimensional data into a lower dimensional…

One challenge that remains open in 3D deep learning is how to efficiently represent 3D data to feed deep networks. Recent works have relied on volumetric or point cloud representations, but such approaches suffer from a number of issues…

Neural fields have gained significant attention in the computer vision community due to their excellent performance in novel view synthesis, geometry reconstruction, and generative modeling. Some of their advantages are a sound theoretic…

A closed-form solution exists in two-class linear discriminant analysis (LDA), which discriminates two Gaussian-distributed classes in a multi-dimensional feature space. In this work, we interpret the multilayer perceptron (MLP) as a…

A vast majority of the current research in the field of Machine Learning is done using algorithms with strong arguments pointing to their biological implausibility such as Backpropagation, deviating the field's focus from understanding its…

Molecular representations fundamentally shape how machine learning systems reason about molecular structure and physical properties. Most existing approaches adopt a discrete pipeline: molecules are encoded as sequences, graphs, or point…

We propose a manifold matching approach to generative models which includes a distribution generator (or data generator) and a metric generator. In our framework, we view the real data set as some manifold embedded in a high-dimensional…

Metric learning plays a critical role in training image retrieval and classification. It is also a key algorithm in representation learning, e.g., for feature learning and its alignment in metric space. Hyperbolic embedding has been…

A morphological perceptron is a multilayer feedforward neural network in which neurons perform elementary operations from mathematical morphology. For multiclass classification tasks, a morphological perceptron with a competitive layer…

Despite the success of deep learning in domains such as image, voice, and graphs, there has been little progress in deep representation learning for domains without a known structure between features. For instance, a tabular dataset of…

This study addresses the challenge of accurately forecasting geometric deviations in manufactured components using advanced 3D surface analysis. Despite progress in modern manufacturing, maintaining dimensional precision remains difficult,…

Geometric deep learning has gained much attention in recent years due to more available data acquired from non-Euclidean domains. Some examples include point clouds for 3D models and wireless sensor networks in communications. Graphs are…

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…