Related papers: Planning Neural Dynamics with Lie Group Embedding …

Symmetric positive definite (SPD) matrices used as feature descriptors in image recognition are usually high dimensional. Traditional manifold learning is only applicable for reducing the dimension of high-dimensional vector-form data. For…

Tiered graph autoencoders provide the architecture and mechanisms for learning tiered latent representations and latent spaces for molecular graphs that explicitly represent and utilize groups (e.g., functional groups). This enables the…

We develop a Mean-Field (MF) view of the learning dynamics of overparametrized Artificial Neural Networks (NN) under data symmetric in law wrt the action of a general compact group $G$. We consider for this a class of generalized shallow…

The present paper links the representation theory of Lie groupoids and infinite-dimensional Lie groups. We show that smooth representations of Lie groupoids give rise to smooth representations of associated Lie groups. The groups envisaged…

We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements…

Statistical neurodynamics studies macroscopic behaviors of randomly connected neural networks. We consider a deep layered feedforward network where input signals are processed layer by layer. The manifold of input signals is embedded in a…

The simulation of complex physical systems using a discretized mesh is a cornerstone of applied mechanics, but traditional numerical solvers are often computationally prohibitive for many-query tasks. While Graph Neural Networks (GNNs) have…

Dynamic brain data, teeming with biological and functional insights, are becoming increasingly accessible through advanced measurements, providing a gateway to understanding the inner workings of the brain in living subjects. However, the…

This paper investigates the challenge of learning image manifolds, specifically pose manifolds, of 3D objects using limited training data. It proposes a DNN approach to manifold learning and for predicting images of objects for novel,…

Group theory has been used in machine learning to provide a theoretically grounded approach for incorporating known symmetry transformations in tasks from robotics to protein modeling. In these applications, equivariant neural networks use…

Disentangled representation learning has seen a surge in interest over recent times, generally focusing on new models which optimise one of many disparate disentanglement metrics. Symmetry Based Disentangled Representation learning…

The success of deep neural networks for pan-sharpening is commonly in a form of black box, lacking transparency and interpretability. To alleviate this issue, we propose a novel model-driven deep unfolding framework with image reasoning…

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…

This work investigates the use of smooth neural networks for modeling dynamic variations of implicit surfaces under the level set equation (LSE). For this, it extends the representation of neural implicit surfaces to the space-time…

Perceptual manifolds arise when a neural population responds to an ensemble of sensory signals associated with different physical features (e.g., orientation, pose, scale, location, and intensity) of the same perceptual object. Object…

The emergence of collective dynamics in neural networks is a mechanism of the animal and human brain for information processing. In this paper, we develop a computational technique using distributed processing elements in a complex network,…

Recurrent neural networks (RNNs) are particularly well-suited for modeling long-term dependencies in sequential data, but are notoriously hard to train because the error backpropagated in time either vanishes or explodes at an exponential…

How can we design neural networks that allow for stable universal approximation of maps between topologically interesting manifolds? The answer is with a coordinate projection. Neural networks based on topological data analysis (TDA) use…

Geometric and Topological Deep Learning are rapidly growing research areas that enhance machine learning through the use of geometric and topological structures. Within this framework, Group Equivariant Non-Expansive Operators (GENEOs) have…

Manifold learning now plays a very important role in machine learning and many relevant applications. Although its superior performance in dealing with nonlinear data distribution, data sparsity is always a thorny knot. There are few…