Related papers: ManifoldFormer: Geometric Deep Learning for Neural…

Autoencoders have emerged as powerful models for visualization and dimensionality reduction based on the fundamental assumption that high-dimensional data is generated from a low-dimensional manifold. A critical challenge in autoencoder…

Graph data often exhibits complex geometric heterogeneity, where structures with varying local curvature, such as tree-like hierarchies and dense communities, coexist within a single network. Existing geometric GNNs, which embed graphs into…

Modern generative modeling methods have demonstrated strong performance in learning complex data distributions from clean samples. In many scientific and imaging applications, however, clean samples are unavailable, and only noisy or…

Artificial neural networks (ANNs) are powerful tools capable of approximating any arbitrary mathematical function, but their interpretability remains limited, rendering them as black box models. To address this issue, numerous methods have…

Most current deep learning models equivariant to $O(n)$ or $SO(n)$ either consider mostly scalar information such as distances and angles or have a very high computational complexity. In this work, we test a few novel message passing graph…

In machine learning, there is a long history of trying to build neural networks that can learn from fewer example data by baking in strong geometric priors. However, it is not always clear a priori what geometric constraints are appropriate…

This study investigates the application of Riemannian geometry-based methods for brain decoding using invasive electrophysiological recordings. Although previously employed in non-invasive, the utility of Riemannian geometry for invasive…

Variational autoencoders (VAEs) and generative adversarial networks (GANs) enjoy an intuitive connection to manifold learning: in training the decoder/generator is optimized to approximate a homeomorphism between the data distribution and…

Many scientific problems require to process data in the form of geometric graphs. Unlike generic graph data, geometric graphs exhibit symmetries of translations, rotations, and/or reflections. Researchers have leveraged such inductive bias…

In this paper, we propose a novel space-time geometric representation of human landmark configurations and derive tools for comparison and classification. We model the temporal evolution of landmarks as parametrized trajectories on the…

Incorporating Euclidean symmetries (e.g. rotation equivariance) as inductive biases into graph neural networks has improved their generalization ability and data efficiency in unbounded physical dynamics modeling. However, in various…

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…

Alzheimer's disease (AD) is a devastating neurodegenerative condition that precedes progressive and irreversible dementia; thus, predicting its progression over time is vital for clinical diagnosis and treatment. Numerous studies have…

Geometrical shape of airfoils, together with the corresponding flight conditions, are crucial factors for aerodynamic performances prediction. The obtained airfoils geometrical features in most existing approaches (e.g., geometrical…

Developing foundation models for electroencephalography (EEG) remains challenging due to the signal's low signal-to-noise ratio and complex spectro-temporal non-stationarity. Existing approaches often overlook the hierarchical latent…

While electroencephalogram (EEG) has been a crucial tool for monitoring the brain and diagnosing neurological disorders (e.g., epilepsy), learning meaningful representations from raw EEG signals remains challenging due to limited…

A fundamental cognitive process is the ability to map value and identity onto objects as we learn about them. Exactly how such mental constructs emerge and what kind of space best embeds this mapping remains incompletely understood. Here we…

Multi-frequency Electrical Impedance Tomography (mfEIT) represents a promising biomedical imaging modality that enables the estimation of tissue conductivities across a range of frequencies. Addressing this challenge, we present a novel…

Generative adversarial networks (GANs) have emerged as a powerful unsupervised method to model the statistical patterns of real-world data sets, such as natural images. These networks are trained to map random inputs in their latent space…

Self-supervised learning has been a powerful training paradigm to facilitate representation learning. In this study, we design a masked autoencoder (MAE) to guide deep learning models to learn electroencephalography (EEG) signal…