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Rapid growth of high-dimensional datasets in fields such as single-cell RNA sequencing and spatial genomics has led to unprecedented opportunities for scientific discovery, but it also presents unique computational and statistical…
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…
The application of Riemannian geometry in the decoding of brain-computer interfaces (BCIs) has swiftly garnered attention because of its straightforwardness, precision, and resilience, along with its aptitude for transfer learning, which…
Electroencephalography (EEG) foundation models hold significant promise for universal Brain-Computer Interfaces (BCIs). However, existing approaches often rely on end-to-end fine-tuning and exhibit limited efficacy under frozen-probing…
The development of EEG decoding algorithms confronts challenges such as data sparsity, subject variability, and the need for precise annotations, all of which are vital for advancing brain-computer interfaces and enhancing the diagnosis of…
We propose a model for time series taking values on a Riemannian manifold and fit it to time series of covariance matrices derived from EEG data for patients suffering from epilepsy. The aim of the study is two-fold: to develop a model with…
Deep generative models have demonstrated successful applications in learning non-linear data distributions through a number of latent variables and these models use a nonlinear function (generator) to map latent samples into the data space.…
Deep learning has achieved a remarkable performance breakthrough in several fields, most notably in speech recognition, natural language processing, and computer vision. In particular, convolutional neural network (CNN) architectures…
We develop Riemannian approaches to variational autoencoders (VAEs) for PDE-type ambient data with regularizing geometric latent dynamics, which we refer to as VAE-DLM, or VAEs with dynamical latent manifolds. We redevelop the VAE framework…
We propose Lie group embedded dynamical neural networks (LieEDNN) and the corresponding learning algorithms based on gradient descent and metric projection on smooth manifold, where we treat Lie group as an intrinsic representation for…
This work presents a novel method of exploring human brain-visual representations, with a view towards replicating these processes in machines. The core idea is to learn plausible computational and biological representations by correlating…
We propose extrinsic and intrinsic deep neural network architectures as general frameworks for deep learning on manifolds. Specifically, extrinsic deep neural networks (eDNNs) preserve geometric features on manifolds by utilizing an…
We develop data-driven methods incorporating geometric and topological information to learn parsimonious representations of nonlinear dynamics from observations. The approaches learn nonlinear state-space models of the dynamics for general…
Deep learning (DL) has been widely investigated in a vast majority of applications in electroencephalography (EEG)-based brain-computer interfaces (BCIs), especially for motor imagery (MI) classification in the past five years. The…
Recent methods in geometric deep learning have introduced various neural networks to operate over data that lie on Riemannian manifolds. Such networks are often necessary to learn well over graphs with a hierarchical structure or to learn…
Multi-domain graph pre-training integrates knowledge from diverse domains to enhance performance in the target domains, which is crucial for building graph foundation models. Despite initial success, existing solutions often fall short of…
Despite significant advances in the field of deep learning in ap-plications to various areas, an explanation of the learning pro-cess of neural network models remains an important open ques-tion. The purpose of this paper is a comprehensive…
In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…
Despite significant advances in the field of deep learning in applications to various fields, explaining the inner processes of deep learning models remains an important and open question. The purpose of this article is to describe and…
Synthesizing geometrical shapes from human brain activities is an interesting and meaningful but very challenging topic. Recently, the advancements of deep generative models like Generative Adversarial Networks (GANs) have supported the…