Related papers: Tangent space spatial filters for interpretable an…

In this paper, we develop a new classification method for manifold-valued data in the framework of probabilistic learning vector quantization. In many classification scenarios, the data can be naturally represented by symmetric positive…

Brain-computer interfaces (BCIs) offer transformative potential, but decoding neural signals presents significant challenges. The core premise of this paper is built around demonstrating methods to elucidate the underlying low-dimensional…

Tractography has become an indispensable part of brain connectivity studies. However, it is currently facing problems with reliability. In particular, a substantial amount of nerve fiber reconstructions (streamlines) in tractograms produced…

When do gradient-based explanation algorithms provide perceptually-aligned explanations? We propose a criterion: the feature attributions need to be aligned with the tangent space of the data manifold. To provide evidence for this…

Classification of sequence data is the topic of interest for dynamic Bayesian models and Recurrent Neural Networks (RNNs). While the former can explicitly model the temporal dependencies between class variables, the latter have a capability…

Approximating a manifold-valued function from samples of input-output pairs consists of modeling the relationship between an input from a vector space and an output on a Riemannian manifold. We propose a function approximation method that…

Robust environment perception is essential for decision-making on robots operating in complex domains. Principled treatment of uncertainty sources in a robot's observation model is necessary for accurate mapping and object detection. This…

The Riemannian geometry is one of the main theoretical pieces in Modern Mathematics and Physics. The study of Riemann Geometry in the relevant literature is performed by using a well defined analytical path. Usually it starts from the…

Brain-computer interface (BCI) technology enables direct interaction between humans and computers by analyzing brain signals. Electroencephalogram (EEG) is one of the non-invasive tools used in BCI systems, providing high temporal…

Riemannian manifolds provide a principled way to model nonlinear geometric structure inherent in data. A Riemannian metric on said manifolds determines geometry-aware shortest paths and provides the means to define statistical models…

A common problem in Bayesian inference is the sampling of target probability distributions at sufficient resolution and accuracy to estimate the probability density, and to compute credible regions. Often by construction, many target…

We develop Riemannian Stein Variational Gradient Descent (RSVGD), a Bayesian inference method that generalizes Stein Variational Gradient Descent (SVGD) to Riemann manifold. The benefits are two-folds: (i) for inference tasks in Euclidean…

In this work we introduce a convolution operation over the tangent bundle of Riemann manifolds in terms of exponentials of the Connection Laplacian operator. We define tangent bundle filters and tangent bundle neural networks (TNNs) based…

Magnetic Resonance Imaging (MRI) is an important diagnostic tool for precise detection of various pathologies. Magnetic Resonance (MR) is more preferred than Computed Tomography (CT) due to the high resolution in MR images which help in…

We propose a data-driven approach using a Restricted Boltzmann Machine (RBM) to solve the Schr\"odinger equation in configuration space. Traditional Configuration Interaction (CI) methods construct the wavefunction as a linear combination…

Accurate classification of brain tumors from magnetic resonance imaging (MRI) plays a critical role in early diagnosis and effective treatment planning. In this study, we propose a deep learning framework based on Vision Transformers (ViT)…

A major goal of neuroscience is to understand brain computations during visual processing in naturalistic settings. A dominant approach is to use image-computable deep neural networks trained with different task objectives as a basis for…

Reconstructing visual stimuli from human brain activity (e.g., fMRI) bridges neuroscience and computer vision by decoding neural representations. However, existing methods often overlook critical brain structure-function relationships,…

Cubic spline interpolation on Euclidean space is a standard topic in numerical analysis, with countless applications in science and technology. In several emerging fields, for example computer vision and quantum control, there is a growing…

Understanding how the brain encodes external stimuli and how these stimuli can be decoded from the measured brain activities are long-standing and challenging questions in neuroscience. In this paper, we focus on reconstructing the complex…