Related papers: Neural active manifolds: nonlinear dimensionality …

Nonlinear manifold learning from unorganized data points is a very challenging unsupervised learning and data visualization problem with a great variety of applications. In this paper we present a new algorithm for manifold learning and…

Dense regression is a widely used approach in computer vision for tasks such as image super-resolution, enhancement, depth estimation, etc. However, the high cost of annotation and labeling makes it challenging to achieve accurate results.…

Models are often given in terms of differential equations to represent physical systems. In the presence of uncertainty, accurate prediction of the behavior of these systems using the models requires understanding the effect of uncertainty…

Neural network (NN) interatomic potentials provide fast prediction of potential energy surfaces, closely matching the accuracy of the electronic structure methods used to produce the training data. However, NN predictions are only reliable…

Accurate quantification of uncertainty in neural network predictions remains a central challenge for scientific applications involving high-dimensional, correlated data. While existing methods capture either aleatoric or epistemic…

Latent dynamics models have emerged as powerful tools for modeling and interpreting neural population activity. Recently, there has been a focus on incorporating simultaneously measured behaviour into these models to further disentangle…

Neural networks (NNs) can achieved high performance in various fields such as computer vision, and natural language processing. However, deploying NNs in resource-constrained safety-critical systems has challenges due to uncertainty in the…

Manifold learning (ML), known also as non-linear dimension reduction, is a set of methods to find the low dimensional structure of data. Dimension reduction for large, high dimensional data is not merely a way to reduce the data; the new…

This paper introduces the Neural Differential Manifold (NDM), a novel neural network architecture that explicitly incorporates geometric structure into its fundamental design. Departing from conventional Euclidean parameter spaces, the NDM…

We address the problem of active mapping with a continually-learned neural scene representation, namely Active Neural Mapping. The key lies in actively finding the target space to be explored with efficient agent movement, thus minimizing…

Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…

Manifold-valued data naturally arises in medical imaging. In cognitive neuroscience, for instance, brain connectomes base the analysis of coactivation patterns between different brain regions on the analysis of the correlations of their…

Uncertainty estimation methods using deep learning approaches strive against separating how uncertain the state of the world manifests to us via measurement (objective end) from the way this gets scrambled with the model specification and…

Quantifying uncertainty in a model's predictions is important as it enables the safety of an AI system to be increased by acting on the model's output in an informed manner. This is crucial for applications where the cost of an error is…

We develop theory for nonlinear dimensionality reduction (NLDR). A number of NLDR methods have been developed, but there is limited understanding of how these methods work and the relationships between them. There is limited basis for using…

In recent years, manifold methods have moved into focus as tools for dimension reduction. Assuming that the high-dimensional data actually lie on or close to a low-dimensional nonlinear manifold, these methods have shown convincing results…

Recently, deep learning has been widely applied in functional data analysis (FDA) with notable empirical success. However, the infinite dimensionality of functional data necessitates an effective dimension reduction approach for functional…

Recently, Neural Radiance Fields (NeRF) has shown promising performances on reconstructing 3D scenes and synthesizing novel views from a sparse set of 2D images. Albeit effective, the performance of NeRF is highly influenced by the quality…

Uncertainty estimation for machine learning models is of high importance in many scenarios such as constructing the confidence intervals for model predictions and detection of out-of-distribution or adversarially generated points. In this…

Invariant manifolds are important constructs for the quantitative and qualitative understanding of nonlinear phenomena in dynamical systems. In nonlinear damped mechanical systems, for instance, spectral submanifolds have emerged as useful…