Related papers: Manifold Function Encoder: Identifying Different F…

Hyperspectral imagery provides rich spectral detail but poses unique challenges because of its high dimensionality in both spatial and spectral domains. We propose \textit{HyperspectralMAE}, a Transformer-based foundation model for…

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…

In numerous robotics and mechanical engineering applications, among others, data is often constrained on smooth manifolds due to the presence of rotational degrees of freedom. Common datadriven and learning-based methods such as neural…

The ever-growing popularity of Kinect and inertial sensors has prompted intensive research efforts on human action recognition. Since human actions can be characterized by multiple feature representations extracted from Kinect and inertial…

Representing a manifold of very high-dimensional data with generative models has been shown to be computationally efficient in practice. However, this requires that the data manifold admits a global parameterization. In order to represent…

The problem of extending a function $f$ defined on a training data $\mathcal{C}$ on an unknown manifold $\mathbb{X}$ to the entire manifold and a tubular neighborhood of this manifold is considered in this paper. For $\mathbb{X}$ embedded…

Manifold learning is a hot research topic in the field of computer science and has many applications in the real world. A main drawback of manifold learning methods is, however, that there is no explicit mappings from the input data…

Function approximation based on data drawn randomly from an unknown distribution is an important problem in machine learning. The manifold hypothesis assumes that the data is sampled from an unknown submanifold of a high dimensional…

Depth estimation from monocular endoscopic images presents significant challenges due to the complexity of endoscopic surgery, such as irregular shapes of human soft tissues, as well as variations in lighting conditions. Existing methods…

A fundamental task in data exploration is to extract simplified low dimensional representations that capture intrinsic geometry in data, especially for faithfully visualizing data in two or three dimensions. Common approaches to this task…

Attentional mechanisms are order-invariant. Positional encoding is a crucial component to allow attention-based deep model architectures such as Transformer to address sequences or images where the position of information matters. In this…

In this paper, a multi-scale Fourier neural operator (MscaleFNO) is proposed to reduce the spectral bias of the FNO in learning the mapping between highly oscillatory functions, with application to the nonlinear mapping between the…

In this manuscript, we define (E, F)-invex set, (E, F)-invex functions, and (E, F)-preinvex functions on Euclidean space. We explore the concepts on the Riemannian manifold. We also detail the fundamental properties of (E, F)-preinvex…

Functional Differential Equations (FDEs) play a fundamental role in many areas of mathematical physics, including fluid dynamics (Hopf characteristic functional equation), quantum field theory (Schwinger-Dyson equation), and statistical…

Non-linear manifold learning enables high-dimensional data analysis, but requires out-of-sample-extension methods to process new data points. In this paper, we propose a manifold learning algorithm based on deep learning to create an…

We prove that every smooth closed manifold admits a smooth real-valued function with only two critical values. We call a function of this type a \emph{Reeb function}. We prove that for a Reeb function we can prescribe the set of minima (or…

We consider the problem of task-agnostic feature upsampling in dense prediction where an upsampling operator is required to facilitate both region-sensitive tasks like semantic segmentation and detail-sensitive tasks such as image matting.…

We propose Hyper-Dimensional Function Encoding (HDFE). Given samples of a continuous object (e.g. a function), HDFE produces an explicit vector representation of the given object, invariant to the sample distribution and density. Sample…

Generating learning-friendly representations for points in space is a fundamental and long-standing problem in ML. Recently, multi-scale encoding schemes (such as Space2Vec and NeRF) were proposed to directly encode any point in 2D/3D…

Autoencoder and its variants have been widely applicated in anomaly detection.The previous work memory-augmented deep autoencoder proposed memorizing normality to detect anomaly, however it neglects the feature discrepancy between different…