相关论文: Robust Tangent Space Estimation via Laplacian Eige…

One of the ultimate goals of Manifold Learning (ML) is to reconstruct an unknown nonlinear low-dimensional manifold embedded in a high-dimensional observation space by a given set of data points from the manifold. We derive a local lower…

While diffusion models enable new approaches for estimating Local Intrinsic Dimension (LID), existing methods fail in high-dimensional spaces where noise from vast normal directions overwhelms the tangent signal. We propose Local Hessian…

Numerically solving partial differential equations (PDEs) can be challenging and computationally expensive. This has led to the development of reduced-order models (ROMs) that are accurate but faster than full order models (FOMs). Recently,…

Bayesian optimization (BO) is a popular method for optimizing expensive black-box functions. BO has several well-documented shortcomings, including computational slowdown with longer optimization runs, poor suitability for non-stationary or…

Accurate state estimation for robotic systems evolving on Lie group manifolds, such as legged robots, is a prerequisite for achieving agile control. However, this task is challenged by nonlinear observation models defined on curved…

The second eigenvalue of the Laplacian matrix and its associated eigenvector are fundamental features of an undirected graph, and as such they have found widespread use in scientific computing, machine learning, and data analysis. In many…

Unsupervised domain adaptation (UDA) requires source domain samples with clean ground truth labels during training. Accurately labeling a large number of source domain samples is time-consuming and laborious. An alternative is to utilize…

Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…

We develop Latent Exploration Score (LES) to mitigate over-exploration in Latent Space Optimization (LSO), a popular method for solving black-box discrete optimization problems. LSO utilizes continuous optimization within the latent space…

The reliability of Deep Learning systems depends on their accuracy but also on their robustness against adversarial perturbations to the input data. Several attacks and defenses have been proposed to improve the performance of Deep Neural…

We investigate the unconstrained global optimization of functions with low effective dimensionality, that are constant along certain (unknown) linear subspaces. Extending the technique of random subspace embeddings in [Wang et al., Bayesian…

The spectral structure of the Laplacian-Beltrami operator (LBO) on manifolds has been widely used in many applications, include spectral clustering, dimensionality reduction, mesh smoothing, compression and editing, shape segmentation,…

We propose a sampling algorithm that achieves superior complexity bounds in all the classical settings (strongly log-concave, log-concave, Logarithmic-Sobolev inequality (LSI), Poincar\'e inequality) as well as more general settings with…

Tensor decomposition has emerged as a prominent technique to learn low-dimensional representation under the supervision of reconstruction error, primarily benefiting data inference tasks like completion and imputation, but not…

Generative AI has demonstrated significant potential in creative design, enabling the rapid generation of visual content and imaginative concepts. Although deep AI models achieve effective featurization in the latent space, navigating the…

In many applications, one has side information, e.g., labels that are provided in a semi-supervised manner, about a specific target region of a large data set, and one wants to perform machine learning and data analysis tasks "nearby" that…

Light detection and ranging (LiDAR)-inertial odometry (LIO) enables accurate localization and mapping for autonomous navigation in various scenes. However, its performance remains sensitive to variations in spatial scale, which refers to…

In this paper, we propose a multiscale method for heterogeneous Stokes problems. The method is based on the Localized Orthogonal Decomposition (LOD) methodology and has approximation properties independent of the regularity of the…

This work proposes a novel deep network architecture to solve the camera Ego-Motion estimation problem. A motion estimation network generally learns features similar to Optical Flow (OF) fields starting from sequences of images. This OF can…

We present the sliding basis computational framework to automatically synthesize heterogeneous (graded or discrete) material fields for parts designed using constrained optimization. Our framework uses the fact that any spatially varying…