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The problem of identifying geometric structure in data is a cornerstone of (unsupervised) learning. As a result, Geometric Representation Learning has been widely applied across scientific and engineering domains. In this work, we…

Manifold learning has been proven to be an effective method for capturing the implicitly intrinsic structure of non-Euclidean data, in which one of the primary challenges is how to maintain the distortion-free (isometry) of the data…

When the system is linear, why should learning be nonlinear? Linear dynamical systems, the analytical backbone of control theory, signal processing and circuit analysis, have exact closed-form solutions via the state transition matrix. Yet…

Unlabeled LiDAR logs, in autonomous driving applications, are inherently a gold mine of dense 3D geometry hiding in plain sight - yet they are almost useless without human labels, highlighting a dominant cost barrier for…

Recent advances in large language models (LLMs) have been driven by pretraining, supervised fine tuning (SFT), and alignment tuning. Among these, SFT plays a crucial role in transforming a model 's general knowledge into structured…

Mutual information (MI) is a general measure of statistical dependence with widespread application across the sciences. However, estimating MI between multi-dimensional variables is challenging because the number of samples necessary to…

Distance metric learning is a successful way to enhance the performance of the nearest neighbor classifier. In most cases, however, the distribution of data does not obey a regular form and may change in different parts of the feature…

Data augmentation is a widely used technique and an essential ingredient in the recent advance in self-supervised representation learning. By preserving the similarity between augmented data, the resulting data representation can improve…

High-dimensional data analysis has been an active area, and the main focuses have been variable selection and dimension reduction. In practice, it occurs often that the variables are located on an unknown, lower-dimensional nonlinear…

Chemists in search of structure-property relationships face great challenges due to limited high quality, concordant datasets. Machine learning (ML) has significantly advanced predictive capabilities in chemical sciences, but these modern…

Deep neural networks for learning Symmetric Positive Definite (SPD) matrices are gaining increasing attention in machine learning. Despite the significant progress, most existing SPD networks use traditional Euclidean classifiers on an…

With the dramatic increase of dimensions in the data representation, extracting latent low-dimensional features becomes of the utmost importance for efficient classification. Aiming at the problems of unclear margin representation and…

High-dimensional, heterogeneous data with complex feature interactions pose significant challenges for traditional predictive modeling approaches. While Projection to Latent Structures (PLS) remains a popular technique, it struggles to…

LiDAR relocalization has attracted increasing attention as it can deliver accurate 6-DoF pose estimation in complex 3D environments. Recent learning-based regression methods offer efficient solutions by directly predicting global poses…

LiDAR-based 3D object detectors have been largely utilized in various applications, including autonomous vehicles or mobile robots. However, LiDAR-based detectors often fail to adapt well to target domains with different sensor…

Building models capable of generating structured output is a key challenge for AI and robotics. While generative models have been explored on many types of data, little work has been done on synthesizing lidar scans, which play a key role…

Autoencoders exhibit impressive abilities to embed the data manifold into a low-dimensional latent space, making them a staple of representation learning methods. However, without explicit supervision, which is often unavailable, the…

We introduce a novel framework that directly learns a spectral basis for shape and manifold analysis from unstructured data, eliminating the need for traditional operator selection, discretization, and eigensolvers. Grounded in…

In this paper we present a fully Bayesian latent variable model which exploits conditional nonlinear(in)-dependence structures to learn an efficient latent representation. The latent space is factorized to represent shared and private…

This paper introduces an efficient multi-linear nonparametric (kernel-based) approximation framework for data regression and imputation, and its application to dynamic magnetic-resonance imaging (dMRI). Data features are assumed to reside…