相关论文: Understanding and Improving UMAP with Geometric an…

Scientific and engineering processes deliver massive high-dimensional data sets that are generated as non-linear transformations of an initial state and few process parameters. Mapping such data to a low-dimensional manifold facilitates…

Model predictive control (MPC) faces significant limitations when applied to systems evolving on nonlinear manifolds, such as robotic attitude dynamics and constrained motion planning, where traditional Euclidean formulations struggle with…

Correlation matrices are fundamental summaries of functional brain networks, yet standard analyses often treat entries independently, ignoring the curved geometry of correlation space. Existing geometric methods frequently lack closed-form…

Lidar-only odometry aims to estimate the trajectory of a mobile platform from a stream of lidar scans. Traditional scan-to map approaches register each scan against a single, evolving map, which propagates registration errors over time. To…

Fine-tuning approaches for Vision-Language Models (VLMs) face a critical three-way trade-off between In-Distribution (ID) accuracy, Out-of-Distribution (OOD) generalization, and adversarial robustness. Existing robust fine-tuning strategies…

Machine learning interatomic potentials (MLIPs) enables molecular dynamics (MD) simulations with ab initio accuracy and has been applied to various fields of physical science. However, the performance and transferability of MLIPs are…

Neural implicit surfaces have become an important technique for multi-view 3D reconstruction but their accuracy remains limited. In this paper, we argue that this comes from the difficulty to learn and render high frequency textures with…

Radar ensures robust sensing capabilities in adverse weather conditions, yet challenges remain due to its high inherent noise level. Existing radar odometry has overcome these challenges with strategies such as filtering spurious points,…

Differentiable vector graphics have enabled powerful gradient-based optimization of vector primitives directly from raster images. However, existing frameworks formulate this as a flat optimization problem, forcing hundreds to thousands of…

Geometric Representation Learning (GRL) aims to approximate the non-Euclidean topology of high-dimensional data through discrete graph structures, grounded in the manifold hypothesis. However, traditional static graph construction methods…

Given a real-valued function $f$ defined over a manifold $M$ embedded in $\mathbb{R}^d$, we are interested in recovering structural information about $f$ from the sole information of its values on a finite sample $P$. Existing methods…

Revealing hidden geometry and topology in noisy data sets is a challenging task. Elastic principal graph is a computationally efficient and flexible data approximator based on embedding a graph into the data space and minimizing the energy…

Simultaneously odometry and mapping using LiDAR data is an important task for mobile systems to achieve full autonomy in large-scale environments. However, most existing LiDAR-based methods prioritize tracking quality over reconstruction…

Traditional LiDAR odometry (LO) systems mainly leverage geometric information obtained from the traversed surroundings to register laser scans and estimate LiDAR ego-motion, while it may be unreliable in dynamic or unstructured…

The approximation of nonlinear kernels via linear feature maps has recently gained interest due to their applications in reducing the training and testing time of kernel-based learning algorithms. Current random projection methods avoid the…

Deep-learning architectures for classification problems involve the cross-entropy loss sometimes assisted with auxiliary loss functions like center loss, contrastive loss and triplet loss. These auxiliary loss functions facilitate better…

Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…

This paper introduces a novel framework for image and video demoir\'eing by integrating Maximum A Posteriori (MAP) estimation with advanced deep learning techniques. Demoir\'eing addresses inherently nonlinear degradation processes, which…

The Mapper algorithm, a technique within topological data analysis (TDA), constructs a simplified graphical representation of high-dimensional data to uncover its underlying shape and structural patterns. The algorithm has attracted…

Moving object segmentation (MOS) on LiDAR point clouds is crucial for autonomous systems like self-driving vehicles. Previous supervised approaches rely heavily on costly manual annotations, while LiDAR sequences naturally capture temporal…