Related papers: UMAP: Uniform Manifold Approximation and Projectio…

Panoptic maps enable robots to reason about both geometry and semantics. However, open-vocabulary models repeatedly produce closely related labels that split panoptic entities and degrade volumetric consistency. The proposed UPPM advances…

The study of universal approximation properties (UAP) for neural networks (NN) has a long history. When the network width is unlimited, only a single hidden layer is sufficient for UAP. In contrast, when the depth is unlimited, the width…

Perceptual aliasing and weak textures pose significant challenges to the task of place recognition, hindering the performance of Simultaneous Localization and Mapping (SLAM) systems. This paper presents a novel model, called UMF (standing…

Efficient topology optimization based on the adaptive auxiliary reduced model reanalysis (AARMR) is proposed to improve computational efficiency and scale. In this method, a projection auxiliary reduced model (PARM) is integrated into the…

Mapper is an algorithm that summarizes the topological information contained in a dataset and provides an insightful visualization. It takes as input a point cloud which is possibly high-dimensional, a filter function on it and an open…

This paper provides a full geometric development of a new technique called un-reduction, for dealing with dynamics and optimal control problems posed on spaces that are unwieldy for numerical implementation. The technique, which was…

Neighbour embeddings (NE) allow the representation of high dimensional datasets into lower dimensional spaces and are often used in data visualisation. In practice, accelerated approximations are employed to handle very large datasets.…

While Unmanned Aerial Vehicles (UAVs) have gained significant traction across various fields, path planning in 3D environments remains a critical challenge, particularly under size, weight, and power (SWAP) constraints. Traditional modular…

The Universal Approximation Theorem (UAT) guarantees universal function approximation but does not explain how residual models distribute approximation across layers. We reframe residual networks as a layer-wise approximation process that…

Modifications to a neural network's input and output layers are often required to accommodate the specificities of most practical learning tasks. However, the impact of such changes on architecture's approximation capabilities is largely…

Despite the widespread use of Uniform Manifold Approximation and Projection (UMAP), the impact of its stochastic optimization process on the results remains underexplored. We observed that it often produces unstable results where the…

Monocular metric depth estimation (MMDE) is a core challenge in computer vision, playing a pivotal role in real-world applications that demand accurate spatial understanding. Although prior works have shown promising zero-shot performance…

We present a benchmark designed to evaluate the predictive capabilities of universal machine learning interatomic potentials across systems of varying dimensionality. Specifically, our benchmark tests zero- (molecules, atomic clusters,…

Deep models suffer from limited generalization capability to unseen domains, which has severely hindered their clinical applicability. Specifically for the retinal vessel segmentation task, although the model is supposed to learn the…

Depth map super-resolution technology aims to improve the spatial resolution of low-resolution depth maps and effectively restore high-frequency detail information. Traditional convolutional neural network has limitations in dealing with…

The increasing demand for high-accuracy depth estimation in autonomous driving and augmented reality applications necessitates advanced neural architectures capable of effectively leveraging multiple data modalities. In this context, we…

We introduce the Linearized Diffusion Map (LDM), a novel linear dimensionality reduction method constructed via a linear approximation of the diffusion-map kernel. LDM integrates the geometric intuition of diffusion-based nonlinear methods…

Nonlinear dimensionality reduction lacks interpretability due to the absence of source features in low-dimensional embedding space. We propose an interpretable method featMAP to preserve source features by tangent space embedding. The core…

The chemical sciences are producing an unprecedented amount of large, high-dimensional data sets containing chemical structures and associated properties. However, there are currently no algorithms to visualize such data while preserving…

U-Nets have been established as a standard architecture for image-to-image learning problems such as segmentation and inverse problems in imaging. For large-scale data, as it for example appears in 3D medical imaging, the U-Net however has…