Related papers: IsUMap: Manifold Learning and Data Visualization l…

This paper describes a novel perspective on the foundations of mathematics: how mathematics may be seen to be largely about 'information compression via the matching and unification of patterns' (ICMUP). ICMUP is itself a novel approach to…

Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…

The Vision Transformer (ViT) architecture has become widely recognized in computer vision, leveraging its self-attention mechanism to achieve remarkable success across various tasks. Despite its strengths, ViT's optimization remains…

Detecting the dimension of a hidden manifold from a point sample has become an important problem in the current data-driven era. Indeed, estimating the shape dimension is often the first step in studying the processes or phenomena…

Constructing 3D representations of object geometry is critical for many robotics tasks, particularly manipulation problems. These representations must be built from potentially noisy partial observations. In this work, we focus on the…

Neural Networks and related Deep Learning methods are currently at the leading edge of technologies used for classifying objects. However, they generally demand large amounts of time and data for model training; and their learned models can…

Robust 3D representation learning forms the perceptual foundation of spatial intelligence, enabling downstream tasks in scene understanding and embodied AI. However, learning such representations directly from unposed multi-view images…

We propose NeuMIP, a neural method for representing and rendering a variety of material appearances at different scales. Classical prefiltering (mipmapping) methods work well on simple material properties such as diffuse color, but fail to…

We present DeepSurfels, a novel hybrid scene representation for geometry and appearance information. DeepSurfels combines explicit and neural building blocks to jointly encode geometry and appearance information. In contrast to established…

The ability to autonomously navigate in unknown environments is important for mobile robots. The map is the core component to achieve this. Most map representations rely on drift-free state estimation and provide a global metric map to…

In medical imaging, most of the image registration methods implicitly assume a one-to-one correspondence between the source and target images (i.e., diffeomorphism). However, this is not necessarily the case when dealing with pathological…

The ability to capture rich representations of combinatorial structures has enabled the application of machine learning to tasks such as analysis and generation of floorplans, terrains, images, and animations. Recent work has primarily…

For many machine learning tasks, the input data lie on a low-dimensional manifold embedded in a high dimensional space and, because of this high-dimensional structure, most algorithms are inefficient. The typical solution is to reduce the…

The restricted isometry property (RIP) is essential for the linear map to guarantee the successful recovery of low-rank matrices. The existing works show that the linear map generated by the measurement matrices with independent and…

Can integrating spectral and curvature signals unlock new potential in graph representation learning? Non-Euclidean geometries, particularly Riemannian manifolds such as hyperbolic (negative curvature) and spherical (positive curvature),…

Intersection homology is a topological invariant which detects finer information in a space than ordinary homology. Using ideas from classical simple homotopy theory, we construct local combinatorial transformations on simplicial complexes…

Open-vocabulary panoptic reconstruction is essential for advanced robotics perception and simulation. However, existing methods based on 3D Gaussian Splatting (3DGS) often struggle to simultaneously achieve geometric accuracy, coherent…

Existing neural field representations for 3D object reconstruction either (1) utilize object-level representations, but suffer from low-quality details due to conditioning on a global latent code, or (2) are able to perfectly reconstruct…

Automatic image annotation is one of the most challenging problems in machine vision areas. The goal of this task is to predict number of keywords automatically for images captured in real data. Many methods are based on visual features in…

Representation learning is typically applied to only one mode of a data matrix, either its rows or columns. Yet in many applications, there is an underlying geometry to both the rows and the columns. We propose utilizing this coupled…