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A well-known perceptual consequence of categorization in humans and other animals, called categorical perception, is notably characterized by a within-category compression and a between-category separation: two items, close in input space,…

Boundary and edge cues are highly beneficial in improving a wide variety of vision tasks such as semantic segmentation, object recognition, stereo, and object proposal generation. Recently, the problem of edge detection has been revisited…

Spectral Embedding (SE) has often been used to map data points from non-linear manifolds to linear subspaces for the purpose of classification and clustering. Despite significant advantages, the subspace structure of data in the original…

In this work we develop a novel approach using deep neural networks to reconstruct the conductivity distribution in elliptic problems from one measurement of the solution over the whole domain. The approach is based on a mixed reformulation…

In this paper, we introduce a shallow (one-hidden-layer) physics-informed neural network for solving partial differential equations on static and evolving surfaces. For the static surface case, with the aid of level set function, the…

Understanding the relation between deep and shallow neural networks is extremely important for the theoretical study of deep learning. In this work, we discover an embedding principle in depth that loss landscape of an NN "contains" all…

Spatial networks are networks whose graph topology is constrained by their embedded spatial space. Understanding the coupled spatial-graph properties is crucial for extracting powerful representations from spatial networks. Therefore,…

Exploiting internal spatial geometric constraints of sparse LiDARs is beneficial to depth completion, however, has been not explored well. This paper proposes an efficient method to learn geometry-aware embedding, which encodes the local…

For graph classification tasks, many traditional kernel methods focus on measuring the similarity between graphs. These methods have achieved great success on resolving graph isomorphism problems. However, in some classification problems,…

In the context of classification problems, Deep Learning (DL) approaches represent state of art. Many DL approaches are based on variations of standard multi-layer feed-forward neural networks. These are also referred to as deep networks.…

In recent years, there has been an increasing interest in using deep learning and neural networks to tackle scientific problems, particularly in solving partial differential equations (PDEs). However, many neural network-based methods, such…

A finite element method for elliptic problems with discontinuous coefficients is presented. The discontinuity is assumed to take place along a closed smooth curve. The proposed method allows to deal with meshes that are not adapted to the…

Neural implicit representations are widely used for 3D shape modeling due to their smoothness and compactness, but traditional MLP-based methods struggle with sharp features, such as edges and corners in CAD models, and require long…

Electrophysiological observation plays a major role in epilepsy evaluation. However, human interpretation of brain signals is subjective and prone to misdiagnosis. Automating this process, especially seizure detection relying on scalp-based…

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…

Graph Convolutional Networks (GCNs) gained traction for graph representation learning, with recent attention on improving performance on heterophilic graphs for various real-world applications. The localized feature aggregation in a typical…

This work introduces a novel, fully robust and highly-scalable, $h$-adaptive aggregated unfitted finite element method for large-scale interface elliptic problems. The new method is based on a recent distributed-memory implementation of the…

The main purpose of the present paper is to study from a numerical analysis point of view some robust methods designed to cope with stiff (highly anisotropic) elliptic problems. The so-called asymptotic-preserving schemes studied in this…

The accurate representation of fine-detailed cloth wrinkles poses significant challenges in computer graphics. The inherently non-uniform structure of cloth wrinkles mandates the employment of intricate discretization strategies, which are…

Almost all materials are anisotropic. In this paper, interface relations of anisotropic elliptic partial differential equations involving discontinuities across interfaces are derived in two and three dimensions. Compared with isotropic…