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Heterogeneous Graph Neural Networks (HGNNs) have exhibited powerful performance in heterogeneous graph learning by aggregating information from various types of nodes and edges. However, existing heterogeneous graph models often struggle to…
3D object detection at long range is crucial for ensuring the safety and efficiency of self driving vehicles, allowing them to accurately perceive and react to objects, obstacles, and potential hazards from a distance. But most current…
Although Deep Neural Networks (DNNs) have shown incredible performance in perceptive and control tasks, several trustworthy issues are still open. One of the most discussed topics is the existence of adversarial perturbations, which has…
Complex networks represented as node adjacency matrices constrains the application of machine learning and parallel algorithms. To address this limitation, network embedding (i.e., graph representation) has been intensively studied to learn…
The construction of $r$-nets offers a powerful tool in computational and metric geometry. We focus on high-dimensional spaces and present a new randomized algorithm which efficiently computes approximate $r$-nets with respect to Euclidean…
A novel Neural Network architecture is proposed using the mathematically and physically rich idea of vector fields as hidden layers to perform nonlinear transformations in the data. The data points are interpreted as particles moving along…
It is difficult to detect and evaluate the number of communities in complex networks, especially when the situation involves with an ambiguous boundary between the inner- and inter-community densities. In this paper, Discrete Nodal Domain…
Various Neural Networks employ time-consuming matrix operations like matrix inversion. Many such matrix operations are faster to compute given the Singular Value Decomposition (SVD). Previous work allows using the SVD in Neural Networks…
Normalized Compression Distance (NCD) is a popular tool that uses compression algorithms to cluster and classify data in a wide range of applications. Existing discussions of NCD's theoretical merit rely on certain theoretical properties of…
This paper proposes the SVDNet for retrieval problems, with focus on the application of person re-identification (re-ID). We view each weight vector within a fully connected (FC) layer in a convolutional neuron network (CNN) as a projection…
In order to make full use of geographic routing techniques developed for sensor networks, nodes must be localized. However, traditional localization and virtual localization techniques are dependent either on expensive and sometimes…
Verification of Neural Networks (NNs) that approximate the solution of Partial Differential Equations (PDEs) is a major milestone towards enhancing their trustworthiness and accelerating their deployment, especially for safety-critical…
In the field of node representation learning the task of interpreting latent dimensions has become a prominent, well-studied research topic. The contribution of this work focuses on appraising the interpretability of another…
Random geometric graphs are a popular choice for a latent points generative model for networks. Their definition is based on a sample of $n$ points $X_1,X_2,\cdots,X_n$ on the Euclidean sphere~$\mathbb{S}^{d-1}$ which represents the latent…
Solving linear programs is often a challenging task in distributed settings. While there are good algorithms for solving packing and covering linear programs in a distributed manner (Kuhn et al.~2006), this is essentially the only class of…
This work begins by establishing a mathematical formalization between different geometrical interpretations of Neural Networks, providing a first contribution. From this starting point, a new interpretation is explored, using the idea of…
The overall neural network (NN) performance is closely related to the properties of its embedding distribution in latent space (LS). It has recently been shown that predefined vector systems, specifically An root system vectors, can be used…
We propose a novel distance to calculate distance between high dimensional vector pairs, utilizing vector quantization generated encodings. Vector quantization based methods are successful in handling large scale high dimensional data.…
Dense high dimensional vectors are becoming increasingly vital in fields such as computer vision, machine learning, and large language models (LLMs), serving as standard representations for multimodal data. Now the dimensionality of these…
Geodesic distances on manifolds have numerous applications in image processing, computer graphics and computer vision. In this work, we introduce an approach called `LGGD' (Learned Generalized Geodesic Distances). This method involves…