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Modeling complex spatial networks with multiscale heterogeneity poses significant mathematical and computational challenges. Lacking explicit PDE discretizations and facing excessive degrees of freedom, conventional methods often become…
Longitudinal network consists of a sequence of temporal edges among multiple nodes, where the temporal edges are observed in real time. It has become ubiquitous with the rise of online social platform and e-commerce, but largely…
In an article, E. Grafarend and B. Schaffrin studied the geometry of non-linear adjustment of the planar trisection problem using the Gauss Markov model and the method of the least squares. This paper develops the same method working on an…
Variational tensor network optimization has become a powerful tool for studying classical statistical models in two dimensions. However, its application to three-dimensional systems remains limited, primarily due to the high computational…
Stereo vision is an effective technique for depth estimation with broad applicability in autonomous urban and highway driving. While various deep learning-based approaches have been developed for stereo, the input data from a binocular…
This paper contributes to a development of randomized methods for neural networks. The proposed learner model is generated incrementally by stochastic configuration (SC) algorithms, termed as Stochastic Configuration Networks (SCNs). In…
A recent line of work has shown that an overparametrized neural network can perfectly fit the training data, an otherwise often intractable nonconvex optimization problem. For (fully-connected) shallow networks, in the best case scenario,…
Directly parameterizing and learning gradients of functions has widespread significance, with specific applications in inverse problems, generative modeling, and optimal transport. This paper introduces gradient networks (GradNets): novel…
This paper studies the estimation of network weights for a class of systems with binary-valued observations. In these systems only quantized observations are available for the network estimation. Furthermore, system states are coupled with…
Nowadays, panoramic images can be easily obtained by panoramic cameras. However, when the panoramic camera orientation is tilted, a non-upright panoramic image will be captured. Existing upright adjustment models focus on how to estimate…
Classical path search assumes complete graphs and scalar optimization metrics, yet real infrastructure networks are incomplete and require multi-dimensional evaluation. We introduce the concept of traversal: a generalization of paths that…
Latent space models are effective tools for statistical modeling and exploration of network data. These models can effectively model real world network characteristics such as degree heterogeneity, transitivity, homophily, etc. Due to their…
Multidimensional scaling (MDS) is a dimensionality reduction tool used for information analysis, data visualization and manifold learning. Most MDS procedures embed data points in low-dimensional Euclidean (flat) domains, such that…
Graph Neural Networks (GNNs) have emerged as the leading paradigm for learning over graph-structured data. However, their performance is limited by issues inherent to graph topology, most notably oversquashing and oversmoothing. Recent…
The most commonly used method for addressing 3D geometric registration is the iterative closet-point algorithm, this approach is incremental and prone to drift over multiple consecutive frames. The Common strategy to address the drift is…
Deep learning and convolutional neural networks in particular are powerful and promising tools for cosmological analysis of large-scale structure surveys. They are already providing similar performance to classical analysis methods using…
Hypergraphs, which use hyperedges to capture groupwise interactions among different entities, have gained increasing attention recently for their versatility in effectively modeling real-world networks. In this paper, we study the problem…
By "parallelogram geometry" we mean the elementary, "commutative", geometry corresponding to vector addition, and by "trapezoid geometry" a certain "non-commutative deformation" of the former. This text presents an elementary approach via…
Employing the ideas of non-linear preconditioning and testing of the classical proximal point method, we formalise common arguments in convergence rate and convergence proofs of optimisation methods to the verification of a simple…
In recent years, it has been convincingly shown that weather forecasting models can be run in single-precision arithmetic. Several models or components thereof have been tested with even lower precision than this. This previous work has…