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Multidimensional fitting (MDF) method is a multivariate data analysis method recently developed and based on the fitting of distances. Two matrices are available: one contains the coordinates of the points and the second contains the…
Recent advances in Neural Radiance Fields (NeRF) have demonstrated significant potential for representing 3D scene appearances as implicit neural networks, enabling the synthesis of high-fidelity novel views. However, the lengthy training…
The recently developed Flexible Local Approximation MEthod (FLAME) produces accurate difference schemes by replacing the usual Taylor expansion with Trefftz functions -- local solutions of the underlying differential equation. This paper…
We introduce a fluid dynamics algorithm that performs with nearly spectral accuracy, but uses finite-differences instead of FFTs to compute gradients and thus executes 10 times faster. The finite differencing is not based on a high-order…
Decentralized learning recently has received increasing attention in machine learning due to its advantages in implementation simplicity and system robustness, data privacy. Meanwhile, the adaptive gradient methods show superior…
We develop efficient and high-order accurate finite difference methods for elliptic partial differential equations in complex geometry in the Difference Potentials framework. The main novelty of the developed schemes is the use of local…
Two main families of node feature augmentation schemes have been explored for enhancing GNNs: random features and spectral positional encoding. Surprisingly, however, there is still no clear understanding of the relation between these two…
We present a real-space formulation and higher-order finite-difference implementation of periodic Orbital-free Density Functional Theory (OF-DFT). Specifically, utilizing a local reformulation of the electrostatic and kernel terms, we…
In this paper, we initiate a study of functional minimization in Federated Learning. First, in the semi-heterogeneous setting, when the marginal distributions of the feature vectors on client machines are identical, we develop the federated…
Gradient-based approximate inference methods, such as Stein variational gradient descent (SVGD), provide simple and general-purpose inference engines for differentiable continuous distributions. However, existing forms of SVGD cannot be…
In \cite{liu2022practical}, a general algorithm is developed to efficiently obtain the best accuracy using the regular refinement. The adaptive refinement allows for obtaining an accuracy with a smaller number of DoFs compared with the…
In 1999, Brodal and Fagerberg (BF) gave an algorithm for maintaining a low outdegree orientation of a dynamic uniformly sparse graph. Specifically, for a dynamic graph on $n$-vertices, with arboricity bounded by $\alpha$ at all times, the…
Spectral discretizations of fractional derivative operators are examined, where the approximation basis is related to the set of Jacobi polynomials. The pseudo-spectral method is implemented by assuming that the grid, used to represent the…
Kernel method has been developed as one of the standard approaches for nonlinear learning, which however, does not scale to large data set due to its quadratic complexity in the number of samples. A number of kernel approximation methods…
Empowered by deep learning, recent methods for material capture can estimate a spatially-varying reflectance from a single photograph. Such lightweight capture is in stark contrast with the tens or hundreds of pictures required by…
Due to recent technological advances, large brain imaging data sets can now be collected. Such data are highly complex so extraction of meaningful information from them remains challenging. Thus, there is an urgent need for statistical…
Federated Learning (FL) enables collaborative model training across distributed clients while preserving data privacy, yet faces challenges in non-independent and identically distributed (non-IID) settings due to client drift, which impairs…
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…
In this paper, we study communication efficient distributed algorithms for distributionally robust federated learning via periodic averaging with adaptive sampling. In contrast to standard empirical risk minimization, due to the minimax…
Federated Learning (FL) is a distributed learning paradigm that enables a large number of resource-limited nodes to collaboratively train a model without data sharing. The non-independent-and-identically-distributed (non-i.i.d.) data…