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Delaunay Triangulation(DT) is one of the important geometric problems that is used in various branches of knowledge such as computer vision, terrain modeling, spatial clustering and networking. Kinetic data structures have become very…
In many mathematical models of physical phenomenons and engineering fields, such as electrical circuits or mechanical multibody systems, which generate the differential algebraic equations (DAEs) systems naturally. In general, the feature…
We give an overview of the theoretical results for matrix block-recursive algorithms in commutative domains and present the results of experiments that we conducted with new parallel programs based on these algorithms on a supercomputer…
Quasi-separable matrices are a class of rank-structured matriceswidely used in numerical linear algebra and of growing interestin computer algebra, with applications in e.g. the linearization ofpolynomial matrices. Various representation…
Graph analytics techniques based on spectral methods process extremely large sparse matrices with millions or even billions of non-zero values. Behind these algorithms lies the Top-K sparse eigenproblem, the computation of the largest…
We present a sorting algorithm that works in-place, executes in parallel, is cache-efficient, avoids branch-mispredictions, and performs work O(n log n) for arbitrary inputs with high probability. The main algorithmic contributions are new…
In the literature, there exist several studies on symbol-based multigrid methods for the solution of linear systems having structured coefficient matrices. In particular, the convergence analysis for such methods has been obtained in an…
Distributed-memory matrix multiplication (MM) is a key element of algorithms in many domains (machine learning, quantum physics). Conventional algorithms for dense MM rely on regular/uniform data decomposition to ensure load balance. These…
Matrix multiplication optimization remains a fundamental challenge in computational mathematics. This work introduces a novel approach that discovers matrix multiplication schemes whose coefficients are restricted to the set $\{-1, 0, 1\}$…
This paper presents the Neural Cache architecture, which re-purposes cache structures to transform them into massively parallel compute units capable of running inferences for Deep Neural Networks. Techniques to do in-situ arithmetic in…
The low-rank matrix approximation problems within a threshold are widely applied in information retrieval, image processing, background estimation of the video sequence problems and so on. This paper presents an adaptive randomized…
This paper deals with maximum entropy completion of partially specified block-circulant matrices. Since positive definite symmetric circulants happen to be covariance matrices of stationary periodic processes, in particular of stationary…
Sparse Convolution (SC) is widely used for processing 3D point clouds that are inherently sparse. Different from dense convolution, SC preserves the sparsity of the input point cloud by only allowing outputs to specific locations. To…
While it is encouraging to witness the recent development in privacy-preserving Machine Learning as a Service (MLaaS), there still exists a significant performance gap for its deployment in real-world applications. We observe the…
The matrix completion problem aims to reconstruct a low-rank matrix based on a revealed set of possibly noisy entries. Prior works consider completing the entire matrix with generalization error guarantees. However, the completion accuracy…
Recent work has demonstrated that using a carefully designed sensing matrix rather than a random one, can improve the performance of compressed sensing. In particular, a well-designed sensing matrix can reduce the coherence between the…
The estimation of high dimensional precision matrices has been a central topic in statistical learning. However, as the number of parameters scales quadratically with the dimension $p$, many state-of-the-art methods do not scale well to…
This paper presents a regularized recursive identification algorithm with simultaneous on-line estimation of both the model parameters and the algorithms hyperparameters. A new kernel is proposed to facilitate the algorithm development. The…
This work proposes a higher-order iterative framework for solving matrix equations, inspired by the structure and functionality of neural networks. A modification of the classical Jacobi iterative method is introduced to compute…
Probabilistic Circuits (PCs) are tractable representations of probability distributions allowing for exact and efficient computation of likelihoods and marginals. Recent advancements have improved the scalability of PCs either by leveraging…