Related papers: Towards a MATLAB Toolbox to compute backstepping k…
Solving systems of linear equations is a fundamental problem, but it can be computationally intensive for classical algorithms in high dimensions. Existing quantum algorithms can achieve exponential speedups for the quantum linear system…
Matrix seriation, the problem of permuting the rows and columns of a matrix to uncover latent structure, is a fundamental technique in data science, particularly in the visualization and analysis of relational data. Applications span…
A recent paper (Neural Networks, {\bf 132} (2020), 253-268) introduces a straightforward and simple kernel based approximation for manifold learning that does not require the knowledge of anything about the manifold, except for its…
Kernel methods are fundamental in machine learning, and faster algorithms for kernel approximation provide direct speedups for many core tasks in machine learning. The polynomial kernel is especially important as other kernels can often be…
Scaling up the sparse matrix-vector multiplication kernel on modern Graphics Processing Units (GPU) has been at the heart of numerous studies in both academia and industry. In this article we present a novel non-parametric, self-tunable,…
Hierarchical matrix approximations have gained significant traction in the machine learning and scientific community as they exploit available low-rank structures in kernel methods to compress the kernel matrix. The resulting compressed…
This paper presents a sequential randomized lowrank matrix factorization approach for incrementally predicting values of an unknown function at test points using the Gaussian Processes framework. It is well-known that in the Gaussian…
The generic matrix multiply (GEMM) function is the core element of high-performance linear algebra libraries used in many computationally-demanding digital signal processing (DSP) systems. We propose an acceleration technique for GEMM based…
We propose in this work a new family of kernels for variable-length time series. Our work builds upon the vector autoregressive (VAR) model for multivariate stochastic processes: given a multivariate time series x, we consider the…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
Within the past years, hardware vendors have started designing low precision special function units in response to the demand of the Machine Learning community and their demand for high compute power in low precision formats. Also the…
In this note, we introduce a family of "power sum" kernels and the corresponding Gaussian processes on symmetric groups $\mathrm{S}_n$. Such processes are bi-invariant: the action of $\mathrm{S}_n$ on itself from both sides does not change…
Algebraic characterization of logic programs has received increasing attention in recent years. Researchers attempt to exploit connections between linear algebraic computation and symbolic computation in order to perform logical inference…
In modern neural networks like Transformers, linear layers require significant memory to store activations during backward pass. This study proposes a memory reduction approach to perform backpropagation through linear layers. Since the…
The main question concerns another recent advance in sequential Monte Carlo, the use of a mixture transition kernel that automatically adapts to the target distribution (Douc et al. 2006). Is there a class of static inference problems for…
We consider scattered data approximation on product regions of equal and different dimensionality. On each of these regions, we assume quasi-uniform but unstructured data sites and construct optimal sparse grids for scattered data…
In this paper, we present a toolbox for structured model reduction developed for MATLAB. In addition to structured model reduction methods using balanced realizations of the subsystems, we introduce a numerical algorithm for structured…
Machine Learning (ML) has widely been used for modeling and predicting physical systems. These techniques offer high expressive power and good generalizability for interpolation within observed data sets. However, the disadvantage of…
We proposed MATEX, a distributed framework for transient simulation of power distribution networks (PDNs). MATEX utilizes matrix exponential kernel with Krylov subspace approximations to solve differential equations of linear circuit.…
Recently, a novel method based on coding partitions [1]-[4] has been used to derive power series expansions to previously intractable problems. In this method the coefficients at $k$ are determined by summing the contributions made by each…