Related papers: Efficient sparse polynomial factoring using the Fu…
In this paper, we present a probabilistic algorithm to multiply two sparse polynomials almost as efficiently as two dense univariate polynomials with a result of approximately the same size. The algorithm depends on unproven heuristics that…
In compressed sensing problems, $\ell_1$ minimization or Basis Pursuit was known to have the best provable phase transition performance of recoverable sparsity among polynomial-time algorithms. It is of great theoretical and practical…
Particle Mesh Ewald (PME) methods accelerated through Fast Fourier Transforms (FFTs) for their reciprocal part are widely used to solve N -body problems over periodic structures with Laplace-like kernels. The FFT dependence of classical PME…
This study presents the derivation of a recursive formula for integrals of products of $N$ Hermite polynomials, establishing a numerically stable scheme for their accurate evaluation in computer codes. The derivation is notably simple and…
We introduce a novel Bayesian hybrid matrix factorisation model (HMF) for data integration, based on combining multiple matrix factorisation methods, that can be used for in- and out-of-matrix prediction of missing values. The model is very…
We develop and implement in this paper a fast sparse assembly algorithm, the fundamental operation which creates a compressed matrix from raw index data. Since it is often a quite demanding and sometimes critical operation, it is of…
This paper describes REAP, a software-hardware approach that enables high performance sparse linear algebra computations on a cooperative CPU-FPGA platform. REAP carefully separates the task of organizing the matrix elements from the…
Shapley values have emerged as a central game-theoretic tool in explainable AI (XAI). However, computing Shapley values exactly requires $2^d$ game evaluations for a model with $d$ features. Lundberg and Lee's KernelSHAP algorithm has…
Current inference systems for Mixture-of-Experts (MoE) models primarily employ static parallelization strategies. However, these static approaches cannot consistently achieve optimal performance across different inference scenarios, as they…
State-of-the-art embeddings often capture distinct yet complementary discriminative features: For instance, one image embedding model may excel at distinguishing fine-grained textures, while another focuses on object-level structure.…
Polynomial multiplication is known to have quasi-linear complexity in both the dense and the sparse cases. Yet no truly linear algorithm has been given in any case for the problem, and it is not clear whether it is even possible. This…
We advocate a new approach of addressing hidden structure problems and finding efficient quantum algorithms. We introduce and investigate the Hidden Symmetry Subgroup Problem (HSSP), which is a generalization of the well-studied Hidden…
Many computer vision applications require robust and efficient estimation of camera geometry from a minimal number of input data measurements, i.e., solving minimal problems in a RANSAC framework. Minimal problems are usually formulated as…
Ensemble methods are commonly used to enhance the generalization performance of machine learning models. However, they present a challenge in deep learning systems due to the high computational overhead required to train an ensemble of deep…
Matrix multiplication is a fundamental kernel in large-scale artificial intelligence and scientific computing, but its performance on conventional electronic accelerators is increasingly constrained by memory bandwidth and energy…
Generalized sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many high performance graph algorithms as well as for some linear solvers, such as algebraic multigrid. Here we show that SpGEMM also yields efficient…
We propose a simulated annealing algorithm specifically tailored to optimise total retrieval times in a multi-level warehouse under complex pre-batched picking constraints. Experiments on real data from a picker-to-parts order picking…
In recent years fused-multiply-add (FMA) units with lower-precision multiplications and higher-precision accumulation have proven useful in machine learning/artificial intelligence applications, most notably in training deep neural networks…
We present a faster interior-point method for optimizing sum-of-squares (SOS) polynomials, which are a central tool in polynomial optimization and capture convex programming in the Lasserre hierarchy. Let $p = \sum_i q^2_i$ be an…
We present a unified framework for the construction of localized exponential integrators that bypasses the traditional trade-off between the accuracy of global spectral methods and the efficiency of sparse finite differences. By evaluating…