Related papers: Efficient sparse polynomial factoring using the Fu…

This paper presents a product to sum approach for a fast and efficient matrix filling in a hierarchical finite-element method (FEM). Due to the existence of a coupling factor arising from the material and Jacobian inhomogeneities in curved…

Many concurrent algorithms require processes to perform fetch-and-add operations on a single memory location, which can be a hot spot of contention. We present a novel algorithm called Aggregating Funnels that reduces this contention by…

Deep representation learning has become one of the most widely adopted approaches for visual search, recommendation, and identification. Retrieval of such representations from a large database is however computationally challenging.…

This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some of the output variables are also input variables, linked by a linear dependency. Fundamental examples…

An algorithm for matrix factorization of polynomials was proposed in \cite{fomatati2022tensor} and it was shown that this algorithm produces better results than the standard method for factoring polynomials on the class of summand-reducible…

Sparse matrix-matrix multiplication (SpGEMM) is a computational primitive that is widely used in areas ranging from traditional numerical applications to recent big data analysis and machine learning. Although many SpGEMM algorithms have…

For many data-processing applications, a comprehensive set of efficient operations for the management of priority values is required. Indexed priority queues are particularly promising to satisfy this requirement by design. In this work, we…

Sequence model based NLP applications can be large. Yet, many applications that benefit from them run on small devices with very limited compute and storage capabilities, while still having run-time constraints. As a result, there is a need…

Ensembling is commonly used in machine learning on tabular data to boost predictive performance and robustness, but larger ensembles often lead to increased hardware demand. We introduce HAPEns, a post-hoc ensembling method that explicitly…

Finding the product of two polynomials is an essential and basic problem in computer algebra. While most previous results have focused on the worst-case complexity, we instead employ the technique of adaptive analysis to give an improvement…

This paper describes a novel approach of packing sparse convolutional neural networks for their efficient systolic array implementations. By combining subsets of columns in the original filter matrix associated with a convolutional layer,…

We present an implementation of Pagh's compressed matrix multiplication algorithm, a randomized algorithm that constructs sketches of matrices to compute an unbiased estimate of their product. By leveraging fast polynomial multiplication…

Finite element methods usually construct basis functions and quadrature rules for multidimensional domains via tensor products of one-dimensional counterparts. While straightforward, this approach results in integration spaces larger than…

This paper describes a new and purely functional implementation technique of binary heaps. A binary heap is a tree-based data structure that implements priority queue operations (insert, remove, minimum/maximum) and guarantees at worst…

Matrix-multiply-accumulate (MMA) units, or tensor cores, are now widespread across modern computing architectures. Yet, their use for particle-grid operators remains limited. In implicit particle methods, mass-matrix assembly is a…

The works presented in this habilitation concern the algorithmics of polynomials. This is a central topic in computer algebra, with numerous applications both within and outside the field - cryptography, error-correcting codes, etc. For…

Hensel's lemma, combined with repeated applications of Weierstrass preparation theorem, allows for the factorization of polynomials with multivariate power series coefficients. We present a complexity analysis for this method and leverage…

Finding the solutions to a system of multivariate polynomial equations is a fundamental problem in mathematics and computer science. It involves evaluating the polynomials at many points, often chosen from a grid. In most current methods,…

We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our…

Computing the product of two sparse matrices (SpGEMM) is a fundamental operation in various combinatorial and graph algorithms as well as various bioinformatics and data analytics applications for computing inner-product similarities. For…