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Since its inception in 2016, Federated Learning (FL) has been gaining tremendous popularity in the machine learning community. Several frameworks have been proposed to facilitate the development of FL algorithms, but researchers often…
Approximate bi-level optimization (ABLO) consists of (outer-level) optimization problems, involving numerical (inner-level) optimization loops. While ABLO has many applications across deep learning, it suffers from time and memory…
Automated feature engineering plays a critical role in improving predictive model performance for tabular learning tasks. Traditional automated feature engineering methods are limited by their reliance on pre-defined transformations within…
Bloom filters are space-efficient probabilistic data structures that are used to test whether an element is a member of a set, and may return false positives. Recently, variations referred to as learned Bloom filters were developed that can…
The deployment of large language models (LLMs) is often constrained by memory bandwidth, where the primary bottleneck is the cost of transferring model parameters from the GPU's global memory to its registers. When coupled with custom…
In a recent work (arXiv-DOI: 1804.08072v1) we introduced the Modified Augmented Lagrangian Method (MALM) for the efficient minimization of objective functions with large quadratic penalty terms. From MALM there results an optimality…
The phase space flow of a dynamical system leading to the solution of Linear Programming (LP) problems is explored as an example of complexity analysis in an analog computation framework. An ensemble of LP problems with $n$ variables and…
Simplification of fractional powers of positive rational numbers and of sums, products and powers of such numbers is taught in beginning algebra. Such numbers can often be expressed in many ways, as this article discusses in some detail.…
An optical flow variational model is proposed for a sequence of images defined on a domain in $\mathbb{R}^2$. We introduce a regularization term given by the $L^1$ norm of a fractional differential operator. To solve the minimization…
The present paper deals with the study of the fluence rate over both healthy and tumor tissues in the presence of focal laser ablation (FLA). We propose new analytical solutions for the coupled partial differential equations (PDE) system,…
The development of randomized algorithms for numerical linear algebra, e.g. for computing approximate QR and SVD factorizations, has recently become an intense area of research. This paper studies one of the most frequently discussed…
We propose a new algorithmic framework, called "partial rejection sampling", to draw samples exactly from a product distribution, conditioned on none of a number of bad events occurring. Our framework builds (perhaps surprising) new…
We present several new algorithms for computing factorization invariant values over affine semigroups. In particular, we give (i) the first known algorithm to compute the delta set of any affine semigroup, (ii) an improved method of…
A reaction-diffusion problem with a Caputo time derivative is considered. An integral discretization scheme on a graded mesh along with a decomposition of the exact solution is proposed. The truncation error estimate of the discretization…
When task-specific labels are not available, it becomes difficult to select an embedding model for a specific target corpus. Existing labelless measures based on kernel estimators or Gaussian mixes fail in high-dimensional space, resulting…
We obtain two new algorithms for partial fraction decompositions; the first is over algebraically closed fields, and the second is over general fields. These algorithms takes $O(M^2)$ time, where $M$ is the degree of the denominator of the…
This paper proposes a new algorithm for Gaussian process classification based on posterior linearisation (PL). In PL, a Gaussian approximation to the posterior density is obtained iteratively using the best possible linearisation of the…
The use of machine learning algorithms to predict behaviors of complex systems is booming. However, the key to an effective use of machine learning tools in multi-physics problems, including combustion, is to couple them to physical and…
Reduced-order plasma models that can efficiently predict plasma behavior across various settings and configurations are highly sought after yet elusive. The demand for such models has surged in the past decade due to their potential to…
We investigate prime factorization from two perspectives: quantum annealing and computational algebraic geometry, specifically Gr\"obner bases. We present a novel scalable algorithm which combines the two approaches and leads to the…