Related papers: Scaling up prime factorization with self-organizin…
We present a new approach to RSA factorization inspired by geometric interpretations and square differences. This method reformulates the problem in terms of the distance between perfect squares and provides a recurrence relation that…
Motivated by the factorization inherent in the original fast multipole method and the improved fast Gauss transform we introduce a factorable form of attention that operates efficiently in high dimensions. This approach reduces the…
Tensor decompositions, which represent an $N$-order tensor using approximately $N$ factors of much smaller dimensions, can significantly reduce the number of parameters. This is particularly beneficial for high-order tensors, as the number…
We propose HAMSI (Hessian Approximated Multiple Subsets Iteration), which is a provably convergent, second order incremental algorithm for solving large-scale partially separable optimization problems. The algorithm is based on a local…
Multiresolution analysis and matrix factorization are foundational tools in computer vision. In this work, we study the interface between these two distinct topics and obtain techniques to uncover hierarchical block structure in symmetric…
We propose the algorithm that solves the symmetric cone programs (SCPs) by iteratively calling the projection and rescaling methods the algorithms for solving exceptional cases of SCP. Although our algorithm can solve SCPs by itself, we…
We present a special-purpose algorithm for factoring semiprimes $N = pq$ in which one prime factor satisfies $p \approx c\,(a/b)^n$ for positive integers $a, b, c, n$ with $a > b$ and $\gcd(a,b) = 1$. Given the correct parameters $(a, b)$,…
A variety of large-scale machine learning problems can be cast as instances of constrained submodular maximization. Existing approaches for distributed submodular maximization have a critical drawback: The capacity - number of instances…
Matrix Factorization (MF) has been widely applied in machine learning and data mining. A large number of algorithms have been studied to factorize matrices. Among them, stochastic gradient descent (SGD) is a commonly used method.…
Factorization machines (FMs) are widely used in recommender systems due to their adaptability and ability to learn from sparse data. However, for the ubiquitous non-interactive features in sparse data, existing FMs can only estimate the…
In-memory database query processing frequently involves substantial data transfers between the CPU and memory, leading to inefficiencies due to Von Neumann bottleneck. Processing-in-Memory (PIM) architectures offer a viable solution to…
We report on the design and implementation of the AC/DC gradient descent solver for a class of optimization problems over normalized databases. AC/DC decomposes an optimization problem into a set of aggregates over the join of the database…
Tuning numerical libraries has become more difficult over time, as systems get more sophisticated. In particular, modern multicore machines make the behaviour of algorithms hard to forecast and model. In this paper, we tackle the issue of…
The availability of working quantum computers has led to several proposals and claims of quantum advantage. In 2023, this has included claims that quantum computers can successfully factor large integers, by optimizing the search for nearby…
The FastECPP algorithm is currently the fastest approach to prove theprimality of general numbers, and has the additional benefit of creatingcertificates that can be checked independently and with a lower complexity.This article shows how…
This paper presents an exact and explicit tensor-network equation for the search of nontrivial divisors of a composite integer, together with an algorithm for its computation. The proposed method is based on the MeLoCoToN approach, which…
Matrix factorization is an inference problem that has acquired importance due to its vast range of applications that go from dictionary learning to recommendation systems and machine learning with deep networks. The study of its fundamental…
In this work, we introduce the concept of an entirely new circuit architecture based on the novel, physics-inspired computing paradigm: Memcomputing. In particular, we focus on digital memcomputing machines (DMMs) that can be designed…
We propose a flexible and theoretically supported framework for scalable nonnegative matrix factorization. The goal is to find nonnegative low-rank components directly from compressed measurements, accessing the original data only once or…
Conic optimization plays a crucial role in many machine learning (ML) problems. However, practical algorithms for conic constrained ML problems with large datasets are often limited to specific use cases, as stochastic algorithms for…