Related papers: Integer Factorization with a Neuromorphic Sieve
Symmetric nonnegative matrix factorization (SNMF) has demonstrated to be a powerful method for data clustering. However, SNMF is mathematically formulated as a non-convex optimization problem, making it sensitive to the initialization of…
Symmetric Nonnegative Matrix Factorization (SymNMF) is a technique in data analysis and machine learning that approximates a symmetric matrix with a product of a nonnegative, low-rank matrix and its transpose. To design faster and more…
Sieving is essential in different number theoretical algorithms. Sieving with large primes violates locality of memory access, thus degrading performance. Our suggestion on how to tackle this problem is to use cyclic data structures in…
We introduce a novel method for encoding integers using smooth real-valued functions whose integral properties implicitly reflect discrete quantities. In contrast to classical representations, where the integer appears as an explicit…
Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…
Due to the complexity of the space of quantum many-body states the computation of expectation values by statistical sampling is, in general, a hard task. Neural network representations of such quantum states which can be physically…
Let $x\ge y>0$ be integers. A positive integer is $y$-smooth if all its prime divisors are at most $y$. Let $\Psi(x,y)$ count the number of $y$-smooth integers up to $x$. We present several algorithms that will generate an integer $n\le x$…
Lenstra's integer factorization algorithm is asymptotically one of the fastest known algorithms, and is ideally suited for parallel computation. We suggest a way in which the algorithm can be speeded up by the addition of a second phase.…
We offer multiplication method for factoring big natural numbers which extends the group of the Fermat's and Lehman's factorization algorithms and has run-time complexity $O(n^{1/3})$. This paper is argued the finiteness of proposed…
Let n be any odd natural number other than a perfect square, in this article it is demonstrated that this new factorization algorithm is much more efficient than the implementation technique [2,3 p.1470], described in this article, of the…
Sorting algorithms are the deciding factor for the performance of common operations such as removal of duplicates or database sort-merge joins. This work focuses on 32-bit integer keys, optionally paired with a 32-bit value. We present a…
We study the problem of edge partitioning, where the goal is to partition the edge set of a graph into several parts. The replication factor of a vertex $v$ is the number of parts that contain edges incident to $v$. The goal is to minimize…
We propose a computationally efficient algorithm for seizure detection. Instead of using a purely data-driven approach, we develop a hybrid model-based/data-driven method, combining convolutional neural networks with factor graph inference.…
Depth factorization and quantization have emerged as two of the principal strategies for designing efficient deep convolutional neural network (CNN) architectures tailored for low-power inference on the edge. However, there is still little…
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…
Unsupervised integrative analysis of multiple data sources has become common place and scalable algorithms are necessary to accommodate ever increasing availability of data. Only few currently methods have estimation speed as their focus,…
We study the problem of large-scale network embedding, which aims to learn latent representations for network mining applications. Previous research shows that 1) popular network embedding benchmarks, such as DeepWalk, are in essence…
This paper considers clustered multi-task compressive sensing, a hierarchical model that solves multiple compressive sensing tasks by finding clusters of tasks that leverage shared information to mutually improve signal reconstruction. The…
In this paper, we create a systematic and automatic procedure for transforming the integer factorization problem into the problem of solving a system of Boolean equations. Surprisingly, the resulting system of Boolean equations takes on a…
The density estimation is one of the core problems in statistics. Despite this, existing techniques like maximum likelihood estimation are computationally inefficient due to the intractability of the normalizing constant. For this reason an…