Related papers: Integer Factorization with a Neuromorphic Sieve
Non-negative matrix factorization (NMF) is a common method for generating topic models from text data. NMF is widely accepted for producing good results despite its relative simplicity of implementation and ease of computation. One…
Nonnegative matrix factorization is a powerful technique to realize dimension reduction and pattern recognition through single-layer data representation learning. Deep learning, however, with its carefully designed hierarchical structure,…
Let $n = \mathrm{p}\!\cdot\!\mathrm{q}$ (p < q) and $\Delta = \lvert p-q \rvert$, where p,q are odd integers, then, it is hypothesized that factorizing this composite n will take O(1) time once the steady state value is reached for any…
This paper proposes new factorizations for computing the Neumann series. The factorizations are based on fast algorithms for small prime sizes series and the splitting of large sizes into several smaller ones. We propose a different basis…
Neural networks are very popular in many areas, but great computing complexity makes it hard to run neural networks on devices with limited resources. To address this problem, quantization methods are used to reduce model size and…
The joint optimization of the integer matrix $\mathbf{A}$ and the power scaling matrix $\mathbf{D}$ is central to achieving the capacity-approaching performance of Integer-Forcing (IF) precoding. This problem, however, is known to be…
The fast assembling of stiffness and mass matrices is a key issue in isogeometric analysis, particularly if the spline degree is increased. We present two algorithms based on the idea of sum factorization, one for matrix assembling and one…
In this paper, we review recent work published over the last 3 years under the umbrella of Neuromorphic engineering to analyze what are the common features among such systems. We see that there is no clear consensus but each system has one…
We present a hardware architecture that uses the Neural Engineering Framework (NEF) to implement large-scale neural networks on Field Programmable Gate Arrays (FPGAs) for performing pattern recognition in real time. NEF is a framework that…
Recent technological developments have led to big data processing, which resulted in significant computational difficulties when solving large-scale linear systems or inverting matrices. As a result, fast approximate iterative matrix…
Neuromorphic computing (NC) introduces a novel algorithmic paradigm representing a major shift from traditional digital computing of Von Neumann architectures. NC emulates or simulates the neural dynamics of brains in the form of Spiking…
Prime numbers are fundamental in number theory and play a significant role in various areas, from pure mathematics to practical applications, including cryptography. In this contribution, we introduce a multithreaded implementation of the…
The proliferation of deep learning applications has intensified the demand for electronic hardware with low energy consumption and fast computing speed. Neuromorphic photonics have emerged as a viable alternative to directly process…
Brain inspired neuromorphic computing has demonstrated remarkable advantages over traditional von Neumann architecture for its high energy efficiency and parallel data processing. However, the limited resolution of synaptic weights degrades…
To factor an integer N, given that it is equal to the product of two primes, it suffices to find an integer d satisfying a certain simple numerical test. In this approach, the factorization problem equates to the problem of designing an…
As robots become smarter and more ubiquitous, optimizing the power consumption of intelligent compute becomes imperative towards ensuring the sustainability of technological advancements. Neuromorphic computing hardware makes use of…
Quantum processors are potentially superior to their classical counterparts for many computational tasks including factorization. Circuit methods as well as adiabatic methods have already been proposed and implemented for finding the…
The number of steps any classical computer requires in order to find the prime factors of an $l$-digit integer $N$ increases exponentially with $l$, at least using algorithms known at present. Factoring large integers is therefore…
Nonnegative Matrix Factorization (NMF) is a widely used technique for data representation. Inspired by the expressive power of deep learning, several NMF variants equipped with deep architectures have been proposed. However, these methods…
A new integer deterministic factorization algorithm, rated at arithmetic operations to $O(N^{1/6+\varepsilon})$ arithmetic operations, is presented in this note. Equivalently, given the least $(\log N)/6$ bits of a factor of the balanced…