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Learning-based hashing algorithms are ``hot topics" because they can greatly increase the scale at which existing methods operate. In this paper, we propose a new learning-based hashing method called ``fast supervised discrete hashing"…

Machine Learning · Computer Science 2019-04-09 Jie Gui , Tongliang Liu , Zhenan Sun , Dacheng Tao , Tieniu Tan

This paper studies the quantum computational complexity of the discrete logarithm (DL) and related group-theoretic problems in the context of generic algorithms -- that is, algorithms that do not exploit any properties of the group…

Quantum Physics · Physics 2024-10-23 Minki Hhan , Takashi Yamakawa , Aaram Yun

We present for the first time an efficient iterative method to directly solve the four-component Dirac-Kohn-Sham (DKS) density functional theory. Due to the existence of the negative energy continuum in the DKS operator, the existing…

Computational Physics · Physics 2013-05-03 Lin Lin , Sihong Shao , Weinan E

Lattice sieving in two or more dimensions has proven to be an indispensable practical aid in integer factorization and discrete log computations involving the number field sieve. The main contribution of this article is to show that a…

Number Theory · Mathematics 2020-01-30 Gary McGuire , Oisin Robinson

The two currently fastest general-purpose integer factorization algorithms are the Quadratic Sieve and the Number Field Sieve. Both techniques are used to find so-called smooth values of certain polynomials, i.e., values that factor…

Number Theory · Mathematics 2024-05-01 Markus Hittmeir

Leveraging transfer learning has recently been shown to be an effective strategy for training large models with Differential Privacy (DP). Moreover, somewhat surprisingly, recent works have found that privately training just the last layer…

Machine Learning · Computer Science 2022-11-28 Harsh Mehta , Walid Krichene , Abhradeep Thakurta , Alexey Kurakin , Ashok Cutkosky

Nonnegative matrix factorization (NMF) has been shown to be identifiable under the separability assumption, under which all the columns(or rows) of the input data matrix belong to the convex cone generated by only a few of these columns(or…

Machine Learning · Statistics 2014-03-25 Jason Gejie Liu , Shuchin Aeron

Deep learning-based hybrid iterative methods (DL-HIM) have emerged as a promising approach for designing fast neural solvers to tackle large-scale sparse linear systems. DL-HIM combine the smoothing effect of simple iterative methods with…

Numerical Analysis · Mathematics 2025-06-09 Chen Cui , Kai Jiang , Yun Liu , Shi Shu

Differentially Private-SGD (DP-SGD) of Abadi et al. (2016) and its variations are the only known algorithms for private training of large scale neural networks. This algorithm requires computation of per-sample gradients norms which is…

Machine Learning · Computer Science 2021-02-08 Zhiqi Bu , Sivakanth Gopi , Janardhan Kulkarni , Yin Tat Lee , Judy Hanwen Shen , Uthaipon Tantipongpipat

This paper revisits an algorithm for isolating real roots of univariate polynomials based on continued fractions. It follows the work of Vincent, Uspen- sky, Collins and Akritas, Johnson and Krandick. We use some tricks, especially a new…

Symbolic Computation · Computer Science 2012-09-18 Liyun Dai , Bican Xia

We introduce a refined differentially private (DP) data structure for kernel density estimation (KDE), offering not only improved privacy-utility tradeoff but also better efficiency over prior results. Specifically, we study the…

Data Structures and Algorithms · Computer Science 2025-03-25 Erzhi Liu , Jerry Yao-Chieh Hu , Alex Reneau , Zhao Song , Han Liu

The Poisson-Nernst-Planck (PNP) equations are one of the most effective model for describing electrostatic interactions and diffusion processes in ion solution systems, and have been widely used in the numerical simulations of biological…

Numerical Analysis · Mathematics 2023-12-19 Yang Liu , Shi Shu , Ying Yang

This paper presents a means with time complexity of at worst O(n^3) to compute the discrete logarithm on cyclic finite groups of integers modulo p. The algorithm makes use of reduction of the problem to that of finding the concurrent zeros…

Data Structures and Algorithms · Computer Science 2009-12-29 Charles Sauerbier

A variety of complex biological, natural and man-made systems exhibit non-Markovian dynamics that can be modeled through fractional order differential equations, yet, we lack sample comlexity aware system identification strategies. Towards…

Systems and Control · Electrical Eng. & Systems 2025-06-23 Xiaole Zhang , Vijay Gupta , Paul Bogdan

A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not…

Quantum Physics · Physics 2017-02-20 Peter W. Shor

Large integer factorization is a prominent research challenge, particularly in the context of quantum computing. This holds significant importance, especially in information security that relies on public key cryptosystems. The classical…

Quantum Physics · Physics 2023-10-24 Imran Khan Tutul , Sara Karimi , Mohammadreza Soltaninia , Junpeng Zhan

We propose a deep signature/log-signature FBSDE algorithm to solve forward-backward stochastic differential equations (FBSDEs) with state and path dependent features. By incorporating the deep signature/log-signature transformation into the…

Machine Learning · Computer Science 2022-08-22 Qi Feng , Man Luo , Zhaoyu Zhang

We present a generic algorithm for computing discrete logarithms in a finite abelian p-group H, improving the Pohlig-Hellman algorithm and its generalization to noncyclic groups by Teske. We then give a direct method to compute a basis for…

Number Theory · Mathematics 2013-02-05 Andrew V. Sutherland

Faster-than-Nyquist (FTN) signaling is a candidate non-orthonormal transmission technique to improve the spectral efficiency (SE) of future communication systems. However, such improvements of the SE are at the cost of additional…

Information Theory · Computer Science 2022-04-18 Sina Abbasi , Ebrahim Bedeer

We present an efficient preconditioning technique for accelerating the fixed point iteration in real-space Kohn-Sham density functional theory (DFT) calculations. The preconditioner uses a low rank approximation of the dielectric matrix…

Materials Science · Physics 2023-03-29 Sambit Das , Vikram Gavini