Related papers: A Geometric Square-Based Approach to RSA Integer F…
We give new results for problems in computational and statistical machine learning using tools from high-dimensional geometry and probability. We break up our treatment into two parts. In Part I, we focus on computational considerations in…
In this paper, we present an approach to integer factorization using distributed representations formed with Vector Symbolic Architectures. The approach formulates integer factorization in a manner such that it can be solved using neural…
Manifold regularization methods for matrix factorization rely on the cluster assumption, whereby the neighborhood structure of data in the input space is preserved in the factorization space. We argue that using the k-neighborhoods of all…
Sparse matrix factorization is the problem of approximating a matrix $\mathbf{Z}$ by a product of $J$ sparse factors $\mathbf{X}^{(J)} \mathbf{X}^{(J-1)} \ldots \mathbf{X}^{(1)}$. This paper focuses on identifiability issues that appear in…
We propose a new ensemble prediction method, Random Subset Averaging (RSA), tailored for settings with many covariates, particularly in the presence of strong correlations. RSA constructs candidate models via binomial random subset strategy…
In this paper, we present attacks on three types of RSA modulus when the least significant bits of the prime factors of RSA modulus satisfy some conditions. Let $p,$ and $q$ be primes of the form $p=a^{m_1}+r_p$ and $q=b^{m_2}+r_q$…
Modern robotics often involves multiple embodied agents operating within a shared environment. Path planning in these cases is considerably more challenging than in single-agent scenarios. Although standard Sampling-based Algorithms (SBAs)…
Integer factorization is one of the vital algorithms discussed as a part of analysis of any black-box cipher suites where the cipher algorithm is based on number theory. The origin of the problem is from Discrete Logarithmic Problem which…
Representational Similarity Analysis (RSA) aims to explore similarities between neural activities of different stimuli. Classical RSA techniques employ the inverse of the covariance matrix to explore a linear model between the neural…
Factorization of numbers with the help of Gauss sums relies on an intimate relationship between the maxima of these functions and the factors. Indeed, when we restrict ourselves to integer arguments of the Gauss sum we profit from a…
We propose a localized divide and conquer algorithm for inverse factorization $S^{-1} = ZZ^*$ of Hermitian positive definite matrices $S$ with localized structure, e.g. exponential decay with respect to some given distance function on the…
Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity…
Given a graph or similarity matrix, we consider the problem of recovering a notion of true distance between the nodes, and so their true positions. We show that this can be accomplished in two steps: matrix factorisation, followed by…
Shor's algorithm is one of the most promising applications of quantum computers. However, since $\sim 10^6$ physical qubits are believed to be required for established approaches, the algorithm will need to be distributed across many…
We consider the Subset Sum Ratio Problem ($SSR$), in which given a set of integers the goal is to find two subsets such that the ratio of their sums is as close to~1 as possible, and introduce a family of variations that capture additional…
Test-time scaling methods improve the capabilities of large language models (LLMs) by increasing the amount of compute used during inference to make a prediction. Inference-time compute can be scaled in parallel by choosing among multiple…
Nonnegative matrix factorization (NMF) is widely used for clustering with strong interpretability. Among general NMF problems, symmetric NMF is a special one that plays an important role in graph clustering where each element measures the…
Integer factorization is a very hard computational problem. Currently no efficient algorithm for integer factorization is publicly known. However, this is an important problem on which it relies the security of many real world cryptographic…
In myriad statistical applications, data are collected from related but heterogeneous sources. These sources share some commonalities while containing idiosyncratic characteristics. One of the most fundamental challenges in such scenarios…
Although Bayesian methods are robust and principled, their application in practice could be limited since they typically rely on computationally intensive Markov Chain Monte Carlo algorithms for their implementation. One possible solution…