Related papers: Hashing Modulo Alpha-Equivalence
Hashing methods have made significant progress in cross-modal retrieval tasks with fast query speed and low storage cost. Among them, deep learning-based hashing achieves better performance on large-scale data due to its excellent…
The symmetric Nonnegative Matrix Factorization (NMF), a special but important class of the general NMF, has found numerous applications in data analysis such as various clustering tasks. Unfortunately, designing fast algorithms for the…
We present a fast algorithm for modular exponentiation when the factorization of the modulus is known. Let $a,n,m$ be positive integers and suppose $m$ factors canonically as $\prod_{i=1}^k p_i^{e_i}$. Choose integer parameters $t_i\in [1,…
A family of comparison-based exact pattern matching algorithms is described. They utilize multi-dimensional arrays in order to process more than one adjacent text window in each iteration of the search cycle. This approach leads to a lower…
Deep hashing has been widely adopted for large-scale image retrieval, with numerous strategies proposed to optimize hash function learning. Pairwise-based methods are effective in learning hash functions that preserve local similarity…
We describe a consistent hashing algorithm which performs multiple lookups per key in a hash table of nodes. It requires no additional storage beyond the hash table, and achieves a peak-to-average load ratio of 1 + epsilon with just 1 +…
The square root modulo problem is a known primitive in designing an asymmetric cryptosystem. It was first attempted by Rabin. Decryption failure of the Rabin cryptosystem caused by the 4-to-1 decryption output is overcome efficiently in…
A Reduction -- an accumulation over a set of values, using an associative and commutative operator -- is a common computation in many numerical computations, including scientific computations, machine learning, computer vision, and…
The classical persistence algorithm computes the unique decomposition of a persistence module implicitly given by an input simplicial filtration. Based on matrix reduction, this algorithm is a cornerstone of the emergent area of topological…
In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…
Let {\alpha} be the maximal value such that the product of an n x n^{\alpha} matrix by an n^{\alpha} x n matrix can be computed with n^{2+o(1)} arithmetic operations. In this paper we show that \alpha>0.30298, which improves the previous…
Greedy algorithms are widely used for problems in machine learning such as feature selection and set function optimization. Unfortunately, for large datasets, the running time of even greedy algorithms can be quite high. This is because for…
We develop a meta-algorithm that, given a polynomial (in one or more variables), and a prime p, produces a fast (logarithmic time) algorithm that takes a positive integer n and outputs the number of times each residue class modulo p appears…
An algebraic number $\beta \in \mathbb{C}$ with no conjugate of modulus 1 can serve as the base of a numeration system $(\beta, \mathcal{A})$ with parallel addition, i.e., the sum of two operands represented in base $\beta$ with digits from…
We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The principal innovation in these algorithms is that they are block-iterative in the…
We develop procedures, based on minimization of the composition $f(x) = h(c(x))$ of a convex function $h$ and smooth function $c$, for solving random collections of quadratic equalities, applying our methodology to phase retrieval problems.…
We ascertain the modularity-like objective function whose optimization is equivalent to the maximum likelihood in annotated networks. We demonstrate that the modularity-like objective function is a linear combination of modularity and…
We introduce harmonization, an ensembling method that combines several "noisy" decoders to generate highly accurate decoding predictions. Harmonized ensembles of MWPM-based decoders achieve lower logical error rates than their individual…
Based on cluster de-synchronization properties of phase oscillators, we introduce an efficient method for the detection and identification of modules in complex networks. The performance of the algorithm is tested on computer generated and…
In this article, we introduce a new parameterized family of topological descriptors, taking the form of candidate decompositions, for multi-parameter persistence modules, and we identify a subfamily of these descriptors, that we call…