相关论文: The Schreier-Sims algorithm for matrix groups

We consider the quantum complexity of estimating matrix elements of unitary irreducible representations of groups. For several finite groups including the symmetric group, quantum Fourier transforms yield efficient solutions to this…

We introduce a concept of a W-graph ideal in a Coxeter group. The main goal of this paper is to describe how to construct a W-graph from a given W-graph ideal. The principal application of this idea is in type A, where it provides an…

We consider robust covariance estimation with group symmetry constraints. Non-Gaussian covariance estimation, e.g., Tyler scatter estimator and Multivariate Generalized Gaussian distribution methods, usually involve non-convex minimization…

Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the…

General-purpose Sparse Matrix-Matrix Multiplication (SpMM) is a fundamental kernel in scientific computing and deep learning. The emergence of new matrix computation units such as Tensor Cores (TCs) brings more opportunities for SpMM…

The simulation of spin models close to critical points of continuous phase transitions is heavily impeded by the occurrence of critical slowing down. A number of cluster algorithms, usually based on the Fortuin-Kasteleyn representation of…

Decoder-only Transformer models such as GPT have demonstrated exceptional performance in text generation, by autoregressively predicting the next token. However, the efficacy of running GPT on current hardware systems is bounded by low…

We propose new sequential simulation-optimization algorithms for general convex optimization via simulation problems with high-dimensional discrete decision space. The performance of each choice of discrete decision variables is evaluated…

We propose a new iteration scheme, the Cauchy-Simplex, to optimize convex problems over the probability simplex $\{w\in\mathbb{R}^n\ |\ \sum_i w_i=1\ \textrm{and}\ w_i\geq0\}$. Specifically, we map the simplex to the positive quadrant of a…

Simon's problem is one of the most important problems demonstrating the power of quantum algorithms, as it greatly inspired the proposal of Shor's algorithm. The generalized Simon's problem is a natural extension of Simon's problem, and…

We consider the problem of minimizing a convex objective which is the sum of a smooth part, with Lipschitz continuous gradient, and a nonsmooth part. Inspired by various applications, we focus on the case when the nonsmooth part is a…

We present an approximation algorithm that takes a pool of pre-trained models as input and produces from it a cascaded model with similar accuracy but lower average-case cost. Applied to state-of-the-art ImageNet classification models, this…

We present a new algorithm for amortized inference in sparse probabilistic graphical models (PGMs), which we call $\Delta$-amortized inference ($\Delta$-AI). Our approach is based on the observation that when the sampling of variables in a…

Genetic algorithms are considered as one of the most efficient search techniques. Although they do not offer an optimal solution, their ability to reach a suitable solution in considerably short time gives them their respectable role in…

The matrix scaling problem, particularly the Sinkhorn-Knopp algorithm, has been studied for over 60 years. In practice, the algorithm often yields high-quality approximations within just a few iterations. Theoretically, however, the…

This note presents an elementary version of Sims's algorithm for computing strong generators of a given perm group, together with a proof of correctness and some notes about appropriate low-level data structures. Upper and lower bounds on…

The increasing availability of graph-structured data motivates the task of optimising over functions defined on the node set of graphs. Traditional graph search algorithms can be applied in this case, but they may be sample-inefficient and…

Recent demonstrations of superconducting quantum computers by Google and IBM and trapped-ion computers from IonQ fueled new research in quantum algorithms, compilation into quantum circuits, and empirical algorithmics. While online access…

Consider the problem of estimating a low-rank matrix when its entries are perturbed by Gaussian noise. If the empirical distribution of the entries of the spikes is known, optimal estimators that exploit this knowledge can substantially…

We improve a recently proposed dynamically driven renormalization group algorithm for cellular automata systems with one absorbing state, introducing spatial correlations in the expression for the transition probabilities. We implement the…