相关论文: Solving N-Queen Problem using Las Vegas Algorithm …

The N-representability problem consists in determining whether, for a given p-body matrix, there exists at least one N-body density matrix from which the p-body matrix can be obtained by contraction, that is, if the given matrix is a p-body…

Convolutional Neural Networks (CNNs) have achieved significant breakthroughs in various fields. However, these advancements have led to a substantial increase in the complexity and size of these networks. This poses a challenge when…

Number the cells of a (possibly infinite) chessboard in some way with the numbers 0, 1, 2, ... Consider the cells in order, placing a queen in a cell if and only if it would not attack any earlier queen. The problem is to determine the…

In deep learning frameworks, weight pruning is a widely used technique for improving computational efficiency by reducing the size of large models. This is especially critical for convolutional operators, which often act as performance…

We generalize the recent results of Chaiken et al. to a rectangular $m\times n$ chessboard. An explicit formula for the number of nonattacking configurations of one-move riders on such a chessboard is calculated in two different ways, one…

In constructive recognition of a representation of a Classical group $G$, much attention has been paid to the natural representation as well as to generic (Black Box) algorithms that treat all representations uniformly. There are…

In his list of open problems, Martin Erickson described a certain game: "Two players alternately put queens on an n x n chess board so that each new queen is not in range of any queen already on the board (the color of the queens is…

In this paper, by combining the algorithm New Q-Newton's method - developed in previous joint work of the author - with Armijo's Backtracking line search, we resolve convergence issues encountered by Newton's method (e.g. convergence to a…

Reducing the size of a neural network (pruning) by removing weights without impacting its performance is an important problem for resource-constrained devices. In the past, pruning was typically accomplished by ranking or penalizing weights…

We consider the resolution of learning problems involving $\ell_0$-regularization via Branch-and-Bound (BnB) algorithms. These methods explore regions of the feasible space of the problem and check whether they do not contain solutions…

Backtracking search algorithms are often used to solve the Constraint Satisfaction Problem (CSP). The efficiency of backtracking search depends greatly on the variable ordering heuristics. Currently, the most commonly used heuristics are…

Stochastic search algorithms are among the most sucessful approaches for solving hard combinatorial problems. A large class of stochastic search approaches can be cast into the framework of Las Vegas Algorithms (LVAs). As the run-time…

Simple regression methods provide robust, near-optimal solutions for optimal switching problems, including high-dimensional ones (up to 50). While the theory requires solving intractable PDE systems, the Longstaff-Schwartz algorithm with…

We shall investigate randomized algorithms for solving large-scale linear inverse problems with general regularizations. We first present some techniques to transform inverse problems of general form into the ones of standard form, then…

We introduce the idea that the P vs NP problem can have a finer structure. Given the NP complete problem of interest, the configurations space of the problem can be divided in (at least) two regions. In one region, polynomial algorithms to…

This paper proposes a new mechanism for pruning a search game-tree in computer chess. The algorithm stores and then reuses chains or sequences of moves, built up from previous searches. These move sequences have a built-in forward-pruning…

Neural network pruning is a widely used strategy for reducing model storage and computing requirements. It allows to lower the complexity of the network by introducing sparsity in the weights. Because taking advantage of sparse matrices is…

Python currently is the dominant language in the field of Machine Learning but is often criticized for being slow to perform certain tasks. In this report, we use the well-known $N$-queens puzzle as a benchmark to show that once compiled…

The ability of Deep Neural Networks to approximate highly complex functions is key to their success. This benefit, however, comes at the expense of a large model size, which challenges its deployment in resource-constrained environments.…

Network compression is crucial to making the deep networks to be more efficient, faster, and generalizable to low-end hardware. Current network compression methods have two open problems: first, there lacks a theoretical framework to…