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How I Solved Sudoku With a Business Rules Engine - KDnuggets

#artificialintelligence

On a family trip a few months back, I was flipping through an airline magazine and landed on the puzzles page. There were three puzzles, "Easy", "Medium", and "Hard". At the top of the page a word that would become my obsession over the next couple of months: "Sudoku". I had heard about Sudoku puzzles, but I had never really considered trying one. I grabbed a pencil from one of the kids and started with the "Easy" puzzle. It took me quite some time (and I tore the paper in one spot after erasing too many times) but I eventually completed the puzzle.


Solving Sudoku with Convolution Neural Network Keras

#artificialintelligence

Then we apply softmax function on the final scores to convert them into probabilities. And the data is classified into a class that has the highest probability value(refer to the following image). But in sudoku, the scenario is different. We have to get 81 numbers for each position in the sudoku game, not just one. And we have a total of 9 classes for each number because a number can fall in a range of 1 to 9. To comply with this design, our network should output (81*9) numbers.


Solving Sudoku with Ant Colony Optimisation

arXiv.org Artificial Intelligence

In this paper we present a new Ant Colony Optimisation-based algorithm for Sudoku, which out-performs existing methods on large instances. Our method includes a novel anti-stagnation operator, which we call Best Value Evaporation.


OptNet: Differentiable Optimization as a Layer in Neural Networks

arXiv.org Artificial Intelligence

This paper presents OptNet, a network architecture that integrates optimization problems (here, specifically in the form of quadratic programs) as individual layers in larger end-to-end trainable deep networks. These layers encode constraints and complex dependencies between the hidden states that traditional convolutional and fully-connected layers often cannot capture. In this paper, we explore the foundations for such an architecture: we show how techniques from sensitivity analysis, bilevel optimization, and implicit differentiation can be used to exactly differentiate through these layers and with respect to layer parameters; we develop a highly efficient solver for these layers that exploits fast GPU-based batch solves within a primal-dual interior point method, and which provides backpropagation gradients with virtually no additional cost on top of the solve; and we highlight the application of these approaches in several problems. In one notable example, we show that the method is capable of learning to play mini-Sudoku (4x4) given just input and output games, with no a priori information about the rules of the game; this highlights the ability of our architecture to learn hard constraints better than other neural architectures.


Sudoku Puzzles

AI Magazine

Each row, each column, and each 3x3 box must contain every number from 1 to 9. Additional number clues can be found by answering these questions:. Each row, each column, and each 3x3 box must contain each of the 9 different letters. If completed properly, a nine letter word will be revealed. Puzzle solutions can be found on page 107.


AI taught to beat Sudoku puzzles. Now how about a time machine to 2005?

#artificialintelligence

AI can now solve some of the hardest Sudoku puzzles to a high degree of accuracy, according to new research that teaches machines to logically reason.


Behind the Magic: How we built the ARKit Sudoku Solver

@machinelearnbot

Magic Sudoku uses a combination of Computer Vision, Machine Learning, and Augmented Reality to give a magical user experience that "just works" when you point your phone at a Sudoku puzzle. All of this happens several times each second. I won't dwell too much on the ARKit portion, the Sudoku solving algorithm, or the actual Machine Learning model itself (there are plenty of tutorials written about those subjects already). What was most interesting to me were the practical aspects I learned while training my first machine learning algorithm. One of the original reasons I chose a Sudoku solver as our first AR app was that I knew classifying digits is basically the "hello world" of Machine Learning.


Behind the Magic: How we built the ARKit Sudoku Solver

#artificialintelligence

Magic Sudoku uses a combination of Computer Vision, Machine Learning, and Augmented Reality to give a magical user experience that "just works" when you point your phone at a Sudoku puzzle. All of this happens several times each second. I won't dwell too much on the ARKit portion, the Sudoku solving algorithm, or the actual Machine Learning model itself (there are plenty of tutorials written about those subjects already). What was most interesting to me were the practical aspects I learned while training my first machine learning algorithm. One of the original reasons I chose a Sudoku solver as our first AR app was that I knew classifying digits is basically the "hello world" of Machine Learning.


Sudoku and Doing Your Best Work – Towards Data Science – Medium

#artificialintelligence

A lot of our lives, both our working lives and our personal lives, are spent doing repetitive, uncreative tasks. Many of these tasks are enjoyable: they include hobbies like gardening or baking that we enjoy for hard-to-articulate reasons. But, they also include things we don't want to do, like laundry or washing the dishes. While we cannot simply program a robot to do the tasks listed above, there are a lot of repetitive tasks, especially ones that don't involve manipulating physical objects, for which we can. For example, scientific software packages like Wolfram Alpha can solve most differential equations automatically, so that humans no longer have to solve them by hand.


Sudoku Science

AITopics Original Links

Millions of people around the world are tackling one of the hardest problems in computer science--without even knowing it. The logic game Sudoku is a miniature version of a longstanding mathematical challenge, and it entices both puzzlers, who see it as an enjoyable plaything, and researchers, who see it as a laboratory for algorithm design. Sudoku has become a worldwide puzzle craze within the past year. Previously known primarily in Japan, it now graces newspapers, Web sites, and best-selling books in dozens of countries. A puzzle consists of a 9-by-9 grid made up of nine 3-by-3 subgrids.