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A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups

arXiv.org Machine Learning

Symmetries and equivariance are fundamental to the generalization of neural networks on domains such as images, graphs, and point clouds. Existing work has primarily focused on a small number of groups, such as the translation, rotation, and permutation groups. In this work we provide a completely general algorithm for solving for the equivariant layers of matrix groups. In addition to recovering solutions from other works as special cases, we construct multilayer perceptrons equivariant to multiple groups that have never been tackled before, including $\mathrm{O}(1,3)$, $\mathrm{O}(5)$, $\mathrm{Sp}(n)$, and the Rubik's cube group. Our approach outperforms non-equivariant baselines, with applications to particle physics and dynamical systems. We release our software library to enable researchers to construct equivariant layers for arbitrary matrix groups.


A Deep Learning Technique, Decoding The Rubik's Cube - ELE Times

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A deep-learning technique that can learn a so-called "fitness function" from a set of sample solutions to a problem has been devised. This technique was initially trained to solve the Rubik's cube, the popular 3-D combination puzzle invented by Hungarian sculptor Ernő Rubik. The aim was to use machine learning to learn to solve the Rubik's cube. Rubik's cube is a very complex puzzle, but any of the vast numbers of combinations is at most 20 steps from a solution. So the approach here is to try and solve the problem by learning to do each of those steps individually. The technique is based on two main approaches: stepwise learning and the use of a deep neural network.


A deep learning technique to solve Rubik's cube and other problems step-by-step

#artificialintelligence

Colin G. Johnson, an associate professor at the University of Nottingham, recently developed a deep-learning technique that can learn a so-called "fitness function" from a set of sample solutions to a problem. This technique, presented in a paper published in Wiley's Expert Systems journal, was initially trained to solve the Rubik's cube, the popular 3-D combination puzzle invented by Hungarian sculptor Ernő Rubik. "The aim of our paper was to use machine learning to learn to solve the Rubik's cube," Colin G. Johnson, one of the researchers who carried out the study, told TechXplore. "Rubik's cube is a very complex puzzle, but any of the vast number of combinations is at most 20 steps from a solution. So the approach we take here is to try and solve the problem by learning to do each of those steps individually."


Finally, I can solve a Rubik's Cube

Engadget

The Rubik's Cube has been around for decades. I've toyed with the cube, probably in the very late '80s or early '90s, but never even imagined being able to solve one; from entirely shuffled, to perfectly ordered. But wouldn't it be satisfying if I could? Fortunately, the internet makes solving what was originally an architecture puzzle, doable for most of us. The world record for solving a cube has plummeted since 2000 from 20 seconds to under five, as pros and enthusiasts synthesized high-speed solutions and turn combinations (called algorithms) and shared them with the world.


This AI can explain how it solves Rubik's Cube--and that's a big deal

#artificialintelligence

However, these AI algorithms cannot explain the thought processes behind their decisions. A computer that masters protein folding and also tells researchers more about the rules of biology is much more useful than a computer that folds proteins without explanation. Therefore, AI researchers like me are now turning our efforts toward developing AI algorithms that can explain themselves in a manner that humans can understand. If we can do this, I believe that AI will be able to uncover and teach people new facts about the world that have not yet been discovered, leading to new innovations. One field of AI, called reinforcement learning, studies how computers can learn from their own experiences.


How To Solve a Rubik's Cube by Using Algorithms

#artificialintelligence

Love it or hate it, The Rubik's cube is one of the world's most popular puzzles. For many, it is an intimidating challenge, but it doesn't need to be. With a few simple algorithms and some perseverance, you too can solve one in short order if you haven't before. Read on to find out how. RELATED: HOW TO CHEAT AND MAKE IT LOOK LIKE YOU CAN SOLVE A RUBIK'S CUBE If you have trouble solving a Rubik's cube, don't fret, you are not alone.


World's smallest Rubik's Cube to be sold in Japan

The Japan Times

Japanese toy-maker MegaHouse Corp. said Wednesday it will launch the world's smallest working Rubik's Cube, weighing about 2 grams and measuring 0.99 centimeter on each side. On the same day, the Bandai Namco Holdings Inc. subsidiary started accepting orders for the product online. It is priced at ¥198,000 in Japan, including delivery costs. Delivery will start in late December. The Rubik's Cube, invented by Erno Rubik from Hungary in 1974, hit store shelves across the world in 1980. In Japan, MegaHouse has shipped out over 14 million cubes.


AI Is Making Our Lives Better In Weird And Wonderful Ways, Here's How

#artificialintelligence

When some people hear the term'artificial intelligence' their initial reaction is to imagine a dystopian future where robots have risen up and overthrown humanity. The truth is, application of AI technology in our day-to-day lives is a lot less sinister. It might not be long before these technologies become common in our everyday lives. It's currently assisting with medical diagnosis, the creation of autonomous cars and to help improve businesses by analysing data and creating accurate forecasts of client or market behaviour. The application of AI is becoming more and more popular in businesses worldwide, with the potential to improve our lives in unexpected ways.


A connected Rubik's Cube will let speed cubers compete remotely

Engadget

In-person competition is a no-go in many disciplines amid the COVID-19 pandemic, but speed cubers will be still able to battle opponents remotely in the Rubik's Cube World Cup. Rubik's has revealed the Connected Cube, which links to your phone or tablet and tracks your solve times and progress in real-time. It's more of a traditional cube than GoCube, which is largely a STEM-focused toy. Both use the same platform and can connect to the Rubik's Arena community, which has almost 47,000 players. As such, amateur and professional cubers can take part in this year's World Cup without having to travel, as long as they have a Connected Cube or GoCube. Qualifiers start August 15th and run through October 10th.


Is Robotics Lagging AI?

#artificialintelligence

The concept of autonomous machines dates back to medieval times, but the research into the practical and potential use of robots began only in the 20th century. Today, there are numerous scholars, inventors, engineers, and technicians that are working to develop machines that mimic human behaviour and manage tasks in a human-like fashion. While artificial intelligence plays a crucial role in the development and advancement of robotics, the rise of general-purpose robots poses a question of whether robotics has begun to lag AI. People often confuse robotics for industrial automation and academia and research. While for most high-end research robots, it has deep learning embedded into them such as computer vision linked objects, feature detection and classification, industrial robots are beginning to include the maturity of camera-based object detection and classification.