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Staying the course: Locating equilibria of dynamical systems on Riemannian manifolds defined by point-clouds

arXiv.org Artificial Intelligence

We introduce a method to successively locate equilibria (steady states) of dynamical systems on Riemannian manifolds. The manifolds need not be characterized by an a priori known atlas or by the zeros of a smooth map. Instead, they can be defined by point-clouds and sampled as needed through an iterative process. If the manifold is an Euclidean space, our method follows isoclines, curves along which the direction of the vector field $X$ is constant. For a generic vector field $X$, isoclines are smooth curves and every equilibrium lies on isoclines. We generalize the definition of isoclines to Riemannian manifolds through the use of parallel transport: generalized isoclines are curves along which the directions of $X$ are parallel transports of each other. As in the Euclidean case, generalized isoclines of generic vector fields $X$ are smooth curves that connect equilibria of $X$. Our algorithm can be regarded as an extension of the method of Newton trajectories to the manifold setting when the manifold is unknown. This work is motivated by computational statistical mechanics, specifically high dimensional (stochastic) differential equations that model the dynamics of molecular systems. Often, these dynamics concentrate near low-dimensional manifolds and have transitions (saddle points with a single unstable direction) between metastable equilibria. We employ iteratively sampled data and isoclines to locate these saddle points. Coupling a black-box sampling scheme (e.g., Markov chain Monte Carlo) with manifold learning techniques (diffusion maps in the case presented here), we show that our method reliably locates equilibria of $X$.


Machine Learning Math: A Complete Guide to Machine Learning for Beginners with Tensorflow. This Book Explains How to Build Artificial Intelligence in Business Applications: ML & AI Academy: 9798647618702: Amazon.com: Books

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You will learn four important things. The first one is how to implement games using gym and how to play games for relaxation and having fun. The second one is that you will learn how to preprocess data in reinforcement learning tasks such as in computer games. For practical machine learning applications, you will spend a great deal of time understanding and refining data, which affects the performance of an AI system a lot. The third one is the deep Q-learning algorithm.


11 Best Udemy Deep Learning Courses, Tutorials and Trainings in 2022

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Are you looking for Best Deep Learning Courses? This is also coming from the same two authors of the first one in this list; this Bestselling Course concentrates on Deep Learning. It will help you understand the intuition behind Artificial Neural Networks, Recurrent Neural Networks, Boltzmann Machines, Self Organizing Maps, and Auto-Encoders. You will also learn how to apply them. This deep learning certification tutorial will give you in-depth knowledge of deep learning.


Advanced Machine Learning Specialization Coursera Review in 2022

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The course starts with linear models and a discussion of stochastic optimization methods that are crucial for training deep neural networks. Here you can study all popular building blocks of neural networks including fully connected layers, convolutional and recurrent layers. Learners will use these building blocks to define complex modern architectures in TensorFlow and Keras frameworks. In the course, you can implement a deep neural network for the task of image captioning.


Review of Deep Learning A-Z Hands-On Artificial Neural Networks

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Are you interested in the field of Deep Learning? Here is the short and useful Review of Deep Learning A-Z Hands-On Artificial Neural Networks. If you are in the intermediate level people who know the basics of Deep Learning and Machine Learning, including the classical algorithms like linear regression or logistic regression and more advanced topics like Artificial Neural Networks, but who want to learn more about it and explore all the different fields of Deep Learning. This is one of the Best Seller courses on Udemy where students enrolled more than 291.3K with 34.9K reviews and 4.6average star ratings. With this top-selling Deep Learning tutorial, you will learn how to create Deep Learning Algorithms in Python from two Machine Learning & Data Science experts.


Mathematics for Machine Learning Coursera Review 2022

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Coursera Mathematics of Machine Learning Specialization offered by Imperial College London (world's top ten Universities) implements your mathematical concepts using real-world data. It is called mathematics is the fundamental block of Machine Learning. Those who don't know machine learning mathematics will not understand the concepts of underlying various fundamental parts of python/R APIs. The specialization has three courses included. Each of these courses has a span of 4–6 weeks.


Recommender Systems with Machine Learning

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This course is a complete package for the beginners to learn the basics of recommender systems, its applications and building it from scratch by using machine learning with python. Every module has engaging content covering necessary theoretical concepts with a complete practical approach is used in along with brief theoretical concepts. At the end of every module, we assign you a quiz, the solution to the quizzes is also available in the next video. We will be starting with the theoretical concepts of recommender systems, after providing you the basic knowledge of recommender systems. You will be able to learn about the important taxonomies of recommender systems which are actually the basic building block of it.


Lifelong and Continual Learning Dialogue Systems

arXiv.org Artificial Intelligence

Dialogue systems, commonly known as chatbots, have gained escalating popularity in recent times due to their wide-spread applications in carrying out chit-chat conversations with users and task-oriented dialogues to accomplish various user tasks. Existing chatbots are usually trained from pre-collected and manually-labeled data and/or written with handcrafted rules. Many also use manually-compiled knowledge bases (KBs). Their ability to understand natural language is still limited, and they tend to produce many errors resulting in poor user satisfaction. Typically, they need to be constantly improved by engineers with more labeled data and more manually compiled knowledge. This book introduces the new paradigm of lifelong learning dialogue systems to endow chatbots the ability to learn continually by themselves through their own self-initiated interactions with their users and working environments to improve themselves. As the systems chat more and more with users or learn more and more from external sources, they become more and more knowledgeable and better and better at conversing. The book presents the latest developments and techniques for building such continual learning dialogue systems that continuously learn new language expressions and lexical and factual knowledge during conversation from users and off conversation from external sources, acquire new training examples during conversation, and learn conversational skills. Apart from these general topics, existing works on continual learning of some specific aspects of dialogue systems are also surveyed. The book concludes with a discussion of open challenges for future research.


AI uses artificial sleep to learn new task without forgetting the last

New Scientist

Artificial intelligence can learn and remember how to do multiple tasks by mimicking the way sleep helps us cement what we learned during waking hours. "There is a huge trend now to bring ideas from neuroscience and biology to improve existing machine learning – and sleep is one of them" says Maxim Bazhenov at the University of California, San Diego. Many AIs can only master one set of well-defined tasks – they can't acquire additional knowledge later on without losing everything they had previously learned. "The issue pops up if you want to develop systems which are capable of so-called lifelong learning," says Pavel Sanda at the Czech Academy of Sciences in the Czech Republic. Lifelong learning is how humans accumulate knowledge to adapt to and solve future challenges.


Fancy writing for AIhub? We are recruiting ambassadors

AIHub

Are you a PhD student or researcher with an interest in science communication? We are recruiting AIhub ambassadors to help us write about the latest news, research, conferences, and more, in the field of artificial intelligence. Ideally you would produce a series of blog posts on aspects of the field that interest you. You could write about some significant research, give a tutorial, or cover a session at a conference. You could draw attention to exciting new developments in the field, interview a researcher, produce a tutorial video, review a paper or book, or summarise recent social media commentary.