Geometric

A simple description and uses of the Geometric distributionPhoto by Moritz Kindler on UnsplashIn this article I want to discuss a common and easy to understand distribution in statistics, the Geometric distribution. This distribution is used in many industries such as finance, sports and commerce. Therefore, it is important to be aware of if you are a Data Scientist.In this post, we will go through its definition, intuition, a bit of mathematics and finally use it in an example problem.The Geometric distribution is a…

Unlocking AI for 360° spherical dataPhoto by Josue Aguazia on UnsplashWhile AI is now commonplace for standard types of data, such as structured, sequential and image data, the application of AI is severly curtailed for other more complex forms of data. These more complex datasets typical exhibit non-trivial geometry.The field of geometric AI, or geometric deep learning, has emerged to extend the remarkable benefits of AI to these more complex — geometric — datasets (for a brief introduction to geometric AI see our…

AI for complex dataPhoto by SIMON LEE on UnsplashDeep learning is hard. While universal approximation theorems show that sufficiently complex neural networks can in principle approximate “anything”, there is no guarantee that we can find good models.Great progress in deep learning has nevertheless been made by judicious choice of model architectures. These model architectures encode inductive biases to give the model a helping hand. One of the most powerful inductive biases is to leverage notions of geometry, giving rise…

Origins of Geometric Deep LearningGeometric Deep Learning approaches a broad class of ML problems from the perspectives of symmetry and invariance, providing a common blueprint for the “zoo” of neural network architectures. In the last post in our series on the origins of Geometric Deep Learning, we look at the precursors of Graph Neural Networks.Image: Shutterstock.In the last post from the “Towards Geometric Deep Learning” series, we discuss how early prototypes of GNNs emerged in the field of chemistry in the 1960s.…

What is Geometric Deep Learning? Let’s learn about various networks in this article. The deep learning algorithms like Recurrent Neural Networks (RNN) and Convolutional Neural Networks (CNN) have done significant work in solving problems of various fields like speech recognition, computer vision, and a lot more in the last few years. Although the results had great accuracy, it mostly worked on euclidean data. But when it comes to Network Science, Physics, Biology, Computer Graphics, and Recommender Systems, we…

Origins of Geometric Deep LearningGeometric Deep Learning approaches a broad class of ML problems from the perspectives of symmetry and invariance, providing a common blueprint for neural network architectures as diverse as CNNs, GNNs, and Transformers. In a new series of posts, we study how these ideas have taken us from ancient Greece to convolutional neural networks.Image: Shutterstock.In the third post from the “Towards Geometric Deep Learning series,” we discuss the first “geometric” neural networks: the Neocognitron…

Origins of Geometric Deep LearningGeometric Deep Learning approaches a broad class of ML problems from the perspectives of symmetry and invariance, providing a common blueprint for neural network architectures as diverse as CNNs, GNNs, and Transformers. In a new series of posts, we study how geometric ideas dating back to ancient Greece have shaped modern deep learning.Image: based on Shutterstock.In the second post from the “Towards Geometric Deep Learning series,” we discuss the early neural network models, and how…

After CNNs exploded in 2012, showing unprecedented levels of prediction accuracy on image classification tasks, a group of researchers from Yann LeCun's team decided to extend their success to other, more exotic domains. Specifically, they started working on generalizing convnets to graphs. Their efforts were described in this influential paper.  Since then, Graph Neural Networks have become a hot area of research within the ML community and beyond. Numerous papers have been published explaining how different kinds and…

Origins of Geometric Deep LearningGeometric Deep Learning approaches a broad class of ML problems from the perspectives of symmetry and invariance, providing a common blueprint for neural network architectures as diverse as CNNs, GNNs, and Transformers. In a new series of posts, we study how these ideas have emerged through history from ancient Greek geometry to Graph Neural Networks.Image: based on Shutterstock.What is in common between snowflakes and the Standard Model? Symmetry. In the first post from the “Towards…

The GDL BlueprintA series of blog posts that summarize the Geometric Deep Learning (GDL) Course, at AMMI program; African Master’s of Machine Intelligence, taught by Michael Bronstein, Joan Bruna, Taco Cohen, and Petar Veličković.The curse of dimensionality represents one of the most challenging problems in high-dimensional learning. In a previous post (Geometric Priors I), we discussed various concepts in machine learning and geometric deep learning, including symmetry, invariant and equivariant networks. In this post,…