geometry
![Brian Piercy](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" fill="%230A66C2"><path d="M20.447 20.452H16.89v-5.569c0-1.328-.027-3.037-1.852-3.037-1.853 0-2.136 1.445-2.136 2.939v5.667H9.351V9h3.414v1.561h.046c.477-.9 1.637-1.85 3.37-1.85 3.601 0 4.267 2.37 4.267 5.455v6.286zM5.337 7.433a1.982 1.982 0 1 1 0-3.964 1.982 1.982 0 0 1 0 3.964zm1.782 13.019H3.555V9h3.564v11.452zM22.225 0H1.771C.792 0 0 .774 0 1.729v20.542C0 23.227.792 24 1.771 24h20.451C23.2 24 24 23.227 24 22.271V1.729C24 .774 23.2 0 22.222 0h.003z"/></svg>)
Generating random points inside a sphere of any dimension.
The last decade has witnessed an experimental revolution in data science and machine learning, epitomised by deep learning methods. Indeed, many high-dimensional learning tasks previously thought to be beyond reach -- such as computer vision, playing Go, or protein folding -- are in fact feasible with appropriate computational scale. Remarkably, the essence of deep learning is built from two simple algorithmic principles: first, the notion of representation or feature learning, whereby adapted, often hierarchical, features capture the appropriate notion of regularity for each task, and second, learning by local gradient-descent type methods, typically implemented as backpropagation. While learning generic functions in high dimensions is a cursed estimation problem, most tasks of interest are not generic, and come with essential pre-defined regularities arising from the underlying low-dimensionality and structure of the physical world. This text is concerned with exposing these regularities through unified geometric principles that can be applied throughout a wide spectrum of applications. Such a 'geometric unification' endeavour, in the spirit of Felix Klein's Erlangen Program, serves a dual purpose: on one hand, it provides a common mathematical framework to study the most successful neural network architectures, such as CNNs, RNNs, GNNs, and Transformers. On the other hand, it gives a constructive procedure to incorporate prior physical knowledge into neural architectures and provide principled way to build future architectures yet to be invented.
A dodecahedron is rounder than an icosahedron, as measured by angle defect, the discrete analog of curvature.
an open source textbook and reference work on algebraic geometry
A cross-framework package for kernels and Gaussian processes on manifolds, graphs, and meshes
An end-to-end deep learning geospatial segmentation project using Pytorch and TorchGeo packages
AI for complex data
Interactive article explaining how curves and surfaces are modeled.
Intuitive Math Descriptions
The geometry puzzles that are lighting up Twitter.