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Tags: #math
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Chentsov's Theorem
The Fisher information is often the default choice of the Riemannian metric for manifolds of probability distributions. In this post, ...
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The Curvature of the Manifold of Gaussian Distributions
The Gaussian probability distribution is central in statistics and machine learning. As it turns out, by equipping the set of ...
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Hessian and Curvatures in Machine Learning: A Differential-Geometric View
In machine learning, especially in neural networks, the Hessian matrix is often treated synonymously with curvatures. But, from calculus alone, ...
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Optimization and Gradient Descent on Riemannian Manifolds
One of the most ubiquitous applications in the field of differential geometry is the optimization problem. In this article we ...
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Minkowski's, Dirichlet's, and Two Squares Theorem
Application of Minkowski's Theorem in geometry problems, Dirichlet's Approximation Theorem, and Two Squares Theorem.
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Reduced Betti number of sphere: Mayer-Vietoris Theorem
A proof of reduced homology of sphere with Mayer-Vietoris sequence.
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Brouwer's Fixed Point Theorem: A Proof with Reduced Homology
A proof of special case (ball) of Brouwer's Fixed Point Theorem with Reduced Homology.