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almostsuremath.com | ||
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terrytao.wordpress.com
In these notes we quickly review the basics of abstract measure theory and integration theory, which were covered in the previous course but will of course be relied upon in the current course. Th... |
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mattbaker.blog
In my last blog post, I discussed a simple proof of the fact that pi is irrational. That pi is in fact transcendental was first proved in 1882 by Ferdinand von Lindemann, who showed that if $latex \alpha$ is a nonzero complex number and $latex e^\alpha$ is algebraic, then $latex \alpha$ must be transcendental. Since... |
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jmanton.wordpress.com
If $latex Y$ is a $latex \sigma(X)$-measurable random variable then there exists a Borel-measurable function $latex f \colon \mathbb{R} \rightarrow \mathbb{R}$ such that $latex Y = f(X)$. The standard proof of this fact leaves several questions unanswered. This note explains what goes wrong when attempting a "direct" proof. It also explains how the standard proof... |
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blog.otoro.net
[AI summary] This text discusses the development of a system for generating large images from latent vectors, combining Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs). It explores the use of Conditional Perceptual Neural Networks (CPPNs) to create images with specific characteristics, such as style and orientation, by manipulating latent vectors. The text also covers the ability to perform arithmetic on latent vectors to generate new images and the potential for creating animations by transitioning between different latent states. The author suggests future research directions, including training on more complex datasets and exploring alternative training objectives beyond Maximum Likelihood. |
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