/explore
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www.themathdoctors.org | ||
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blog.zerolimits.dev
A blog about the most random things you can think of. |
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fa.bianp.net
There's a fascinating link between minimization of quadratic functions and polynomials. A link that goes deep and allows to phrase optimization problems in the language of polynomials and vice versa. Using this connection, we can tap into centuries of research in the theory of polynomials and shed new light on ... |
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jaydaigle.net
We continue our exploration of what numbers are, and where mathematicians keep finding weird ones. In the first three parts we extended the natural numbers in two ways: algebraically and analytically. Those approaches gave overlapping but distinct sets of numbers. This week we combine them to get the complex numbers, and see some hints of why the complex numbers are so useful-and so frustrating. |
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lilianweng.github.io
So far, I've written about two types of generative models, GAN and VAE. Neither of them explicitly learns the probability density function of real data, $p(\mathbf{x})$ (where $\mathbf{x} \in \mathcal{D}$) - because it is really hard! Taking the generative model with latent variables as an example, $p(\mathbf{x}) = \int p(\mathbf{x}\vert\mathbf{z})p(\mathbf{z})d\mathbf{z}$ can hardly be calculated as it is intractable to go through all possible values of the latent code $\mathbf{z}$. |
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