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fa.bianp.net | ||
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fabricebaudoin.blog
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| | | | | In this section, we consider a diffusion operator $latex L=\sum_{i,j=1}^n \sigma_{ij} (x) \frac{\partial^2}{ \partial x_i \partial x_j} +\sum_{i=1}^n b_i (x)\frac{\partial}{\partial x_i}, $ where $latex b_i$ and $latex \sigma_{ij}$ are continuous functions on $latex \mathbb{R}^n$ and for every $latex x \in \mathbb{R}^n$, the matrix $latex (\sigma_{ij}(x))_{1\le i,j\le n}$ is a symmetric and non negative matrix. Our... | |
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francisbach.com
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| | | | | [AI summary] This mathematical post explores the geometry of positive semi-definite matrices using the von Neumann entropy and related Bregman divergences to derive concentration inequalities for random matrices. | |
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www.jeremykun.com
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| | | | | This proof assumes knowledge of complex analysis, specifically the notions of analytic functions and Liouville's Theorem (which we will state below). The fundamental theorem of algebra has quite a few number of proofs (enough to fill a book!). In fact, it seems a new tool in mathematics can prove its worth by being able to prove the fundamental theorem in a different way. This series of proofs of the fundamental theorem also highlights how in mathematics there are many many ways to prove a single theorem... | |
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teddykoker.com
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| | | Google AI recently released a paper, Rethinking Attention with Performers (Choromanski et al., 2020), which introduces Performer, a Transformer architecture which estimates the full-rank-attention mechanism using orthogonal random features to approximate the softmax kernel with linear space and time complexity. In this post we will investigate how this works, and how it is useful for the machine learning community. | ||
