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Mathematics
Yaroslav Bulatov's user avatar
Yaroslav Bulatov's user avatar
Yaroslav Bulatov's user avatar
Yaroslav Bulatov
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Google (OCR team) -> Google Brain -> OpenAI -> PyTorch team (Facebook)

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70
Matrices commute if and only if they share a common basis of eigenvectors?
Oct 7, 2010
15
How do Lagrange multipliers work to find the lowest value of a function subject to a constraint?
Aug 10, 2010
13
Inverse of integral transform $f(s)=\int_0^\infty g(x) \exp(-s g(x)) \mathbb{d}x$
Sep 5, 2021
13
Proving $\sqrt{1-x^2}\ge \operatorname{erf}(\sqrt{-\log x})$
Oct 14, 2010
12
Why is $AA^TAA^TAA^TAA^T$ larger than $AAAAA^TA^TA^TA^T$ for Gaussian $A$?
Feb 19
11
Average value of $\frac{x'A^2x}{x'A^3x}$ over surface of $n$-dimensional sphere
Aug 19, 2021
11
Computing $\int _0^{\infty }e^{-b x} x^{b-1} \log \left((1-a x)^2\right)dx$ or $ \mathbb E \log\left[(c- \chi^2_{2b} )^2\right]$
Jan 12
10
Showing $\operatorname{Tr}\left(I-\frac{1}{\|A\|^2}A^TA\right)\ge\operatorname{Tr}\prod_i \left(I-\frac{1}{\|a_i\|^2}a_i^T a_i\right)$
yesterday
9
Behavior of inverse of $f(s)=\frac{1}{H_n}\sum_{i=1}^n \left(1-\frac{1}{i}\right)^s\frac{1}{i}$
Jun 22, 2021
9
Proving $1-\exp(-4x^2/ \pi) \ge \text{erf}(x)^2$
Oct 15, 2010
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