I have a question about how the averaging works when doing mini-batch gradient descent. I think I now understood the general gradient descent algorithm, but only for online learning. When doing mini-batch gradient descent, do I have to: forward propagate calculate error calculate all gradients...

I'm trying to solve $Id=s\log^2(A)$ where $Id$ is the identity matrix, $s$ is a natural number, and $A$ is a two-by-two matrix for which the matrix logarithm is defined. I'm getting the solutions: $$A=\begin{pmatrix} e^{\frac{1}{\sqrt{s}}} & 0 \\ 0 & e^{\frac{1}{\sqrt{s}}} \end{pmatrix}.$$ Are t...

Problem: $\alpha$ and $\beta$ are two mutually orthogonal probability measures in the sense that for some Borel subset $E\subset[0,1]$, $\alpha(E)=0$ and $\beta(E)=1$. If $F(x)=\alpha\{[0,x]\}$ and $G(x)=\beta\{[0,x]\}$ for $0<x\leq 1$, show that for any $\varepsilon>0$, there is finite collectio...