Explore >> Select a destination
|
You are here 
|
almostsuremath.com | ||
| | | | |
djalil.chafai.net
|
|
| | | | | The logarithmic potential is a classical object of potential theory intimately connected with the two dimensional Laplacian. It appears also in free probability theory via the free entropy, and in partial differential equations e.g. Patlak-Keller-Segel models. This post concerns only it usage for the spectra of non Hermitian random matrices. Let \( {\mathcal{P}(\mathbb{C})} \) be the set of probability measures... | |
| | | | |
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... | |
| | | | |
mkatkov.wordpress.com
|
|
| | | | | For probability space $latex (\Omega, \mathcal{F}, \mathbb{P})$ with $latex A \in \mathcal{F}$ the indicator random variable $latex {\bf 1}_A : \Omega \rightarrow \mathbb{R} = \left\{ \begin{array}{cc} 1, & \omega \in A \\ 0, & \omega \notin A \end{array} \right.$ Than expected value of the indicator variable is the probability of the event $latex \omega \in... | |
| | | | |
neuralnetworksanddeeplearning.com
|
|
| | | [AI summary] The text provides an in-depth explanation of the backpropagation algorithm in neural networks. It starts by discussing the concept of how small changes in weights propagate through the network to affect the final cost, leading to the derivation of the partial derivatives required for gradient descent. The explanation includes a heuristic argument based on tracking the perturbation of weights through the network, resulting in a chain of partial derivatives. The text also touches on the historical context of how backpropagation was discovered, emphasizing the process of simplifying complex proofs and the role of using weighted inputs (z-values) as intermediate variables to streamline the derivation. Finally, it concludes with a citation and licens... | ||
