\chapter*{Notation Conventions}

\begin{itemize}
    \item[] $x$, $y$, $\epsilon$ \dotfill Scalar variables
    \item[] $\bfx$, $\bfy$, $\bm{\epsilon}$ \dotfill Vector variables
    \item[] $\bfx^{(l)}$ \dotfill Activity vector of layer $l$ of a neural network
    \item[] $\bfx(i)$ \dotfill $i$-th vector sample in a dataset
    \item[] $\bfx_k$ \dotfill $k$-dimensional subvector of $\bfx$ or $k$-th sample in a sequence of vectors
    \item[] $x_i$ \dotfill $i$-th dimension of a vector 
    \item[] $\dot{\bfx}$ \dotfill Dynamics of a variable $\bfx$ 
    \item[] $\bfA$, $\bm{\Theta}$ \dotfill Matrix
    \item[] $\bfA_{mn}$ \dotfill $m\times n$ submatrix of $\bfA$
    \item[] $A_{ij}$ \dotfill Matrix element at the $i$-th row and $j$-th column
    \item[] $\mathcal{F}, \mathcal{L}$ \dotfill Objective function 
    \item[] $\mathbb{R}^{d_1\times d_2}$ \dotfill Matrix of size $d_1\times d_2$ of real numbers
    \item[] $\mathbb{E}_p$ \dotfill Expectation over a distribution $p$ 
    \item[] $\mathcal{N}(\bm{\mu},\bm{\Sigma})$ \dotfill Multivariate Gaussian distribution with mean $\bm{\mu}$ and covariance $\bm{\Sigma}$
    \item[] $\frac{\partial \mathcal{F}}{\partial \bfx}$ \dotfill Partial derivative of $\mathcal{F}$ with respect to $\bfx$ 
    
\end{itemize}








