$$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Self-defined math definitions
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Math symbol commands
\newcommand{\intd}{\,\mathrm{d}} % Symbol 'd' used in integration, such as 'dx'
\newcommand{\diff}{\,\mathrm{d}} % Symbol 'd' used in differentiation
\newcommand{\grad}{\nabla} % Gradient operator
\newcommand{\laplacian}{\nabla^2} % Laplacian operator
\newcommand{\partiald}[2]{\frac{\partial #1}{\partial #2}} % Partial derivative
\newcommand{\dd}[2]{\frac{\mathrm{d}#1}{\mathrm{d}#2}} % Total derivative
% Common functions
\newcommand{\expf}{\mathrm{e}^{}} % Exponential function (e.g., expf(x))
\newcommand{\logf}{\ln} % Natural logarithm
\newcommand{\sinc}{\mathrm{sinc}} % Sinc function
% Neural network notation
\newcommand{\h}{\mathbf{h}} % Hidden state vector
\newcommand{\x}{\mathbf{x}} % Input vector
\newcommand{\W}{\mathbf{W}} % Weight matrix
\newcommand{\U}{\mathbf{U}} % Input weight matrix
\newcommand{\b}{\mathbf{b}} % Bias vector
% Other useful macros
\newcommand{\eqdef}{\triangleq} % Define equality
\newcommand{\approxdef}{\overset{\text{def}}{=}} % Approximate definition
\newcommand{\trans}{^\top} % Transpose
\newcommand{\inv}{^{-1}} % Inverse
\newcommand{\norm}[1]{\left\lVert#1\right\rVert} % Norm
\newcommand{\abs}[1]{\left|#1\right|} % Absolute value
\newcommand{\floor}[1]{\left\lfloor#1\right\rfloor} % Floor
\newcommand{\ceil}[1]{\left\lceil#1\right\rceil} % Ceiling
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% End of self-defined math definitions
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
$$
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