\newcommand{\par}[1] {\left({#1}\right)}
\newcommand{\arr}[1] {\left[{#1}\right]}
\newcommand{\hsh}[1] {\left\{{#1}\right\}}
\newcommand{\abs}[1] {\left|{#1}\right|}

\newcommand{\basisCanon} {\mathbf{\hat{e}}}
\newcommand{\basisCanonElement}[1][i] {\basisCanon_{#1}}

\newcommand{\varietyAffine}[2][X] {\mathscr{#1}\par{#2}}

\newcommand{\smol} {\epsilon}
\newcommand{\derivativeDirectionalSimple}[3][f] {{#1}'\par{#2_0; #3}}
\newcommand{\derivativeDirectional}[3][f] {\frac{d #1 \par{#2_0; #3}}{d \smol}}
\newcommand{\derivativePartial}[3][f] {\frac{\partial #1 \par{#2_0}}{\partial x_{#3}}}
\newcommand{\derivativePartialOutput}[4][f] {\frac{\partial #1_{#3} \par{#2_0}}{\partial x_{#4}}}
\newcommand{\derivativeGradientSimple}[2][f] {\nabla_{#1} \par{#2_0}}
\newcommand{\continueField}[1][1] {\mathcal{C}^{#1}}
\newcommand{\hessianSimple}[2][f] {\mathbf{\nabla}^2_{#1} \par{#2_0}}
\newcommand{\hessianElement}[4][f] {\frac{\partial^2 #1 \par{#2}}{\partial #2_{#3}\ \cdot\ \partial #2_{#4}}}
\newcommand{\iacobianSimple}[2][f] {\mathbf{J}_{#1} \par{#2}}

\newcommand{\fmlDataset} {\mathbf{D}}
\newcommand{\fmlDatasetSize} {P}
\newcommand{\fmlDatasetTrain} {\fmlDataset_{train}}
\newcommand{\fmlDatasetValidate} {\fmlDataset_{validate}}
\newcommand{\fmlDatasetTest} {\fmlDataset_{test}}
\newcommand{\fmlInputs} {\mathbf{X}}
\newcommand{\fmlIndex} {i}
\newcommand{\fmlInput}[1][\fmlIndex] {\mathbf{x}_{#1}}
\newcommand{\fmlInputSize} {n}
\newcommand{\fmlInputField}[1][\fmlInputSize] {\mathbb{X}^{#1}}
\newcommand{\fmlElementIndex} {j}
\newcommand{\fmlInputElement}[1][\fmlIndex\fmlElementIndex] {x_{#1}}
\newcommand{\fmlInputElementField} {\mathbb{X}}
\newcommand{\fmlOutputs} {\mathbf{y}}
\newcommand{\fmlOutput}[1][\fmlIndex] {y_{#1}}
\newcommand{\fmlOutputField} {\mathbb{Y}}
\newcommand{\fmlClassifier} {f}
\newcommand{\fmlModel} {\fmlClassifier^*}
\newcommand{\fmlHypothesisSpace} {\mathcal{H}}
\newcommand{\fmlComplexity} {c}
\newcommand{\fmlComplexityCoefficient} {\lambda}
\newcommand{\fmlLoss} {V}
