Strengthening Deep Neural Networks

Appendix A. Mathematics Terminology Reference

To serve as either a refresher or an introduction, Table A-1 summarizes the key mathematical terminology in the context in which it is used in this book.

Table A-1. Mathematics terminology summary

Terminology	Description
x	A nonbold variable refers to a scalar.
x	A variable in bold refers to a vector.
y = f(x; Θ)	The result of function f on the vector input x, where f is dependent on the parameters Θ. In the context of this book, this represents the output of a DNN model for a particular input: f represents the DNN model algorithm, Θ represents its parameters determined during training, and x is the input to the model.
C(f(x; Θ), y)	The result of function C given f(x; Θ) and the vector y. In the context of this book, this represents the cost (or loss) of the DNN model for a particular input with respect to the required output y.
xi	The element i of vector x.
$\frac{dy}{dx}$	The derivative of y with respect to x.
$\frac{\partial y}{\partial x}$	The partial derivative of y with respect to x, wh - ere x is one of the variables that affects y.
${\nabla }_{x}f$	The nabla (upside-down Greek delta) symbol means “gradient.” ${\nabla }_{x}f$ refers to the vector of partial derivatives of the function f for the vector x. Put more simply, this means the effect that a very small change to the value of x has on the function f.
{1, 2, . . . L}	The set of numbers from 1 to L.
ℝ	The set of real numbers.
{x : P(x)}	The set of all values of x for which P(x) is true, ...