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The $\nabla$ symbol when seen in front of a vector-valued function
like $\nabla f(x)$ refers to the function's gradient.
$\odot$ [Hadamard Product]({% link terms/hadamard-product.md %})
This circle-dot symbol can mean a few different things, depending on context.
Typically in machine learning literature, it refers to the Hadamard product
(component-wise multiplication for matrices).
$\sigma$ Sigma
The $\sigma$ symbol is often used to represent the standard deviation
of a probability distribution.
When used as a function that takes in a value, e.g. $\sigma(x)$,
then it refers to the logistic sigmoid function.
The XOR operator is a logical operator that takes two terms. It returns
true when both inputs differ.
For example, $a \oplus b$ is only true when $a$ is true and $b$ is false,
or when $b$ is false and when $a$ is true.
Put another way, $a \oplus b$ will be false when both $a$ and $b$ are false,
or when both $a$ and $b$ are true. See Exclusive or on Wikipedia for more
information.
$[x]_+$ , bracket operator, max operator
The bracket operator $[x]_+$ where an expression $x$ is surrounded by a plus sign and a subscript is equivalent to $\max(0,X)$. See 8 for more information.