f(⋅) Center-dot notation in functions

Some papers will use a center dot (or interpunct) to represent that any value can be inserted as the value of a function.

For example, argmaxf(⋅) means the same as argmaxxf(x)

See Mathematics StackExchange for more information.

∇ Gradient

The ∇ symbol when seen in front of a vector-valued function like ∇f(x) refers to the function’s gradient.

⊙ Hadamard Product

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).

σ Sigma

The σ 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. σ(x), then it refers to the logistic sigmoid function.

Wikipedia has a more complete list of the symbol’s uses

⊕ XOR, exclusive-or, exclusive disjunction

The XOR operator is a logical operator that takes two terms. It returns true when both inputs differ.

For example, a⊕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⊕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.