Ramp function

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The ramp function is a unary real function, whose graph is shaped like a ramp. It can be expressed by numerous definitions, for example "0 for negative inputs, output equals input for non-negative inputs". The term "ramp" can also be used for other functions obtained by scaling and shifting, and the function in this article is the unit ramp function (slope 1, starting at 0). In mathematics, the ramp function is also known as the positive part. In machine learning, it is commonly known as a ReLU activation function or a rectifier in analogy to half-wave rectification in electrical engineering. In statistics (when used as a likelihood function) it is known as a tobit model. This function has numerous applications in mathematics and engineering, and goes by various names, depending on the context. There are differentiable variants of the ramp function. The ramp function (R(x) : R → R0) may be defined analytically in several ways. Possible definitions are: It could approximated as close as desired by choosing an increasing positive value a > 0 {\displaystyle a>0} .