Piecewise function that clamps its input to be non-negative
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Graph of the ramp function
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[1][2] 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.
^Brownlee, Jason (8 January 2019). "A Gentle Introduction to the Rectified Linear Unit (ReLU)". Machine Learning Mastery. Retrieved 8 April 2021.
^Liu, Danqing (30 November 2017). "A Practical Guide to ReLU". Medium. Retrieved 8 April 2021.
The rampfunction is a unary real function, whose graph is shaped like a ramp. It can be expressed by numerous definitions, for example "0 for negative...
function: H ( x ) := 1 x ≥ 0 = 1 R + ( x ) {\displaystyle H(x):=\mathbf {1} _{x\geq 0}=\mathbf {1} _{\mathbb {R} _{+}}(x)} the derivative of the ramp...
can obviously be used to approximate the rampfunction, or first approximate the ReLU, then the rampfunction. if σ {\displaystyle \sigma } is "squashing"...
known as the softplus function and (with scaling) is a smooth approximation of the rampfunction, just as the logistic function (with scaling) is a smooth...
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0. ⟨x−a⟩1{\displaystyle \langle x-a\rangle ^{1}} is also called the Rampfunction. Integrating ⟨x−a⟩n{\displaystyle \langle x-a\rangle ^{n}} can be done...
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Arjun Rampal (born 26 November 1972) is an Indian actor, model, film producer and television personality who works in Hindi films. He made his acting debut...
specifications for a general-purpose function generator are: Produces sine, square, triangular, sawtooth (ramp), and pulse output. Arbitrary waveform...
negative part of any function with values in a linearly ordered group. The unit rampfunction is the positive part of the identity function. Given a measurable...
Macaulay brackets are a notation used to describe the rampfunction { x } = { 0 , x < 0 x , x ≥ 0. {\displaystyle \{x\}={\begin{cases}0,&x<0\\x,&x\geq...
A ramp meter, ramp signal, or metering light is a device, usually a basic traffic light or a two-section signal light (red and green only, no yellow) together...
is also known as a rampfunction and is analogous to half-wave rectification in electrical engineering. This activation function was first introduced...
n{\displaystyle n} of summation is understood to range over all the integers. The rampfunction can be expressed R(x)=x⋅[x≥0].{\displaystyle R(x)=x\cdot [x\geq 0].}...
azaenolate which can be alkylated by alkyl halides. The hydrazines SAMP and RAMPfunction as chiral auxiliary. Several methods are known to recover carbonyl compounds...
a ramp waveform. The convention is that a sawtooth wave ramps upward and then sharply drops. In a reverse (or inverse) sawtooth wave, the wave ramps downward...
An intake ramp is a rectangular, plate-like device within the air intake of a jet engine, designed to generate a number of shock waves to aid the inlet...
a highway or highway ramp that was partially or fully constructed, but went unused or was later closed. An unused roadway or ramp may often be referred...
in n variables. Macaulay brackets, a notation used to describe the rampfunction. Macaulay Duration, a special case of bond duration, named after Frederick...
In solid-state physics, the work function (sometimes spelled workfunction) is the minimum thermodynamic work (i.e., energy) needed to remove an electron...
interchange contain ramps. In left-hand drive countries, the rampsfunction the same as in right-hand drive countries, but ramps with the same designation...
"The Logical Song" and released it as a single in 2001 under the title "Ramp! (The Logical Song)"; for later releases, including those in the UK and Australia...
stickhandling in tight spaces. Ice hockey portal Field hockey stick Rampfunction, often called a "hockey stick" due to similar shape Hockey stick graph...
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