!!! Overview [{$pagename}] ([ReLU]) performs a threshold operation to each element of the input, where any value less than zero is set to zero. !! [{$pagename}] [Artificial Neural networks] In the context of [Artificial Neural networks], the [{$pagename}] is an [Activation Function] defined as the positive part of its argument: %%prettify {{{ a = f(x) = max(0,x) }}} /% where x is the input to a [Artificial Neuron]. This is also known as a ramp function and is analogous to half-wave rectification in electrical engineering. [{$pagename}] [Activation Function] was first introduced to a dynamical network by Hahnloser et al. in a 2000 paper in Nature with strong biological motivations and mathematical justifications. [{$pagename}] has been used in convolutional networks[3] more effectively than the widely used logistic [sigmoid function] (which is inspired by probability theory and its more practical counterpart, the [hyperbolic tangent]. The rectifier is, as of 2017, the most popular activation function for [Deep Neural networks]. A [Artificial Neuron] employing the rectifier is also called a [{$pagename}]. A smooth approximation to the rectifier is the analytic function !! [{$pagename}] in [Python] %%prettify {{{ def relu(x, derivative=False): if (derivative == True): for i in range(0, len(x)): for k in range(len(x[i])): if x[i][k] > 0: x[i][k] = 1 else: x[i][k] = 0 return x for i in range(0, len(x)): for k in range(0, len(x[i])): if x[i][k] > 0: pass # do nothing since it would be effectively replacing x with x else: x[i][k] = 0 return x }}} /% !! More Information There might be more information for this subject on one of the following: [{ReferringPagesPlugin before='*' after='\n' }] ---- * [#1] - [Rectifier_(neural_networks)|Wikipedia:Rectifier_(neural_networks)|target='_blank'] - based on information obtained 2017-12-10-