File:Perceptron-unit.svg

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DescriptionPerceptron-unit.svg	English: An artificial neuron. It has input nodes $x_{0},\dots ,x_{n}$ , weights $w_{0},\dots ,w_{n}$ . The input signals get multiplied with the weights. The results are summed up. Then the activation function $\varphi$ is applied (e.g. sigmoid, tanh, ReLU, ...). This is then the output $o$ of the artificial neuron. Overall, the perceptron unit is a function $f(x_{0},\dots ,x_{n})=\varphi (\sum _{i=0}^{n}w_{i}x_{i})$ . Typical choices for activation functions $\varphi$ are the sigmoid function $\varphi (x)={\frac {1}{1+e^{-x}}}$ or ReLU $\varphi (x)=\max(0,x)$ . The input $x_{0}$ is called the bias and is constant 1, so $x_{0}=1$ . Input-Neuronen Hidden-Neuron Deutsch: Ein künstliches Neuron. Es hat Eingabeknoten $x_{0},\dots ,x_{n}$ , Gewichte $w_{0},\dots ,w_{n}$ . Die Eingabesignale werden jeweils mit den Gewichten multipliziert. Die Ergebnisse werden aufsummiert. Dann wird auf die Summe die Aktiviertungsfunktion $\varphi$ (z.B. die Sigmoid-Funktion, tanh, ReLU, ...) angewendet. Die Perzeptron-Einheit beschreibt also eine Funktion $f(x_{0},\dots ,x_{n})=\varphi (\sum _{i=0}^{n}w_{i}x_{i})$ . Zwei typische Aktivierungsfunktionen $\varphi$ sind die Sigmoidfunktion $\varphi (x)={\frac {1}{1+e^{-x}}}$ und ReLU $\varphi (x)=\max(0,x)$ . Der Eingabeknoten $x_{0}$ wird Bias genannt und ist konstant 1, also $x_{0}=1$ . Input-Neuronen Hidden-Neuron
Date	21 July 2014
Source	Own work
Author	MartinThoma

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	Date/Time	Dimensions	User	Comment
current	16:08, 6 June 2016	639 × 576 (48 KB)	MartinThoma (talk \| contribs)	Font to Path as Wikimedia Commons does not render it correct
	16:06, 6 June 2016	639 × 576 (48 KB)	MartinThoma (talk \| contribs)	Add "=1" to x_0
	11:08, 24 May 2016	639 × 576 (46 KB)	MartinThoma (talk \| contribs)	Raised \phi; rotated 0, 1, 3; changed dashing of line between \sum and \phi
	13:54, 13 January 2016	639 × 576 (48 KB)	MartinThoma (talk \| contribs)	{{Information \|Description ={{en\|1=An artificial neuron. It has input nodes <math>x_0, \dots, x_n</math>, weights <math>w_0, \dots, w_n</math>. The input signals get multiplied with the weights. The results are summed up. Then the activation functio...

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