پرسپترون

الپرسپترون Perceptron هو أحد أبسط أنواع الشبكات العصبونية أمامية التغذية Feed-Forward ، حيث لا يحتوي على طبقة عصبونات خفية بل تنتقل المعلومات المدخلة من الطبقة الأمامية إلى النهائية مباشرة. أول من استحدث شبكة الپرسپترون كان فرانك روزنبلات عام 1957 في جامعة كورنل.

التعريف

يستخدم الپرسپترون القيم الذاتية للمصفوفات لتمثل الشبكات العصبونية أمامية التغذية وهو a tertiary classifier that maps its input ${\displaystyle{\displaystyle x}}$ (a binary vector) to an output value ${\displaystyle{\displaystyle f(x)}}$ (a single binary value) across the matrix.

{\displaystyle{\displaystyle f(x)={\begin{cases}1&{\text{if }}w\cdot x+b>0\\ 0&{\text{else}}\end{cases}}}}

where ${\displaystyle{\displaystyle w}}$ is a vector of real-valued weights and ${\displaystyle{\displaystyle w\cdot x}}$ is the dot product (which computes a weighted sum). ${\displaystyle{\displaystyle b}}$ is the 'bias', a constant term that does not depend on any input value.

مثال

A perceptron (X₁, X₂ input, X₀*W₀=b, TH=0.5) learns how to perform a NAND function:

		المـُدخل				Initial			المـُخرج							النهائي
Threshold	معدل التعلم	Sensor values			المـُخرج المرغوب	الأوزان			المحسوب			المجموع	الشبكة	الخطأ	التصحيح	الأوزان
TH	LR	X0	X1	X2	Z	w0	w1	w2	C0	C1	C2	S	N	E	R	W0	W1	W2
									X0 x w0	X1 x w1	X2 x w2	C0+C1+C2	IF(S>TH,1,0)	Z-N	LR x E
0.5	0.1	1	0	0	1	0	0	0	0	0	0	0	0	1	+0.1	0.1	0	0
0.5	0.1	1	0	1	1	0.1	0	0	0.1	0	0	0.1	0	1	+0.1	0.2	0	0.1
0.5	0.1	1	1	0	1	0.2	0	0.1	0.2	0	0	0.2	0	1	+0.1	0.3	0.1	0.1
0.5	0.1	1	1	1	0	0.3	0.1	0.1	0.3	0.1	0.1	0.5	0	0	0	0.3	0.1	0.1
0.5	0.1	1	0	0	1	0.3	0.1	0.1	0.3	0	0	0.3	0	1	+0.1	0.4	0.1	0.1
0.5	0.1	1	0	1	1	0.4	0.1	0.1	0.4	0	0.1	0.5	0	1	+0.1	0.5	0.1	0.2
0.5	0.1	1	1	0	1	0.5	0.1	0.2	0.5	0.1	0	0.6	1	0	0	0.5	0.1	0.2
0.5	0.1	1	1	1	0	0.5	0.1	0.2	0.5	0.1	0.2	0.8	1	-1	-0.1	0.4	0	0.1
0.5	0.1	1	0	0	1	0.4	0	0.1	0.4	0	0	0.4	0	1	+0.1	0.5	0	0.1
0.5	0.1	1	0	1	1	0.5	0	0.1	0.5	0	0.1	0.6	1	0	0	0.5	0	0.1
0.5	0.1	1	1	0	1	0.5	0	0.1	0.5	0	0	0.5	0	1	+0.1	0.6	0.1	0.1
0.5	0.1	1	1	1	0	0.6	0.1	0.1	0.6	0.1	0.1	0.8	1	-1	-0.1	0.5	0	0
0.5	0.1	1	0	0	1	0.5	0	0	0.5	0	0	0.5	0	1	+0.1	0.6	0	0
0.5	0.1	1	0	1	1	0.6	0	0	0.6	0	0	0.6	1	0	0	0.6	0	0
0.5	0.1	1	1	0	1	0.6	0	0	0.6	0	0	0.6	1	0	0	0.6	0	0
0.5	0.1	1	1	1	0	0.6	0	0	0.6	0	0	0.6	1	-1	-0.1	0.5	-0.1	-0.1
0.5	0.1	1	0	0	1	0.5	-0.1	-0.1	0.5	0	0	0.5	0	1	+0.1	0.6	-0.1	-0.1
0.5	0.1	1	0	1	1	0.6	-0.1	-0.1	0.6	0	-0.1	0.5	0	1	+0.1	0.7	-0.1	0
0.5	0.1	1	1	0	1	0.7	-0.1	0	0.7	-0.1	0	0.6	1	0	0	0.7	-0.1	0
0.5	0.1	1	1	1	0	0.7	-0.1	0	0.7	-0.1	0	0.6	1	-1	-0.1	0.6	-0.2	-0.1
0.5	0.1	1	0	0	1	0.6	-0.2	-0.1	0.6	0	0	0.6	1	0	0	0.6	-0.2	-0.1
0.5	0.1	1	0	1	1	0.6	-0.2	-0.1	0.6	0	-0.1	0.5	0	1	+0.1	0.7	-0.2	0
0.5	0.1	1	1	0	1	0.7	-0.2	0	0.7	-0.2	0	0.5	0	1	+0.1	0.8	-0.1	0
0.5	0.1	1	1	1	0	0.8	-0.1	0	0.8	-0.1	0	0.7	1	-1	-0.1	0.7	-0.2	-0.1
0.5	0.1	1	0	0	1	0.7	-0.2	-0.1	0.7	0	0	0.7	1	0	0	0.7	-0.2	-0.1
0.5	0.1	1	0	1	1	0.7	-0.2	-0.1	0.7	0	-0.1	0.6	1	0	0	0.7	-0.2	-0.1
0.5	0.1	1	1	0	1	0.7	-0.2	-0.1	0.7	-0.2	0	0.5	0	1	+0.1	0.8	-0.1	-0.1
0.5	0.1	1	1	1	0	0.8	-0.1	-0.1	0.8	-0.1	-0.1	0.6	1	-1	-0.1	0.7	-0.2	-0.2
0.5	0.1	1	0	0	1	0.7	-0.2	-0.2	0.7	0	0	0.7	1	0	0	0.7	-0.2	-0.2
0.5	0.1	1	0	1	1	0.7	-0.2	-0.2	0.7	0	-0.2	0.5	0	1	+0.1	0.8	-0.2	-0.1
0.5	0.1	1	1	0	1	0.8	-0.2	-0.1	0.8	-0.2	0	0.6	1	0	0	0.8	-0.2	-0.1
0.5	0.1	1	1	1	0	0.8	-0.2	-0.1	0.8	-0.2	-0.1	0.5	0	0	0	0.8	-0.2	-0.1
0.5	0.1	1	0	0	1	0.8	-0.2	-0.1	0.8	0	0	0.8	1	0	0	0.8	-0.2	-0.1
0.5	0.1	1	0	1	1	0.8	-0.2	-0.1	0.8	0	-0.1	0.7	1	0	0	0.8	-0.2	-0.1

Note: Initial weight equals final weight of previous iteration. A too high learning rate makes the perceptron periodically oscillate around the solution. A possible enhancement is to use ${\displaystyle{\displaystyle LR^{n}}}$ starting with n=1 and incrementing it by 1 when a loop in learning is found.