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.

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التعريف

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

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

where $w$ is a vector of real-valued weights and $w\cdot x$ is the dot product (which computes a weighted sum). $b$ 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 $LR^{n}$ starting with n=1 and incrementing it by 1 when a loop in learning is found.