Small Basic - Multilayered Perceptron

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This is the continued story from Small Basic - Artificial Neuron.

Last time, I told about simple perceptron (artificial neuron) can become such as OR, AND and NAND operations.  Single perceptron is able to be drawn as following graph.  The horizontal axis is x1 and the vertical axis is x2.  The light area means y=0 and the dark area means y=1.  So, in following graph, if (x1, x2) is (1, 1) then y=1.

Screen shot of a program Graph 0.5 - AND

If setting any b, w1 and w2 parameters, single perceptron can't become XOR (exclusive or) nor EQV (equivalent).  But by combining multiple perceptrons, XOR and EQV can be implemented.  The graph blow is showing XOR constructed with AND, NAND and OR perceptrons.

Screen shot of a program Graph 0.5 - XOR

The graph drawing program above is uploaded as RQX345-3.

Computer logic is constructed with multilayered logical gates such as AND, OR, XOR.  So, with multilayered perceptrons, we can also construct a computer.  But, why perceptrons are used instead of logical gates.  I'd like to talk the reason in the future blog posts.

Let's learn with Small Basic!