Hi,

I build with the neuron from Drosophila a network,

that can recognice prime numbers with 5 neurons up to 255 in binary notation

Dietmar

prim.html

Edited 7 hours ago7 hr by Dietmar

@xper

Can you please enable, that my prim.html is clickable and can be seen at once, direct in my post?

It would be really crazy nice

Dietmar

Of coure, that didn't help on the clickable, lol.

Hi,

eight input switches and five neurons.

• OFF = 0

• ON = 1

The eight switches represent these values:

Switch:  x0  x1  x2  x3  x4  x5  x6   x7
Value:    1   2   4   8  16  32  64  128

Add the values of the switches that are ON. This gives the number to test.

For example, switching ON 128, 8 and 1 gives:

128 + 8 + 1 = 137

This lets us enter every number from 0 to 255.

What does a neuron do?

It adds and subtracts the signals it receives. If the total reaches its threshold, it switches ON. Otherwise, it stays OFF.

For example:

5*x1 means:
Add 5 if switch x1 is ON.
Add nothing if switch x1 is OFF.

-4*x2 means:
Subtract 4 if switch x2 is ON.
Subtract nothing if switch x2 is OFF.

The outputs of the five neurons are called h1, h2, h3, h4 and h5. They are always 0 or 1.

Calculate the neurons in order: 1, 2, 3, 4, 5.

Neuron 1 calculates:

S1 = -x0 + 5*x1 + 3*x2 + x3 + 2*x4 - x5 + 4*x6 + x7

If S1 >= 7, then h1 = 1.
Otherwise, h1 = 0.

Neuron 2 also uses the result from Neuron 1:

S2 = 2*x0 + x1 - 4*x2 + 3*x3 - 3*x4 + 7*x5 - 4*x6 + 3*x7
     + 5*h1

If S2 >= 6, then h2 = 1.
Otherwise, h2 = 0.

Neuron 3 calculates:

S3 = -3*x0 - 2*x1 + 2*x3 + x4 + 3*x5 + x6 - 2*x7
     + 5*h1 + 6*h2

If S3 >= 4, then h3 = 1.
Otherwise, h3 = 0.

Neuron 4 calculates:

S4 = 13*x0 + 4*x1 - 7*x2 + 9*x3 - 8*x4 + 6*x5 - 10*x6 + 6*x7
     + 5*h1 - 13*h2 - 7*h3

If S4 >= 4, then h4 = 1.
Otherwise, h4 = 0.

Neuron 5 gives the final answer:

S5 = 2*x1 + 6*x2 - 3*x3 + 4*x4 + 4*x5 + 7*x6 - 5*x7
     - 5*h1 + 10*h2 - 9*h3 + 13*h4

If S5 >= 15, then h5 = 1: PRIME.
Otherwise, h5 = 0: NOT PRIME.

Here, * means multiplication and >= means “greater than or equal to”. Reaching the threshold exactly is enough to switch ON.

A neuron passes only its ON/OFF result to the next neurons. For example, if Neuron 2 has a total of 8, its output is h2 = 1, not 8.

For our example, 137:

Neuron:   1   2   3   4   5
Output:   0   1   0   1   1

The last neuron is ON, so 137 is prime.

For 169:

Neuron:   1   2   3   4   5
Output:   0   1   1   1   0

The last neuron is OFF, so 169 is not prime. Indeed, 169 = 13*13.

All 256 possible inputs were tested: 54 primes, 202 non-primes, zero errors. The network also correctly handles 0, 1 and 2.

There are five neurons in total, including the final output neuron.

Dietmar