threshold-parity5

5-bit parity function. Outputs 1 if odd number of inputs are high.

Function

parity5(a, b, c, d, e) = a XOR b XOR c XOR d XOR e

Architecture

Hybrid tree-cascade: parity5 = XOR(XOR(XOR(a,b), XOR(c,d)), e)

Four XOR2 gates:

• xor_ab: XOR(a, b) - parallel with xor_cd
• xor_cd: XOR(c, d) - parallel with xor_ab
• xor_abcd: XOR(xor_ab, xor_cd)
• xor_final: XOR(xor_abcd, e)

Parameters

Inputs	5
Outputs	1
Neurons	12
Layers	6
Parameters	36
Magnitude	40

Usage

from safetensors.torch import load_file

w = load_file('model.safetensors')

def xor2(a, b, prefix):
    or_out = int(a * w[f'{prefix}.or.weight'][0] + b * w[f'{prefix}.or.weight'][1] + w[f'{prefix}.or.bias'] >= 0)
    nand_out = int(a * w[f'{prefix}.nand.weight'][0] + b * w[f'{prefix}.nand.weight'][1] + w[f'{prefix}.nand.bias'] >= 0)
    return int(or_out * w[f'{prefix}.and.weight'][0] + nand_out * w[f'{prefix}.and.weight'][1] + w[f'{prefix}.and.bias'] >= 0)

def parity5(a, b, c, d, e):
    xor_ab = xor2(a, b, 'xor_ab')
    xor_cd = xor2(c, d, 'xor_cd')
    xor_abcd = xor2(xor_ab, xor_cd, 'xor_abcd')
    return xor2(xor_abcd, e, 'xor_final')

print(parity5(1, 0, 1, 0, 1))  # 1 (odd)
print(parity5(1, 1, 1, 1, 0))  # 0 (even)

License

MIT