threshold-parity4

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

Function

parity4(a, b, c, d) = a XOR b XOR c XOR d

Architecture

Tree structure: parity(a,b,c,d) = XOR(XOR(a,b), XOR(c,d))

Three XOR2 gates, each using OR-NAND-AND structure:

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

Layer structure:

1. or1, nand1 (a,b) and or2, nand2 (c,d) in parallel
2. and1 (xor_ab) and and2 (xor_cd)
3. or3, nand3 (on xor outputs)
4. and3 (final output)

Parameters

Inputs	4
Outputs	1
Neurons	9
Layers	4
Parameters	27
Magnitude	30

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 parity4(a, b, c, d):
    return xor2(xor2(a, b, 'xor_ab'), xor2(c, d, 'xor_cd'), 'xor_final')

print(parity4(1, 0, 1, 0))  # 0 (even)
print(parity4(1, 1, 1, 0))  # 1 (odd)

License

MIT