threshold-parity3

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

Function

parity3(a, b, c) = a XOR b XOR c

Truth Table

a	b	c	out
0	0	0	0
0	0	1	1
0	1	0	1
0	1	1	0
1	0	0	1
1	0	1	0
1	1	0	0
1	1	1	1

Architecture

Cascade of two XOR2 gates: parity(a,b,c) = XOR(XOR(a,b), c)

Each XOR2 uses OR-NAND-AND structure:

• OR: fires if either input is 1
• NAND: fires if not both inputs are 1
• AND: fires if both OR and NAND fire (XOR condition)

Layers:

1. xor1.or, xor1.nand (on inputs a, b)
2. xor1.and (combines layer 1)
3. xor2.or, xor2.nand (on xor1 output and c)
4. xor2.and (final output)

Parameters

Inputs	3
Outputs	1
Neurons	6
Layers	4
Parameters	18
Magnitude	20

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 parity3(a, b, c):
    return xor2(xor2(a, b, 'xor1'), c, 'xor2')

print(parity3(1, 0, 1))  # 0 (even parity)
print(parity3(1, 1, 1))  # 1 (odd parity)

License

MIT