threshold-parity8

threshold-parity8

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

Function

parity8(b0..b7) = b0 XOR b1 XOR b2 XOR b3 XOR b4 XOR b5 XOR b6 XOR b7

Architecture

Balanced tree of 7 XOR2 gates:

b0 b1  b2 b3  b4 b5  b6 b7
  \/     \/     \/     \/
 xor01  xor23  xor45  xor67   (Level 1: 4 gates)
    \    /       \    /
   xor0123      xor4567       (Level 2: 2 gates)
        \        /
        xor_final             (Level 3: 1 gate)

Each XOR2 uses OR-NAND-AND structure (3 neurons, 9 params, magnitude 10).

Parameters

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 parity8(bits):
    x01 = xor2(bits[0], bits[1], 'xor_01')
    x23 = xor2(bits[2], bits[3], 'xor_23')
    x45 = xor2(bits[4], bits[5], 'xor_45')
    x67 = xor2(bits[6], bits[7], 'xor_67')
    x0123 = xor2(x01, x23, 'xor_0123')
    x4567 = xor2(x45, x67, 'xor_4567')
    return xor2(x0123, x4567, 'xor_final')

print(parity8([1, 0, 1, 0, 1, 0, 1, 0]))  # 0 (even)
print(parity8([1, 1, 1, 0, 0, 0, 0, 0]))  # 1 (odd)

License

MIT