threshold-equals2

2-bit equality comparator. Outputs 1 if 2-bit A equals 2-bit B.

Function

equals2(a1, a0, b1, b0) = 1 if (a1,a0) == (b1,b0), else 0

Architecture

Checks if each bit pair matches using XNOR, then ANDs the results.

XNOR(x, y) = (x AND y) OR (NOT x AND NOT y)

Layer 1: (4 neurons on raw inputs)

• and1: a1 AND b1
• nor1: NOR(a1, b1)
• and0: a0 AND b0
• nor0: NOR(a0, b0)

Layer 2: (2 neurons)

• xnor1: OR(and1, nor1) - bit 1 matches
• xnor0: OR(and0, nor0) - bit 0 matches

Layer 3: (1 neuron)

• eq: AND(xnor1, xnor0) - both bits match

Parameters

Inputs	4 (a1, a0, b1, b0)
Outputs	1
Neurons	7
Layers	3
Parameters	31
Magnitude	18

Usage

from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

# Check if 2 == 2 (binary 10 == 10)
# a1=1, a0=0, b1=1, b0=0
# Result: 1 (equal)

License

MIT