|
|
"""
|
|
|
Threshold Network for XNOR Gate
|
|
|
|
|
|
A formally verified two-layer threshold network computing equivalence.
|
|
|
XNOR is not linearly separable, requiring at least 2 layers.
|
|
|
Architecture: Layer1 computes NOR and AND, Layer2 computes OR of results.
|
|
|
"""
|
|
|
|
|
|
import torch
|
|
|
from safetensors.torch import load_file
|
|
|
|
|
|
|
|
|
class ThresholdXNOR:
|
|
|
"""
|
|
|
XNOR gate implemented as a 2-layer threshold network.
|
|
|
|
|
|
Layer 1: NOR (neuron 1) and AND (neuron 2) in parallel
|
|
|
Layer 2: OR of layer 1 outputs
|
|
|
|
|
|
XNOR(x,y) = OR(NOR(x,y), AND(x,y))
|
|
|
"""
|
|
|
|
|
|
def __init__(self, weights_dict):
|
|
|
self.l1_n1_weight = weights_dict['layer1.neuron1.weight']
|
|
|
self.l1_n1_bias = weights_dict['layer1.neuron1.bias']
|
|
|
self.l1_n2_weight = weights_dict['layer1.neuron2.weight']
|
|
|
self.l1_n2_bias = weights_dict['layer1.neuron2.bias']
|
|
|
self.l2_weight = weights_dict['layer2.weight']
|
|
|
self.l2_bias = weights_dict['layer2.bias']
|
|
|
|
|
|
def __call__(self, x1, x2):
|
|
|
inputs = torch.tensor([float(x1), float(x2)])
|
|
|
|
|
|
nor_out = ((inputs * self.l1_n1_weight).sum() + self.l1_n1_bias >= 0).float()
|
|
|
and_out = ((inputs * self.l1_n2_weight).sum() + self.l1_n2_bias >= 0).float()
|
|
|
|
|
|
layer1_out = torch.tensor([nor_out, and_out])
|
|
|
output = ((layer1_out * self.l2_weight).sum() + self.l2_bias >= 0).float()
|
|
|
|
|
|
return output
|
|
|
|
|
|
@classmethod
|
|
|
def from_safetensors(cls, path="model.safetensors"):
|
|
|
return cls(load_file(path))
|
|
|
|
|
|
|
|
|
def forward(x1, x2, weights):
|
|
|
"""
|
|
|
Forward pass with Heaviside activation.
|
|
|
|
|
|
Args:
|
|
|
x1, x2: Input values (0 or 1)
|
|
|
weights: Dict with layer weights and biases
|
|
|
|
|
|
Returns:
|
|
|
XNOR(x1, x2)
|
|
|
"""
|
|
|
inputs = torch.tensor([float(x1), float(x2)])
|
|
|
|
|
|
nor_out = ((inputs * weights['layer1.neuron1.weight']).sum() + weights['layer1.neuron1.bias'] >= 0).float()
|
|
|
and_out = ((inputs * weights['layer1.neuron2.weight']).sum() + weights['layer1.neuron2.bias'] >= 0).float()
|
|
|
|
|
|
layer1_out = torch.tensor([nor_out, and_out])
|
|
|
output = ((layer1_out * weights['layer2.weight']).sum() + weights['layer2.bias'] >= 0).float()
|
|
|
|
|
|
return output
|
|
|
|
|
|
|
|
|
if __name__ == "__main__":
|
|
|
weights = load_file("model.safetensors")
|
|
|
model = ThresholdXNOR(weights)
|
|
|
|
|
|
print("XNOR Gate Truth Table:")
|
|
|
print("-" * 25)
|
|
|
for x1 in [0, 1]:
|
|
|
for x2 in [0, 1]:
|
|
|
out = int(model(x1, x2).item())
|
|
|
expected = 1 - (x1 ^ x2)
|
|
|
status = "OK" if out == expected else "FAIL"
|
|
|
print(f"XNOR({x1}, {x2}) = {out} [{status}]")
|
|
|
|
