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"""
Threshold Network for Implication Gate
A formally verified single-neuron threshold network computing material conditional.
Weights are integer-constrained and activation uses the Heaviside step function.
"""
import torch
from safetensors.torch import load_file
class ThresholdImplies:
"""
Implication gate implemented as a threshold neuron.
Circuit: output = (w1*x + w2*y + bias >= 0)
With weights=[-1,1], bias=0: fails only when x=1 and y=0.
"""
def __init__(self, weights_dict):
self.weight = weights_dict['weight']
self.bias = weights_dict['bias']
def __call__(self, x, y):
inputs = torch.tensor([float(x), float(y)])
weighted_sum = (inputs * self.weight).sum() + self.bias
return (weighted_sum >= 0).float()
@classmethod
def from_safetensors(cls, path="model.safetensors"):
return cls(load_file(path))
def forward(x, weights):
"""
Forward pass with Heaviside activation.
Args:
x: Input tensor of shape [..., 2]
weights: Dict with 'weight' and 'bias' tensors
Returns:
Implies(x[0], x[1])
"""
x = torch.as_tensor(x, dtype=torch.float32)
weighted_sum = (x * weights['weight']).sum(dim=-1) + weights['bias']
return (weighted_sum >= 0).float()
if __name__ == "__main__":
weights = load_file("model.safetensors")
model = ThresholdImplies(weights)
print("Implication Gate Truth Table:")
print("-" * 30)
for x in [0, 1]:
for y in [0, 1]:
out = int(model(x, y).item())
expected = 1 if (x == 0 or y == 1) else 0
status = "OK" if out == expected else "FAIL"
print(f"Implies({x}, {y}) = {out} [{status}]")
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