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