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"""
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Threshold Network for Biconditional Gate
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A formally verified two-layer threshold network computing logical equivalence (iff).
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Biconditional is not linearly separable, requiring at least 2 layers.
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Architecture: Layer1 computes NOR and AND, Layer2 computes OR of results.
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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 ThresholdBiImplies:
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"""
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Biconditional gate implemented as a 2-layer threshold network.
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Layer 1: NOR (neuron 1) and AND (neuron 2) in parallel
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Layer 2: OR of layer 1 outputs
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BiImplies(x,y) = OR(NOR(x,y), AND(x,y)) = (x iff y)
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"""
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def __init__(self, weights_dict):
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self.l1_n1_weight = weights_dict['layer1.neuron1.weight']
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self.l1_n1_bias = weights_dict['layer1.neuron1.bias']
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self.l1_n2_weight = weights_dict['layer1.neuron2.weight']
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self.l1_n2_bias = weights_dict['layer1.neuron2.bias']
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self.l2_weight = weights_dict['layer2.weight']
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self.l2_bias = weights_dict['layer2.bias']
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def __call__(self, x1, x2):
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inputs = torch.tensor([float(x1), float(x2)])
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nor_out = ((inputs * self.l1_n1_weight).sum() + self.l1_n1_bias >= 0).float()
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and_out = ((inputs * self.l1_n2_weight).sum() + self.l1_n2_bias >= 0).float()
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layer1_out = torch.tensor([nor_out, and_out])
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output = ((layer1_out * self.l2_weight).sum() + self.l2_bias >= 0).float()
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return output
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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(x1, x2, weights):
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"""
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Forward pass with Heaviside activation.
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Args:
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x1, x2: Input values (0 or 1)
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weights: Dict with layer weights and biases
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Returns:
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BiImplies(x1, x2) = (x1 iff x2)
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"""
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inputs = torch.tensor([float(x1), float(x2)])
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nor_out = ((inputs * weights['layer1.neuron1.weight']).sum() + weights['layer1.neuron1.bias'] >= 0).float()
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and_out = ((inputs * weights['layer1.neuron2.weight']).sum() + weights['layer1.neuron2.bias'] >= 0).float()
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layer1_out = torch.tensor([nor_out, and_out])
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output = ((layer1_out * weights['layer2.weight']).sum() + weights['layer2.bias'] >= 0).float()
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return output
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if __name__ == "__main__":
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weights = load_file("model.safetensors")
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model = ThresholdBiImplies(weights)
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print("Biconditional Gate Truth Table:")
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print("-" * 30)
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for x1 in [0, 1]:
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for x2 in [0, 1]:
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out = int(model(x1, x2).item())
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expected = 1 if x1 == x2 else 0
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status = "OK" if out == expected else "FAIL"
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print(f"BiImplies({x1}, {x2}) = {out} [{status}]")
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