| """
|
| Threshold Network for XOR Gate
|
|
|
| A formally verified two-layer threshold network computing exclusive or.
|
| XOR is not linearly separable, requiring at least 2 layers.
|
| Architecture: Layer1 computes OR and NAND, Layer2 computes AND of results.
|
| """
|
|
|
| import torch
|
| from safetensors.torch import load_file
|
|
|
|
|
| class ThresholdXOR:
|
| """
|
| XOR gate implemented as a 2-layer threshold network.
|
|
|
| Layer 1: OR (neuron 1) and NAND (neuron 2) in parallel
|
| Layer 2: AND of layer 1 outputs
|
|
|
| XOR(x,y) = AND(OR(x,y), NAND(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)])
|
|
|
| or_out = ((inputs * self.l1_n1_weight).sum() + self.l1_n1_bias >= 0).float()
|
| nand_out = ((inputs * self.l1_n2_weight).sum() + self.l1_n2_bias >= 0).float()
|
|
|
| layer1_out = torch.tensor([or_out, nand_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:
|
| XOR(x1, x2)
|
| """
|
| inputs = torch.tensor([float(x1), float(x2)])
|
|
|
| or_out = ((inputs * weights['layer1.neuron1.weight']).sum() + weights['layer1.neuron1.bias'] >= 0).float()
|
| nand_out = ((inputs * weights['layer1.neuron2.weight']).sum() + weights['layer1.neuron2.bias'] >= 0).float()
|
|
|
| layer1_out = torch.tensor([or_out, nand_out])
|
| output = ((layer1_out * weights['layer2.weight']).sum() + weights['layer2.bias'] >= 0).float()
|
|
|
| return output
|
|
|
|
|
| if __name__ == "__main__":
|
| weights = load_file("model.safetensors")
|
| model = ThresholdXOR(weights)
|
|
|
| print("XOR Gate Truth Table:")
|
| print("-" * 25)
|
| for x1 in [0, 1]:
|
| for x2 in [0, 1]:
|
| out = int(model(x1, x2).item())
|
| expected = x1 ^ x2
|
| status = "OK" if out == expected else "FAIL"
|
| print(f"XOR({x1}, {x2}) = {out} [{status}]")
|
|
|
