| | """
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| | Threshold Network for NOR Gate
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| |
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| | A formally verified single-neuron threshold network computing negated disjunction.
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| | Weights are integer-constrained and activation uses the Heaviside step function.
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| | NOR is functionally complete - any Boolean function can be built from NOR gates.
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| | """
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| |
|
| | import torch
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| | from safetensors.torch import load_file
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| |
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| |
|
| | class ThresholdNOR:
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| | """
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| | NOR gate implemented as a threshold neuron.
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| |
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| | Circuit: output = (w1*x1 + w2*x2 + bias >= 0)
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| | With weights=[-1,-1], bias=0: fires only when both inputs are 0.
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| | """
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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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| |
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| | def __call__(self, x1, x2):
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| | inputs = torch.tensor([float(x1), float(x2)])
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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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| |
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| |
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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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| |
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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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| |
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| | Returns:
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| | NOR(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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| |
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| |
|
| | if __name__ == "__main__":
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| | weights = load_file("model.safetensors")
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| | model = ThresholdNOR(weights)
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| |
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| | print("NOR Gate Truth Table:")
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| | print("-" * 25)
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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 - (x1 | x2)
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| | status = "OK" if out == expected else "FAIL"
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| | print(f"NOR({x1}, {x2}) = {out} [{status}]")
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| |
|
