| """
|
| Threshold Network for NAND Gate
|
|
|
| A formally verified single-neuron threshold network computing negated conjunction.
|
| Weights are integer-constrained and activation uses the Heaviside step function.
|
| NAND is functionally complete - any Boolean function can be built from NAND gates.
|
| """
|
|
|
| import torch
|
| from safetensors.torch import load_file
|
|
|
|
|
| class ThresholdNAND:
|
| """
|
| NAND gate implemented as a threshold neuron.
|
|
|
| Circuit: output = (w1*x1 + w2*x2 + bias >= 0)
|
| With weights=[-1,-1], bias=1: fires unless both inputs are 1.
|
| """
|
|
|
| def __init__(self, weights_dict):
|
| self.weight = weights_dict['weight']
|
| self.bias = weights_dict['bias']
|
|
|
| def __call__(self, x1, x2):
|
| inputs = torch.tensor([float(x1), float(x2)])
|
| 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:
|
| NAND(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 = ThresholdNAND(weights)
|
|
|
| print("NAND Gate Truth Table:")
|
| print("-" * 25)
|
| for x1 in [0, 1]:
|
| for x2 in [0, 1]:
|
| out = int(model(x1, x2).item())
|
| expected = 1 - (x1 & x2)
|
| status = "OK" if out == expected else "FAIL"
|
| print(f"NAND({x1}, {x2}) = {out} [{status}]")
|
|
|
