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""" |
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Threshold Network for 4-input AND Gate |
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A formally verified single-neuron threshold network computing 4-way logical conjunction. |
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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 ThresholdAND4: |
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""" |
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4-input AND gate implemented as a threshold neuron. |
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Circuit: output = (w1*x1 + w2*x2 + w3*x3 + w4*x4 + bias >= 0) |
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With weights=[1,1,1,1], bias=-4: only (1,1,1,1) reaches threshold. |
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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, x1, x2, x3, x4): |
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inputs = torch.tensor([float(x1), float(x2), float(x3), float(x4)]) |
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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 [..., 4] |
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weights: Dict with 'weight' and 'bias' tensors |
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Returns: |
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AND(x[0], x[1], x[2], x[3]) |
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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 = ThresholdAND4(weights) |
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print("4-input AND Gate Truth Table:") |
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print("-" * 35) |
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correct = 0 |
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for x1 in [0, 1]: |
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for x2 in [0, 1]: |
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for x3 in [0, 1]: |
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for x4 in [0, 1]: |
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out = int(model(x1, x2, x3, x4).item()) |
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expected = x1 & x2 & x3 & x4 |
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status = "OK" if out == expected else "FAIL" |
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if out == expected: |
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correct += 1 |
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print(f"AND4({x1}, {x2}, {x3}, {x4}) = {out} [{status}]") |
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print(f"\nTotal: {correct}/16 correct") |
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