| | """
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| | Threshold Network for Parity Computation
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| |
|
| | A ternary threshold network that computes the parity (XOR) of 8 binary inputs.
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| | Weights are constrained to {-1, 0, +1} and activations use the Heaviside step function.
|
| | """
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| |
|
| | import json
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| | import torch
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| | import torch.nn as nn
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| |
|
| |
|
| | class ThresholdNetwork(nn.Module):
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| | """
|
| | Binary threshold network with ternary weights.
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| |
|
| | Architecture: 8 -> 32 -> 16 -> 1
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| | Weights: {-1, 0, +1}
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| | Activation: Heaviside (x >= 0 -> 1, else 0)
|
| | """
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| |
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| | def __init__(self, n_bits=8, hidden1=32, hidden2=16):
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| | super().__init__()
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| | self.n_bits = n_bits
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| | self.hidden1 = hidden1
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| | self.hidden2 = hidden2
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| |
|
| | self.layer1_weight = nn.Parameter(torch.zeros(hidden1, n_bits))
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| | self.layer1_bias = nn.Parameter(torch.zeros(hidden1))
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| | self.layer2_weight = nn.Parameter(torch.zeros(hidden2, hidden1))
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| | self.layer2_bias = nn.Parameter(torch.zeros(hidden2))
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| | self.output_weight = nn.Parameter(torch.zeros(1, hidden2))
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| | self.output_bias = nn.Parameter(torch.zeros(1))
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| |
|
| | def forward(self, x):
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| | """Forward pass with Heaviside activation."""
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| | x = x.float()
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| | x = (torch.nn.functional.linear(x, self.layer1_weight, self.layer1_bias) >= 0).float()
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| | x = (torch.nn.functional.linear(x, self.layer2_weight, self.layer2_bias) >= 0).float()
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| | x = (torch.nn.functional.linear(x, self.output_weight, self.output_bias) >= 0).float()
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| | return x.squeeze(-1)
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| |
|
| | @classmethod
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| | def from_safetensors(cls, path):
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| | """Load model from SafeTensors file."""
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| | from safetensors.torch import load_file
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| |
|
| | weights = load_file(path)
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| |
|
| | hidden1 = weights['layer1.weight'].shape[0]
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| | hidden2 = weights['layer2.weight'].shape[0]
|
| | n_bits = weights['layer1.weight'].shape[1]
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| |
|
| | model = cls(n_bits=n_bits, hidden1=hidden1, hidden2=hidden2)
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| | model.layer1_weight.data = weights['layer1.weight']
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| | model.layer1_bias.data = weights['layer1.bias']
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| | model.layer2_weight.data = weights['layer2.weight']
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| | model.layer2_bias.data = weights['layer2.bias']
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| | model.output_weight.data = weights['output.weight']
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| | model.output_bias.data = weights['output.bias']
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| |
|
| | return model
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| |
|
| |
|
| | def parity(x):
|
| | """Ground truth parity function."""
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| | return (x.sum(dim=-1) % 2).float()
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| |
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| |
|
| | if __name__ == '__main__':
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| | model = ThresholdNetwork.from_safetensors('model.safetensors')
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| |
|
| | test_inputs = torch.tensor([
|
| | [0, 0, 0, 0, 0, 0, 0, 0],
|
| | [1, 0, 0, 0, 0, 0, 0, 0],
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| | [1, 1, 0, 0, 0, 0, 0, 0],
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| | [1, 1, 1, 0, 0, 0, 0, 0],
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| | [1, 1, 1, 1, 1, 1, 1, 1],
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| | ], dtype=torch.float32)
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| |
|
| | outputs = model(test_inputs)
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| | expected = parity(test_inputs)
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| |
|
| | print("Input -> Output (Expected)")
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| | for i in range(len(test_inputs)):
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| | bits = test_inputs[i].int().tolist()
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| | print(f"{bits} -> {int(outputs[i].item())} ({int(expected[i].item())})")
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| |
|
