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