| ---
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| license: mit
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| tags:
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| - pytorch
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| - safetensors
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| - threshold-logic
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| - neuromorphic
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| - voting
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| ---
|
|
|
| # threshold-4outof6
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|
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| At-least-4-of-6 threshold gate. Fires when 4 or more of the 6 inputs are high.
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|
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| ## Function
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|
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| ```
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| 4outof6(x0, x1, x2, x3, x4, x5) = 1 if (x0 + x1 + x2 + x3 + x4 + x5) >= 4
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| ```
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|
|
| ## Truth Table (selected)
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|
|
| | Hamming Weight | Output |
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| |:--------------:|:------:|
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| | 0 | 0 |
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| | 1 | 0 |
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| | 2 | 0 |
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| | 3 | 0 |
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| | 4 | 1 |
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| | 5 | 1 |
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| | 6 | 1 |
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|
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| ## Mechanism
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| Single threshold neuron with uniform weights. The bias of -4 sets the firing threshold:
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|
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| - Sum = (number of 1s) + (-4)
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| - Fires when sum >= 0, i.e., when Hamming weight >= 4
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|
|
| ## k-out-of-6 Family
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|
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| | Circuit | Bias | Fires when |
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| |---------|------|------------|
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| | 1-out-of-6 | -1 | HW >= 1 |
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| | 2-out-of-6 | -2 | HW >= 2 |
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| | 3-out-of-6 | -3 | HW >= 3 (majority) |
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| | 4-out-of-6 | -4 | HW >= 4 |
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| | 5-out-of-6 | -5 | HW >= 5 |
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| | 6-out-of-6 | -6 | HW = 6 (AND) |
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|
|
| ## Parameters
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|
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| | | |
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| |---|---|
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| | Weights | [1, 1, 1, 1, 1, 1] |
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| | Bias | -4 |
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| | Inputs | 6 |
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| | Outputs | 1 |
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| | Neurons | 1 |
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| | Layers | 1 |
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| | Parameters | 7 |
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| | Magnitude | 10 |
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|
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| ## Usage
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|
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| ```python
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| from safetensors.torch import load_file
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| import torch
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|
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| w = load_file('model.safetensors')
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|
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| def at_least_4_of_6(bits):
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| inputs = torch.tensor([float(b) for b in bits])
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| return int((inputs @ w['neuron.weight'].T + w['neuron.bias'] >= 0).item())
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|
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| print(at_least_4_of_6([1, 1, 1, 1, 0, 0, 0])) # 0 or 1 depending on k
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| ```
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|
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| ## License
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| MIT
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|
