At most 2 of 3 threshold circuit (NAND3), magnitude 5

README.md

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+---
+license: mit
+tags:
+- pytorch
+- safetensors
+- threshold-logic
+- neuromorphic
+---
+
+# threshold-atmost2outof3
+
+At most 2 of 3 inputs high. Equivalent to 3-input NAND gate.
+
+## Function
+
+atmost2outof3(a, b, c) = 1 if (a + b + c) <= 2, else 0
+
+Equivalently: NAND(a, b, c) = NOT(a AND b AND c)
+
+## Truth Table
+
+| a | b | c | sum | out |
+|---|---|---|-----|-----|
+| 0 | 0 | 0 | 0 | 1 |
+| 0 | 0 | 1 | 1 | 1 |
+| 0 | 1 | 0 | 1 | 1 |
+| 0 | 1 | 1 | 2 | 1 |
+| 1 | 0 | 0 | 1 | 1 |
+| 1 | 0 | 1 | 2 | 1 |
+| 1 | 1 | 0 | 2 | 1 |
+| 1 | 1 | 1 | 3 | 0 |
+
+## Architecture
+
+Single neuron: weights [-1, -1, -1], bias 2
+
+Fires when: -a - b - c + 2 >= 0, i.e., sum <= 2
+
+## Parameters
+
+| | |
+|---|---|
+| Inputs | 3 |
+| Outputs | 1 |
+| Neurons | 1 |
+| Layers | 1 |
+| Parameters | 4 |
+| Magnitude | 5 |
+
+## Usage
+
+```python
+from safetensors.torch import load_file
+import torch
+
+w = load_file('model.safetensors')
+
+def atmost2of3(a, b, c):
+    inp = torch.tensor([float(a), float(b), float(c)])
+    return int((inp @ w['neuron.weight'].T + w['neuron.bias'] >= 0).item())
+
+print(atmost2of3(1, 1, 0))  # 1 (sum=2)
+print(atmost2of3(1, 1, 1))  # 0 (sum=3)
+```
+
+## License
+
+MIT

config.json

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+{
+  "name": "threshold-atmost2outof3",
+  "description": "At most 2 of 3 inputs high (3-input NAND)",
+  "inputs": 3,
+  "outputs": 1,
+  "neurons": 1,
+  "layers": 1,
+  "parameters": 4
+}

create_safetensors.py

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+import torch
+from safetensors.torch import save_file
+
+weights = {
+    'neuron.weight': torch.tensor([[-1.0, -1.0, -1.0]], dtype=torch.float32),
+    'neuron.bias': torch.tensor([2.0], dtype=torch.float32)
+}
+save_file(weights, 'model.safetensors')
+
+def test(a, b, c):
+    inp = torch.tensor([float(a), float(b), float(c)])
+    return int((inp @ weights['neuron.weight'].T + weights['neuron.bias'] >= 0).item())
+
+print("Verifying atmost2outof3...")
+errors = 0
+for i in range(8):
+    a, b, c = (i >> 2) & 1, (i >> 1) & 1, i & 1
+    result = test(a, b, c)
+    expected = 1 if (a + b + c) <= 2 else 0
+    if result != expected:
+        errors += 1
+if errors == 0:
+    print("All 8 test cases passed!")
+print(f"Magnitude: {sum(t.abs().sum().item() for t in weights.values()):.0f}")

model.py

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+import torch
+from safetensors.torch import load_file
+
+def load_model(path='model.safetensors'):
+    return load_file(path)
+
+def atmost2of3(a, b, c, weights):
+    """Returns 1 if at most 2 of 3 inputs are high (NAND)"""
+    inp = torch.tensor([float(a), float(b), float(c)])
+    return int((inp @ weights['neuron.weight'].T + weights['neuron.bias'] >= 0).item())
+
+if __name__ == '__main__':
+    w = load_model()
+    print('atmost2outof3 (NAND3) truth table:')
+    for i in range(8):
+        a, b, c = (i >> 2) & 1, (i >> 1) & 1, i & 1
+        print(f'  {a}{b}{c} -> {atmost2of3(a, b, c, w)}')