Exactly 1 of 3 threshold circuit, magnitude 12

README.md

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+---
+license: mit
+tags:
+- pytorch
+- safetensors
+- threshold-logic
+- neuromorphic
+---
+
+# threshold-exactly1outof3
+
+Exactly 1 of 3 inputs high.
+
+## Function
+
+exactly1outof3(a, b, c) = 1 if (a + b + c) == 1, else 0
+
+## Truth Table
+
+| a | b | c | sum | out |
+|---|---|---|-----|-----|
+| 0 | 0 | 0 | 0 | 0 |
+| 0 | 0 | 1 | 1 | 1 |
+| 0 | 1 | 0 | 1 | 1 |
+| 0 | 1 | 1 | 2 | 0 |
+| 1 | 0 | 0 | 1 | 1 |
+| 1 | 0 | 1 | 2 | 0 |
+| 1 | 1 | 0 | 2 | 0 |
+| 1 | 1 | 1 | 3 | 0 |
+
+## Architecture
+
+Two layers (not linearly separable):
+
+**Layer 1:**
+- N1: weights [1, 1, 1], bias -1 (fires when sum >= 1)
+- N2: weights [-1, -1, -1], bias 1 (fires when sum <= 1)
+
+**Layer 2:**
+- AND: weights [1, 1], bias -2 (fires when both N1 and N2 fire)
+
+## Parameters
+
+| | |
+|---|---|
+| Inputs | 3 |
+| Outputs | 1 |
+| Neurons | 3 |
+| Layers | 2 |
+| Parameters | 11 |
+| Magnitude | 12 |
+
+## Usage
+
+```python
+from safetensors.torch import load_file
+import torch
+
+w = load_file('model.safetensors')
+
+def exactly1of3(a, b, c):
+    inp = torch.tensor([float(a), float(b), float(c)])
+    l1 = (inp @ w['layer1.weight'].T + w['layer1.bias'] >= 0).float()
+    out = (l1 @ w['layer2.weight'].T + w['layer2.bias'] >= 0).float()
+    return int(out.item())
+
+print(exactly1of3(0, 0, 1))  # 1 (sum=1)
+print(exactly1of3(0, 1, 1))  # 0 (sum=2)
+```
+
+## License
+
+MIT

config.json

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+{
+  "name": "threshold-exactly1outof3",
+  "description": "Exactly 1 of 3 inputs high",
+  "inputs": 3,
+  "outputs": 1,
+  "neurons": 3,
+  "layers": 2,
+  "parameters": 11
+}

create_safetensors.py

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+import torch
+from safetensors.torch import save_file
+
+# Layer 1: N1 (sum >= 1), N2 (sum <= 1)
+# Layer 2: AND(N1, N2)
+weights = {
+    'layer1.weight': torch.tensor([
+        [1.0, 1.0, 1.0],   # N1: sum >= 1
+        [-1.0, -1.0, -1.0] # N2: sum <= 1
+    ], dtype=torch.float32),
+    'layer1.bias': torch.tensor([-1.0, 1.0], dtype=torch.float32),
+    'layer2.weight': torch.tensor([[1.0, 1.0]], dtype=torch.float32),
+    'layer2.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)])
+    l1 = (inp @ weights['layer1.weight'].T + weights['layer1.bias'] >= 0).float()
+    out = (l1 @ weights['layer2.weight'].T + weights['layer2.bias'] >= 0).float()
+    return int(out.item())
+
+print("Verifying exactly1outof3...")
+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) == 1 else 0
+    if result != expected:
+        errors += 1
+        print(f"ERROR: {a}{b}{c} -> {result}, expected {expected}")
+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 exactly1of3(a, b, c, weights):
+    """Returns 1 if exactly 1 of 3 inputs is high"""
+    inp = torch.tensor([float(a), float(b), float(c)])
+    l1 = (inp @ weights['layer1.weight'].T + weights['layer1.bias'] >= 0).float()
+    out = (l1 @ weights['layer2.weight'].T + weights['layer2.bias'] >= 0).float()
+    return int(out.item())
+
+if __name__ == '__main__':
+    w = load_model()
+    print('exactly1outof3 truth table:')
+    for i in range(8):
+        a, b, c = (i >> 2) & 1, (i >> 1) & 1, i & 1
+        print(f'  {a}{b}{c} -> {exactly1of3(a, b, c, w)}')