Exactly 2 of 4 threshold circuit, magnitude 16

README.md

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+---
+license: mit
+tags:
+- pytorch
+- safetensors
+- threshold-logic
+- neuromorphic
+---
+
+# threshold-exactly2outof4
+
+Exactly 2 of 4 inputs high.
+
+## Function
+
+exactly2outof4(a, b, c, d) = 1 if (a + b + c + d) == 2, else 0
+
+## Truth Table
+
+| a | b | c | d | sum | out |
+|---|---|---|---|-----|-----|
+| 0 | 0 | 0 | 0 | 0 | 0 |
+| 0 | 0 | 0 | 1 | 1 | 0 |
+| 0 | 0 | 1 | 1 | 2 | 1 |
+| 0 | 1 | 0 | 1 | 2 | 1 |
+| 1 | 0 | 0 | 1 | 2 | 1 |
+| 0 | 1 | 1 | 0 | 2 | 1 |
+| 1 | 0 | 1 | 0 | 2 | 1 |
+| 1 | 1 | 0 | 0 | 2 | 1 |
+| 0 | 1 | 1 | 1 | 3 | 0 |
+| 1 | 1 | 1 | 1 | 4 | 0 |
+
+## Architecture
+
+```
+Layer 1:
+  N1: [1,1,1,1] b=-2  (fires when sum >= 2)
+  N2: [-1,-1,-1,-1] b=2  (fires when sum <= 2)
+
+Layer 2:
+  AND: [1,1] b=-2  (fires when both N1 and N2 fire)
+```
+
+## Parameters
+
+| | |
+|---|---|
+| Inputs | 4 |
+| Outputs | 1 |
+| Neurons | 3 |
+| Layers | 2 |
+| Parameters | 13 |
+| Magnitude | 16 |
+
+## Usage
+
+```python
+from safetensors.torch import load_file
+import torch
+
+w = load_file('model.safetensors')
+
+def exactly2of4(a, b, c, d):
+    inp = torch.tensor([float(a), float(b), float(c), float(d)])
+    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(exactly2of4(0, 0, 1, 1))  # 1
+print(exactly2of4(0, 1, 1, 1))  # 0
+```
+
+## License
+
+MIT

config.json

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+{
+  "name": "threshold-exactly2outof4",
+  "description": "Exactly 2 of 4 inputs high",
+  "inputs": 4,
+  "outputs": 1,
+  "neurons": 3,
+  "layers": 2,
+  "parameters": 13
+}

create_safetensors.py

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+import torch
+from safetensors.torch import save_file
+
+# exactly2: (sum >= 2) AND (sum <= 2)
+weights = {
+    'layer1.weight': torch.tensor([
+        [1.0, 1.0, 1.0, 1.0],   # N1: sum >= 2
+        [-1.0, -1.0, -1.0, -1.0] # N2: sum <= 2
+    ], dtype=torch.float32),
+    'layer1.bias': torch.tensor([-2.0, 2.0], 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 exactly2of4(a, b, c, d):
+    inp = torch.tensor([float(a), float(b), float(c), float(d)])
+    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 exactly2outof4...")
+errors = 0
+for i in range(16):
+    a, b, c, d = (i >> 3) & 1, (i >> 2) & 1, (i >> 1) & 1, i & 1
+    result = exactly2of4(a, b, c, d)
+    expected = 1 if (a + b + c + d) == 2 else 0
+    if result != expected:
+        errors += 1
+        print(f"ERROR: {a}{b}{c}{d} -> {result}, expected {expected}")
+if errors == 0:
+    print("All 16 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 exactly2of4(a, b, c, d, weights):
+    inp = torch.tensor([float(a), float(b), float(c), float(d)])
+    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('exactly2outof4 truth table:')
+    for i in range(16):
+        a, b, c, d = (i >> 3) & 1, (i >> 2) & 1, (i >> 1) & 1, i & 1
+        s = a + b + c + d
+        print(f'  {a}{b}{c}{d} (sum={s}) -> {exactly2of4(a, b, c, d, w)}')