Exactly 4 of 5 threshold circuit, magnitude 22

README.md

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+---
+license: mit
+tags:
+- pytorch
+- safetensors
+- threshold-logic
+- neuromorphic
+---
+
+# threshold-exactly4outof5
+
+Exactly 4 of 5 inputs high.
+
+## Function
+
+exactly4outof5(a, b, c, d, e) = 1 if (a + b + c + d + e) == 4, else 0
+
+## Truth Table (selected)
+
+| sum | out |
+|-----|-----|
+| 0 | 0 |
+| 1 | 0 |
+| 2 | 0 |
+| 3 | 0 |
+| 4 | 1 |
+| 5 | 0 |
+
+## Architecture
+
+Two layers required (exactly-k is not linearly separable).
+
+**Layer 1:**
+- N1: sum >= 4 (weights [1,1,1,1,1], bias -4)
+- N2: sum <= 4 (weights [-1,-1,-1,-1,-1], bias 4)
+
+**Layer 2:**
+- AND(N1, N2): weights [1,1], bias -2
+
+## Parameters
+
+| | |
+|---|---|
+| Inputs | 5 |
+| Outputs | 1 |
+| Neurons | 3 |
+| Layers | 2 |
+| Parameters | 15 |
+| Magnitude | 22 |
+
+## Usage
+
+```python
+from safetensors.torch import load_file
+import torch
+
+w = load_file('model.safetensors')
+
+def exactly4of5(a, b, c, d, e):
+    inp = torch.tensor([float(a), float(b), float(c), float(d), float(e)])
+    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(exactly4of5(1, 1, 1, 1, 0))  # 1 (sum=4)
+print(exactly4of5(1, 1, 1, 1, 1))  # 0 (sum=5)
+```
+
+## License
+
+MIT

config.json

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+{
+  "name": "threshold-exactly4outof5",
+  "description": "Exactly 4 of 5 inputs high",
+  "inputs": 5,
+  "outputs": 1,
+  "neurons": 3,
+  "layers": 2,
+  "parameters": 15
+}

create_safetensors.py

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+import torch
+from safetensors.torch import save_file
+
+weights = {
+    'layer1.weight': torch.tensor([
+        [1.0, 1.0, 1.0, 1.0, 1.0],   # N1: sum >= 4
+        [-1.0, -1.0, -1.0, -1.0, -1.0]  # N2: sum <= 4
+    ], dtype=torch.float32),
+    'layer1.bias': torch.tensor([-4.0, 4.0], 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 exactly4of5(a, b, c, d, e):
+    inp = torch.tensor([float(a), float(b), float(c), float(d), float(e)])
+    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 exactly4outof5...")
+errors = 0
+for i in range(32):
+    bits = [(i >> j) & 1 for j in range(5)]
+    result = exactly4of5(*bits)
+    expected = 1 if sum(bits) == 4 else 0
+    if result != expected:
+        errors += 1
+        print(f"ERROR: {bits} -> {result}, expected {expected}")
+if errors == 0:
+    print("All 32 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 exactly4of5(a, b, c, d, e, weights):
+    inp = torch.tensor([float(a), float(b), float(c), float(d), float(e)])
+    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('exactly4outof5 selected outputs:')
+    for s in range(6):
+        bits = [(1 if j < s else 0) for j in range(5)]
+        print(f'  sum={s}: {bits} -> {exactly4of5(*bits, w)}')