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README.md

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+---
+license: mit
+tags:
+- pytorch
+- safetensors
+- threshold-logic
+- neuromorphic
+---
+
+# threshold-atmost4outof8
+
+At-most-4-out-of-8 detector. Fires when half or fewer inputs are active. The non-majority detector.
+
+## Circuit
+
+```
+  x₀ x₁ x₂ x₃ x₄ x₅ x₆ x₇
+   │  │  │  │  │  │  │  │
+   └──┴──┴──┴──┼──┴──┴──┴──┘
+               ▼
+          ┌─────────┐
+          │ w: -1×8 │
+          │ b:  +4  │
+          └─────────┘
+               │
+               ▼
+           HW ≤ 4?
+```
+
+## The Majority Complement
+
+This is NOT(Majority):
+
+| HW | Majority (≥5) | AtMost4 (≤4) |
+|----|---------------|--------------|
+| 0-4 | 0 | 1 |
+| 5-8 | 1 | 0 |
+
+Exactly one fires for any input. They partition the input space.
+
+## Includes Ties
+
+| HW | AtMost3 | **AtMost4** | AtMost5 |
+|----|---------|-------------|---------|
+| 3 | 1 | 1 | 1 |
+| 4 | 0 | **1** | 1 |
+| 5 | 0 | 0 | 1 |
+
+AtMost4 is the first in the family to include the tie case (HW = 4).
+
+## Coverage
+
+Fires on more than half of all inputs:
+
+| HW | C(8,k) | AtMost4? |
+|----|--------|----------|
+| 0 | 1 | Yes |
+| 1 | 8 | Yes |
+| 2 | 28 | Yes |
+| 3 | 56 | Yes |
+| 4 | 70 | Yes |
+| 5-8 | 93 | No |
+
+Total: 1 + 8 + 28 + 56 + 70 = **163** of 256 inputs (63.7%).
+
+## Dual of AtLeast4
+
+| Circuit | Condition | Fires on |
+|---------|-----------|----------|
+| AtLeast4 | HW ≥ 4 | 163 inputs |
+| **AtMost4** | HW ≤ 4 | 163 inputs |
+
+Both fire on 163 inputs, but different sets. Their intersection is exactly HW = 4 (70 inputs).
+
+## Parameters
+
+| Component | Value |
+|-----------|-------|
+| Weights | all -1 |
+| Bias | +4 |
+| **Total** | **9 parameters** |
+
+## Usage
+
+```python
+from safetensors.torch import load_file
+import torch
+
+w = load_file('model.safetensors')
+
+def atmost4(bits):
+    inp = torch.tensor([float(b) for b in bits])
+    return int((inp * w['weight']).sum() + w['bias'] >= 0)
+
+# Tie (4 active): included
+print(atmost4([1,1,1,1,0,0,0,0]))  # 1
+
+# Majority (5 active): excluded
+print(atmost4([1,1,1,1,1,0,0,0]))  # 0
+```
+
+## Files
+
+```
+threshold-atmost4outof8/
+├── model.safetensors
+├── model.py
+├── config.json
+└── README.md
+```
+
+## License
+
+MIT

config.json

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+{
+  "name": "threshold-atmost4outof8",
+  "description": "At-most-4-out-of-8 detector as threshold circuit",
+  "inputs": 8,
+  "outputs": 1,
+  "neurons": 1,
+  "layers": 1,
+  "parameters": 9
+}

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 atmost4(bits, weights):
+    """At-most-4-out-of-8: fires when half or fewer inputs are active."""
+    inp = torch.tensor([float(b) for b in bits])
+    return int((inp * weights['weight']).sum() + weights['bias'] >= 0)
+
+if __name__ == '__main__':
+    w = load_model()
+    print('AtMost4OutOf8: HW <= 4')
+    for hw in range(9):
+        bits = [1]*hw + [0]*(8-hw)
+        print(f'HW={hw}: {atmost4(bits, w)}')

model.safetensors

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+version https://git-lfs.github.com/spec/v1
+oid sha256:a3aa78ce3e02ebb13fec291f4aa80813bc4c28f0525d24885d41cd6448c289b5
+size 164