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README.md

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+---
+license: mit
+tags:
+- pytorch
+- safetensors
+- threshold-logic
+- neuromorphic
+---
+
+# threshold-atmost2outof8
+
+At-most-2-out-of-8 detector. Fires when two or fewer inputs are active. The error-tolerance bound.
+
+## Circuit
+
+```
+  x₀ x₁ x₂ x₃ x₄ x₅ x₆ x₇
+   │  │  │  │  │  │  │  │
+   └──┴──┴──┴──┼──┴──┴──┴──┘
+               ▼
+          ┌─────────┐
+          │ w: -1×8 │
+          │ b:  +2  │
+          └─────────┘
+               │
+               ▼
+           HW ≤ 2?
+```
+
+## The Double-Error Budget
+
+This circuit allows:
+
+- Zero active inputs (silence)
+- One active input (single event)
+- Two active inputs (pair/double event)
+
+Three or more is considered "too many."
+
+## Mechanism
+
+```
+sum = -HW + 2
+```
+
+| HW | Sum | Output |
+|----|-----|--------|
+| 0 | +2 | 1 |
+| 1 | +1 | 1 |
+| 2 | 0 | 1 |
+| 3 | -1 | 0 |
+| 4+ | < -1 | 0 |
+
+The bias of +2 grants a budget of two active inputs.
+
+## Error Detection Context
+
+In coding theory:
+
+- A code with minimum distance d can detect d-1 errors
+- AtMost2 accepts patterns with ≤2 bit flips from all-zeros
+- Useful for validating that corruption is within correctable limits
+
+| Scenario | This circuit |
+|----------|--------------|
+| No errors | Pass |
+| Single-bit error | Pass |
+| Double-bit error | Pass |
+| Triple+ error | Fail |
+
+## Dual of AtLeast6
+
+| Circuit | Condition | Sparse/Dense |
+|---------|-----------|--------------|
+| AtLeast6 | HW ≥ 6 | Dense |
+| **AtMost2** | HW ≤ 2 | Sparse |
+
+Bitwise NOT maps AtMost2 inputs to AtLeast6 inputs.
+
+## Coverage
+
+| HW | C(8,k) | AtMost2? |
+|----|--------|----------|
+| 0 | 1 | Yes |
+| 1 | 8 | Yes |
+| 2 | 28 | Yes |
+| 3-8 | 219 | No |
+
+Fires on 1 + 8 + 28 = **37** of 256 inputs (14.5%).
+
+## Parameters
+
+| Component | Value |
+|-----------|-------|
+| Weights | all -1 |
+| Bias | +2 |
+| **Total** | **9 parameters** |
+
+## Usage
+
+```python
+from safetensors.torch import load_file
+import torch
+
+w = load_file('model.safetensors')
+
+def atmost2(bits):
+    inp = torch.tensor([float(b) for b in bits])
+    return int((inp * w['weight']).sum() + w['bias'] >= 0)
+
+# Double event: allowed
+print(atmost2([1,0,0,0,1,0,0,0]))  # 1
+
+# Triple event: rejected
+print(atmost2([1,0,0,1,1,0,0,0]))  # 0
+```
+
+## Files
+
+```
+threshold-atmost2outof8/
+├── model.safetensors
+├── model.py
+├── config.json
+└── README.md
+```
+
+## License
+
+MIT

config.json

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+{
+  "name": "threshold-atmost2outof8",
+  "description": "At-most-2-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 atmost2(bits, weights):
+    """At-most-2-out-of-8: fires when 0, 1, or 2 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('AtMost2OutOf8 truth table:')
+    for hw in range(9):
+        bits = [1]*hw + [0]*(8-hw)
+        result = atmost2(bits, w)
+        print(f'HW={hw}: {result}')

model.safetensors

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+version https://git-lfs.github.com/spec/v1
+oid sha256:d0f31cb8e47c2c4efedd3551f5df6d3bc3ff16bf73ec97e7ccdbea9e67b0c071
+size 164