Rename from tiny-Majority-verified

README.md

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+---
+license: mit
+tags:
+- pytorch
+- safetensors
+- threshold-logic
+- neuromorphic
+---
+
+# threshold-majority
+
+Strict majority detector for 8 inputs. Fires when more than half are active.
+
+## Circuit
+
+```
+  x₀ x₁ x₂ x₃ x₄ x₅ x₆ x₇
+   │  │  │  │  │  │  │  │
+   └──┴──┴──┴──┼──┴──┴──┴──┘
+               ▼
+          ┌─────────┐
+          │ w: all 1│
+          │ b:  -5  │
+          └─────────┘
+               │
+               ▼
+           HW ≥ 5?
+```
+
+## Mechanism
+
+- Sum = (number of 1s) - 5
+- Fires when Hamming weight ≥ 5 (more 1s than 0s)
+
+A tie (4-4) doesn't count as majority. You need strictly more than half.
+
+Functionally identical to threshold-5outof8.
+
+## Duality with Minority
+
+| Circuit | Weights | Bias | Fires when |
+|---------|---------|------|------------|
+| **Majority** | all +1 | -5 | HW ≥ 5 |
+| Minority | all -1 | +3 | HW ≤ 3 |
+
+Majority: "enough votes to pass"
+Minority: "not enough votes to block"
+
+These are not complements (they don't sum to 1). The gap at HW=4 belongs to neither.
+
+## Parameters
+
+| | |
+|---|---|
+| Weights | [1, 1, 1, 1, 1, 1, 1, 1] |
+| Bias | -5 |
+| Total | 9 parameters |
+
+## Usage
+
+```python
+from safetensors.torch import load_file
+import torch
+
+w = load_file('model.safetensors')
+
+def majority(bits):
+    inputs = torch.tensor([float(b) for b in bits])
+    return int((inputs * w['weight']).sum() + w['bias'] >= 0)
+```
+
+## Files
+
+```
+threshold-majority/
+├── model.safetensors
+├── model.py
+├── config.json
+└── README.md
+```
+
+## License
+
+MIT

config.json

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+{
+  "model_type": "threshold_network",
+  "task": "majority_gate",
+  "architecture": "8 -> 1",
+  "input_size": 8,
+  "output_size": 1,
+  "num_neurons": 1,
+  "num_parameters": 9,
+  "threshold": 5,
+  "activation": "heaviside",
+  "weight_constraints": "integer",
+  "verification": {
+    "method": "coq_proof",
+    "exhaustive": true,
+    "inputs_tested": 256
+  },
+  "accuracy": {
+    "all_inputs": "256/256",
+    "percentage": 100.0
+  },
+  "github": "https://github.com/CharlesCNorton/coq-circuits"
+}

model.py

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+"""
+Threshold Network for Majority Gate
+
+A formally verified single-neuron threshold network computing 8-bit majority.
+Outputs 1 when 5 or more of the 8 inputs are true (strict majority).
+"""
+
+import torch
+from safetensors.torch import load_file
+
+
+class ThresholdMajority:
+    """
+    Majority gate implemented as a threshold neuron.
+
+    Circuit: output = (sum of inputs + bias >= 0)
+    With all weights=1, bias=-5: fires when hamming weight >= 5.
+    """
+
+    def __init__(self, weights_dict):
+        self.weight = weights_dict['weight']
+        self.bias = weights_dict['bias']
+
+    def __call__(self, bits):
+        inputs = torch.tensor([float(b) for b in bits])
+        weighted_sum = (inputs * self.weight).sum() + self.bias
+        return (weighted_sum >= 0).float()
+
+    @classmethod
+    def from_safetensors(cls, path="model.safetensors"):
+        return cls(load_file(path))
+
+
+def forward(x, weights):
+    """
+    Forward pass with Heaviside activation.
+
+    Args:
+        x: Input tensor of shape [..., 8]
+        weights: Dict with 'weight' and 'bias' tensors
+
+    Returns:
+        1 if majority (5+ of 8) are true, else 0
+    """
+    x = torch.as_tensor(x, dtype=torch.float32)
+    weighted_sum = (x * weights['weight']).sum(dim=-1) + weights['bias']
+    return (weighted_sum >= 0).float()
+
+
+if __name__ == "__main__":
+    weights = load_file("model.safetensors")
+    model = ThresholdMajority(weights)
+
+    print("Majority Gate Tests:")
+    print("-" * 40)
+
+    test_cases = [
+        [0,0,0,0,0,0,0,0],
+        [1,0,0,0,0,0,0,0],
+        [1,1,1,1,0,0,0,0],
+        [1,1,1,1,1,0,0,0],
+        [1,1,1,1,1,1,0,0],
+        [1,1,1,1,1,1,1,1],
+    ]
+
+    for bits in test_cases:
+        hw = sum(bits)
+        out = int(model(bits).item())
+        expected = 1 if hw >= 5 else 0
+        status = "OK" if out == expected else "FAIL"
+        print(f"HW={hw}: Majority({bits}) = {out}  [{status}]")

model.safetensors

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+oid sha256:7d01848d8d9961c12dac0b923a1f92f6d03ac7395cc8957bbc1b24c5aa37094c
+size 164