Rename from tiny-mod8-verified

README.md

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+---
+license: mit
+tags:
+- pytorch
+- safetensors
+- threshold-logic
+- neuromorphic
+- modular-arithmetic
+---
+
+# threshold-mod8
+
+Computes Hamming weight mod 8 directly on inputs. Single-layer circuit.
+
+## Circuit
+
+```
+  x₀ x₁ x₂ x₃ x₄ x₅ x₆ x₇
+   │  │  │  │  │  │  │  │
+   │  │  │  │  │  │  │  │
+   w: 1  1  1  1  1  1  1 -7
+   └──┴──┴──┴──┼──┴──┴──┴──┘
+               ▼
+          ┌─────────┐
+          │ b:  0   │
+          └─────────┘
+               │
+               ▼
+           HW mod 8
+```
+
+## Algebraic Insight
+
+Position 8 gets weight 1-8 = -7:
+
+- Positions 1-7: weight +1
+- Position 8: weight -7
+
+```
+HW=0: sum=0 → 0 mod 8
+...
+HW=7: sum=7 → 7 mod 8
+HW=8: sum=0 → 0 mod 8  (reset: 1+1+1+1+1+1+1-7=0)
+```
+
+The only non-trivial case is HW=8, which resets to 0.
+
+## Parameters
+
+| | |
+|---|---|
+| Weights | [1, 1, 1, 1, 1, 1, 1, -7] |
+| Bias | 0 |
+| Total | 9 parameters |
+
+## Usage
+
+```python
+from safetensors.torch import load_file
+import torch
+
+w = load_file('model.safetensors')
+
+def mod8(bits):
+    inputs = torch.tensor([float(b) for b in bits])
+    return int((inputs * w['weight']).sum() + w['bias'])
+```
+
+## Files
+
+```
+threshold-mod8/
+├── model.safetensors
+├── model.py
+├── config.json
+└── README.md
+```
+
+## License
+
+MIT

config.json

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+{
+  "model_type": "threshold_network",
+  "task": "mod8_classification",
+  "architecture": "8 -> 1",
+  "input_size": 8,
+  "output_size": 1,
+  "num_neurons": 1,
+  "num_parameters": 9,
+  "modulus": 8,
+  "activation": "heaviside",
+  "weight_constraints": "integer",
+  "weight_pattern": "[1, 1, 1, 1, 1, 1, 1, -7]",
+  "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 MOD-8 Circuit
+
+A formally verified threshold network computing Hamming weight mod 8.
+Uses the algebraic weight pattern [1, 1, 1, 1, 1, 1, 1, -7].
+"""
+
+import torch
+from safetensors.torch import load_file
+
+
+class ThresholdMod8:
+    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
+
+    @classmethod
+    def from_safetensors(cls, path="model.safetensors"):
+        return cls(load_file(path))
+
+
+if __name__ == "__main__":
+    weights = load_file("model.safetensors")
+    model = ThresholdMod8(weights)
+
+    print("MOD-8 Circuit Tests:")
+    for hw in range(9):
+        bits = [1]*hw + [0]*(8-hw)
+        out = model(bits).item()
+        print(f"HW={hw}: weighted_sum={out:.0f}, HW mod 8 = {hw % 8}")

model.safetensors

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+version https://git-lfs.github.com/spec/v1
+oid sha256:44a0290658bd88ba3c0b3d387c2e159270787c0db94e9ea8745cdeb639c352a6
+size 164