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README.md

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+---
+license: mit
+tags:
+- pytorch
+- safetensors
+- threshold-logic
+- neuromorphic
+- comparison
+---
+
+# threshold-equal
+
+4-bit equality comparator. Returns 1 if a = b, 0 otherwise.
+
+## Circuit
+
+```
+  a0  b0      a1  b1      a2  b2      a3  b3
+   │   │       │   │       │   │       │   │
+   └─┬─┘       └─┬─┘       └─┬─┘       └─┬─┘
+     ▼           ▼           ▼           ▼
+  ┌─────┐     ┌─────┐     ┌─────┐     ┌─────┐
+  │XOR 0│     │XOR 1│     │XOR 2│     │XOR 3│   Layer 1-2
+  └─────┘     └─────┘     └─────┘     └─────┘
+     │           │           │           │
+     └───────────┴─────┬─────┴───────────┘
+                       ▼
+                  ┌─────────┐
+                  │   NOR   │              Layer 3
+                  │ w: -1×4 │
+                  │ b:  0   │
+                  └─────────┘
+                       │
+                       ▼
+                    (a = b)
+```
+
+## Mechanism
+
+1. **XOR each bit pair**: XOR(a_i, b_i) = 1 if bits differ, 0 if same
+2. **NOR all XORs**: Fires only when all XORs are 0 (all bits match)
+
+The NOR gate acts as a "zero detector" - it fires when all its inputs are silent.
+
+## XOR Structure (each)
+
+```
+    a   b
+    │   │
+    ├─┬─┤
+    │ │ │
+    ▼ │ ▼
+┌────┐│┌────┐
+│ OR │││NAND│
+└────┘│└────┘
+    │ │ │
+    └─┼─┘
+      ▼
+  ┌──────┐
+  │ AND  │
+  └──────┘
+      │
+      ▼
+   XOR out
+```
+
+## Truth Table (sample)
+
+| a | b | a = b |
+|---|---|-------|
+| 0 | 0 | 1 |
+| 0 | 1 | 0 |
+| 5 | 5 | 1 |
+| 5 | 10 | 0 |
+| 15 | 15 | 1 |
+| 7 | 8 | 0 |
+
+All 256 input combinations verified correct.
+
+## Architecture
+
+| Component | Neurons | Parameters |
+|-----------|---------|------------|
+| XOR × 4 | 12 | 36 |
+| NOR | 1 | 5 |
+| **Total** | **13** | **41** |
+
+**Layers: 3** (XOR: 2, NOR: 1)
+
+## Comparison Family
+
+| Circuit | Condition | Implementation |
+|---------|-----------|----------------|
+| LessThan | a < b | borrow_out of (a - b) |
+| **Equal** | a = b | NOR of all XOR bits |
+| GreaterThan | a > b | LessThan(b, a) |
+
+## Usage
+
+```python
+from safetensors.torch import load_file
+
+w = load_file('model.safetensors')
+
+def equal(a, b):
+    """a, b: 4-bit lists [a0,a1,a2,a3] (LSB first)
+    Returns: 1 if a == b, 0 otherwise"""
+    # See model.py for full implementation
+    pass
+
+# Example: 7 == 7?
+a = [1, 1, 1, 0]  # 7 in LSB-first
+b = [1, 1, 1, 0]  # 7 in LSB-first
+result = equal(a, b)  # Returns 1
+```
+
+## Files
+
+```
+threshold-equal/
+├── model.safetensors
+├── model.py
+├── config.json
+└── README.md
+```
+
+## License
+
+MIT

config.json

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+{
+  "name": "threshold-equal",
+  "description": "4-bit equality comparator as threshold circuit",
+  "inputs": 8,
+  "outputs": 1,
+  "neurons": 13,
+  "layers": 3,
+  "parameters": 41
+}

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 xor_gate(a, b, w, idx):
+    inp = torch.tensor([float(a), float(b)])
+    l1 = (inp @ w[f'xor{idx}.layer1.weight'].T + w[f'xor{idx}.layer1.bias'] >= 0).float()
+    return int((l1 @ w[f'xor{idx}.layer2.weight'].T + w[f'xor{idx}.layer2.bias'] >= 0).item())
+
+def equal(a, b, weights):
+    """4-bit equality comparator.
+    a, b: lists of 4 bits each (LSB first)
+    Returns: 1 if a == b, 0 otherwise
+    """
+    xors = [xor_gate(a[i], b[i], weights, i) for i in range(4)]
+    xor_vec = torch.tensor([float(x) for x in xors])
+    return int((xor_vec @ weights['nor.weight'].T + weights['nor.bias'] >= 0).item())
+
+if __name__ == '__main__':
+    w = load_model()
+    print('4-bit Equal Comparator')
+    print('a == b tests:')
+    tests = [(0, 0), (0, 1), (5, 5), (5, 10), (15, 15), (7, 8)]
+    for a_val, b_val in tests:
+        a = [(a_val >> i) & 1 for i in range(4)]
+        b = [(b_val >> i) & 1 for i in range(4)]
+        result = equal(a, b, w)
+        print(f'{a_val:2d} == {b_val:2d} = {result}')

model.safetensors

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