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README.md

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+---
+license: mit
+tags:
+- pytorch
+- safetensors
+- threshold-logic
+- neuromorphic
+- prefix
+- parallel
+---
+
+# threshold-prefix-or
+
+4-bit parallel prefix OR operation. Computes running OR from MSB to each position. Used in leading-one detection and any-ones-above detection.
+
+## Circuit
+
+```
+    x3      x2      x1      x0
+     │       │       │       │
+     ▼       ▼       ▼       ▼
+   ┌───┐   ┌───┐   ┌───┐   ┌───┐
+   │y3 │   │y2 │   │y1 │   │y0 │
+   │>=1│   │>=1│   │>=1│   │>=1│
+   └───┘   └───┘   └───┘   └───┘
+     │       │       │       │
+     ▼       ▼       ▼       ▼
+   (x3)  (x3|x2) (x3|x2|x1) (all)
+```
+
+## Function
+
+```
+prefix_or(x3, x2, x1, x0) -> (y3, y2, y1, y0)
+
+y3 = x3
+y2 = x3 OR x2
+y1 = x3 OR x2 OR x1
+y0 = x3 OR x2 OR x1 OR x0
+```
+
+Each output yi is the OR of all inputs from x3 down to xi.
+
+## Truth Table (selected)
+
+| x3 x2 x1 x0 | y3 y2 y1 y0 | Meaning |
+|-------------|-------------|---------|
+| 0 0 0 0 | 0 0 0 0 | All zeros |
+| 0 0 0 1 | 0 0 0 1 | Only LSB set |
+| 0 0 1 0 | 0 0 1 1 | First one at pos 1 |
+| 0 1 0 0 | 0 1 1 1 | First one at pos 2 |
+| 1 0 0 0 | 1 1 1 1 | First one at MSB |
+| 1 1 1 1 | 1 1 1 1 | All ones |
+| 1 0 1 0 | 1 1 1 1 | Mixed pattern |
+
+## Mechanism
+
+**Single-layer parallel implementation:**
+
+| Output | Condition | Weights | Bias |
+|--------|-----------|---------|------|
+| y3 | x3 >= 1 | [1,0,0,0] | -1 |
+| y2 | x3 + x2 >= 1 | [1,1,0,0] | -1 |
+| y1 | x3 + x2 + x1 >= 1 | [1,1,1,0] | -1 |
+| y0 | x3 + x2 + x1 + x0 >= 1 | [1,1,1,1] | -1 |
+
+All use bias -1 (fires when at least one relevant input is 1).
+
+## Parameters
+
+| | |
+|---|---|
+| Inputs | 4 |
+| Outputs | 4 |
+| Neurons | 4 |
+| Layers | 1 |
+| Parameters | 20 |
+| Magnitude | 14 |
+
+## Applications
+
+- **Leading-one detection:** Transition from 0→1 in output marks MSB position
+- **Any-bit-set prefix:** y_i = 1 means some bit from MSB to position i is set
+- **Carry kill detection:** In adders, prefix-OR of "kill" signals
+
+## Usage
+
+```python
+from safetensors.torch import load_file
+import torch
+
+w = load_file('model.safetensors')
+
+def prefix_or(x3, x2, x1, x0):
+    inp = torch.tensor([float(x3), float(x2), float(x1), float(x0)])
+    y3 = int((inp @ w['y3.weight'].T + w['y3.bias'] >= 0).item())
+    y2 = int((inp @ w['y2.weight'].T + w['y2.bias'] >= 0).item())
+    y1 = int((inp @ w['y1.weight'].T + w['y1.bias'] >= 0).item())
+    y0 = int((inp @ w['y0.weight'].T + w['y0.bias'] >= 0).item())
+    return y3, y2, y1, y0
+
+print(prefix_or(0, 0, 1, 0))  # (0, 0, 1, 1)
+print(prefix_or(1, 0, 0, 0))  # (1, 1, 1, 1)
+```
+
+## License
+
+MIT

config.json

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+{
+  "name": "threshold-prefix-or",
+  "description": "4-bit parallel prefix OR operation",
+  "inputs": 4,
+  "outputs": 4,
+  "neurons": 4,
+  "layers": 1,
+  "parameters": 20
+}

create_safetensors.py

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+import torch
+from safetensors.torch import save_file
+
+weights = {}
+
+# y3 = x3 (at least 1 of [x3])
+weights['y3.weight'] = torch.tensor([[1.0, 0.0, 0.0, 0.0]], dtype=torch.float32)
+weights['y3.bias'] = torch.tensor([-1.0], dtype=torch.float32)
+
+# y2 = x3 OR x2 (at least 1 of [x3,x2])
+weights['y2.weight'] = torch.tensor([[1.0, 1.0, 0.0, 0.0]], dtype=torch.float32)
+weights['y2.bias'] = torch.tensor([-1.0], dtype=torch.float32)
+
+# y1 = x3 OR x2 OR x1
+weights['y1.weight'] = torch.tensor([[1.0, 1.0, 1.0, 0.0]], dtype=torch.float32)
+weights['y1.bias'] = torch.tensor([-1.0], dtype=torch.float32)
+
+# y0 = x3 OR x2 OR x1 OR x0
+weights['y0.weight'] = torch.tensor([[1.0, 1.0, 1.0, 1.0]], dtype=torch.float32)
+weights['y0.bias'] = torch.tensor([-1.0], dtype=torch.float32)
+
+save_file(weights, 'model.safetensors')
+
+def prefix_or(x3, x2, x1, x0):
+    inp = torch.tensor([float(x3), float(x2), float(x1), float(x0)])
+    y3 = int((inp @ weights['y3.weight'].T + weights['y3.bias'] >= 0).item())
+    y2 = int((inp @ weights['y2.weight'].T + weights['y2.bias'] >= 0).item())
+    y1 = int((inp @ weights['y1.weight'].T + weights['y1.bias'] >= 0).item())
+    y0 = int((inp @ weights['y0.weight'].T + weights['y0.bias'] >= 0).item())
+    return y3, y2, y1, y0
+
+print("Verifying prefix-or...")
+errors = 0
+for i in range(16):
+    x3, x2, x1, x0 = (i >> 3) & 1, (i >> 2) & 1, (i >> 1) & 1, i & 1
+    y3, y2, y1, y0 = prefix_or(x3, x2, x1, x0)
+    exp_y3 = x3
+    exp_y2 = x3 | x2
+    exp_y1 = x3 | x2 | x1
+    exp_y0 = x3 | x2 | x1 | x0
+    if (y3, y2, y1, y0) != (exp_y3, exp_y2, exp_y1, exp_y0):
+        errors += 1
+if errors == 0:
+    print("All 16 test cases passed!")
+else:
+    print(f"FAILED: {errors} errors")
+print(f"Magnitude: {sum(t.abs().sum().item() for t in weights.values()):.0f}")

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 prefix_or(x3, x2, x1, x0, w):
+    inp = torch.tensor([float(x3), float(x2), float(x1), float(x0)])
+    y3 = int((inp @ w['y3.weight'].T + w['y3.bias'] >= 0).item())
+    y2 = int((inp @ w['y2.weight'].T + w['y2.bias'] >= 0).item())
+    y1 = int((inp @ w['y1.weight'].T + w['y1.bias'] >= 0).item())
+    y0 = int((inp @ w['y0.weight'].T + w['y0.bias'] >= 0).item())
+    return y3, y2, y1, y0
+
+if __name__ == '__main__':
+    w = load_model()
+    print('Prefix-OR selected tests:')
+    for i in [0b0000, 0b0001, 0b0010, 0b0100, 0b1000, 0b1111]:
+        x3, x2, x1, x0 = (i >> 3) & 1, (i >> 2) & 1, (i >> 1) & 1, i & 1
+        y3, y2, y1, y0 = prefix_or(x3, x2, x1, x0, w)
+        print(f'{x3}{x2}{x1}{x0} -> {y3}{y2}{y1}{y0}')

model.safetensors

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+oid sha256:c6b9ad2e7e465c9072afabbb5b75d29573cf77ff1f53f100436888b0477f3633
+size 592