4-bit left shift, magnitude 7

README.md

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+---
+license: mit
+tags:
+- pytorch
+- safetensors
+- threshold-logic
+- neuromorphic
+---
+
+# threshold-shiftleft4
+
+4-bit logical left shift by 1 bit.
+
+## Function
+
+shiftleft4(a3, a2, a1, a0) = [a2, a1, a0, 0]
+
+MSB (a3) is discarded, 0 shifts in at LSB.
+
+## Examples
+
+| Input | Output |
+|-------|--------|
+| 0001 | 0010 |
+| 0101 | 1010 |
+| 1000 | 0000 |
+| 1111 | 1110 |
+
+## Architecture
+
+Single layer with 4 neurons copying bits to shifted positions.
+
+| Output | Source | Weights [a3,a2,a1,a0] | Bias |
+|--------|--------|------------------------|------|
+| y3 | a2 | [0, 1, 0, 0] | -1 |
+| y2 | a1 | [0, 0, 1, 0] | -1 |
+| y1 | a0 | [0, 0, 0, 1] | -1 |
+| y0 | 0 | [0, 0, 0, 0] | -1 |
+
+## Parameters
+
+| | |
+|---|---|
+| Inputs | 4 |
+| Outputs | 4 |
+| Neurons | 4 |
+| Layers | 1 |
+| Parameters | 8 |
+| Magnitude | 7 |
+
+## License
+
+MIT

config.json

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+{
+  "name": "threshold-shiftleft4",
+  "description": "4-bit left shift by 1",
+  "inputs": 4,
+  "outputs": 4,
+  "neurons": 4,
+  "layers": 1,
+  "parameters": 8
+}

create_safetensors.py

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+import torch
+from safetensors.torch import save_file
+
+weights = {}
+
+# Input order: [a3, a2, a1, a0]
+# Left shift: output = [a2, a1, a0, 0]
+
+# y3 = a2
+weights['y3.weight'] = torch.tensor([[0.0, 1.0, 0.0, 0.0]], dtype=torch.float32)
+weights['y3.bias'] = torch.tensor([-1.0], dtype=torch.float32)
+
+# y2 = a1
+weights['y2.weight'] = torch.tensor([[0.0, 0.0, 1.0, 0.0]], dtype=torch.float32)
+weights['y2.bias'] = torch.tensor([-1.0], dtype=torch.float32)
+
+# y1 = a0
+weights['y1.weight'] = torch.tensor([[0.0, 0.0, 0.0, 1.0]], dtype=torch.float32)
+weights['y1.bias'] = torch.tensor([-1.0], dtype=torch.float32)
+
+# y0 = 0 (constant)
+weights['y0.weight'] = torch.tensor([[0.0, 0.0, 0.0, 0.0]], dtype=torch.float32)
+weights['y0.bias'] = torch.tensor([-1.0], dtype=torch.float32)
+
+save_file(weights, 'model.safetensors')
+
+# Verify
+def shiftleft4(a3, a2, a1, a0):
+    inp = torch.tensor([float(a3), float(a2), float(a1), float(a0)])
+    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 shiftleft4...")
+errors = 0
+for i in range(16):
+    a3, a2, a1, a0 = (i >> 3) & 1, (i >> 2) & 1, (i >> 1) & 1, i & 1
+    result = shiftleft4(a3, a2, a1, a0)
+    expected = [a2, a1, a0, 0]
+    if result != expected:
+        errors += 1
+        print(f"ERROR: {a3}{a2}{a1}{a0} -> {result}, expected {expected}")
+
+if errors == 0:
+    print("All 16 test cases passed!")
+
+mag = sum(t.abs().sum().item() for t in weights.values())
+print(f"Magnitude: {mag:.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 shiftleft4(a3, a2, a1, a0, w):
+    """Left shift by 1 bit. MSB is lost, 0 shifts in at LSB."""
+    inp = torch.tensor([float(a3), float(a2), float(a1), float(a0)])
+    return [int((inp @ w[f'y{i}.weight'].T + w[f'y{i}.bias'] >= 0).item()) for i in [3,2,1,0]]
+
+if __name__ == '__main__':
+    w = load_model()
+    print('shiftleft4 examples:')
+    for val in [0b0001, 0b0101, 0b1000, 0b1111]:
+        a3, a2, a1, a0 = (val >> 3) & 1, (val >> 2) & 1, (val >> 1) & 1, val & 1
+        result = shiftleft4(a3, a2, a1, a0, w)
+        print(f'  {a3}{a2}{a1}{a0} << 1 = {"".join(map(str, result))}')