1-bit less-than-or-equal comparator, magnitude 2

README.md

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+---
+license: mit
+tags:
+- pytorch
+- safetensors
+- threshold-logic
+- neuromorphic
+---
+
+# threshold-lessthanorequal
+
+1-bit less-than-or-equal comparator. Outputs 1 when a <= b.
+
+## Function
+
+lte(a, b) = 1 if a <= b, else 0
+
+Equivalent to: NOT(a) OR b (implication)
+
+## Truth Table
+
+| a | b | a <= b |
+|---|---|--------|
+| 0 | 0 | 1 |
+| 0 | 1 | 1 |
+| 1 | 0 | 0 |
+| 1 | 1 | 1 |
+
+## Architecture
+
+Single neuron: weights [-1, 1], bias 0
+
+Fires when: -a + b >= 0, i.e., b >= a
+
+## Parameters
+
+| | |
+|---|---|
+| Inputs | 2 |
+| Outputs | 1 |
+| Neurons | 1 |
+| Layers | 1 |
+| Parameters | 3 |
+| Magnitude | 2 |
+
+## Usage
+
+```python
+from safetensors.torch import load_file
+import torch
+
+w = load_file('model.safetensors')
+
+def lte(a, b):
+    inp = torch.tensor([float(a), float(b)])
+    return int((inp @ w['neuron.weight'].T + w['neuron.bias'] >= 0).item())
+
+print(lte(0, 1))  # 1
+print(lte(1, 0))  # 0
+```
+
+## License
+
+MIT

config.json

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+{
+  "name": "threshold-lessthanorequal",
+  "description": "1-bit less-than-or-equal comparator",
+  "inputs": 2,
+  "outputs": 1,
+  "neurons": 1,
+  "layers": 1,
+  "parameters": 3
+}

create_safetensors.py

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+import torch
+from safetensors.torch import save_file
+
+# a <= b is equivalent to -a + b >= 0
+weights = {
+    'neuron.weight': torch.tensor([[-1.0, 1.0]], dtype=torch.float32),
+    'neuron.bias': torch.tensor([0.0], dtype=torch.float32)
+}
+save_file(weights, 'model.safetensors')
+
+def lte(a, b):
+    inp = torch.tensor([float(a), float(b)])
+    return int((inp @ weights['neuron.weight'].T + weights['neuron.bias'] >= 0).item())
+
+print("Verifying lessthanorequal...")
+errors = 0
+for a in [0, 1]:
+    for b in [0, 1]:
+        result = lte(a, b)
+        expected = 1 if a <= b else 0
+        if result != expected:
+            errors += 1
+            print(f"ERROR: {a} <= {b} -> {result}, expected {expected}")
+if errors == 0:
+    print("All 4 test cases passed!")
+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 lte(a, b, weights):
+    inp = torch.tensor([float(a), float(b)])
+    return int((inp @ weights['neuron.weight'].T + weights['neuron.bias'] >= 0).item())
+
+if __name__ == '__main__':
+    w = load_model()
+    print('lessthanorequal truth table:')
+    for a in [0, 1]:
+        for b in [0, 1]:
+            print(f'  {a} <= {b} -> {lte(a, b, w)}')