Add weighted threshold circuit

1 neuron, 1 layer, 5 parameters, magnitude 16.

.gitattributes

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+*.safetensors filter=lfs diff=lfs merge=lfs -text

README.md

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+---
+license: mit
+tags:
+- pytorch
+- safetensors
+- threshold-logic
+- neuromorphic
+- weighted-voting
+---
+
+# threshold-weighted
+
+Weighted threshold function demonstrating non-uniform input weights.
+
+## Function
+
+y = 1 iff 4·x3 + 3·x2 + 2·x1 + 1·x0 >= 6
+
+Each input has a different "voting power":
+- x3: weight 4 (most influential)
+- x2: weight 3
+- x1: weight 2
+- x0: weight 1 (least influential)
+
+Maximum weighted sum = 10, threshold = 6 (weighted majority).
+
+## Truth Table (selected rows)
+
+| x3 | x2 | x1 | x0 | w_sum | y |
+|----|----|----|-----|-------|---|
+| 0 | 0 | 0 | 0 | 0 | 0 |
+| 0 | 1 | 1 | 1 | 6 | **1** |
+| 1 | 0 | 0 | 0 | 4 | 0 |
+| 1 | 0 | 1 | 0 | 6 | **1** |
+| 1 | 1 | 0 | 0 | 7 | **1** |
+| 1 | 1 | 1 | 1 | 10 | **1** |
+
+Note: x3 alone (weight 4) isn't enough, but x3 + x1 (weight 6) passes.
+
+## Architecture
+
+Single threshold neuron:
+
+```
+x3 ──(×4)──┐
+x2 ──(×3)──┼──► Σ ──► (≥6?) ──► y
+x1 ──(×2)──┤
+x0 ──(×1)──┘
+```
+
+## Parameters
+
+| | |
+|---|---|
+| Inputs | 4 |
+| Outputs | 1 |
+| Neurons | 1 |
+| Layers | 1 |
+| Parameters | 5 |
+| Magnitude | 16 |
+
+## Theory
+
+This is the fundamental building block of threshold logic. Any linearly separable Boolean function can be computed by a single weighted threshold neuron. Non-linearly-separable functions (like XOR) require multiple layers.
+
+The general form: y = 1 iff Σ(wi·xi) >= θ
+
+## Applications
+
+- Weighted voting systems
+- Credit scoring
+- Risk assessment
+- Neural network layers
+
+## Usage
+
+```python
+from safetensors.torch import load_file
+import torch
+
+w = load_file('model.safetensors')
+
+def weighted(x3, x2, x1, x0):
+    inp = torch.tensor([float(x3), float(x2), float(x1), float(x0)])
+    return int((inp @ w['y.weight'].T + w['y.bias'] >= 0).item())
+
+# weighted(1, 0, 1, 0) = 1  # 4+2=6 >= 6
+# weighted(1, 0, 0, 1) = 0  # 4+1=5 < 6
+```
+
+## License
+
+MIT

config.json

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+{
+  "name": "threshold-weighted",
+  "description": "Weighted threshold function (4,3,2,1 >= 6)",
+  "inputs": 4,
+  "outputs": 1,
+  "neurons": 1,
+  "layers": 1,
+  "parameters": 5
+}

create_safetensors.py

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+import torch
+from safetensors.torch import save_file
+
+weights = {}
+
+# Weighted Threshold Function
+# Inputs: x3, x2, x1, x0 with weights 4, 3, 2, 1
+# Output: y = 1 iff 4*x3 + 3*x2 + 2*x1 + 1*x0 >= 6
+#
+# This represents weighted voting where different inputs have different influence.
+# Maximum sum = 4+3+2+1 = 10
+# Threshold = 6 (need majority of weighted votes)
+#
+# Single neuron implementation!
+
+weights['y.weight'] = torch.tensor([[4.0, 3.0, 2.0, 1.0]], dtype=torch.float32)
+weights['y.bias'] = torch.tensor([-6.0], dtype=torch.float32)
+
+save_file(weights, 'model.safetensors')
+
+def weighted_threshold(x3, x2, x1, x0):
+    inp = torch.tensor([float(x3), float(x2), float(x1), float(x0)])
+    y = int((inp @ weights['y.weight'].T + weights['y.bias'] >= 0).item())
+    return y
+
+def reference(x3, x2, x1, x0):
+    weighted_sum = 4*x3 + 3*x2 + 2*x1 + 1*x0
+    return 1 if weighted_sum >= 6 else 0
+
+print("Verifying Weighted Threshold (4,3,2,1 >= 6)...")
+errors = 0
+for i in range(16):
+    x3, x2, x1, x0 = (i >> 3) & 1, (i >> 2) & 1, (i >> 1) & 1, i & 1
+    result = weighted_threshold(x3, x2, x1, x0)
+    expected = reference(x3, x2, x1, x0)
+    if result != expected:
+        errors += 1
+        print(f"ERROR: ({x3},{x2},{x1},{x0}) -> {result}, expected {expected}")
+
+if errors == 0:
+    print("All 16 test cases passed!")
+else:
+    print(f"FAILED: {errors} errors")
+
+print("\nTruth Table:")
+print("x3 x2 x1 x0 | w_sum | y")
+print("-" * 26)
+for i in range(16):
+    x3, x2, x1, x0 = (i >> 3) & 1, (i >> 2) & 1, (i >> 1) & 1, i & 1
+    y = weighted_threshold(x3, x2, x1, x0)
+    ws = 4*x3 + 3*x2 + 2*x1 + 1*x0
+    print(f" {x3}  {x2}  {x1}  {x0}  |   {ws:2d}  | {y}")
+
+mag = sum(t.abs().sum().item() for t in weights.values())
+print(f"\nMagnitude: {mag:.0f}")
+print(f"Parameters: {sum(t.numel() for t in weights.values())}")
+print(f"Neurons: {len([k for k in weights.keys() if 'weight' in k])}")

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 weighted_threshold(x3, x2, x1, x0, weights):
+    """Weighted threshold: 4*x3 + 3*x2 + 2*x1 + 1*x0 >= 6."""
+    inp = torch.tensor([float(x3), float(x2), float(x1), float(x0)])
+    y = int((inp @ weights['y.weight'].T + weights['y.bias'] >= 0).item())
+    return y
+
+if __name__ == '__main__':
+    w = load_model()
+    print('Weighted Threshold (weights: 4,3,2,1, threshold: 6):')
+    for i in range(16):
+        x3, x2, x1, x0 = (i >> 3) & 1, (i >> 2) & 1, (i >> 1) & 1, i & 1
+        y = weighted_threshold(x3, x2, x1, x0, w)
+        ws = 4*x3 + 3*x2 + 2*x1 + 1*x0
+        print(f'  {x3}{x2}{x1}{x0} (sum={ws:2d}) -> {y}')

model.safetensors

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+version https://git-lfs.github.com/spec/v1
+oid sha256:baf960db67b51595173a3ee0dbc62325a01c1cbc699b389ca8234cf40e26b192
+size 156