16:1 multiplexer threshold circuit, magnitude 145

README.md

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+---
+license: mit
+tags:
+- pytorch
+- safetensors
+- threshold-logic
+- neuromorphic
+---
+
+# threshold-mux16
+
+16:1 multiplexer. Selects one of 16 data inputs based on 4-bit select signal.
+
+## Function
+
+MUX16(d0..d15, s3,s2,s1,s0) = d[s] where s = 8*s3 + 4*s2 + 2*s1 + s0
+
+## Architecture
+
+```
+d0..d15 (16 data)   s3 s2 s1 s0 (4 select)
+    |                    |
+    +--------------------+
+    |
+    v
+[N0]  d0  AND (s=0000)  ----+
+[N1]  d1  AND (s=0001)  ----|
+[N2]  d2  AND (s=0010)  ----|
+  ...                        +---> [OR] ---> output
+[N14] d14 AND (s=1110)  ----|
+[N15] d15 AND (s=1111)  ----+
+```
+
+## Layer 1 Weights
+
+Each neuron Ni fires when di=1 AND s=i:
+- Weight on di: +1
+- Weight on each select bit: +1 if that bit is 1 in i, else -1
+- Bias: -(1 + popcount(i))
+
+## Parameters
+
+| | |
+|---|---|
+| Inputs | 20 (16 data + 4 select) |
+| Outputs | 1 |
+| Neurons | 17 |
+| Layers | 2 |
+| Parameters | 373 |
+| Magnitude | 145 |
+
+## Usage
+
+```python
+from safetensors.torch import load_file
+import torch
+
+w = load_file('model.safetensors')
+
+def mux16(data, s3, s2, s1, s0):
+    inp = torch.tensor([float(d) for d in data] +
+                       [float(s3), float(s2), float(s1), float(s0)])
+    l1 = (inp @ w['layer1.weight'].T + w['layer1.bias'] >= 0).float()
+    out = (l1 @ w['layer2.weight'].T + w['layer2.bias'] >= 0).float()
+    return int(out.item())
+
+# Select d10 (s=1010)
+data = [0]*16
+data[10] = 1
+print(mux16(data, 1, 0, 1, 0))  # 1
+```
+
+## License
+
+MIT

config.json

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+{
+  "name": "threshold-mux16",
+  "description": "16:1 multiplexer as threshold circuit",
+  "inputs": 20,
+  "outputs": 1,
+  "neurons": 17,
+  "layers": 2,
+  "parameters": 373
+}

create_safetensors.py

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+import torch
+from safetensors.torch import save_file
+
+weights = {}
+
+# Input order: d0..d15, s3, s2, s1, s0 (20 inputs)
+# Layer 1: 16 neurons, each selects di when s = i
+# Layer 2: OR gate
+
+layer1_weights = []
+layer1_biases = []
+
+for i in range(16):
+    w = [0.0] * 20
+    # Data input weight
+    w[i] = 1.0
+    # Select weights: +1 if bit should be 1, -1 if bit should be 0
+    s3_bit = (i >> 3) & 1
+    s2_bit = (i >> 2) & 1
+    s1_bit = (i >> 1) & 1
+    s0_bit = i & 1
+    w[16] = 1.0 if s3_bit else -1.0  # s3
+    w[17] = 1.0 if s2_bit else -1.0  # s2
+    w[18] = 1.0 if s1_bit else -1.0  # s1
+    w[19] = 1.0 if s0_bit else -1.0  # s0
+    # Bias: -(1 + popcount(i))
+    bias = -(1 + bin(i).count('1'))
+    layer1_weights.append(w)
+    layer1_biases.append(bias)
+
+weights['layer1.weight'] = torch.tensor(layer1_weights, dtype=torch.float32)
+weights['layer1.bias'] = torch.tensor(layer1_biases, dtype=torch.float32)
+
+# Layer 2: OR gate
+weights['layer2.weight'] = torch.tensor([[1.0] * 16], dtype=torch.float32)
+weights['layer2.bias'] = torch.tensor([-1.0], dtype=torch.float32)
+
+save_file(weights, 'model.safetensors')
+
+# Verify
+def mux16(data, s3, s2, s1, s0):
+    inp = torch.tensor([float(d) for d in data] + [float(s3), float(s2), float(s1), float(s0)])
+    l1 = (inp @ weights['layer1.weight'].T + weights['layer1.bias'] >= 0).float()
+    out = (l1 @ weights['layer2.weight'].T + weights['layer2.bias'] >= 0).float()
+    return int(out.item())
+
+print("Verifying MUX16...")
+errors = 0
+test_count = 0
+for s in range(16):
+    s3, s2, s1, s0 = (s >> 3) & 1, (s >> 2) & 1, (s >> 1) & 1, s & 1
+    # Test with selected data = 1, others = 0
+    data = [0] * 16
+    data[s] = 1
+    result = mux16(data, s3, s2, s1, s0)
+    if result != 1:
+        errors += 1
+        print(f"ERROR: s={s}, d[{s}]=1 -> {result}, expected 1")
+    test_count += 1
+
+    # Test with selected data = 0
+    data[s] = 0
+    result = mux16(data, s3, s2, s1, s0)
+    if result != 0:
+        errors += 1
+        print(f"ERROR: s={s}, d[{s}]=0 -> {result}, expected 0")
+    test_count += 1
+
+if errors == 0:
+    print(f"All {test_count} test cases passed!")
+else:
+    print(f"FAILED: {errors} errors")
+
+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 mux16(data, s3, s2, s1, s0, weights):
+    """16:1 Multiplexer: returns data[s] where s = 8*s3 + 4*s2 + 2*s1 + s0"""
+    inp = torch.tensor([float(d) for d in data] + [float(s3), float(s2), float(s1), float(s0)])
+    l1 = (inp @ weights['layer1.weight'].T + weights['layer1.bias'] >= 0).float()
+    out = (l1 @ weights['layer2.weight'].T + weights['layer2.bias'] >= 0).float()
+    return int(out.item())
+
+if __name__ == '__main__':
+    w = load_model()
+    print('MUX16 verification:')
+    for s in range(16):
+        s3, s2, s1, s0 = (s >> 3) & 1, (s >> 2) & 1, (s >> 1) & 1, s & 1
+        data = [0] * 16
+        data[s] = 1
+        result = mux16(data, s3, s2, s1, s0, w)
+        print(f'  s={s:2d} ({s3}{s2}{s1}{s0}), d[{s}]=1 -> {result}')