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README.md

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+---
+license: mit
+tags:
+- pytorch
+- safetensors
+- threshold-logic
+- neuromorphic
+- arithmetic
+- multiplier
+- compressor
+---
+
+# threshold-4to2-compressor
+
+4:2 compressor for high-speed multiplier trees. Reduces 4 input bits plus carry-in to 2 output bits plus carry-out while preserving arithmetic value.
+
+## Circuit
+
+```
+   x      y      z      w      cin
+   │      │      │      │       │
+   └──┬───┴──┬───┴──┬───┘       │
+      │      │      │           │
+      ▼      │      │           │
+   ┌─────┐   │      │           │
+   │XOR  │   │      │           │
+   │(x,y)│   │      │           │
+   └──┬──┘   │      │           │
+      │      │      │           │
+      ▼      ▼      │           │
+   ┌─────────────┐  │           │
+   │  XOR(xy,z)  │  │           │
+   └──────┬──────┘  │           │
+          │         │           │
+          ▼         ▼           │
+       ┌──────────────┐         │
+       │  XOR(xyz,w)  │         │
+       └──────┬───────┘         │
+              │                 │
+              ▼                 ▼
+           ┌─────────────────────┐
+           │    XOR(xyzw, cin)   │───► Sum
+           └─────────────────────┘
+
+   cout = MAJ(x,y,z)     (independent of w, cin)
+   carry = MAJ(XOR(x,y,z), w, cin)
+```
+
+## Function
+
+```
+compress_4to2(x, y, z, w, cin) -> (sum, carry, cout)
+
+Invariant: x + y + z + w + cin = sum + 2*carry + 2*cout
+```
+
+## Truth Table (partial - 32 combinations)
+
+| x | y | z | w | cin | sum | carry | cout | verify |
+|---|---|---|---|-----|-----|-------|------|--------|
+| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0=0 |
+| 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1=1 |
+| 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 2=2 |
+| 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 3=3 |
+| 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 4=4 |
+| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 5=5 |
+
+Input sum range: 0 to 5
+Output encoding: sum + 2*carry + 2*cout (range 0-5)
+
+## Mechanism
+
+The 4:2 compressor is built from two cascaded 3:2 compressors with a twist:
+
+**Stage 1: Compress (x, y, z)**
+- sum1 = x XOR y XOR z
+- cout = MAJ(x, y, z)  ← This goes to next column
+
+**Stage 2: Compress (sum1, w, cin)**
+- sum = sum1 XOR w XOR cin
+- carry = MAJ(sum1, w, cin)  ← This goes to next column
+
+Key insight: The cout is computed early and can propagate horizontally while sum/carry are still being computed.
+
+## Architecture
+
+| Component | Function | Neurons | Layers |
+|-----------|----------|---------|--------|
+| XOR(x,y) | First pair | 3 | 2 |
+| XOR(xy,z) | Add third | 3 | 2 |
+| MAJ(x,y,z) | cout | 1 | 1 |
+| XOR(xyz,w) | Add fourth | 3 | 2 |
+| XOR(xyzw,cin) | sum | 3 | 2 |
+| MAJ(xyz,w,cin) | carry | 1 | 1 |
+
+**Total: 14 neurons**
+
+## Parameters
+
+| | |
+|---|---|
+| Inputs | 5 (x, y, z, w, cin) |
+| Outputs | 3 (sum, carry, cout) |
+| Neurons | 14 |
+| Layers | 8 |
+| Parameters | 44 |
+| Magnitude | 46 |
+
+## Delay Analysis
+
+Critical path for sum: 4 XOR stages = 8 layers
+Critical path for carry: 4 XOR stages + 1 MAJ = 9 layers
+Critical path for cout: 1 MAJ = 1 layer (very fast!)
+
+The early cout enables fast horizontal carry propagation in multiplier arrays.
+
+## Usage
+
+```python
+from safetensors.torch import load_file
+import torch
+
+w = load_file('model.safetensors')
+
+def compress_4to2(x, y, z, w_in, cin):
+    # Implementation details in model.py
+    pass
+
+# Example: sum of 5 bits
+s, carry, cout = compress_4to2(1, 1, 1, 1, 1)
+print(f"1+1+1+1+1 = {s} + 2*{carry} + 2*{cout} = {s + 2*carry + 2*cout}")
+# Output: 1+1+1+1+1 = 1 + 2*1 + 2*1 = 5
+```
+
+## Applications
+
+- Booth multipliers (radix-4)
+- Wallace/Dadda tree reduction
+- FMA (fused multiply-add) units
+- High-performance DSP
+
+## Comparison with 3:2 Compressor
+
+| Property | 3:2 | 4:2 |
+|----------|-----|-----|
+| Inputs | 3 | 5 (4 + cin) |
+| Outputs | 2 | 3 (2 + cout) |
+| Reduction ratio | 3→2 | 4→2 per column |
+| Neurons | 7 | 14 |
+| Tree depth for n bits | O(log₁.₅ n) | O(log₂ n) |
+
+4:2 compressors provide faster reduction in multiplier trees.
+
+## Files
+
+```
+threshold-4to2-compressor/
+├── model.safetensors
+├── model.py
+├── create_safetensors.py
+├── config.json
+└── README.md
+```
+
+## License
+
+MIT

config.json

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+{
+  "name": "threshold-4to2-compressor",
+  "description": "4:2 compressor for high-speed multiplier trees",
+  "inputs": 5,
+  "outputs": 3,
+  "neurons": 14,
+  "layers": 8,
+  "parameters": 44
+}

create_safetensors.py

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+import torch
+from safetensors.torch import save_file
+
+weights = {}
+
+# 4:2 Compressor
+# Inputs: x, y, z, w, cin
+# Outputs: sum, carry, cout
+# Invariant: x + y + z + w + cin = sum + 2*carry + 2*cout
+
+def add_xor(prefix):
+    weights[f'{prefix}.or.weight'] = torch.tensor([[1.0, 1.0]], dtype=torch.float32)
+    weights[f'{prefix}.or.bias'] = torch.tensor([-1.0], dtype=torch.float32)
+    weights[f'{prefix}.nand.weight'] = torch.tensor([[-1.0, -1.0]], dtype=torch.float32)
+    weights[f'{prefix}.nand.bias'] = torch.tensor([1.0], dtype=torch.float32)
+    weights[f'{prefix}.and.weight'] = torch.tensor([[1.0, 1.0]], dtype=torch.float32)
+    weights[f'{prefix}.and.bias'] = torch.tensor([-2.0], dtype=torch.float32)
+
+# XOR chain for sum: x XOR y XOR z XOR w XOR cin
+add_xor('xor_xy')      # XOR(x, y)
+add_xor('xor_xyz')     # XOR(xy, z)
+add_xor('xor_xyzw')    # XOR(xyz, w)
+add_xor('xor_sum')     # XOR(xyzw, cin) -> sum
+
+# MAJ(x, y, z) -> cout (at-least-2-of-3)
+weights['cout.weight'] = torch.tensor([[1.0, 1.0, 1.0]], dtype=torch.float32)
+weights['cout.bias'] = torch.tensor([-2.0], dtype=torch.float32)
+
+# MAJ(xyz, w, cin) -> carry (at-least-2-of-3)
+weights['carry.weight'] = torch.tensor([[1.0, 1.0, 1.0]], dtype=torch.float32)
+weights['carry.bias'] = torch.tensor([-2.0], dtype=torch.float32)
+
+save_file(weights, 'model.safetensors')
+
+def xor2(a, b, prefix):
+    inp = torch.tensor([float(a), float(b)])
+    or_out = int((inp @ weights[f'{prefix}.or.weight'].T + weights[f'{prefix}.or.bias'] >= 0).item())
+    nand_out = int((inp @ weights[f'{prefix}.nand.weight'].T + weights[f'{prefix}.nand.bias'] >= 0).item())
+    l1 = torch.tensor([float(or_out), float(nand_out)])
+    return int((l1 @ weights[f'{prefix}.and.weight'].T + weights[f'{prefix}.and.bias'] >= 0).item())
+
+def compress_4to2(x, y, z, w, cin):
+    # XOR chain for sum
+    xy = xor2(x, y, 'xor_xy')
+    xyz = xor2(xy, z, 'xor_xyz')
+    xyzw = xor2(xyz, w, 'xor_xyzw')
+    sum_out = xor2(xyzw, cin, 'xor_sum')
+
+    # cout = MAJ(x, y, z)
+    inp_cout = torch.tensor([float(x), float(y), float(z)])
+    cout = int((inp_cout @ weights['cout.weight'].T + weights['cout.bias'] >= 0).item())
+
+    # carry = MAJ(xyz, w, cin)
+    inp_carry = torch.tensor([float(xyz), float(w), float(cin)])
+    carry = int((inp_carry @ weights['carry.weight'].T + weights['carry.bias'] >= 0).item())
+
+    return sum_out, carry, cout
+
+print("Verifying 4:2 compressor...")
+errors = 0
+for x in [0, 1]:
+    for y in [0, 1]:
+        for z in [0, 1]:
+            for w in [0, 1]:
+                for cin in [0, 1]:
+                    s, carry, cout = compress_4to2(x, y, z, w, cin)
+                    input_sum = x + y + z + w + cin
+                    output_sum = s + 2 * carry + 2 * cout
+                    if input_sum != output_sum:
+                        errors += 1
+                        print(f"ERROR: {x}+{y}+{z}+{w}+{cin}={input_sum}, but got {output_sum}")
+
+if errors == 0:
+    print("All 32 test cases passed!")
+else:
+    print(f"FAILED: {errors} errors")
+
+print(f"Magnitude: {sum(t.abs().sum().item() for t in weights.values()):.0f}")
+print(f"Parameters: {sum(t.numel() for t in weights.values())}")

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 xor2(a, b, prefix, w):
+    inp = torch.tensor([float(a), float(b)])
+    or_out = int((inp @ w[f'{prefix}.or.weight'].T + w[f'{prefix}.or.bias'] >= 0).item())
+    nand_out = int((inp @ w[f'{prefix}.nand.weight'].T + w[f'{prefix}.nand.bias'] >= 0).item())
+    l1 = torch.tensor([float(or_out), float(nand_out)])
+    return int((l1 @ w[f'{prefix}.and.weight'].T + w[f'{prefix}.and.bias'] >= 0).item())
+
+def compress_4to2(x, y, z, w_in, cin, weights):
+    """4:2 compressor: x+y+z+w+cin = sum + 2*carry + 2*cout."""
+    xy = xor2(x, y, 'xor_xy', weights)
+    xyz = xor2(xy, z, 'xor_xyz', weights)
+    xyzw = xor2(xyz, w_in, 'xor_xyzw', weights)
+    sum_out = xor2(xyzw, cin, 'xor_sum', weights)
+
+    inp_cout = torch.tensor([float(x), float(y), float(z)])
+    cout = int((inp_cout @ weights['cout.weight'].T + weights['cout.bias'] >= 0).item())
+
+    inp_carry = torch.tensor([float(xyz), float(w_in), float(cin)])
+    carry = int((inp_carry @ weights['carry.weight'].T + weights['carry.bias'] >= 0).item())
+
+    return sum_out, carry, cout
+
+if __name__ == '__main__':
+    w = load_model()
+    print('4:2 Compressor selected tests:')
+    print('x y z w cin | sum carry cout | verify')
+    print('------------+----------------+-------')
+    for total in range(6):
+        # Generate a combination with this total
+        for x in [0, 1]:
+            for y in [0, 1]:
+                for z in [0, 1]:
+                    for w_in in [0, 1]:
+                        for cin in [0, 1]:
+                            if x + y + z + w_in + cin == total:
+                                s, carry, cout = compress_4to2(x, y, z, w_in, cin, w)
+                                check = 'OK' if total == s + 2*carry + 2*cout else 'FAIL'
+                                print(f'{x} {y} {z} {w_in}  {cin}  |  {s}    {carry}     {cout}   | {check}')
+                                break
+                    else:
+                        continue
+                    break
+                else:
+                    continue
+                break
+            else:
+                continue
+            break

model.safetensors

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