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---
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license: mit
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tags:
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- pytorch
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- safetensors
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- threshold-logic
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- neuromorphic
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- arithmetic
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---
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# threshold-halfsubtractor
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Subtracts two 1-bit inputs, producing difference and borrow. The subtraction counterpart to the half adder.
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## Circuit
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```
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a b a b
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│ │ │ │
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├───┬───┤ └─┬─┘
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│ │ │ │
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▼ │ ▼ ▼
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┌──────┐│┌──────┐ ┌───────┐
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│ OR │││ NAND │ │ ¬a ∧ b│
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│w:1,1 │││w:-1,-1│ │w:-1,1 │
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│b: -1 │││b: +1 │ │b: -1 │
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└──────┘│└──────┘ └───────┘
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│ │ │ │
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└───┼───┘ │
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▼ │
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┌──────┐ │
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│ AND │ │
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│w: 1,1│ │
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│b: -2 │ │
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└──────┘ │
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│ │
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▼ ▼
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diff borrow
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```
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The diff output uses XOR (2 layers). The borrow output detects when we subtract 1 from 0.
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## Truth Table
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| a | b | diff | borrow |
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|---|---|------|--------|
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| 0 | 0 | 0 | 0 |
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| 0 | 1 | 1 | 1 |
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| 1 | 0 | 1 | 0 |
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| 1 | 1 | 0 | 0 |
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Binary: a - b = diff - (borrow × 2)
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## Mechanism
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**Diff (XOR):** Same as the half adder's sum. The difference bit is 1 when exactly one input is 1.
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**Borrow:** Uses weights [-1, +1] with bias -1. This fires only when a=0 and b=1:
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- a=0, b=0: -0 + 0 - 1 = -1 < 0 → no borrow
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- a=0, b=1: -0 + 1 - 1 = 0 ≥ 0 → borrow
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- a=1, b=0: -1 + 0 - 1 = -2 < 0 → no borrow
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- a=1, b=1: -1 + 1 - 1 = -1 < 0 → no borrow
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The borrow is NOT(a) AND b - we borrow when subtracting 1 from 0.
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## Components
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| Output | Function | Neurons | Layers |
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|--------|----------|---------|--------|
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| diff | XOR(a, b) | 3 | 2 |
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| borrow | ¬a ∧ b | 1 | 1 |
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**Total: 4 neurons, 12 parameters**
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## Contrast with Half Adder
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| Circuit | Output 2 | Function | Weights |
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|---------|----------|----------|---------|
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| HalfAdder | carry | a ∧ b | [1, 1], b=-2 |
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| HalfSubtractor | borrow | ¬a ∧ b | [-1, 1], b=-1 |
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The only difference: borrow has an inhibitory weight on a.
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## Usage
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```python
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from safetensors.torch import load_file
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import torch
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w = load_file('model.safetensors')
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def half_subtractor(a, b):
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inp = torch.tensor([float(a), float(b)])
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# XOR for diff
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l1 = (inp @ w['xor.layer1.weight'].T + w['xor.layer1.bias'] >= 0).float()
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diff = int((l1 @ w['xor.layer2.weight'].T + w['xor.layer2.bias'] >= 0).item())
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# Borrow
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borrow = int((inp @ w['borrow.weight'].T + w['borrow.bias'] >= 0).item())
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return diff, borrow
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```
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## Files
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```
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threshold-halfsubtractor/
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├── model.safetensors
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├── model.py
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├── config.json
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└── README.md
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```
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## License
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MIT
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