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license: mit
tags:
- pytorch
- safetensors
- threshold-logic
- neuromorphic
- comparison
---
# threshold-lessthan
8-bit less-than comparator. Returns 1 if a < b, 0 otherwise.
## Circuit
```
a0 b0 a1 b1 a2 b2 a3 b3 a4 b4 a5 b5 a6 b6 a7 b7
│ │ 0 │ │ │ │ │ │ │ │ │ │ │ │ │ │
└┬┘│ └┬┘ └┬┘ └┬┘ └┬┘ └┬┘ └┬┘ └┬┘
▼ │ ▼ ▼ ▼ ▼ ▼ ▼ ▼
┌───┐│ ┌───┐ ┌───┐ ┌───┐ ┌───┐ ┌───┐ ┌───┐ ┌───┐
│FS0│┴──│FS1│────│FS2│────│FS3│────│FS4│────│FS5│────│FS6│────│FS7│──►(a<b)
└───┘ └───┘ └───┘ └───┘ └───┘ └───┘ └───┘ └───┘
│ │ │ │ │ │ │ │
▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼
d0 d1 d2 d3 d4 d5 d6 d7
(difference bits unused - only final borrow matters)
```
Uses 8 cascaded full subtractors. The final borrow output indicates a < b.
## Mechanism
The circuit computes a - b using subtraction:
- If a ≥ b: no borrow propagates, result is non-negative
- If a < b: borrow propagates out, indicating underflow
The difference bits (d0-d7) are computed but unused. Only the final borrow matters.
## Truth Table (sample)
| a | b | a < b |
|---|---|-------|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 0 |
| 127 | 128 | 1 |
| 255 | 0 | 0 |
| 0 | 255 | 1 |
| 100 | 100 | 0 |
| 99 | 100 | 1 |
## Full Subtractor Structure
```
a b
│ │
└───┬───┘
▼
┌─────────┐
│ HS1 │
└─────────┘
│ │
d1 b1
│ \
│ bin \
└──┬──┘ \
▼ \
┌─────────┐ \
│ HS2 │ │
└─────────┘ │
│ │ │
d b2 │
│ │
└──┬───┘
▼
┌──────┐
│ OR │
└──────┘
│
▼
bout
```
## Architecture
| Component | Per FS | Total (8 FSs) |
|-----------|--------|---------------|
| Neurons | 9 | 72 |
| Parameters | 27 | 216 |
**Layers: 32** (8 FSs × 4 layers each)
## Comparison Family
| Circuit | Condition | Implementation |
|---------|-----------|----------------|
| **LessThan** | a < b | borrow_out of (a - b) |
| Equal | a = b | NOR of all XOR bits |
| GreaterThan | a > b | LessThan(b, a) |
## Usage
```python
from safetensors.torch import load_file
w = load_file('model.safetensors')
def less_than(a, b):
"""a, b: 8-bit lists [a0..a7] (LSB first)
Returns: 1 if a < b, 0 otherwise"""
# See model.py for full implementation
pass
# Example: 99 < 100?
a = [(99 >> i) & 1 for i in range(8)]
b = [(100 >> i) & 1 for i in range(8)]
result = less_than(a, b) # Returns 1
```
## Files
```
threshold-lessthan/
├── model.safetensors
├── model.py
├── config.json
└── README.md
```
## License
MIT
|