threshold-greaterthan

8-bit greater-than comparator. Returns 1 if a > b, 0 otherwise.

Circuit

b0 a0    b1 a1    b2 a2    b3 a3    b4 a4    b5 a5    b6 a6    b7 a7
 │ │ 0    │ │      │ │      │ │      │ │      │ │      │ │      │ │
 └┬┘│     └┬┘      └┬┘      └┬┘      └┬┘      └┬┘      └┬┘      └┬┘
  ▼ │      ▼        ▼        ▼        ▼        ▼        ▼        ▼
┌───┐│  ┌───┐    ┌───┐    ┌───┐    ┌───┐    ┌───┐    ┌───┐    ┌───┐
│FS0│┴──│FS1│────│FS2│────│FS3│────│FS4│────│FS5│────│FS6│────│FS7│──►(a>b)
└───┘   └───┘    └───┘    └───┘    └───┘    └───┘    └───┘    └───┘

Note: inputs are swapped compared to LessThan. Computes b - a.

Mechanism

The circuit computes b - a using subtraction:

• If b ≥ a: no borrow propagates → a ≤ b → output 0
• If b < a: borrow propagates out → a > b → output 1

This is equivalent to LessThan(b, a).

Truth Table (sample)

a	b	a > b
0	0	0
1	0	1
0	1	0
128	127	1
0	255	0
255	0	1
100	100	0
100	99	1

Full Subtractor Structure

        b       a           (note: b first, a second)
        │       │
        └───┬───┘
            ▼
       ┌─────────┐
       │   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	borrow_out of (b - a)

Usage

from safetensors.torch import load_file

w = load_file('model.safetensors')

def greater_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: 100 > 99?
a = [(100 >> i) & 1 for i in range(8)]
b = [(99 >> i) & 1 for i in range(8)]
result = greater_than(a, b)  # Returns 1

Files

threshold-greaterthan/
├── model.safetensors
├── model.py
├── config.json
└── README.md

License

MIT