threshold-popcount4

4-bit population count. Counts the number of 1 bits in a 4-bit input.

Function

popcount4(a, b, c, d) = binary count of 1 bits

Output [y2, y1, y0] is the 3-bit binary representation of the count (0-4).

Truth Table

a	b	c	d	count	y2	y1	y0
0	0	0	0	0	0	0	0
0	0	0	1	1	0	0	1
0	0	1	1	2	0	1	0
0	1	1	1	3	0	1	1
1	1	1	1	4	1	0	0

Architecture

         a   b   c   d
         |   |   |   |
    +----+---+---+---+----+
    |                     |
Layer 1:                  |
    y2 = (sum >= 4)       |
    ge2 = (sum >= 2)      |
    le3 = (sum <= 3)      |
    XOR(a,b) components   |
    XOR(c,d) components   |
    |                     |
Layer 2:                  |
    y1 = AND(ge2, le3)    |
    xor_ab = XOR(a,b)     |
    xor_cd = XOR(c,d)     |
    |                     |
Layer 3:                  |
    XOR(xor_ab, xor_cd)   |
    components            |
    |                     |
Layer 4:                  |
    y0 = XOR(xor_ab, xor_cd)

• y2 (MSB): 1 when count = 4
• y1: 1 when count is 2 or 3
• y0 (LSB): 1 when count is odd (parity = XOR4)

Parameters

Inputs	4
Outputs	3
Neurons	13
Layers	4
Parameters	53
Magnitude	55

Usage

from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

# See model.py for full implementation
# popcount4(1, 0, 1, 1) returns [0, 1, 1] (count=3 = binary 011)

License

MIT