threshold-3to8decoder

3-to-8 binary decoder. Converts 3-bit binary input to one-hot 8-bit output. A single-layer threshold circuit.

Circuit

       a₂      a₁      a₀
        │       │       │
        ├───────┼───────┤
        │       │       │
    ┌───┴───┬───┴───┬───┴───┐
    │       │       │       │
    ▼       ▼       ▼       ▼
┌──────┐┌──────┐┌──────┐┌──────┐
│  y₀  ││  y₁  ││  y₂  ││ ...  │
│-1,-1,-1││-1,-1,+1││-1,+1,-1││      │
│b:  0 ││b: -1 ││b: -1 ││      │
└──────┘└──────┘└──────┘└──────┘
    │       │       │       │
    ▼       ▼       ▼       ▼
   y₀      y₁      y₂  ... y₇

One-Hot Encoding

Each input value activates exactly one output:

Input	a₂a₁a₀	Output y₀y₁y₂y₃y₄y₅y₆y₇
0	000	10000000
1	001	01000000
2	010	00100000
3	011	00010000
4	100	00001000
5	101	00000100
6	110	00000010
7	111	00000001

Mechanism

Each output yᵢ acts as a "pattern matcher" for input = i:

• Weight +1 for bit positions that should be 1
• Weight -1 for bit positions that should be 0
• Bias = -(number of 1 bits in i)

Example for y₅ (binary 101):

weights: [+1, -1, +1]  (match 1, reject 0, match 1)
bias: -2              (need 2 matches to fire)

When input = 101: sum = 1·1 + (-1)·0 + 1·1 = 2, fires When input = 111: sum = 1·1 + (-1)·1 + 1·1 = 1, doesn't fire

The Matching Principle

The circuit computes "how well does input match pattern i?"

• Perfect match: score = (number of 1s in i)
• One bit wrong: score = (number of 1s in i) - 1

The bias ensures only perfect matches pass.

Weight Patterns

Output	Binary	Weights	Bias
y₀	000	[-1, -1, -1]	0
y₁	001	[-1, -1, +1]	-1
y₂	010	[-1, +1, -1]	-1
y₃	011	[-1, +1, +1]	-2
y₄	100	[+1, -1, -1]	-1
y₅	101	[+1, -1, +1]	-2
y₆	110	[+1, +1, -1]	-2
y₇	111	[+1, +1, +1]	-3

Single-Layer Elegance

Unlike traditional logic (which uses AND, OR, NOT combinations), threshold logic can decode in one layer. Each output neuron directly computes "does input match me?"

Architecture

8 neurons, 32 parameters, 1 layer

All neurons run in parallel - no dependencies.

Usage

from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

def decode(a2, a1, a0):
    inp = torch.tensor([float(a2), float(a1), float(a0)])
    return [int((inp * w[f'y{i}.weight']).sum() + w[f'y{i}.bias'] >= 0)
            for i in range(8)]

# Input 5 -> output 5 is hot
outputs = decode(1, 0, 1)
print(outputs)  # [0, 0, 0, 0, 0, 1, 0, 0]

Files

threshold-3to8decoder/
├── model.safetensors
├── model.py
├── config.json
└── README.md

License

MIT