threshold-priorityencoder

8-to-3 priority encoder. Outputs the binary index of the highest-priority active input.

Circuit

  x₀ x₁ x₂ x₃ x₄ x₅ x₆ x₇
   │  │  │  │  │  │  │  │
   └──┴──┴──┴──┼──┴──┴──┴──┘
               │
    ┌──────────┼──────────┐
    │          │          │
    ▼          ▼          ▼
┌──────┐   ┌──────┐   ┌──────┐
│win₀  │...│win₃  │...│win₇  │    Layer 1: Winner detectors
│+1,0..│   │inhibit│   │just  │    (8 neurons)
│b=-1  │   │higher │   │x₇    │
└──────┘   └──────┘   └──────┘
    │          │          │
    └────┬─────┴────┬─────┘
         │          │
    ┌────┴────┐┌────┴────┐
    │  y₀ OR  ││  y₂ OR  │        Layer 2: Output encoding
    │ 1,3,5,7 ││ 4,5,6,7 │        (4 neurons)
    └─────────┘└─────────┘
         │          │
         ▼          ▼
        y₀   y₁   y₂   valid

Mechanism

Winner Detection: Each position has a neuron that fires only when:

1. That input is active (weight +1)
2. No higher-priority input is active (weight -1 on each higher input)

winner₅: fires when x₅=1 AND x₆=0 AND x₇=0
weights: [0, 0, 0, 0, 0, +1, -1, -1]
bias: -1

Output Encoding: The 3-bit output is assembled by OR-ing the appropriate winners:

• y₀ = OR(win₁, win₃, win₅, win₇) — odd indices
• y₁ = OR(win₂, win₃, win₆, win₇) — indices with bit 1 set
• y₂ = OR(win₄, win₅, win₆, win₇) — indices with bit 2 set

Truth Table (samples)

Active inputs	Winner	Output (y₂y₁y₀)	Index
x₀ only	win₀	000	0
x₃ only	win₃	011	3
x₇ only	win₇	111	7
x₀, x₃	win₃	011	3
x₂, x₅, x₆	win₆	110	6
all	win₇	111	7
none	none	000	0*

*valid=0 when no inputs active

Priority Convention

Highest index wins. x₇ has absolute priority over all others.

Input	Priority
x₇	Highest
x₆	...
...	...
x₀	Lowest

Architecture

Layer	Neurons	Function
1	8	Winner detectors
2	4	Output OR gates (y₀, y₁, y₂, valid)

Total: 12 neurons, 96 parameters, 2 layers

The Inhibition Principle

The key insight: each winner neuron is inhibited by all higher-priority inputs.

winner₃ weights: [0, 0, 0, +1, -1, -1, -1, -1]
                          x₃  x₄  x₅  x₆  x₇

If any of x₄-x₇ is active, the negative weight cancels x₃'s contribution.

Usage

from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

def priority_encode(bits):
    """Returns (y2, y1, y0, valid)"""
    # See model.py for full implementation
    pass

# Multiple active: highest wins
bits = [1, 0, 1, 0, 0, 1, 0, 0]  # x0, x2, x5 active
y2, y1, y0, valid = priority_encode(bits)
# Result: (1, 0, 1, 1) = index 5

Files

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

License

MIT