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:
- That input is active (weight +1)
- 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
1from safetensors.torch import load_file
2import torch
3
4w = load_file('model.safetensors')
5
6def priority_encode(bits):
7 """Returns (y2, y1, y0, valid)"""
8 # See model.py for full implementation
9 pass
10
11# Multiple active: highest wins
12bits = [1, 0, 1, 0, 0, 1, 0, 0] # x0, x2, x5 active
13y2, y1, y0, valid = priority_encode(bits)
14# Result: (1, 0, 1, 1) = index 5
Files
threshold-priorityencoder/
├── model.safetensors
├── model.py
├── config.json
└── README.md
License
MIT
