threshold-winnertakeall

4-input Winner-Take-All network. A single active input "wins" and produces output. Ties produce no winner.

Circuit

   x₀      x₁      x₂      x₃
    │       │       │       │
    ├───────┼───────┼───────┤
    │       │       │       │
    ▼       ▼       ▼       ▼
┌──────┐┌──────┐┌──────┐┌──────┐
│  y₀  ││  y₁  ││  y₂  ││  y₃  │
│+1 -1 ││-1 +1 ││-1 -1 ││-1 -1 │
│-1 -1 ││-1 -1 ││+1 -1 ││-1 +1 │
│b: -1 ││b: -1 ││b: -1 ││b: -1 │
└──────┘└──────┘└──────┘└──────┘
    │       │       │       │
    ▼       ▼       ▼       ▼
   y₀      y₁      y₂      y₃

Competitive Dynamics

Each output neuron has:

• +1 weight for its own input (self-excitation)
• -1 weight for all other inputs (lateral inhibition)
• -1 bias (requires activation to fire)

This creates competition: each neuron tries to fire, but activity from others suppresses it.

Truth Table

Inputs	Outputs	Interpretation
0000	0000	No input, no winner
1000	1000	x₀ wins
0100	0100	x₁ wins
0010	0010	x₂ wins
0001	0001	x₃ wins
1100	0000	Tie - no winner
1010	0000	Tie - no winner
1111	0000	All active - no winner

The Inhibition Principle

For y₀ to fire:

sum = (+1)·x₀ + (-1)·x₁ + (-1)·x₂ + (-1)·x₃ - 1
    = x₀ - x₁ - x₂ - x₃ - 1

This fires only when x₀=1 and all others=0:

• x₀=1, others=0: sum = 1 - 0 - 0 - 0 - 1 = 0 ≥ 0 ✓
• x₀=1, x₁=1: sum = 1 - 1 - 0 - 0 - 1 = -1 < 0 ✗

Exactly-One Detection

WTA is equivalent to "Exactly-1-of-4 with position encoding":

HW	WTA Output
0	0000
1	One-hot (winner)
2+	0000 (tie)

Biological Analogy

This mimics lateral inhibition in neural circuits:

• Retinal ganglion cells compete via inhibitory interneurons
• The strongest signal suppresses neighbors
• Sharpens contrast and selects dominant features

Architecture

4 neurons, 20 parameters, 1 layer

All neurons compute in parallel. No recurrence needed for binary inputs.

Usage

from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

def wta(inputs):
    inp = torch.tensor([float(x) for x in inputs])
    return [int((inp * w[f'y{i}.weight']).sum() + w[f'y{i}.bias'] >= 0)
            for i in range(4)]

print(wta([0,1,0,0]))  # [0, 1, 0, 0] - x1 wins
print(wta([1,1,0,0]))  # [0, 0, 0, 0] - tie

Files

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

License

MIT