threshold-minority

Sparse activation detector. Fires when few inputs are active (3 or fewer of 8).

Circuit

  x₀ x₁ x₂ x₃ x₄ x₅ x₆ x₇
   │  │  │  │  │  │  │  │
   └──┴──┴──┴──┼──┴──┴──┴──┘
               ▼
          ┌──────────┐
          │ w: all -1│
          │ b:  +3   │
          └──────────┘
               │
               ▼
           HW ≤ 3?

Mechanism

Negative weights flip the logic. Each active input subtracts from the sum:

• Sum = -HW + 3 = 3 - (number of 1s)
• Fires when HW ≤ 3

HW	Sum	Output
0	+3	1
1	+2	1
2	+1	1
3	0	1
4	-1	0
...	...	0

Duality with Majority

Circuit	Weights	Bias	Fires when
Majority	all +1	-5	HW ≥ 5
Minority	all -1	+3	HW ≤ 3

These aren't complements. At HW=4, both are silent. This is the "tie zone" - neither majority nor minority.

Parameters

Weights	[-1, -1, -1, -1, -1, -1, -1, -1]
Bias	+3
Total	9 parameters

Usage

from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

def minority(bits):
    inputs = torch.tensor([float(b) for b in bits])
    return int((inputs * w['weight']).sum() + w['bias'] >= 0)

Files

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

License

MIT