---
license: mit
tags:
- pytorch
- safetensors
- threshold-logic
- neuromorphic
---

# 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

```python
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