README.md

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

# threshold-majority

Strict majority detector for 8 inputs. Fires when more than half are active.

## Circuit

```
  x₀ x₁ x₂ x₃ x₄ x₅ x₆ x₇
   │  │  │  │  │  │  │  │
   └──┴──┴──┴──┼──┴──┴──┴──┘
               ▼
          ┌─────────┐
          │ w: all 1│
          │ b:  -5  │
          └─────────┘
               │
               ▼
           HW ≥ 5?
```

## Mechanism

- Sum = (number of 1s) - 5
- Fires when Hamming weight ≥ 5 (more 1s than 0s)

A tie (4-4) doesn't count as majority. You need strictly more than half.

Functionally identical to threshold-5outof8.

## Duality with Minority

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

Majority: "enough votes to pass"
Minority: "not enough votes to block"

These are not complements (they don't sum to 1). The gap at HW=4 belongs to neither.

## Parameters

| | |
|---|---|
| Weights | [1, 1, 1, 1, 1, 1, 1, 1] |
| Bias | -5 |
| Total | 9 parameters |

## Optimality

Exhaustive enumeration of all 27,298,155 weight configurations at magnitudes 0-13 confirms this circuit is **already at minimum magnitude (13)**. There is exactly one valid configuration at magnitude 13, and no valid configurations exist below it.

## Usage

```python
from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

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

## Files

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

## License

MIT