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

# threshold-or4

A 1-of-4 threshold gate. Any single active input is enough to fire.

## Circuit

```
  x1  x2  x3  x4
   │   │   │   │
   └───┴───┴───┘
         │
         ▼
    ┌─────────┐
    │w: 1,1,1,1│
    │ b: -1   │
    └─────────┘
         │
         ▼
   OR4(x1,x2,x3,x4)
```

## Mechanism

Same weights as AND4, but bias -1 instead of -4. A single vote suffices:

| x1 | x2 | x3 | x4 | sum | output |
|----|----|----|-----|-----|--------|
| 0 | 0 | 0 | 0 | -1 | 0 |
| 0 | 0 | 0 | 1 | 0 | 1 |
| ... | ... | ... | ... | ... | 1 |
| 1 | 1 | 1 | 1 | 3 | 1 |

## Parameters

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

## Optimality

Exhaustive enumeration of all 1,683 weight configurations at magnitudes 0-5 confirms this circuit is **at minimum magnitude (5)**. There is exactly 1 valid configuration at magnitude 5, and no valid configurations exist below it.

| Magnitude | Valid Configs |
|-----------|---------------|
| 0-4 | 0 |
| 5 | 1 |

## Properties

- Linearly separable (single neuron suffices)
- De Morgan dual: OR4(x1,x2,x3,x4) = NOT(AND4(NOT(x1), NOT(x2), NOT(x3), NOT(x4)))

## Usage

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

w = load_file('model.safetensors')

def or4_gate(x1, x2, x3, x4):
    inputs = torch.tensor([float(x1), float(x2), float(x3), float(x4)])
    return int((inputs * w['weight']).sum() + w['bias'] >= 0)

assert or4_gate(0, 0, 0, 0) == 0
assert or4_gate(0, 0, 0, 1) == 1
assert or4_gate(1, 1, 1, 1) == 1
```

## Files

```
threshold-or4/
├── model.safetensors
├── model.py
├── config.json
├── create_safetensors.py
└── README.md
```

## License

MIT