README.md

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

# threshold-or3

3-input OR gate. Fires when at least one input is active. The 1-of-3 threshold gate.

## Circuit

```
    a   b   c
    │   │   │
    └───┼───┘
        │
        ▼
   ┌─────────┐
   │ w: 1,1,1│
   │ b:  -1  │
   └─────────┘
        │
        ▼
   OR(a,b,c)
```

## The Existence Test

3-input OR detects "at least one active":

| Inputs | Sum | Output |
|--------|-----|--------|
| **000** | **-1** | **0** |
| 001 | 0 | 1 |
| 010 | 0 | 1 |
| 011 | +1 | 1 |
| 100 | 0 | 1 |
| 101 | +1 | 1 |
| 110 | +1 | 1 |
| 111 | +2 | 1 |

Only complete silence fails.

## Same Weights, Different Threshold

AND and OR use identical weights but different biases:

| Gate | Weights | Bias | Meaning |
|------|---------|------|---------|
| OR(a,b,c) | [1, 1, 1] | -1 | Need 1+ vote |
| MAJ(a,b,c) | [1, 1, 1] | -2 | Need 2+ votes |
| AND(a,b,c) | [1, 1, 1] | -3 | Need 3 votes |

The bias is the threshold. OR is the most permissive.

## De Morgan Dual

OR(a,b,c) = NOT(AND(NOT(a), NOT(b), NOT(c)))

But threshold logic computes OR directly - no inversion needed.

## Parameters

| Component | Value |
|-----------|-------|
| Weights | [1, 1, 1] |
| Bias | -1 |
| **Total** | **4 parameters** |

## Optimality

Exhaustive enumeration of all 321 weight configurations at magnitudes 0-4 confirms this circuit is **already at minimum magnitude (4)**. There is exactly one valid configuration at magnitude 4, and no valid configurations exist below it.

## Usage

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

w = load_file('model.safetensors')

def or3(a, b, c):
    inp = torch.tensor([float(a), float(b), float(c)])
    return int((inp * w['weight']).sum() + w['bias'] >= 0)

print(or3(0, 0, 1))  # 1
print(or3(0, 0, 0))  # 0
```

## Files

```
threshold-or3/
├── model.safetensors
├── model.py
├── config.json
└── README.md
```

## License

MIT