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

# threshold-nor

The silence detector. Fires only when both inputs are quiet.

## Circuit

```
    x   y
    │   │
    └─┬─┘
      ▼
  ┌────────┐
  │w: -1,-1│
  │ b:  0  │
  └────────┘
      │
      ▼
   NOR(x,y)
```

## Mechanism

With bias 0, we start exactly at threshold. Any input subtracts, pushing us below:

| x | y | sum | output |
|---|---|-----|--------|
| 0 | 0 | 0 | 1 |
| 0 | 1 | -1 | 0 |
| 1 | 0 | -1 | 0 |
| 1 | 1 | -2 | 0 |

NOR is OR with inverted output. It's also NOT extended to two inputs: NOR(x,x) = NOT(x).

## Parameters

| | |
|---|---|
| Weights | [-1, -1] |
| Bias | 0 |
| Total | 3 parameters |

## Optimality

Exhaustive enumeration of all 7 weight configurations at magnitudes 0-2 confirms this circuit is **already at minimum magnitude (2)**. There is exactly one valid configuration at magnitude 2, and no valid configurations exist below it.

## Functional Completeness

Like NAND, NOR can build any Boolean function:

- NOT(x) = NOR(x, x)
- OR(x,y) = NOT(NOR(x,y)) = NOR(NOR(x,y), NOR(x,y))
- AND(x,y) = NOR(NOT(x), NOT(y))

NOR logic was used in the Apollo Guidance Computer.

## Usage

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

w = load_file('model.safetensors')

def nor_gate(x, y):
    inputs = torch.tensor([float(x), float(y)])
    return int((inputs * w['weight']).sum() + w['bias'] >= 0)
```

## Files

```
threshold-nor/
├── model.safetensors
├── model.py
├── config.json
└── README.md
```

## License

MIT