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

# threshold-nor3

3-input NOR gate. Fires only when all inputs are silent. The silence detector.

## Circuit

```
    a   b   c
    │   │   │
    └───┼───┘
        │
        ▼
   ┌──────────┐
   │w: -1,-1,-1│
   │ b:   0   │
   └──────────┘
        │
        ▼
   NOR(a,b,c)
```

## The Perfect Silence Test

3-input NOR fires only on complete absence:

| Inputs | Sum | Output |
|--------|-----|--------|
| **000** | **0** | **1** |
| 001 | -1 | 0 |
| 010 | -1 | 0 |
| 011 | -2 | 0 |
| 100 | -1 | 0 |
| 101 | -2 | 0 |
| 110 | -2 | 0 |
| 111 | -3 | 0 |

Any activity silences the gate.

## Zero-Budget Design

With bias 0, we start exactly at threshold:

```
sum = -a - b - c + 0 = -HW
fires when -HW >= 0
fires when HW = 0
```

No tolerance. The slightest input pushes us below threshold.

## Functional Completeness

Like NAND, NOR is universal:

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

NOR logic powered the Apollo Guidance Computer.

## Extension of 2-input NOR

| Gate | Weights | Bias |
|------|---------|------|
| NOR(a,b) | [-1, -1] | 0 |
| **NOR(a,b,c)** | [-1, -1, -1] | 0 |
| NOR(a,b,c,d) | [-1, -1, -1, -1] | 0 |

All have bias 0. Only the number of inputs changes.

## Parameters

| Component | Value |
|-----------|-------|
| Weights | [-1, -1, -1] |
| Bias | 0 |
| **Total** | **4 parameters** |

## Optimality

Exhaustive enumeration of all 129 weight configurations at magnitudes 0-3 confirms this circuit is **already at minimum magnitude (3)**. There is exactly one valid configuration at magnitude 3, and no valid configurations exist below it.

## Usage

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

w = load_file('model.safetensors')

def nor3(a, b, c):
    inp = torch.tensor([float(a), float(b), float(c)])
    return int((inp * w['weight']).sum() + w['bias'] >= 0)

print(nor3(0, 0, 0))  # 1
print(nor3(0, 0, 1))  # 0
```

## Files

```
threshold-nor3/
├── model.safetensors
├── model.py
├── config.json
└── README.md
```

## License

MIT