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

# threshold-and

A 2-of-2 threshold gate. Both inputs must be active to reach the firing threshold.

## Circuit

```
    x   y
    │   │
    └─┬─┘
      ▼
  ┌───────┐
  │ w: 1,1│
  │ b: -2 │
  └───────┘
      │
      ▼
   AND(x,y)
```

## Mechanism

Each input contributes +1 to the sum. The bias of -2 means exactly two contributions are required to reach zero:

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

The bias acts as a vote threshold. With bias -2, you need 2 votes.

## Parameters

| | |
|---|---|
| Weights | [1, 1] |
| Bias | -2 |
| Total | 3 parameters |

## Optimality

Exhaustive enumeration of all 129 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.

## Properties

- Linearly separable (unlike XOR)
- Commutative, associative, idempotent
- Generalizes to n-input AND with weights all 1, bias -n

## Usage

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

w = load_file('model.safetensors')

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

## Files

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

## License

MIT