metadata
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
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