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phanerozoic/
threshold-and

Name: threshold-and
Rating: 2.5 (11 reviews)

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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

phanerozoic/threshold-and