phanerozoic / threshold-and

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:

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

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