threshold-1outof8

At-least-one detector for 8 inputs. Equivalent to an 8-input OR gate.

Circuit

  x₀ x₁ x₂ x₃ x₄ x₅ x₆ x₇
   │  │  │  │  │  │  │  │
   └──┴──┴──┴──┼──┴──┴──┴──┘
               ▼
          ┌─────────┐
          │ w: all 1│
          │ b:  -1  │
          └─────────┘
               │
               ▼
            HW ≥ 1

Mechanism

With uniform weights of 1 and bias -1, the neuron fires when at least one input is active:

• Sum = (number of 1s) - 1
• Fires when sum ≥ 0, i.e., when Hamming weight ≥ 1

This is the loosest threshold in the k-out-of-8 family.

k-out-of-8 Family

Circuit	Bias	Fires when
1-out-of-8	-1	HW ≥ 1 (this)
2-out-of-8	-2	HW ≥ 2
...	...	...
8-out-of-8	-8	HW = 8

All share weights [1,1,1,1,1,1,1,1]. Only the bias differs.

Parameters

Weights	[1, 1, 1, 1, 1, 1, 1, 1]
Bias	-1
Total	9 parameters

Usage

from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

def at_least_1(bits):
    inputs = torch.tensor([float(b) for b in bits])
    return int((inputs * w['weight']).sum() + w['bias'] >= 0)

Files

threshold-1outof8/
├── model.safetensors
├── model.py
├── config.json
└── README.md

License

MIT