threshold-1outof6

At-least-one detector for 6 inputs. Equivalent to a 6-input OR gate. The loosest threshold in the k-out-of-6 family.

Circuit

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

Function

1outof6(x0, x1, x2, x3, x4, x5) = 1 if (x0 + x1 + x2 + x3 + x4 + x5) >= 1

Returns 1 when at least one input is high (Hamming weight >= 1).

Truth Table (selected)

Inputs	HW	Output
000000	0	0
000001	1	1
000010	1	1
010101	3	1
111111	6	1

Only the all-zeros input produces 0.

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

k-out-of-6 Family

Circuit	Bias	Fires when
1-out-of-6	-1	HW >= 1 (this)
2-out-of-6	-2	HW >= 2
3-out-of-6	-3	HW >= 3
4-out-of-6	-4	HW >= 4
5-out-of-6	-5	HW >= 5
6-out-of-6	-6	HW = 6

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

Parameters

Weights	[1, 1, 1, 1, 1, 1]
Bias	-1
Inputs	6
Outputs	1
Neurons	1
Layers	1
Parameters	7
Magnitude	7

Usage

from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

def at_least_1_of_6(bits):
    inputs = torch.tensor([float(b) for b in bits])
    return int((inputs @ w['neuron.weight'].T + w['neuron.bias'] >= 0).item())

# Examples
print(at_least_1_of_6([0, 0, 0, 0, 0, 0]))  # 0
print(at_least_1_of_6([0, 0, 0, 0, 0, 1]))  # 1
print(at_least_1_of_6([1, 0, 1, 0, 1, 0]))  # 1

Applications

• Any-input-active detection
• Interrupt pending flags
• Error aggregation
• Valid signal generation

Files

threshold-1outof6/
├── model.safetensors
├── model.py
├── create_safetensors.py
├── config.json
└── README.md

License

MIT