threshold-atmost7outof8

At-most-7-out-of-8 detector. Fires when fewer than all inputs are active. This is 8-input NAND.

Circuit

  x₀ x₁ x₂ x₃ x₄ x₅ x₆ x₇
   │  │  │  │  │  │  │  │
   └──┴──┴──┴──┼──┴──┴──┴──┘
               ▼
          ┌─────────┐
          │ w: -1×8 │
          │ b:  +7  │
          └─────────┘
               │
               ▼
         NOT(all)?

The Unanimity Detector (Inverted)

This circuit is the complement of 8-input AND:

HW	AND (all 8)	AtMost7 (NAND)
0-7	0	1
8	1	0

It fires on 255 of 256 inputs. Only complete unanimity silences it.

Equivalence to 8-input NAND

Circuit	Condition	Weights	Bias
8-input AND	HW = 8	all +1	-8
8-input NAND	HW < 8	all -1	+7

They are complements. Both use the same number of parameters but opposite logic.

Functional Completeness

NAND is functionally complete - any Boolean function can be built from NAND alone:

• NOT(x) = NAND(x, x, x, x, x, x, x, x)
• But for 2-input NAND we'd need to tie inputs

This 8-input NAND can simulate 2-input NAND by fixing 6 inputs to 1.

The Single Failure Case

Scenario	AtMost7
All systems go	0
Any system down	1

If you interpret 1 as "operational," AtMost7 fires whenever there's at least one failure.

Dual of AtLeast1 (OR)

Circuit	Condition	Fires on
AtLeast1 (OR)	HW ≥ 1	255 inputs
AtMost7 (NAND)	HW ≤ 7	255 inputs

Both fire on almost everything. One misses all-zeros; the other misses all-ones.

Parameters

Component	Value
Weights	all -1
Bias	+7
Total	9 parameters

Usage

from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

def atmost7(bits):
    """Also known as 8-input NAND"""
    inp = torch.tensor([float(b) for b in bits])
    return int((inp * w['weight']).sum() + w['bias'] >= 0)

# Almost all active
print(atmost7([1,1,1,1,1,1,1,0]))  # 1

# All active (unanimity)
print(atmost7([1,1,1,1,1,1,1,1]))  # 0

Files

threshold-atmost7outof8/
├── model.safetensors
├── model.py
├── config.json
└── README.md

License

MIT