threshold-atmost3outof8

At-most-3-out-of-8 detector. Fires when three or fewer inputs are active. Identical to Minority.

Circuit

  x₀ x₁ x₂ x₃ x₄ x₅ x₆ x₇
   │  │  │  │  │  │  │  │
   └──┴──┴──┴──┼──┴──┴──┴──┘
               ▼
          ┌─────────┐
          │ w: -1×8 │
          │ b:  +3  │
          └─────────┘
               │
               ▼
           HW ≤ 3?

Equivalence to Minority

This circuit is functionally identical to threshold-minority:

Circuit	Condition	Implementation
Minority	HW ≤ 3	w: all -1, b: +3
AtMost3	HW ≤ 3	w: all -1, b: +3

Both detect "strictly fewer than half." The naming differs by framing:

• "Minority" emphasizes the voting interpretation
• "AtMost3" emphasizes the counting bound

The Tie Boundary

HW	AtMost3	Interpretation
0-3	1	Minority (< 50%)
4	0	Tie (= 50%)
5-8	0	Majority (> 50%)

AtMost3 excludes ties. Four active inputs is not "at most 3."

Dual of AtLeast5 (Majority)

Circuit	Condition	Meaning
AtLeast5	HW ≥ 5	Majority
AtMost3	HW ≤ 3	Minority

These are not complements - the tie zone (HW = 4) belongs to neither.

Coverage

HW	C(8,k)	AtMost3?
0	1	Yes
1	8	Yes
2	28	Yes
3	56	Yes
4-8	163	No

Fires on 1 + 8 + 28 + 56 = 93 of 256 inputs (36.3%).

Parameters

Component	Value
Weights	all -1
Bias	+3
Total	9 parameters

Usage

from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

def atmost3(bits):
    inp = torch.tensor([float(b) for b in bits])
    return int((inp * w['weight']).sum() + w['bias'] >= 0)

# Three active: minority
print(atmost3([1,1,1,0,0,0,0,0]))  # 1

# Four active: tie, not minority
print(atmost3([1,1,1,1,0,0,0,0]))  # 0

Files

threshold-atmost3outof8/
├── model.safetensors
├── model.py
├── config.json
└── README.md

License

MIT