threshold-atmost2outof8

At-most-2-out-of-8 detector. Fires when two or fewer inputs are active. The error-tolerance bound.

Circuit

  x₀ x₁ x₂ x₃ x₄ x₅ x₆ x₇
   │  │  │  │  │  │  │  │
   └──┴──┴──┴──┼──┴──┴──┴──┘
               ▼
          ┌─────────┐
          │ w: -1×8 │
          │ b:  +2  │
          └─────────┘
               │
               ▼
           HW ≤ 2?

The Double-Error Budget

This circuit allows:

• Zero active inputs (silence)
• One active input (single event)
• Two active inputs (pair/double event)

Three or more is considered "too many."

Mechanism

sum = -HW + 2

HW	Sum	Output
0	+2	1
1	+1	1
2	0	1
3	-1	0
4+	< -1	0

The bias of +2 grants a budget of two active inputs.

Error Detection Context

In coding theory:

• A code with minimum distance d can detect d-1 errors
• AtMost2 accepts patterns with ≤2 bit flips from all-zeros
• Useful for validating that corruption is within correctable limits

Scenario	This circuit
No errors	Pass
Single-bit error	Pass
Double-bit error	Pass
Triple+ error	Fail

Dual of AtLeast6

Circuit	Condition	Sparse/Dense
AtLeast6	HW ≥ 6	Dense
AtMost2	HW ≤ 2	Sparse

Bitwise NOT maps AtMost2 inputs to AtLeast6 inputs.

Coverage

HW	C(8,k)	AtMost2?
0	1	Yes
1	8	Yes
2	28	Yes
3-8	219	No

Fires on 1 + 8 + 28 = 37 of 256 inputs (14.5%).

Parameters

Component	Value
Weights	all -1
Bias	+2
Total	9 parameters

Usage

from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

def atmost2(bits):
    inp = torch.tensor([float(b) for b in bits])
    return int((inp * w['weight']).sum() + w['bias'] >= 0)

# Double event: allowed
print(atmost2([1,0,0,0,1,0,0,0]))  # 1

# Triple event: rejected
print(atmost2([1,0,0,1,1,0,0,0]))  # 0

Files

threshold-atmost2outof8/
├── model.safetensors
├── model.py
├── config.json
└── README.md

License

MIT