---
license: mit
tags:
- pytorch
- safetensors
- threshold-logic
- neuromorphic
---

# 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

```python
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