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

# threshold-1outof8

At-least-one detector for 8 inputs. Equivalent to an 8-input OR gate.

## Circuit

```
  x₀ x₁ x₂ x₃ x₄ x₅ x₆ x₇
   │  │  │  │  │  │  │  │
   └──┴──┴──┴──┼──┴──┴──┴──┘
               ▼
          ┌─────────┐
          │ w: all 1│
          │ b:  -1  │
          └─────────┘
               │
               ▼
            HW ≥ 1
```

## 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

This is the loosest threshold in the k-out-of-8 family.

## k-out-of-8 Family

| Circuit | Bias | Fires when |
|---------|------|------------|
| **1-out-of-8** | **-1** | **HW ≥ 1 (this)** |
| 2-out-of-8 | -2 | HW ≥ 2 |
| ... | ... | ... |
| 8-out-of-8 | -8 | HW = 8 |

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

## Parameters

| | |
|---|---|
| Weights | [1, 1, 1, 1, 1, 1, 1, 1] |
| Bias | -1 |
| Total | 9 parameters |

## Usage

```python
from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

def at_least_1(bits):
    inputs = torch.tensor([float(b) for b in bits])
    return int((inputs * w['weight']).sum() + w['bias'] >= 0)
```

## Files

```
threshold-1outof8/
├── model.safetensors
├── model.py
├── config.json
└── README.md
```

## License

MIT