README.md

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

# threshold-mod4

Computes Hamming weight mod 4 directly on inputs. Single-layer circuit using repeated weight pattern.

## Circuit

```
  x₀ x₁ x₂ x₃ x₄ x₅ x₆ x₇
   │  │  │  │  │  │  │  │
   │  │  │  │  │  │  │  │
   w: 1  1  1 -3  1  1  1 -3
   └──┴──┴──┴──┼──┴──┴──┴──┘
               ▼
          ┌─────────┐
          │ b:  0   │
          └─────────┘
               │
               ▼
           HW mod 4
```

## Algebraic Insight

The pattern `(1, 1, 1, -3)` repeats twice across 8 inputs:

- Positions 1-3: weight +1 each
- Position 4: weight -3 (reset: 1+1+1-3 = 0)
- Positions 5-7: weight +1 each
- Position 8: weight -3 (reset again)

Every 4 bits, the sum resets. For 8 bits, two complete cycles.

```
HW=0: sum=0 → 0 mod 4
HW=1: sum=1 → 1 mod 4
HW=2: sum=2 → 2 mod 4
HW=3: sum=3 → 3 mod 4
HW=4: sum=0 → 0 mod 4  (reset)
...
```

## Parameters

| | |
|---|---|
| Weights | [1, 1, 1, -3, 1, 1, 1, -3] |
| Bias | 0 |
| Total | 9 parameters |

## MOD-m Family

| m | Weight pattern |
|---|----------------|
| 3 | (1, 1, -2) |
| **4** | **(1, 1, 1, -3)** |
| 5 | (1, 1, 1, 1, -4) |
| m | (1, ..., 1, 1-m) with m-1 ones |

## Usage

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

w = load_file('model.safetensors')

def mod4(bits):
    inputs = torch.tensor([float(b) for b in bits])
    return int((inputs * w['weight']).sum() + w['bias'])
```

## Files

```
threshold-mod4/
├── model.safetensors
├── model.py
├── config.json
└── README.md
```

## License

MIT