threshold-mod6

Computes Hamming weight mod 6 directly on inputs. Single-layer circuit.

Circuit

  x₀ x₁ x₂ x₃ x₄ x₅ x₆ x₇
   │  │  │  │  │  │  │  │
   │  │  │  │  │  │  │  │
   w: 1  1  1  1  1 -5  1  1
   └──┴──┴──┴──┼──┴──┴──┴──┘
               ▼
          ┌─────────┐
          │ b:  0   │
          └─────────┘
               │
               ▼
           HW mod 6

Algebraic Insight

For 8 inputs and mod 6, position 6 gets weight 1-6 = -5:

• Positions 1-5: weight +1
• Position 6: weight -5 (reset: 1+1+1+1+1-5 = 0)
• Positions 7-8: weight +1

HW=0: sum=0 → 0 mod 6
HW=1: sum=1 → 1 mod 6
...
HW=5: sum=5 → 5 mod 6
HW=6: sum=0 → 0 mod 6  (reset)
HW=7: sum=1 → 1 mod 6
HW=8: sum=2 → 2 mod 6

Parameters

Weights	[1, 1, 1, 1, 1, -5, 1, 1]
Bias	0
Total	9 parameters

Usage

from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

def mod6(bits):
    inputs = torch.tensor([float(b) for b in bits])
    return int((inputs * w['weight']).sum() + w['bias'])

Files

threshold-mod6/
├── model.safetensors
├── model.py
├── config.json
└── README.md

License

MIT