threshold-mod8

Computes Hamming weight mod 8 directly on inputs. Single-layer circuit.

Circuit

  x₀ x₁ x₂ x₃ x₄ x₅ x₆ x₇
   │  │  │  │  │  │  │  │
   │  │  │  │  │  │  │  │
   w: 1  1  1  1  1  1  1 -7
   └──┴──┴──┴──┼──┴──┴──┴──┘
               ▼
          ┌─────────┐
          │ b:  0   │
          └─────────┘
               │
               ▼
           HW mod 8

Algebraic Insight

Position 8 gets weight 1-8 = -7:

• Positions 1-7: weight +1
• Position 8: weight -7

HW=0: sum=0 → 0 mod 8
...
HW=7: sum=7 → 7 mod 8
HW=8: sum=0 → 0 mod 8  (reset: 1+1+1+1+1+1+1-7=0)

The only non-trivial case is HW=8, which resets to 0.

Parameters

Weights	[1, 1, 1, 1, 1, 1, 1, -7]
Bias	0
Total	9 parameters

Usage

from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

def mod8(bits):
    inputs = torch.tensor([float(b) for b in bits])
    return int((inputs * w['weight']).sum() + w['bias'])

Files

threshold-mod8/
├── model.safetensors
├── model.py
├── config.json
└── README.md

License

MIT