metadata
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
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