Who Said Neural Networks Aren't Linear? The Linearizer Framework

This repository provides the code implementation for the paper “Who Said Neural Networks Aren’t Linear?” , which introduces the Linearizer Framework.

Overview

Neural networks are famously nonlinear, but linearity is defined relative to vector spaces (f: X → Y). This project introduces Linearizers - architectures that sandwich a linear operator (A) between two invertible neural networks:

f(x) = g⁻¹ᵧ(Agₓ(x)).

This framework lets classic linear-algebra tools like SVD, pseudoinverse, and projections, operate on nonlinear mappings.

Applications enabled by the framework and showed in the paper:

• One-Step Generation: Reduce diffusion sampling from hundreds of steps to a single linearized step.
• Style Transfer Interpolations: Modular, controllable style transfer interpolations via linear transformations in the latent linear space.
• IGN: Coming soon / TODO.

We provide complete, runnable implementations for the listed applications in this repository.

Project Structure

linearizer/
├── one_step/           # One-step generation application
│   ├── data/          # Data loading utilities
│   ├── modules/       # Core model components
│   ├── utils/         # Training and sampling utilities
│   ├── train_one_step.py
│   └── test_one_step.py
├── style_transfer/    # Style transfer application
│   ├── modules/       # Style transfer models
│   ├── utils/         # Visualization utilities
│   ├── train_style_transfer.py
│   └── style_intrepolations.py
├── ign/               # Coming Soon
└── common/           # Shared components
    └── song__unet.py # UNet architecture

Installation Requirements

Python Environment

1. Create conda environment:

   conda create -n linearizer python=3.9
   conda activate linearizer
   

2. Install dependencies:

   pip install -r requirements.txt
   

Getting Started

Navigate to the specific application directories (one_step/, ign/ or style_transfer/) for detailed usage instructions.