Model-centric Data Manifold: the Data Through the Eyes of the Model

This repository contains the code used to perform the experiments of the paper "Model-centric Data manifold: the Data Through the Eyes of the Model".

Getting started

The repository contains:

• a checkpoint directory containing a checkpoint of a CNN partially trained on MNIST and a checkpoint of a VGG11-like network partially trained on CIFAR-10;
• the package model_manifold that includes functions to move along a leaf of the foliation as well as to move across different leaves;
• many scripts needed to perform every single experiment on MNIST reported in the paper.

Prerequisites

In order to run the code you need to have Python 3.6 or above installed. We have performed our experiments with Python 3.9.1.

Remember to install all requirements with

python3 -m pip install -r requirements.txt

Training on MNIST

To reproduce our training on MNIST, run

python3 mnist_training.py

The command above trains the CNN defined in mnist_networks.py. It saves the checkpoints in the checkpoint directory. The graph of the mean trace of the local data matrix during training is saved in the same directory.

Many configuration parameters can be modified using the script CLI. To inspect those parameters it is sufficient to display the help page with

python3 mnist_training.py --help

Visualizing paths on the foliation

The experiments reported in the paper can be reproduced executing the scripts mnist_kernel.py, mnist_data_leaf.py, mnist_noise_leaf.py.

All those scripts take a model checkpoint as input and they compute paths in the data domain according to the foliation induced by the model.

The scripts have two effects:

• they export a .gif animation of the evolution in the outputs directory;
• they save an image reporting intermediate steps of the evolution in the outputs directory.

The scripts have these optional parameters:

• --start: the index in the MNIST test set of the source image;
• --end: the index in the MNIST test set of the destination image (if needed);
• --seed: random seed to control the sampling of source and destination image;
• --output-dir: output directory.

If --start (or --end) is not specified, it is chosen at random.

Moving across leaves in the foliation

To move across leaves in the foliation, the data should evolve along directions in the kernel of the local data matrix. In this experiment, we take a valid image in MNIST test set and a random direction and we let the image evolve along the projection of such direction on the kernel of the data matrix.

You can reproduce the experiment running

python3 mnist_kernel.py checkpoint/medium_cnn_10.pt 

Here we report some outputs of the script.

Moving along the data leaf

To move along the data leaf, data should evolve along directions orthogonal to the kernel of the local data matrix. In this experiment, we take two valid images in MNIST test set and we let the source image evolve to reach the destination image.

You can reproduce the experiment running

python3 mnist_data_leaf.py checkpoint/medium_cnn_10.pt 

Here we report some outputs of the script.

Adding the boolean flag --flip, it is possible to verify that also flipped digits (images that sometimes resemble latin letters) belong to the data leaf, since it is possible to join them with a valid digit.

In this case the command becomes

python3 mnist_data_leaf.py checkpoint/small_cnn_01.pt --flip

Here we report some outputs of this command.

Moving across leaves in the foliation then along a noisy leaf

We combine the two experiments above to verify that movements along a leaf preserve the noise in the image.

You can reproduce the experiment running

python3 mnist_noise_leaf.py checkpoint/medium_cnn_10.pt 

Here we report some outputs of the script.