Measuring (in)variances in Convolutional Neural Networks Internal Representations

This repository contains the code necessary to obtain the experimental results published in the article Measuring (in)variances in Convolutional Neural Networks Internal Representations

Institutional repository version (open access)

Bibtex entry

@inbook{inbook, author = {Quiroga, Facundo and Torrents-Barrena, Jordina and Lanzarini, Laura and Puig, Domenec}, year = {2019}, month = {07}, pages = {98-109}, title = {Measuring (in)variances in Convolutional Networks}, isbn = {978-3-030-27712-3}, doi = {10.1007/978-3-030-27713-0_9} }

Abstract

`Convolutional neural networks (CNN) offer state-of-the-art performance in various computer vision tasks such as activity recognition, face detection, medical image analysis, among others. Many of those tasks need invariance to image transformations (i.e., rotations, translations or scaling).

By definition, convolutional layers are only equivariant to translation. Max pooling operations can empower CNNs with partial invariance, but full invariance to translation (or other transformations) requires additional schemes such as training with data augmentation, specialized layers, or both. However, there is no clear understanding of how these schemes work or should be applied. Indeed, they are only focused on the invariance of the CNNs' output with respect to the transformation, but do not delve into the internal representation of the network invariances.

This work proposes a versatile, straightforward and interpretable measure to quantify the (in)variance of CNN activations with respect to transformations of the input. Intermediate output values of feature maps and fully connected layers are also analyzed with respect to different input transformations. Our technique is validated on rotation transformations and compared with the relative (in)variance of several networks. More specifically, ResNet, AllConvolutional and VGG architectures were trained on CIFAR10 and MNIST databases with / without rotational data augmentation.

Experiments reveal that rotation (in)variance of CNN outputs is class conditional. A distribution analysis also shows that lower layers are the most invariant, which seems to go against previous guidelines that recommend placing invariances near the network output and equivariances near the input. `

What can you do with this code

You can train a model on the MNIST or CIFAR10 datasets. Two models will be generated for each training; a rotated model, for which the dataset's samples were randomly rotated before, and an unrotated model, for which they weren't modified at all.

The available models are Resnet, VGG16, AllConvolutional network and a simple Convolutional Network

Afterwards, you can measure the (in)variance of each activation of the networks, and visualize them as heatmaps or plots.

How to run

These instructions have been tested on a modern ubuntu-based distro (>=18) with python version>=3.6.

• Clone the repository and cd to it:

  • git clone https://github.com/facundoq/rotational_variance.git
  • cd rotational_variance

• Create a virtual environment and activate it (requires python3 with the venv module and pip):

  • python3 -m venv .env
  • source .env/bin/activate

• Install libraries

  • pip install -r requirements.txt

• Run the experiments with python experiment> <model> <dataset>

  • experiment_rotation.py trains two models with the dataset: one with the vanilla version, the other with a data-augmented version via rotations.
  • experiment_variance.py calculates the variance of the activations of the model for the rotated and unrotated model/dataset combinations. Results are saved by default to ~/variance_results/
  • plot_variances_models.py generates plots of the variances for each/model dataset combination found in ~/variance_results/. Both stratified/non-stratified versions of the measure are included in the plots.

• The folder plots contains the results for any given model/dataset combination