Exercise: Interpretable machine learning in python

Task 1: Input optimization.

Open the src/input_opt.py file. The network ./data/weights.pkl contains network weights pre-trained on MNIST. Turn the network optimization problem around, and find an input that makes a particular output neuron extremely happy. In other words maximize,

$$\max_\mathbf{x} y_i = f(\mathbf{x}, \theta) .$$

Use jax.value_and_grad to find the gradients of the network input $\mathbf{x}$. Start with a jnp.ones network input of shape [1, 28, 28, 1] and iteratively optimize it. Normalize by subtracting the mean and deviding by the standard deviation at every step. Execute your script with python src/input_opt.py

Task 2 Integrated Gradients (Optional):

Reuse your MNIST digit recognition code. Implement IG as discussed in the lecture. Recall the equation

$$\text{IntegratedGrads}_i(x) = (x_i - x_i') \cdot \sum_{k=1}^m \frac{\partial F (x' + \frac{k}{m} \cdot (x - x'))}{\partial x_i}.$$

F partial xi denotes the gradients with respect to the input color-channels i. x prime denotes a baseline black image. And x symbolizes an input we are interested in. Finally, m denotes the number of summation steps from the black baseline image to the interesting input.

Follow the TODOs in ./src/mnist_integrated.py and then run scripts/integrated_gradients.slurm.

Task 3 - Deepfake detection (Optional):

In this exercise we will consider 128 by 128-pixel fake images from StyleGAN and pictures of real people from the Flickr-Faces-HQ dataset.

Flickr-Faces-HQ images depict real people, such as the person below:

Generative adversarial networks allow the generation of fake images at scale. Does the picture below seem real?

How can we identify the fake? Given that modern neural networks can generate hundreds of fake images per second can we create a classifier to automate the process?

3.1 Getting started:

1. Move to the data folder in your terminal. Download ffhq_style_gan.zip on bender using the command

   gdown https://drive.google.com/uc?id=1MOHKuEVqURfCKAN9dwp1o2tuR19OTQCF

   If gdown is not installed, type pip install gdown and then try again.
2. Type export UNZIP_DISABLE_ZIPBOMB_DETECTION=TRUE to make unzipping big archives possible.
3. Extract the image pairs here by executing unzip ffhq_style_gan.zip in the terminal.

The desired outcome is to have a folder called ffhq_style_gan in the project data-folder.

3.2 Analyzing the data

The load_folder function from the util module loads both real and fake data. Code to load the data is already present in the deepfake_interpretation.py file.

Compute log-scaled frequency domain representations of samples from both sources via

$$\mathbf{F}_I = \log_e (| \mathcal{F}_{2d}(\mathbf(I)) | + \epsilon ), \text{ with } \mathbf{I} \in \mathbb{R}^{h,w,c}, \epsilon \approx 0$$

Above $h$, $w$ and $c$ denote image height, width and columns. $log$ denotes the natural logarithm, and bars denote the absolute value. A small epsilon is added for numerical stability.

Use the numpy functions jnp.log, jnp.abs, jnp.fft.fft2. By default, fft2 transforms the last two axes. The last axis contains the color channels in this case. We are looking to transform the rows and columns.

Plot mean spectra for real and fake images as well as their difference over the entire validation or test sets. For that complete the TODOs in src/deepfake_interpretation.py and run the script scripts/train.slurm.

3.3 Training and interpreting a linear classifier

Train a linear classifier consisting of a single nn.Dense-layer on the log-scaled Fourier coefficients using Flax. Plot the result. What do you see?