This is the website for the Tutorials of the Machine Learning for Physicists course, taught by Prof. Florian Marquardt at the University of Erlangen-Nuremberg during the summer term 2019. Please refer to the lectures website to watch the videos and download the lecture note pdfs for the course.
Tutorial sessions will take place in the same Lecture Hall of the lectures, from 18.00 to 19.30 on the following dates:
We need to install the following software and python packages:
Hi! Today I will be your personal tutor and I will guide you through the configuration of your system! This is a computer-generated face made with a neural network. Produced by a GAN (generative adversarial network) StyleGAN (Dec 2018) - Karras et al. and Nvidia Original GAN (2014) - Goodfellow et al. See here for more information
We will use the MiniConda package and environment management system. To perform the installation, use the following procedure:
chmod 777 [filename])
and run it in the terminal with ./[filename].
conda create --name neuralnets
conda activate neuralnets
conda install jupyter h5py hdf5 matplotlib mkl-service numpy scipy tensorflow
You can now run Jupyter Notebook from the Application Menu. If you don't find it, you can run it by opening again the Anaconda Prompt, activating again the neuralnets environment and typing jupyter notebook .
Please run the following test notebook within Jupyter to check if all the packages were correctly installed
If you encounter a problem which you cannot solve by yourself during the installation, have questions reguarding the lectures or the exercises, please write an email to one of the assistants. We will try to take care of the problem within a reasonable time.
See also the Python Cheat Sheet
for loops when working with arrays
Feed forward neural network with random weight initialization This is how a neural network with many layers, two inputs and one output looks like before training. A convenient choice of the parameters of this network allows to reproduce any arbitrary function.
How can we implement logical operations such as AND, OR, NOT, XOR with neural networks?
Train a neural network that approximates a given function. We manually implement the backpropagation algorithm.
Build a neural network which learns to reproduce a given image
Build a convolutional neural network that classifies the digits from the MNIST dataset. The dataset contains training, validation and test images with their correct labels. Implemented in Keras.
Manually choose the weights of the neural network to approximate a 2d function with arbitrary precision. We can use logical operations between the output of the neurons. In this example we use a deep network (more than one layer)
Manually choose the weights of the neural network so that it approximates a square.
Manually choose the weights of the neural network so that it approximates a given convex shape.
Build a neural network which learns to reproduce a given image
Same example as above but with a dense neural network instead of a convolutional one.
Train a network that is able to distinguish between a circle and a square
Logical operations with neural network The figure shows how to implement a logic AND with a single artificial neuron with sigmoid activation function. How can we implement the other logical gates?
Backpropagation algorithm The backpropagation algorithm is the procedure we can employ to calculate the derivatives of the cost function with respect to its parameters. We need them in order to update the parameters of the neural network through the Gradient Descent algorithm. Without backpropagation, deep neural network could not be trained in an efficient way.
Reproduce a given image. Train a neural network that tries to reproduce a given image. If the network is not big enough, the best possible approximation will be returned. This is a sort of image compression if the amount of parameters of the network is smaller than the number of pixels of the image. Try reproduce bigger images with less parameters in order to get a compressed description of the image.
Convolutional neural network used to train a digit classifier. We give the input image as a 28x28x1 array (single channel i.e. b/w). We apply a first convolutional layer with 8 filters (which extract 8 different features). Then, we apply a subsampling layer, which combines into one pixel regions of 2x2 pixels. We repeat again the same structure with another convolutional layer followed by a subsampling layer. Finally, we flatten the output of the network so that instead of 8 channels of 7x7 pictures we get a single channel with 392 neurons. We apply a dense layer with 10 neurons with a sigmoid activation function in order to return probabilities.
In this tutorial, we will train a very simple autoencodeer. We discretize a function in N_points and give it as input to the autoencoder. We want the output to be the function itself. However, since there is a very small layer in the middle of the autoencoder (bottleneck), the task is not trivial. In other words, the central layer will contain a compressed representation of the function. In particular, we choose a set of random gaussians with different mean mu and standard deviation sigma as functions.
We implement the example on Andrej Karpathy blog on a collection of Physics articles.
Create an autoencoder that, given images of random circles with noise produces noiseless circles.
Autoencoder: Example of autoencoder neural network
Denoising autoencoder. Example of denoising autoencoder. Given random noisy circles, the network should produce noiseless circles.
LSTM Character-level text generation See here for more information.
In this tutorial, we will focus on Reinforcement Learning. We will explore together the standard Q-Learning and
Policy Gradient algorithms. We apply them to a classical problem: the Cartpole.
Please install the Cartpole simulation library with the command
pip install gym
Apply RL to solve the challenge of finding, as fast as possible, a "treasure" in:You can start from the example notebook we provide below (try to correct it).Use the labyrinth generator on Wikipedia "Maze Generation Algorithm"
- a fixed given labyrinth
- an arbitrary labyrinth (in each run, the player finds itself in another labyrinth)
Reinforcement Learning Train a network that decides the action to take based on reward.
The Cartpole Problem The Cartpole is an inverted pendulum with the center of mass above its pivot point. It is unstable and falls over. It can be controlled by moving the cart. The goal of the problem is to keep the pole balanced by moving the cart left or right, by applying appropriate forces to the pivot point. For more information, see this blog post
Escape from the maze
In this tutorial, we will show simple applications of Restricted Boltzmann Machines.
Below you can find the complete notebooks:Please use this section below to provide us an anonymous feedback. Thank you!
