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Accurate Learning with Neural Networks - from Theory to Practice

Accompanying code for the ICLR 2023 paper 'Learning ReLU Networks to high uniform accuracy is intractable'. Implemented in PyTorch, experiment execution and tracking using Ray Tune and Weights & Biases.

Illustration of a learned neural network with small average but large uniform error.

Install

This code was tested with Python 3.9.7. All necessary packages are specified in requirements.txt and can be installed with:

pip install -r requirements.txt.

You can test your setup by running python main.py.

If you want to automatically log metrics and plots to Weights & Biases (W&B), you need to log in:

wandb login --anonymously

Omit the flag --anonymously if you already have a W&B account. The link to the project can be found in the output of the code and one can verify this by running python main.py again.

Conda-Example

Using (Ana)conda, a typical installation with GPU support could look like:

conda create --name t2p python=3.9.7 pip -y
conda activate t2p
conda install pytorch=1.11 cudatoolkit=11.3 -c pytorch -y
conda install plotly=5.6.0 -c plotly -y
pip install -r requirements_conda.txt

Usually, one wants to (at least) install (py)torch and plotly using conda. The remaining requirements can be found in requirements_conda.txt. See here for more details on the PyTorch installation based on compute platform and OS.

How-To

We specify our experiments using .yaml files in the folder specs and we provide specifications for the following experiments:

  1. Learning a sinusoidal function:

    python main.py -e specs/1d_sine/exp_0.yaml

  2. One-dimensional teacher-student setting (each experiment uses a different batch-size):

    python main.py -e specs/1d_5x32/exp_0.yaml

    python main.py -e specs/1d_5x32/exp_1.yaml

    python main.py -e specs/1d_5x32/exp_2.yaml

  3. Three-dimensional teacher-student setting (each experiment uses a different batch-size):

    python main.py -e specs/3d_5x32/exp_0.yaml

    python main.py -e specs/3d_5x32/exp_1.yaml

    python main.py -e specs/3d_5x32/exp_2.yaml

Note that each training uses a single GPU by default. This can be changed using the key resources_per_trial in the respective experiment specification. You can resume an experiment by adding the flag -r specs/runner_resume.yaml.

Analysis

The Jupyter notebook theory2practice.ipynb shows how to track the experiments on TensorBoard and provides utility functions to analyse and plot the results.