Code, based on the PyTorch framework, for reproducing the experiments in Implicit Regularization in Deep Learning May Not Be Explainable by Norms.

Tested with python 3.7.

pip install -r requirements.txt

The following command will run a matrix completion experiment for the setting analyzed in the paper:

python dmf_multiple_experiments_runner.py

• Experiment parameters can be customized inside the script's code.
• Another option is to run dmf_experiment_runner.py with the desired arguments.
• A folder with checkpoints, metric plots and a log file will be automatically created under the directory specified by the output_dir parameter (default is "outputs/dmf").

To plot the unobserved entry (in absolute value) against the loss you can run:

python dmf_results_plotter.py \
-experiments_checkpoint_paths <experiment_checkpoint_path1> <experiment_checkpoint_path2> ... \
-experiments_names <experiment_name1> <experiment_name2> ...

• The parameter experiments_checkpoint_paths accepts multiple paths. Each path points to a checkpoint file created during training, which can be found under the corresponding experiment directory in a subdirectory named "checkpoints".
• For each checkpoint path given, a matching experiment name needs to be supplied (included as the label in the plot).
• Other options allow to add a plot title and save the figure to a file (see code, or run script with -h flag for further details).

Example plots:

Generating data for general matrix sensing/completion tasks is done using dmf_data_generator.py. Afterwards, it is necessary to modify the dataset path parameter (you might want to change some of the other run parameters as well, e.g. the number of samples to use).

The following command runs tensor completion experiments:

python tc_multiple_experiments_runner.py

• Customization of the run parameters is possible inside the script's code, with tc_experiment_runner.py allowing to pass the parameters as run arguments.
• A folder for each experiment, with checkpoints, metric plots and a log file, will be automatically created under the directory specified by the output_dir parameter (default is "outputs/tc/r1").

To plot the reconstruction error and tensor rank against the # of observations you can run the following command:

python tc_results_plotter.py -experiments_dir <experiment_dir>

• The experiments_dir parameter accepts a directory which contains multiple experiments. For example, after running tc_multiple_experiments_runner.py, the relevant directory is "outputs/tc/r1".
• Experiments are grouped according to initialization standard deviation.
• It is also possible to supply a plot title and save the figure to a file (see code, or run script with -h flag for further details).

Note that the code scans the given directories for trained models using string templates, hence, for compatibility its best to use tc_multiple_experiments_runner for running experiments.

Example plots:

To generate new tensor completion datasets use tc_data_generator.py.

For citing the paper:

@article{razin2020implicit,
  title={Implicit Regularization in Deep Learning May Not Be Explainable by Norms},
  author={Razin, Noam and Cohen, Nadav},
  journal={arXiv preprint arXiv:2005.06398},
  year={2020}
}