mfouda / kV-Margin

Code for Measuring Generalization with Optimal Transport

Measuring Generalization with Optimal Transport

Understanding the generalization of deep neural networks is one of the most important tasks in deep learning. Although much progress has been made, theoretical error bounds still often behave disparately from empirical observations. In this work, we develop margin-based generalization bounds, where the margins are normalized with optimal transport costs between independent random subsets sampled from the training distribution. In particular, the optimal transport cost can be interpreted as a generalization of variance which captures the structural properties of the learned feature space. Our bounds robustly predict the generalization error, given training data and network parameters, on large scale datasets. Theoretically, we demonstrate that the concentration and separation of features play crucial roles in generalization, supporting empirical results in the literature.

Measuring Generalization with Optimal Transport arXiv [paper]
Ching-Yao Chuang, Youssef Mroueh, Kristjan Greenewald, Antonio Torralba, and Stefanie Jegelka

Prerequisites

• Python 3.7
• NumPy
• Tensorflow 1.15.0
• POT

PGDL Dataset

Download the dataset from the official Predicting Generalization in Deep Learning (PGDL) repo. The evaluation tool and instructions can be found here. The folders, kV-Margin and kV-GN-Margin, contain the implementation of our k-variance normalized margins (see complexity.py).

To evaluate our kV-Margin or kv-GN-Margin, download data and run

python ingestion_program/ingestion.py **path/to/inptu_data** **path/to/prediction** ingestion_program kV-Margin

To compute the score of your submission locally, you can run the scoring program:

python scoring_program/score.py **path/to/reference_data** **path/to/prediction** **path/to/output**

One can modify the shallow argument in complexity.py to choose shallow (1st) or deep layer (8th) feature to compute the margins.

Results

random seed = 0	task1	task2	task4	task5	task6	task7	task8	task9
kv-Margin 1st	5.83	29.11	36.45	17.51	6.27	2.11	1.89	13.89
kv-Margin 8th	29.72	27.19	6.01	15.10	0.81	1.71	0.37	1.43
kv-GN-Margin 1st	18.17	45.24	30.78	15.66	4.48	3.91	0.58	21.85
kv-GN-Margin 8th	41.09	46.28	6.71	15.99	1.11	5.93	0.66	8.14

Citation

If you find this repo useful for your research, please consider citing the paper

@article{chuang2021measuring,
  title={Measuring Generalization with Optimal Transport},
  author={Chuang, Ching-Yao and Mroueh, Youssef and Greenewald, Kristjan and Torralba, Antonio and Jegelka, Stefanie},
  journal={arXiv preprint arXiv:2106.03314},
  year={2021}
}

For any questions, please contact Ching-Yao Chuang ([e-mail]).