Next Steps for Interpolation

tags: [ proj:interpolation , interpolation , machine_learning , _adversarial_training , _robustness ]

Let’s record the kinds of experimental data that we are interested in for [[project-interpolation]].

1. Replicating what’s been shown in the literature

• In the Zhang et al. (⊕2019Zhang, Chiyuan, Benjamin Recht, Samy Bengio, Moritz Hardt, and Oriol Vinyals. 2019. “Understanding deep learning requires rethinking generalization.” In 5th International Conference on Learning Representations, Iclr 2017 - Conference Track Proceedings. University of California, Berkeley, Berkeley, United States.) paper, they show that if you randomize the training data labels (in a classification problem), then you can still get zero training loss.
  • the point here is that the classical ideas of understanding the performance of machine learning methods (VC dimension) break down11 Though, I always get confused about this. Probably should reread one of the blog posts of Aroras..
• In some more recent work (Belkin et al. ⊕2019Belkin, Mikhail, Daniel Hsu, Siyuan Ma, and Soumik Mandal. 2019. “Reconciling modern machine-learning practice and the classical biasvariance trade-off.” Proceedings of the National Academy of Sciences 116 (32): 15849–54.), it was cited that if you randomize some of the training labels, you can basically still get the same generalization performance.
  • unclear to me if these two results are the same.
  • I vaguely remember there was some place that talked about the relevance to #robustness or #adversarial_training.
• establish that for standard problems (like CIFAR/MNIST/*), if you perturb the data (some percentage, or be clever about picking the points), then you’re going to maintain test performance.

2. New Ideas

• We conjecture that what’s going on is that there
  • show that this