arXiv subjects

Dimitris Tsipras

Publications and source records attributed to Dimitris Tsipras.

22 records · Page 2Linked to original sources

arXiv2019

How Does Batch Normalization Help Optimization?

Batch Normalization (BatchNorm) is a widely adopted technique that enables faster and more stable training of deep neural networks (DNNs). Despite its pervasiveness, the exact reasons for BatchNorm's effectiveness are still poorly understood. The popular belief is that this effectiveness stems from controlling the change of the layers' input distributions during training to reduce the so-called "internal covariate shift". In this work, we demonstrate that such distributional stability of layer inputs has little to do with the success of BatchNorm. Instead, we uncover a more fundamental impact of BatchNorm on the training process: it makes the optimization landscape significantly smoother. This smoothness induces a more predictive and stable behavior of the gradients, allowing for faster training.

stat.ML↗

arXiv2019

On Evaluating Adversarial Robustness

Correctly evaluating defenses against adversarial examples has proven to be extremely difficult. Despite the significant amount of recent work attempting to design defenses that withstand adaptive attacks, few have succeeded; most papers that propose defenses are quickly shown to be incorrect. We believe a large contributing factor is the difficulty of performing security evaluations. In this paper, we discuss the methodological foundations, review commonly accepted best practices, and suggest new methods for evaluating defenses to adversarial examples. We hope that both researchers developing defenses as well as readers and reviewers who wish to understand the completeness of an evaluation consider our advice in order to avoid common pitfalls.

cs.LG↗

arXiv2018

Adversarially Robust Generalization Requires More Data

Machine learning models are often susceptible to adversarial perturbations of their inputs. Even small perturbations can cause state-of-the-art classifiers with high "standard" accuracy to produce an incorrect prediction with high confidence. To better understand this phenomenon, we study adversarially robust learning from the viewpoint of generalization. We show that already in a simple natural data model, the sample complexity of robust learning can be significantly larger than that of "standard" learning. This gap is information theoretic and holds irrespective of the training algorithm or the model family. We complement our theoretical results with experiments on popular image classification datasets and show that a similar gap exists here as well. We postulate that the difficulty of training robust classifiers stems, at least partially, from this inherently larger sample complexity.

cs.LG↗

arXiv2017

Matrix Scaling and Balancing via Box Constrained Newton's Method and Interior Point Methods

In this paper, we study matrix scaling and balancing, which are fundamental problems in scientific computing, with a long line of work on them that dates back to the 1960s. We provide algorithms for both these problems that, ignoring logarithmic factors involving the dimension of the input matrix and the size of its entries, both run in time $\widetilde{O}\left(m\log κ\log^2 (1/ε)\right)$ where $ε$ is the amount of error we are willing to tolerate. Here, $κ$ represents the ratio between the largest and the smallest entries of the optimal scalings. This implies that our algorithms run in nearly-linear time whenever $κ$ is quasi-polynomial, which includes, in particular, the case of strictly positive matrices. We complement our results by providing a separate algorithm that uses an interior-point method and runs in time $\widetilde{O}(m^{3/2} \log (1/ε))$. In order to establish these results, we develop a new second-order optimization framework that enables us to treat both problems in a unified and principled manner. This framework identifies a certain generalization of linear system solving that we can use to efficiently minimize a broad class of functions, which we call second-order robust. We then show that in the context of the specific functions capturing matrix scaling and balancing, we can leverage and generalize the work on Laplacian system solving to make the algorithms obtained via this framework very efficient.

cs.DS↗