140 research outputs found
Learning Generative Models across Incomparable Spaces
Generative Adversarial Networks have shown remarkable success in learning a
distribution that faithfully recovers a reference distribution in its entirety.
However, in some cases, we may want to only learn some aspects (e.g., cluster
or manifold structure), while modifying others (e.g., style, orientation or
dimension). In this work, we propose an approach to learn generative models
across such incomparable spaces, and demonstrate how to steer the learned
distribution towards target properties. A key component of our model is the
Gromov-Wasserstein distance, a notion of discrepancy that compares
distributions relationally rather than absolutely. While this framework
subsumes current generative models in identically reproducing distributions,
its inherent flexibility allows application to tasks in manifold learning,
relational learning and cross-domain learning.Comment: International Conference on Machine Learning (ICML
Wasserstein Adversarial Robustness
Deep models, while being extremely flexible and accurate, are surprisingly vulnerable to ``small, imperceptible'' perturbations known as adversarial attacks. While the majority of existing attacks focus on measuring perturbations under the metric, Wasserstein distance, which takes geometry in pixel space into account, has long been known to be a suitable metric for measuring image quality and has recently risen as a compelling alternative to the metric in adversarial attacks. However, constructing an effective attack under the Wasserstein metric is computationally much more challenging and calls for better optimization algorithms. We address this gap in two ways: (a) we develop an exact yet efficient projection operator to enable a stronger projected gradient attack; (b) we show that the Frank-Wolfe method equipped with a suitable linear minimization oracle works extremely fast under Wasserstein constraints. Our algorithms not only converge faster but also generate much stronger attacks. For instance, we decrease the accuracy of a residual network on CIFAR-10 to 3.4% within a Wasserstein perturbation ball of radius 0.005, in contrast to 65.6% using the previous Wasserstein attack based on an approximate projection operator. Furthermore, employing our stronger attacks in adversarial training significantly improves the robustness of adversarially trained models. Our algorithms are applicable to general Wasserstein constrained optimization problems in other domains beyond adversarial robustness
Improved Image Wasserstein Attacks and Defenses
Robustness against image perturbations bounded by a ball have been
well-studied in recent literature. Perturbations in the real-world, however,
rarely exhibit the pixel independence that threat models assume. A
recently proposed Wasserstein distance-bounded threat model is a promising
alternative that limits the perturbation to pixel mass movements. We point out
and rectify flaws in previous definition of the Wasserstein threat model and
explore stronger attacks and defenses under our better-defined framework.
Lastly, we discuss the inability of current Wasserstein-robust models in
defending against perturbations seen in the real world. Our code and trained
models are available at https://github.com/edwardjhu/improved_wasserstein .Comment: Best paper award at ICLR Trustworthy ML Workshop 202
Sinkhorn Distributionally Robust Optimization
We study distributionally robust optimization (DRO) with Sinkhorn distance --
a variant of Wasserstein distance based on entropic regularization. We derive
convex programming dual reformulation for a general nominal distribution.
Compared with Wasserstein DRO, it is computationally tractable for a larger
class of loss functions, and its worst-case distribution is more reasonable for
practical applications. To solve the dual reformulation, we develop a
stochastic mirror descent algorithm using biased gradient oracles and analyze
its convergence rate. Finally, we provide numerical examples using synthetic
and real data to demonstrate its superior performance.Comment: 56 pages, 8 figure
Amortized Projection Optimization for Sliced Wasserstein Generative Models
Seeking informative projecting directions has been an important task in
utilizing sliced Wasserstein distance in applications. However, finding these
directions usually requires an iterative optimization procedure over the space
of projecting directions, which is computationally expensive. Moreover, the
computational issue is even more severe in deep learning applications, where
computing the distance between two mini-batch probability measures is repeated
several times. This nested loop has been one of the main challenges that
prevent the usage of sliced Wasserstein distances based on good projections in
practice. To address this challenge, we propose to utilize the
learning-to-optimize technique or amortized optimization to predict the
informative direction of any given two mini-batch probability measures. To the
best of our knowledge, this is the first work that bridges amortized
optimization and sliced Wasserstein generative models. In particular, we derive
linear amortized models, generalized linear amortized models, and non-linear
amortized models which are corresponding to three types of novel mini-batch
losses, named amortized sliced Wasserstein. We demonstrate the favorable
performance of the proposed sliced losses in deep generative modeling on
standard benchmark datasets.Comment: Accepted to NeurIPS 2022, 22 pages, 6 figures, 8 table
- β¦