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Kun Xu 0004

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6 papers

1 author row

ICML Conference 2021 Conference Paper

Variational (Gradient) Estimate of the Score Function in Energy-based Latent Variable Models

Fan Bao
Kun Xu 0004
Chongxuan Li
Lanqing Hong
Jun Zhu 0001
Bo Zhang 0010

This paper presents new estimates of the score function and its gradient with respect to the model parameters in a general energy-based latent variable model (EBLVM). The score function and its gradient can be expressed as combinations of expectation and covariance terms over the (generally intractable) posterior of the latent variables. New estimates are obtained by introducing a variational posterior to approximate the true posterior in these terms. The variational posterior is trained to minimize a certain divergence (e. g. , the KL divergence) between itself and the true posterior. Theoretically, the divergence characterizes upper bounds of the bias of the estimates. In principle, our estimates can be applied to a wide range of objectives, including kernelized Stein discrepancy (KSD), score matching (SM)-based methods and exact Fisher divergence with a minimal model assumption. In particular, these estimates applied to SM-based methods outperform existing methods in learning EBLVMs on several image datasets.

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ICLR Conference 2020 Conference Paper

Mixup Inference: Better Exploiting Mixup to Defend Adversarial Attacks

Tianyu Pang
Kun Xu 0004
Jun Zhu 0001

It has been widely recognized that adversarial examples can be easily crafted to fool deep networks, which mainly root from the locally non-linear behavior nearby input examples. Applying mixup in training provides an effective mechanism to improve generalization performance and model robustness against adversarial perturbations, which introduces the globally linear behavior in-between training examples. However, in previous work, the mixup-trained models only passively defend adversarial attacks in inference by directly classifying the inputs, where the induced global linearity is not well exploited. Namely, since the locality of the adversarial perturbations, it would be more efficient to actively break the locality via the globality of the model predictions. Inspired by simple geometric intuition, we develop an inference principle, named mixup inference (MI), for mixup-trained models. MI mixups the input with other random clean samples, which can shrink and transfer the equivalent perturbation if the input is adversarial. Our experiments on CIFAR-10 and CIFAR-100 demonstrate that MI can further improve the adversarial robustness for the models trained by mixup and its variants.

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ICLR Conference 2020 Conference Paper

Rethinking Softmax Cross-Entropy Loss for Adversarial Robustness

Tianyu Pang
Kun Xu 0004
Yinpeng Dong
Chao Du
Ning Chen 0002
Jun Zhu 0001

Previous work shows that adversarially robust generalization requires larger sample complexity, and the same dataset, e.g., CIFAR-10, which enables good standard accuracy may not suffice to train robust models. Since collecting new training data could be costly, we focus on better utilizing the given data by inducing the regions with high sample density in the feature space, which could lead to locally sufficient samples for robust learning. We first formally show that the softmax cross-entropy (SCE) loss and its variants convey inappropriate supervisory signals, which encourage the learned feature points to spread over the space sparsely in training. This inspires us to propose the Max-Mahalanobis center (MMC) loss to explicitly induce dense feature regions in order to benefit robustness. Namely, the MMC loss encourages the model to concentrate on learning ordered and compact representations, which gather around the preset optimal centers for different classes. We empirically demonstrate that applying the MMC loss can significantly improve robustness even under strong adaptive attacks, while keeping state-of-the-art accuracy on clean inputs with little extra computation compared to the SCE loss.

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ICLR Conference 2020 Conference Paper

To Relieve Your Headache of Training an MRF, Take AdVIL

Chongxuan Li
Chao Du
Kun Xu 0004
Max Welling
Jun Zhu 0001
Bo Zhang 0010

We propose a black-box algorithm called {\it Adversarial Variational Inference and Learning} (AdVIL) to perform inference and learning on a general Markov random field (MRF). AdVIL employs two variational distributions to approximately infer the latent variables and estimate the partition function of an MRF, respectively. The two variational distributions provide an estimate of the negative log-likelihood of the MRF as a minimax optimization problem, which is solved by stochastic gradient descent. AdVIL is proven convergent under certain conditions. On one hand, compared with contrastive divergence, AdVIL requires a minimal assumption about the model structure and can deal with a broader family of MRFs. On the other hand, compared with existing black-box methods, AdVIL provides a tighter estimate of the log partition function and achieves much better empirical results.

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ICML Conference 2020 Conference Paper

Understanding and Stabilizing GANs' Training Dynamics Using Control Theory

Kun Xu 0004
Chongxuan Li
Jun Zhu 0001
Bo Zhang 0010

Generative adversarial networks (GANs) are effective in generating realistic images but the training is often unstable. There are existing efforts that model the training dynamics of GANs in the parameter space but the analysis cannot directly motivate practically effective stabilizing methods. To this end, we present a conceptually novel perspective from control theory to directly model the dynamics of GANs in the frequency domain and provide simple yet effective methods to stabilize GAN’s training. We first analyze the training dynamic of a prototypical Dirac GAN and adopt the widely-used closed-loop control (CLC) to improve its stability. We then extend CLC to stabilize the training dynamic of normal GANs, which can be implemented as an L2 regularizer on the output of the discriminator. Empirical results show that our method can effectively stabilize the training and obtain state-of-the-art performance on data generation tasks.

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ICML Conference 2019 Conference Paper

Improving Adversarial Robustness via Promoting Ensemble Diversity

Tianyu Pang
Kun Xu 0004
Chao Du
Ning Chen 0002
Jun Zhu 0001

Though deep neural networks have achieved significant progress on various tasks, often enhanced by model ensemble, existing high-performance models can be vulnerable to adversarial attacks. Many efforts have been devoted to enhancing the robustness of individual networks and then constructing a straightforward ensemble, e. g. , by directly averaging the outputs, which ignores the interaction among networks. This paper presents a new method that explores the interaction among individual networks to improve robustness for ensemble models. Technically, we define a new notion of ensemble diversity in the adversarial setting as the diversity among non-maximal predictions of individual members, and present an adaptive diversity promoting (ADP) regularizer to encourage the diversity, which leads to globally better robustness for the ensemble by making adversarial examples difficult to transfer among individual members. Our method is computationally efficient and compatible with the defense methods acting on individual networks. Empirical results on various datasets verify that our method can improve adversarial robustness while maintaining state-of-the-art accuracy on normal examples.

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