arXiv subjects

Yifei Wang

Publications and source records attributed to Yifei Wang.

At least 217 records · Page 12Linked to original sources

arXiv2022

When Adversarial Training Meets Vision Transformers: Recipes from Training to Architecture

Vision Transformers (ViTs) have recently achieved competitive performance in broad vision tasks. Unfortunately, on popular threat models, naturally trained ViTs are shown to provide no more adversarial robustness than convolutional neural networks (CNNs). Adversarial training is still required for ViTs to defend against such adversarial attacks. In this paper, we provide the first and comprehensive study on the adversarial training recipe of ViTs via extensive evaluation of various training techniques across benchmark datasets. We find that pre-training and SGD optimizer are necessary for ViTs' adversarial training. Further considering ViT as a new type of model architecture, we investigate its adversarial robustness from the perspective of its unique architectural components. We find, when randomly masking gradients from some attention blocks or masking perturbations on some patches during adversarial training, the adversarial robustness of ViTs can be remarkably improved, which may potentially open up a line of work to explore the architectural information inside the newly designed models like ViTs. Our code is available at https://github.com/mo666666/When-Adversarial-Training-Meets-Vision-Transformers.

cs.CV↗

arXiv2022

Improving Out-of-Distribution Generalization by Adversarial Training with Structured Priors

Deep models often fail to generalize well in test domains when the data distribution differs from that in the training domain. Among numerous approaches to address this Out-of-Distribution (OOD) generalization problem, there has been a growing surge of interest in exploiting Adversarial Training (AT) to improve OOD performance. Recent works have revealed that the robust model obtained by conducting sample-wise AT also retains transferability to biased test domains. In this paper, we empirically show that sample-wise AT has limited improvement on OOD performance. Specifically, we find that AT can only maintain performance at smaller scales of perturbation while Universal AT (UAT) is more robust to larger-scale perturbations. This provides us with clues that adversarial perturbations with universal (low dimensional) structures can enhance the robustness against large data distribution shifts that are common in OOD scenarios. Inspired by this, we propose two AT variants with low-rank structures to train OOD-robust models. Extensive experiments on DomainBed benchmark show that our proposed approaches outperform Empirical Risk Minimization (ERM) and sample-wise AT. Our code is available at https://github.com/NOVAglow646/NIPS22-MAT-and-LDAT-for-OOD.

cs.LG↗

arXiv2022

Motif-based Graph Representation Learning with Application to Chemical Molecules

This work considers the task of representation learning on the attributed relational graph (ARG). Both the nodes and edges in an ARG are associated with attributes/features allowing ARGs to encode rich structural information widely observed in real applications. Existing graph neural networks offer limited ability to capture complex interactions within local structural contexts, which hinders them from taking advantage of the expression power of ARGs. We propose Motif Convolution Module (MCM), a new motif-based graph representation learning technique to better utilize local structural information. The ability to handle continuous edge and node features is one of MCM's advantages over existing motif-based models. MCM builds a motif vocabulary in an unsupervised way and deploys a novel motif convolution operation to extract the local structural context of individual nodes, which is then used to learn higher-level node representations via multilayer perceptron and/or message passing in graph neural networks. When compared with other graph learning approaches to classifying synthetic graphs, our approach is substantially better in capturing structural context. We also demonstrate the performance and explainability advantages of our approach by applying it to several molecular benchmarks.

cs.LG↗

arXiv2022

Optimization-Induced Graph Implicit Nonlinear Diffusion

Due to the over-smoothing issue, most existing graph neural networks can only capture limited dependencies with their inherently finite aggregation layers. To overcome this limitation, we propose a new kind of graph convolution, called Graph Implicit Nonlinear Diffusion (GIND), which implicitly has access to infinite hops of neighbors while adaptively aggregating features with nonlinear diffusion to prevent over-smoothing. Notably, we show that the learned representation can be formalized as the minimizer of an explicit convex optimization objective. With this property, we can theoretically characterize the equilibrium of our GIND from an optimization perspective. More interestingly, we can induce new structural variants by modifying the corresponding optimization objective. To be specific, we can embed prior properties to the equilibrium, as well as introducing skip connections to promote training stability. Extensive experiments show that GIND is good at capturing long-range dependencies, and performs well on both homophilic and heterophilic graphs with nonlinear diffusion. Moreover, we show that the optimization-induced variants of our models can boost the performance and improve training stability and efficiency as well. As a result, our GIND obtains significant improvements on both node-level and graph-level tasks.

cs.LG↗

arXiv2022

Accelerated Information Gradient flow

We present a framework for Nesterov's accelerated gradient flows in probability space to design efficient mean-field Markov chain Monte Carlo (MCMC) algorithms for Bayesian inverse problems. Here four examples of information metrics are considered, including Fisher-Rao metric, Wasserstein-2 metric, Kalman-Wasserstein metric and Stein metric. For both Fisher-Rao and Wasserstein-2 metrics, we prove convergence properties of accelerated gradient flows. In implementations, we propose a sampling-efficient discrete-time algorithm for Wasserstein-2, Kalman-Wasserstein and Stein accelerated gradient flows with a restart technique. We also formulate a kernel bandwidth selection method, which learns the gradient of logarithm of density from Brownian-motion samples. Numerical experiments, including Bayesian logistic regression and Bayesian neural network, show the strength of the proposed methods compared with state-of-the-art algorithms.

math.OC↗

arXiv2022

A DTCWT-SVD Based Video Watermarking resistant to frame rate conversion

Videos can be easily tampered, copied and redistributed by attackers for illegal and monetary usage. Such behaviors severely jeopardize the interest of content owners. Despite huge efforts made in digital video watermarking for copyright protection, typical distortions in video transmission including signal attacks, geometric attacks and temporal synchronization attacks can still easily erase the embedded signal. Among them, temporal synchronization attacks which include frame dropping, frame insertion and frame rate conversion is one of the most prevalent attacks. To address this issue, we present a new video watermarking based on joint Dual-Tree Cosine Wavelet Transformation (DTCWT) and Singular Value Decomposition (SVD), which is resistant to frame rate conversion. We first extract a set of candidate coefficient by applying SVD decomposition after DTCWT transform. Then, we simulate the watermark embedding by adjusting the shape of candidate coefficient. Finally, we perform group-level watermarking that includes moderate temporal redundancy to resist temporal desynchronization attacks. Extensive experimental results show that the proposed scheme is more resilient to temporal desynchronization attacks and performs better than the existing blind video watermarking schemes.

cs.MM↗

arXiv2022

Chaos is a Ladder: A New Theoretical Understanding of Contrastive Learning via Augmentation Overlap

Recently, contrastive learning has risen to be a promising approach for large-scale self-supervised learning. However, theoretical understanding of how it works is still unclear. In this paper, we propose a new guarantee on the downstream performance without resorting to the conditional independence assumption that is widely adopted in previous work but hardly holds in practice. Our new theory hinges on the insight that the support of different intra-class samples will become more overlapped under aggressive data augmentations, thus simply aligning the positive samples (augmented views of the same sample) could make contrastive learning cluster intra-class samples together. Based on this augmentation overlap perspective, theoretically, we obtain asymptotically closed bounds for downstream performance under weaker assumptions, and empirically, we propose an unsupervised model selection metric ARC that aligns well with downstream accuracy. Our theory suggests an alternative understanding of contrastive learning: the role of aligning positive samples is more like a surrogate task than an ultimate goal, and the overlapped augmented views (i.e., the chaos) create a ladder for contrastive learning to gradually learn class-separated representations. The code for computing ARC is available at https://github.com/zhangq327/ARC.

cs.LG↗

arXiv2022

Optimal Neural Network Approximation of Wasserstein Gradient Direction via Convex Optimization

The computation of Wasserstein gradient direction is essential for posterior sampling problems and scientific computing. The approximation of the Wasserstein gradient with finite samples requires solving a variational problem. We study the variational problem in the family of two-layer networks with squared-ReLU activations, towards which we derive a semi-definite programming (SDP) relaxation. This SDP can be viewed as an approximation of the Wasserstein gradient in a broader function family including two-layer networks. By solving the convex SDP, we obtain the optimal approximation of the Wasserstein gradient direction in this class of functions. Numerical experiments including PDE-constrained Bayesian inference and parameter estimation in COVID-19 modeling demonstrate the effectiveness of the proposed method.

cs.LG↗

arXiv2022

A stochastic Stein Variational Newton method

Stein variational gradient descent (SVGD) is a general-purpose optimization-based sampling algorithm that has recently exploded in popularity, but is limited by two issues: it is known to produce biased samples, and it can be slow to converge on complicated distributions. A recently proposed stochastic variant of SVGD (sSVGD) addresses the first issue, producing unbiased samples by incorporating a special noise into the SVGD dynamics such that asymptotic convergence is guaranteed. Meanwhile, Stein variational Newton (SVN), a Newton-like extension of SVGD, dramatically accelerates the convergence of SVGD by incorporating Hessian information into the dynamics, but also produces biased samples. In this paper we derive, and provide a practical implementation of, a stochastic variant of SVN (sSVN) which is both asymptotically correct and converges rapidly. We demonstrate the effectiveness of our algorithm on a difficult class of test problems -- the Hybrid Rosenbrock density -- and show that sSVN converges using three orders of magnitude fewer gradient evaluations of the log likelihood than its stochastic SVGD counterpart. Our results show that sSVN is a promising approach to accelerating high-precision Bayesian inference tasks with modest-dimension, $d\sim\mathcal{O}(10)$.

stat.ML↗

arXiv2022

Knowledgebra: An Algebraic Learning Framework for Knowledge Graph

Knowledge graph (KG) representation learning aims to encode entities and relations into dense continuous vector spaces such that knowledge contained in a dataset could be consistently represented. Dense embeddings trained from KG datasets benefit a variety of downstream tasks such as KG completion and link prediction. However, existing KG embedding methods fell short to provide a systematic solution for the global consistency of knowledge representation. We developed a mathematical language for KG based on an observation of their inherent algebraic structure, which we termed as Knowledgebra. By analyzing five distinct algebraic properties, we proved that the semigroup is the most reasonable algebraic structure for the relation embedding of a general knowledge graph. We implemented an instantiation model, SemE, using simple matrix semigroups, which exhibits state-of-the-art performance on standard datasets. Moreover, we proposed a regularization-based method to integrate chain-like logic rules derived from human knowledge into embedding training, which further demonstrates the power of the developed language. As far as we know, by applying abstract algebra in statistical learning, this work develops the first formal language for general knowledge graphs, and also sheds light on the problem of neural-symbolic integration from an algebraic perspective.

cs.LG↗

arXiv2022

A Unified Contrastive Energy-based Model for Understanding the Generative Ability of Adversarial Training

Adversarial Training (AT) is known as an effective approach to enhance the robustness of deep neural networks. Recently researchers notice that robust models with AT have good generative ability and can synthesize realistic images, while the reason behind it is yet under-explored. In this paper, we demystify this phenomenon by developing a unified probabilistic framework, called Contrastive Energy-based Models (CEM). On the one hand, we provide the first probabilistic characterization of AT through a unified understanding of robustness and generative ability. On the other hand, our unified framework can be extended to the unsupervised scenario, which interprets unsupervised contrastive learning as an important sampling of CEM. Based on these, we propose a principled method to develop adversarial learning and sampling methods. Experiments show that the sampling methods derived from our framework improve the sample quality in both supervised and unsupervised learning. Notably, our unsupervised adversarial sampling method achieves an Inception score of 9.61 on CIFAR-10, which is superior to previous energy-based models and comparable to state-of-the-art generative models.

cs.LG↗

arXiv2022

The Hidden Convex Optimization Landscape of Two-Layer ReLU Neural Networks: an Exact Characterization of the Optimal Solutions

We prove that finding all globally optimal two-layer ReLU neural networks can be performed by solving a convex optimization program with cone constraints. Our analysis is novel, characterizes all optimal solutions, and does not leverage duality-based analysis which was recently used to lift neural network training into convex spaces. Given the set of solutions of our convex optimization program, we show how to construct exactly the entire set of optimal neural networks. We provide a detailed characterization of this optimal set and its invariant transformations. As additional consequences of our convex perspective, (i) we establish that Clarke stationary points found by stochastic gradient descent correspond to the global optimum of a subsampled convex problem (ii) we provide a polynomial-time algorithm for checking if a neural network is a global minimum of the training loss (iii) we provide an explicit construction of a continuous path between any neural network and the global minimum of its sublevel set and (iv) characterize the minimal size of the hidden layer so that the neural network optimization landscape has no spurious valleys. Overall, we provide a rich framework for studying the landscape of neural network training loss through convexity.

cs.LG↗

arXiv2021

Fooling Adversarial Training with Inducing Noise

Adversarial training is widely believed to be a reliable approach to improve model robustness against adversarial attack. However, in this paper, we show that when trained on one type of poisoned data, adversarial training can also be fooled to have catastrophic behavior, e.g., $<1\%$ robust test accuracy with $>90\%$ robust training accuracy on CIFAR-10 dataset. Previously, there are other types of noise poisoned in the training data that have successfully fooled standard training ($15.8\%$ standard test accuracy with $99.9\%$ standard training accuracy on CIFAR-10 dataset), but their poisonings can be easily removed when adopting adversarial training. Therefore, we aim to design a new type of inducing noise, named ADVIN, which is an irremovable poisoning of training data. ADVIN can not only degrade the robustness of adversarial training by a large margin, for example, from $51.7\%$ to $0.57\%$ on CIFAR-10 dataset, but also be effective for fooling standard training ($13.1\%$ standard test accuracy with $100\%$ standard training accuracy). Additionally, ADVIN can be applied to preventing personal data (like selfies) from being exploited without authorization under whether standard or adversarial training.

cs.LG↗

arXiv2021

Dissecting the Diffusion Process in Linear Graph Convolutional Networks

Graph Convolutional Networks (GCNs) have attracted more and more attentions in recent years. A typical GCN layer consists of a linear feature propagation step and a nonlinear transformation step. Recent works show that a linear GCN can achieve comparable performance to the original non-linear GCN while being much more computationally efficient. In this paper, we dissect the feature propagation steps of linear GCNs from a perspective of continuous graph diffusion, and analyze why linear GCNs fail to benefit from more propagation steps. Following that, we propose Decoupled Graph Convolution (DGC) that decouples the terminal time and the feature propagation steps, making it more flexible and capable of exploiting a very large number of feature propagation steps. Experiments demonstrate that our proposed DGC improves linear GCNs by a large margin and makes them competitive with many modern variants of non-linear GCNs.

cs.LG↗

arXiv2021

Residual Relaxation for Multi-view Representation Learning

Multi-view methods learn representations by aligning multiple views of the same image and their performance largely depends on the choice of data augmentation. In this paper, we notice that some other useful augmentations, such as image rotation, are harmful for multi-view methods because they cause a semantic shift that is too large to be aligned well. This observation motivates us to relax the exact alignment objective to better cultivate stronger augmentations. Taking image rotation as a case study, we develop a generic approach, Pretext-aware Residual Relaxation (Prelax), that relaxes the exact alignment by allowing an adaptive residual vector between different views and encoding the semantic shift through pretext-aware learning. Extensive experiments on different backbones show that our method can not only improve multi-view methods with existing augmentations, but also benefit from stronger image augmentations like rotation.

cs.LG↗

arXiv2021

The Convex Geometry of Backpropagation: Neural Network Gradient Flows Converge to Extreme Points of the Dual Convex Program

We study non-convex subgradient flows for training two-layer ReLU neural networks from a convex geometry and duality perspective. We characterize the implicit bias of unregularized non-convex gradient flow as convex regularization of an equivalent convex model. We then show that the limit points of non-convex subgradient flows can be identified via primal-dual correspondence in this convex optimization problem. Moreover, we derive a sufficient condition on the dual variables which ensures that the stationary points of the non-convex objective are the KKT points of the convex objective, thus proving convergence of non-convex gradient flows to the global optimum. For a class of regular training data distributions such as orthogonal separable data, we show that this sufficient condition holds. Therefore, non-convex gradient flows in fact converge to optimal solutions of a convex optimization problem. We present numerical results verifying the predictions of our theory for non-convex subgradient descent.

cs.LG↗

arXiv2021

Predicting the Stereoselectivity of Chemical Transformations by Machine Learning

Stereoselective reactions (both chemical and enzymatic reactions) have been essential for origin of life, evolution, human biology and medicine. Since late 1960s, there have been numerous successes in the exciting new frontier of asymmetric catalysis. However, most industrial and academic asymmetric catalysis nowadays do follow the trial-and-error model, since the energetic difference for success or failure in asymmetric catalysis is incredibly small. Our current understanding about stereoselective reactions is mostly qualitative that stereoselectivity arises from differences in steric effects and electronic effects in multiple competing mechanistic pathways. Quantitatively understanding and modulating the stereoselectivity of for a given chemical reaction still remains extremely difficult. As a proof of principle, we herein present a novel machine learning technique, which combines a LASSO model and two Random Forest model via two Gaussian Mixture models, for quantitatively predicting stereoselectivity of chemical reactions. Compared to the recent ground-breaking approach [1], our approach is able to capture interactions between features and exploit complex data distributions, which are important for predicting stereoselectivity. Experimental results on a recently published dataset demonstrate that our approach significantly outperform [1]. The insight obtained from our results provide a solid foundation for further exploration of other synthetically valuable yet mechanistically intriguing stereoselective reactions.

cs.LG↗

arXiv2021

Reparameterized Sampling for Generative Adversarial Networks

Recently, sampling methods have been successfully applied to enhance the sample quality of Generative Adversarial Networks (GANs). However, in practice, they typically have poor sample efficiency because of the independent proposal sampling from the generator. In this work, we propose REP-GAN, a novel sampling method that allows general dependent proposals by REParameterizing the Markov chains into the latent space of the generator. Theoretically, we show that our reparameterized proposal admits a closed-form Metropolis-Hastings acceptance ratio. Empirically, extensive experiments on synthetic and real datasets demonstrate that our REP-GAN largely improves the sample efficiency and obtains better sample quality simultaneously.

stat.ML↗