arXiv subjects

Yifei Wang

Publications and source records attributed to Yifei Wang.

At least 217 records · Page 12Linked to original sources

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↗

arXiv2021

Adaptive Newton Sketch: Linear-time Optimization with Quadratic Convergence and Effective Hessian Dimensionality

We propose a randomized algorithm with quadratic convergence rate for convex optimization problems with a self-concordant, composite, strongly convex objective function. Our method is based on performing an approximate Newton step using a random projection of the Hessian. Our first contribution is to show that, at each iteration, the embedding dimension (or sketch size) can be as small as the effective dimension of the Hessian matrix. Leveraging this novel fundamental result, we design an algorithm with a sketch size proportional to the effective dimension and which exhibits a quadratic rate of convergence. This result dramatically improves on the classical linear-quadratic convergence rates of state-of-the-art sub-sampled Newton methods. However, in most practical cases, the effective dimension is not known beforehand, and this raises the question of how to pick a sketch size as small as the effective dimension while preserving a quadratic convergence rate. Our second and main contribution is thus to propose an adaptive sketch size algorithm with quadratic convergence rate and which does not require prior knowledge or estimation of the effective dimension: at each iteration, it starts with a small sketch size, and increases it until quadratic progress is achieved. Importantly, we show that the embedding dimension remains proportional to the effective dimension throughout the entire path and that our method achieves state-of-the-art computational complexity for solving convex optimization programs with a strongly convex component.

math.OC↗

arXiv2021

Effect of High-k Dielectric Layer on 1/f Noise Behavior in Graphene Field-Effect Transistors

We report the 1/f noise characteristics at low-frequency in graphene field-effect transistors that utilized a high-k dielectric tantalum oxide encapsulated layer (a few nanometers thick) placed by atomic layer deposition on Si3N4. A low-noise level of ~ 2.2 x 10^(-10) Hz-1 has been obtained at f = 10 Hz. The origin and physical mechanism of the noise can be interpreted by the McWhorter context, where fluctuations in the carrier number contribute dominantly to the low-frequency noise. Optimizing fabrication processes reduced the number of charged impurities in the graphene field-effect transistors. The study has provided insights into the underlying physical mechanisms of the noise at low-frequency for reducing the noise in graphene-based devices.

cond-mat.mtrl-sci↗

arXiv2021

Projected Wasserstein gradient descent for high-dimensional Bayesian inference

We propose a projected Wasserstein gradient descent method (pWGD) for high-dimensional Bayesian inference problems. The underlying density function of a particle system of WGD is approximated by kernel density estimation (KDE), which faces the long-standing curse of dimensionality. We overcome this challenge by exploiting the intrinsic low-rank structure in the difference between the posterior and prior distributions. The parameters are projected into a low-dimensional subspace to alleviate the approximation error of KDE in high dimensions. We formulate a projected Wasserstein gradient flow and analyze its convergence property under mild assumptions. Several numerical experiments illustrate the accuracy, convergence, and complexity scalability of pWGD with respect to parameter dimension, sample size, and processor cores.

cs.LG↗

arXiv2020

Electrical Tuning of Phase Change Antennas and Metasurfaces

The success of semiconductor electronics is built on the creation of compact, low-power switching elements that offer routing, logic, and memory functions. The availability of nanoscale optical switches could have a similarly transformative impact on the development of dynamic and programmable metasurfaces, optical neural networks, and quantum information processing. Phase change materials are uniquely suited to enable their creation as they offer high-speed electrical switching between amorphous and crystalline states with notably different optical properties. Their high refractive index has also been harnessed to fashion them into compact optical antennas. Here, we take the next important step by realizing electrically-switchable phase change antennas and metasurfaces that offer strong, reversible, non-volatile, multi-phase switching and spectral tuning of light scattering in the visible and near-infrared spectral ranges. Their successful implementation relies on a careful joint thermal and optical optimization of the antenna elements that comprise an Ag strip that simultaneously serves as a plasmonic resonator and a miniature heating stage.

physics.optics↗

arXiv2020

Information Newton's flow: second-order optimization method in probability space

We introduce a framework for Newton's flows in probability space with information metrics, named information Newton's flows. Here two information metrics are considered, including both the Fisher-Rao metric and the Wasserstein-2 metric. A known fact is that overdamped Langevin dynamics correspond to Wasserstein gradient flows of Kullback-Leibler (KL) divergence. Extending this fact to Wasserstein Newton's flows, we derive Newton's Langevin dynamics. We provide examples of Newton's Langevin dynamics in both one-dimensional space and Gaussian families. For the numerical implementation, we design sampling efficient variational methods in affine models and reproducing kernel Hilbert space (RKHS) to approximate Wasserstein Newton's directions. We also establish convergence results of the proposed information Newton's method with approximated directions. Several numerical examples from Bayesian sampling problems are shown to demonstrate the effectiveness of the proposed method.

math.OC↗

arXiv2020

Optimizing AD Pruning of Sponsored Search with Reinforcement Learning

Industrial sponsored search system (SSS) can be logically divided into three modules: keywords matching, ad retrieving, and ranking. During ad retrieving, the ad candidates grow exponentially. A query with high commercial value might retrieve a great deal of ad candidates such that the ranking module could not afford. Due to limited latency and computing resources, the candidates have to be pruned earlier. Suppose we set a pruning line to cut SSS into two parts: upstream and downstream. The problem we are going to address is: how to pick out the best $K$ items from $N$ candidates provided by the upstream to maximize the total system's revenue. Since the industrial downstream is very complicated and updated quickly, a crucial restriction in this problem is that the selection scheme should get adapted to the downstream. In this paper, we propose a novel model-free reinforcement learning approach to fixing this problem. Our approach considers downstream as a black-box environment, and the agent sequentially selects items and finally feeds into the downstream, where revenue would be estimated and used as a reward to improve the selection policy. To the best of our knowledge, this is first time to consider the system optimization from a downstream adaption view. It is also the first time to use reinforcement learning techniques to tackle this problem. The idea has been successfully realized in Baidu's sponsored search system, and online long time A/B test shows remarkable improvements on revenue.

cs.LG↗