An SDE Framework for Adversarial Training, with Convergence and Robustness Analysis

Adversarial training has gained great popularity as one of the most effective defenses for deep neural networks against adversarial perturbations on data points. Consequently, research interests have grown in understanding the convergence and robustness of adversarial training. This paper considers the min-max game of adversarial training by alternating stochastic gradient descent. It approximates the training process with a continuous-time stochastic-differential-equation (SDE). In particular, the error bound and convergence analysis is established. This SDE framework allows direct comparison between adversarial training and stochastic gradient descent; and confirms analytically the robustness of adversarial training from a (new) gradient-flow viewpoint. This analysis is then corroborated via numerical studies. To demonstrate the versatility of this SDE framework for algorithm design and parameter tuning, a stochastic control problem is formulated for learning rate adjustment, where the advantage of adaptive learning rate over fixed learning rate in terms of training loss is demonstrated through numerical experiments.

Discriminative-Generative Dual Memory Video Anomaly Detection

Recently, people tried to use a few anomalies for video anomaly detection (VAD) instead of only normal data during the training process. A side effect of data imbalance occurs when a few abnormal data face a vast number of normal data. The latest VAD works use triplet loss or data re-sampling strategy to lessen this problem. However, there is still no elaborately designed structure for discriminative VAD with a few anomalies. In this paper, we propose a DiscRiminative-gEnerative duAl Memory (DREAM) anomaly detection model to take advantage of a few anomalies and solve data imbalance. We use two shallow discriminators to tighten the normal feature distribution boundary along with a generator for the next frame prediction. Further, we propose a dual memory module to obtain a sparse feature representation in both normality and abnormality space. As a result, DREAM not only solves the data imbalance problem but also learn a reasonable feature space. Further theoretical analysis shows that our DREAM also works for the unknown anomalies. Comparing with the previous methods on UCSD Ped1, UCSD Ped2, CUHK Avenue, and ShanghaiTech, our model outperforms all the baselines with no extra parameters. The ablation study demonstrates the effectiveness of our dual memory module and discriminative-generative network.

Generative Adversarial Network: Some Analytical Perspectives

Ever since its debut, generative adversarial networks (GANs) have attracted tremendous amount of attention. Over the past years, different variations of GANs models have been developed and tailored to different applications in practice. Meanwhile, some issues regarding the performance and training of GANs have been noticed and investigated from various theoretical perspectives. This subchapter will start from an introduction of GANs from an analytical perspective, then move on the training of GANs via SDE approximations and finally discuss some applications of GANs in computing high dimensional MFGs as well as tackling mathematical finance problems.

Reinforcement learning for linear-convex models with jumps via stability analysis of feedback controls

We study finite-time horizon continuous-time linear-convex reinforcement learning problems in an episodic setting. In this problem, the unknown linear jump-diffusion process is controlled subject to nonsmooth convex costs. We show that the associated linear-convex control problems admit Lipchitz continuous optimal feedback controls and further prove the Lipschitz stability of the feedback controls, i.e., the performance gap between applying feedback controls for an incorrect model and for the true model depends Lipschitz-continuously on the magnitude of perturbations in the model coefficients; the proof relies on a stability analysis of the associated forward-backward stochastic differential equation. We then propose a novel least-squares algorithm which achieves a regret of the order $O(\sqrt{N\ln N})$ on linear-convex learning problems with jumps, where $N$ is the number of learning episodes; the analysis leverages the Lipschitz stability of feedback controls and concentration properties of sub-Weibull random variables.

Delay Analysis of Wireless Federated Learning Based on Saddle Point Approximation and Large Deviation Theory

Federated learning (FL) is a collaborative machine learning paradigm, which enables deep learning model training over a large volume of decentralized data residing in mobile devices without accessing clients' private data. Driven by the ever increasing demand for model training of mobile applications or devices, a vast majority of FL tasks are implemented over wireless fading channels. Due to the time-varying nature of wireless channels, however, random delay occurs in both the uplink and downlink transmissions of FL. How to analyze the overall time consumption of a wireless FL task, or more specifically, a FL's delay distribution, becomes a challenging but important open problem, especially for delay-sensitive model training. In this paper, we present a unified framework to calculate the approximate delay distributions of FL over arbitrary fading channels. Specifically, saddle point approximation, extreme value theory (EVT), and large deviation theory (LDT) are jointly exploited to find the approximate delay distribution along with its tail distribution, which characterizes the quality-of-service of a wireless FL system. Simulation results will demonstrate that our approximation method achieves a small approximation error, which vanishes with the increase of training accuracy.

Edge-Labeling based Directed Gated Graph Network for Few-shot Learning

Existing graph-network-based few-shot learning methods obtain similarity between nodes through a convolution neural network (CNN). However, the CNN is designed for image data with spatial information rather than vector form node feature. In this paper, we proposed an edge-labeling-based directed gated graph network (DGGN) for few-shot learning, which utilizes gated recurrent units to implicitly update the similarity between nodes. DGGN is composed of a gated node aggregation module and an improved gated recurrent unit (GRU) based edge update module. Specifically, the node update module adopts a gate mechanism using activation of edge feature, making a learnable node aggregation process. Besides, improved GRU cells are employed in the edge update procedure to compute the similarity between nodes. Further, this mechanism is beneficial to gradient backpropagation through the GRU sequence across layers. Experiment results conducted on two benchmark datasets show that our DGGN achieves a comparable performance to the-state-of-art methods.

Universal Silicon Microwave Photonic Spectral Shaper

Optical modulation plays arguably the utmost important role in microwave photonic (MWP) systems. Precise synthesis of modulated optical spectra dictates virtually all aspects of MWP system quality including loss, noise figure, linearity, and the types of functionality that can be executed. But for such a critical function, the versatility to generate and transform analog optical modulation is severely lacking, blocking the pathways to truly unique MWP functions including ultra-linear links and low-loss high rejection filters. Here we demonstrate versatile RF photonic spectrum synthesis in an all-integrated silicon photonic circuit, enabling electrically-tailorable universal analog modulation transformation. We show a series of unprecedented RF filtering experiments through monolithic integration of the spectrum-synthesis circuit with a network of reconfigurable ring resonators.

Entropy Regularization for Mean Field Games with Learning

Entropy regularization has been extensively adopted to improve the efficiency, the stability, and the convergence of algorithms in reinforcement learning. This paper analyzes both quantitatively and qualitatively the impact of entropy regularization for Mean Field Game (MFG) with learning in a finite time horizon. Our study provides a theoretical justification that entropy regularization yields time-dependent policies and, furthermore, helps stabilizing and accelerating convergence to the game equilibrium. In addition, this study leads to a policy-gradient algorithm for exploration in MFG. Under this algorithm, agents are able to learn the optimal exploration scheduling, with stable and fast convergence to the game equilibrium.

DanceIt: Music-inspired Dancing Video Synthesis

Close your eyes and listen to music, one can easily imagine an actor dancing rhythmically along with the music. These dance movements are usually made up of dance movements you have seen before. In this paper, we propose to reproduce such an inherent capability of the human-being within a computer vision system. The proposed system consists of three modules. To explore the relationship between music and dance movements, we propose a cross-modal alignment module that focuses on dancing video clips, accompanied on pre-designed music, to learn a system that can judge the consistency between the visual features of pose sequences and the acoustic features of music. The learned model is then used in the imagination module to select a pose sequence for the given music. Such pose sequence selected from the music, however, is usually discontinuous. To solve this problem, in the spatial-temporal alignment module we develop a spatial alignment algorithm based on the tendency and periodicity of dance movements to predict dance movements between discontinuous fragments. In addition, the selected pose sequence is often misaligned with the music beat. To solve this problem, we further develop a temporal alignment algorithm to align the rhythm of music and dance. Finally, the processed pose sequence is used to synthesize realistic dancing videos in the imagination module. The generated dancing videos match the content and rhythm of the music. Experimental results and subjective evaluations show that the proposed approach can perform the function of generating promising dancing videos by inputting music.

Kernel-based L_2-Boosting with Structure Constraints

Developing efficient kernel methods for regression is very popular in the past decade. In this paper, utilizing boosting on kernel-based weaker learners, we propose a novel kernel-based learning algorithm called kernel-based re-scaled boosting with truncation, dubbed as KReBooT. The proposed KReBooT benefits in controlling the structure of estimators and producing sparse estimate, and is near overfitting resistant. We conduct both theoretical analysis and numerical simulations to illustrate the power of KReBooT. Theoretically, we prove that KReBooT can achieve the almost optimal numerical convergence rate for nonlinear approximation. Furthermore, using the recently developed integral operator approach and a variant of Talagrand's concentration inequality, we provide fast learning rates for KReBooT, which is a new record of boosting-type algorithms. Numerically, we carry out a series of simulations to show the promising performance of KReBooT in terms of its good generalization, near over-fitting resistance and structure constraints.