arXiv subjects
Publications and source records attributed to Dongsheng Li.
In this paper, we establish boundary $W^{2,δ}$ estimates for $u\in S(λ,Λ,f)$ on $C^{1,α}$ domains with $f\in L^p$ as $n<p<\infty$ and $C^{1,α}$ boundary values. Instead of straightening out the boundary, our main idea is to obtain boundary $W^{2,δ}$ estimates from interior $W^{2,δ_0}$ estimates and Whitney decomposition for some $δ\leq δ_0$.
Capturing the dynamics in user preference is crucial to better predict user future behaviors because user preferences often drift over time. Many existing recommendation algorithms -- including both shallow and deep ones -- often model such dynamics independently, i.e., user static and dynamic preferences are not modeled under the same latent space, which makes it difficult to fuse them for recommendation. This paper considers the problem of embedding a user's sequential behavior into the latent space of user preferences, namely translating sequence to preference. To this end, we formulate the sequential recommendation task as a dictionary learning problem, which learns: 1) a shared dictionary matrix, each row of which represents a partial signal of user dynamic preferences shared across users; and 2) a posterior distribution estimator using a deep autoregressive model integrated with Gated Recurrent Unit (GRU), which can select related rows of the dictionary to represent a user's dynamic preferences conditioned on his/her past behaviors. Qualitative studies on the Netflix dataset demonstrate that the proposed method can capture the user preference drifts over time and quantitative studies on multiple real-world datasets demonstrate that the proposed method can achieve higher accuracy compared with state-of-the-art factorization and neural sequential recommendation methods. The code is available at https://github.com/cchao0116/S2PNM-TKDE2021.
In large-scale online services, crucial metrics, a.k.a., key performance indicators (KPIs), are monitored periodically to check their running statuses. Generally, KPIs are aggregated along multiple dimensions and derived by complex calculations among fundamental metrics from the raw data. Once abnormal KPI values are observed, root cause analysis (RCA) can be applied to identify the reasons for anomalies, so that we can troubleshoot quickly. Recently, several automatic RCA techniques were proposed to localize the related dimensions (or a combination of dimensions) to explain the anomalies. However, their analyses are limited to the data on the abnormal metric and ignore the data of other metrics which may be also related to the anomalies, leading to imprecise or even incorrect root causes. To this end, we propose a cross-metric multi-dimensional root cause analysis method, named CMMD, which consists of two key components: 1) relationship modeling, which utilizes graph neural network (GNN) to model the unknown complex calculation among metrics and aggregation function among dimensions from historical data; 2) root cause localization, which adopts the genetic algorithm to efficiently and effectively dive into the raw data and localize the abnormal dimension(s) once the KPI anomalies are detected. Experiments on synthetic datasets, public datasets and online production environment demonstrate the superiority of our proposed CMMD method compared with baselines. Currently, CMMD is running as an online service in Microsoft Azure.
It is hard to train Recurrent Neural Network (RNN) with stable convergence and avoid gradient vanishing and exploding problems, as the weights in the recurrent unit are repeated from iteration to iteration. Moreover, RNN is sensitive to the initialization of weights and bias, which brings difficulties in training. The Alternating Direction Method of Multipliers (ADMM) has become a promising algorithm to train neural networks beyond traditional stochastic gradient algorithms with the gradient-free features and immunity to unsatisfactory conditions. However, ADMM could not be applied to train RNN directly since the state in the recurrent unit is repetitively updated over timesteps. Therefore, this work builds a new framework named ADMMiRNN upon the unfolded form of RNN to address the above challenges simultaneously. We also provide novel update rules and theoretical convergence analysis. We explicitly specify essential update rules in the iterations of ADMMiRNN with constructed approximation techniques and solutions to each sub-problem instead of vanilla ADMM. Numerical experiments are conducted on MNIST, IMDb, and text classification tasks. ADMMiRNN achieves convergent results and outperforms the compared baselines. Furthermore, ADMMiRNN trains RNN more stably without gradient vanishing or exploding than stochastic gradient algorithms. We also provide a distributed paralleled algorithm regarding ADMMiRNN, named P-ADMMiRNN, including Synchronous Parallel ADMMiRNN (SP-ADMMiRNN) and Asynchronous Parallel ADMMiRNN (AP-ADMMiRNN), which is the first to train RNN with ADMM in an asynchronous parallel manner. The source code is publicly available.
Invariant risk minimization (IRM) has recently emerged as a promising alternative for domain generalization. Nevertheless, the loss function is difficult to optimize for nonlinear classifiers and the original optimization objective could fail when pseudo-invariant features and geometric skews exist. Inspired by IRM, in this paper we propose a novel formulation for domain generalization, dubbed invariant information bottleneck (IIB). IIB aims at minimizing invariant risks for nonlinear classifiers and simultaneously mitigating the impact of pseudo-invariant features and geometric skews. Specifically, we first present a novel formulation for invariant causal prediction via mutual information. Then we adopt the variational formulation of the mutual information to develop a tractable loss function for nonlinear classifiers. To overcome the failure modes of IRM, we propose to minimize the mutual information between the inputs and the corresponding representations. IIB significantly outperforms IRM on synthetic datasets, where the pseudo-invariant features and geometric skews occur, showing the effectiveness of proposed formulation in overcoming failure modes of IRM. Furthermore, experiments on DomainBed show that IIB outperforms $13$ baselines by $0.9\%$ on average across $7$ real datasets.
Fine-tuning pretrained models is a common practice in domain generalization (DG) tasks. However, fine-tuning is usually computationally expensive due to the ever-growing size of pretrained models. More importantly, it may cause over-fitting on source domain and compromise their generalization ability as shown in recent works. Generally, pretrained models possess some level of generalization ability and can achieve decent performance regarding specific domains and samples. However, the generalization performance of pretrained models could vary significantly over different test domains even samples, which raises challenges for us to best leverage pretrained models in DG tasks. In this paper, we propose a novel domain generalization paradigm to better leverage various pretrained models, named specialized ensemble learning for domain generalization (SEDGE). It first trains a linear label space adapter upon fixed pretrained models, which transforms the outputs of the pretrained model to the label space of the target domain. Then, an ensemble network aware of model specialty is proposed to dynamically dispatch proper pretrained models to predict each test sample. Experimental studies on several benchmarks show that SEDGE achieves significant performance improvements comparing to strong baselines including state-of-the-art method in DG tasks and reduces the trainable parameters by ~99% and the training time by ~99.5%.
In this paper, a new method is represented to investigate boundary $W^{2,p}$ estimates for elliptic equations, which is, roughly speaking, to derive boundary $W^{2,p}$ estimates from interior $W^{2,p}$ estimates by Whitney decomposition. Using it, $W^{2,p}$ estimates on $C^{1,α}$ domains are obtained for nondivergence form linear elliptic equations and further more, fully nonlinear elliptic equations are also considered.
Continuous-depth neural networks, such as the Neural Ordinary Differential Equations (ODEs), have aroused a great deal of interest from the communities of machine learning and data science in recent years, which bridge the connection between deep neural networks and dynamical systems. In this article, we introduce a new sort of continuous-depth neural network, called the Neural Piecewise-Constant Delay Differential Equations (PCDDEs). Here, unlike the recently proposed framework of the Neural Delay Differential Equations (DDEs), we transform the single delay into the piecewise-constant delay(s). The Neural PCDDEs with such a transformation, on one hand, inherit the strength of universal approximating capability in Neural DDEs. On the other hand, the Neural PCDDEs, leveraging the contributions of the information from the multiple previous time steps, further promote the modeling capability without augmenting the network dimension. With such a promotion, we show that the Neural PCDDEs do outperform the several existing continuous-depth neural frameworks on the one-dimensional piecewise-constant delay population dynamics and real-world datasets, including MNIST, CIFAR10, and SVHN.
In this paper, we consider a different data format for images: vector graphics. In contrast to raster graphics which are widely used in image recognition, vector graphics can be scaled up or down into any resolution without aliasing or information loss, due to the analytic representation of the primitives in the document. Furthermore, vector graphics are able to give extra structural information on how low-level elements group together to form high level shapes or structures. These merits of graphic vectors have not been fully leveraged in existing methods. To explore this data format, we target on the fundamental recognition tasks: object localization and classification. We propose an efficient CNN-free pipeline that does not render the graphic into pixels (i.e. rasterization), and takes textual document of the vector graphics as input, called YOLaT (You Only Look at Text). YOLaT builds multi-graphs to model the structural and spatial information in vector graphics, and a dual-stream graph neural network is proposed to detect objects from the graph. Our experiments show that by directly operating on vector graphics, YOLaT out-performs raster-graphic based object detection baselines in terms of both average precision and efficiency.
The interplay between topology and magnetism is essential for realizing novel topological states including the axion insulator, the magnetic Weyl semimetal, etc. An intrinsically ferromagnetic topological material with only the topological bands at the charge neutrality energy has so far remained elusive. By rationally designing the natural heterostructure consisting of [MnBi2Te4] septuple layers and [Bi2Te3] quintuple layers, we report MnBi8Te13 as the first intrinsic ferromagnetic topological material with clean low-energy band structure. Based on the thermodynamic, transport and neutron diffraction measurements, our data show that despite the adjacent [MnBi2Te4] being 44.1 Å apart, MnBi8Te13 manifests long-range ferromagnetism below 10.5 K with strong coupling between magnetism and charge carriers. Our first-principles calculations and angle-resolved photoemission spectroscopy measurements further demonstrate that MnBi8Te13 is an intrinsic ferromagnetic axion state. Therefore, MnBi8Te13 serves as an ideal system to investigate rich emergent phenomena, including the quantized anomalous Hall effect and quantized topological magnetoelectric effect.
Distributed stochastic gradient descent (SGD) approach has been widely used in large-scale deep learning, and the gradient collective method is vital to ensure the training scalability of the distributed deep learning system. Collective communication such as AllReduce has been widely adopted for the distributed SGD process to reduce the communication time. However, AllReduce incurs large bandwidth resources while most gradients are sparse in many cases since many gradient values are zeros and should be efficiently compressed for bandwidth saving. To reduce the sparse gradient communication overhead, we propose Sparse-Sketch Reducer (S2 Reducer), a novel sketch-based sparse gradient aggregation method with convergence guarantees. S2 Reducer reduces the communication cost by only compressing the non-zero gradients with count-sketch and bitmap, and enables the efficient AllReduce operators for parallel SGD training. We perform extensive evaluation against four state-of-the-art methods over five training models. Our results show that S2 Reducer converges to the same accuracy, reduces 81\% sparse communication overhead, and achieves 1.8$ \times $ speedup compared to state-of-the-art approaches.
Time series data generation has drawn increasing attention in recent years. Several generative adversarial network (GAN) based methods have been proposed to tackle the problem usually with the assumption that the targeted time series data are well-formatted and complete. However, real-world time series (RTS) data are far away from this utopia, e.g., long sequences with variable lengths and informative missing data raise intractable challenges for designing powerful generation algorithms. In this paper, we propose a novel generative framework for RTS data - RTSGAN to tackle the aforementioned challenges. RTSGAN first learns an encoder-decoder module which provides a mapping between a time series instance and a fixed-dimension latent vector and then learns a generation module to generate vectors in the same latent space. By combining the generator and the decoder, RTSGAN is able to generate RTS which respect the original feature distributions and the temporal dynamics. To generate time series with missing values, we further equip RTSGAN with an observation embedding layer and a decide-and-generate decoder to better utilize the informative missing patterns. Experiments on the four RTS datasets show that the proposed framework outperforms the previous generation methods in terms of synthetic data utility for downstream classification and prediction tasks.
Heavy ball momentum is crucial in accelerating (stochastic) gradient-based optimization algorithms for machine learning. Existing heavy ball momentum is usually weighted by a uniform hyperparameter, which relies on excessive tuning. Moreover, the calibrated fixed hyperparameter may not lead to optimal performance. In this paper, to eliminate the effort for tuning the momentum-related hyperparameter, we propose a new adaptive momentum inspired by the optimal choice of the heavy ball momentum for quadratic optimization. Our proposed adaptive heavy ball momentum can improve stochastic gradient descent (SGD) and Adam. SGD and Adam with the newly designed adaptive momentum are more robust to large learning rates, converge faster, and generalize better than the baselines. We verify the efficiency of SGD and Adam with the new adaptive momentum on extensive machine learning benchmarks, including image classification, language modeling, and machine translation. Finally, we provide convergence guarantees for SGD and Adam with the proposed adaptive momentum.
The energy consumption of deep learning models is increasing at a breathtaking rate, which raises concerns due to potential negative effects on carbon neutrality in the context of global warming and climate change. With the progress of efficient deep learning techniques, e.g., model compression, researchers can obtain efficient models with fewer parameters and smaller latency. However, most of the existing efficient deep learning methods do not explicitly consider energy consumption as a key performance indicator. Furthermore, existing methods mostly focus on the inference costs of the resulting efficient models, but neglect the notable energy consumption throughout the entire life cycle of the algorithm. In this paper, we present the first large-scale energy consumption benchmark for efficient computer vision models, where a new metric is proposed to explicitly evaluate the full-cycle energy consumption under different model usage intensity. The benchmark can provide insights for low carbon emission when selecting efficient deep learning algorithms in different model usage scenarios.
This paper revisits the temporal difference (TD) learning algorithm for the policy evaluation tasks in reinforcement learning. Typically, the performance of TD(0) and TD($λ$) is very sensitive to the choice of stepsizes. Oftentimes, TD(0) suffers from slow convergence. Motivated by the tight link between the TD(0) learning algorithm and the stochastic gradient methods, we develop a provably convergent adaptive projected variant of the TD(0) learning algorithm with linear function approximation that we term AdaTD(0). In contrast to the TD(0), AdaTD(0) is robust or less sensitive to the choice of stepsizes. Analytically, we establish that to reach an $ε$ accuracy, the number of iterations needed is $\tilde{O}(ε^{-2}\ln^4\frac{1}ε/\ln^4\frac{1}ρ)$ in the general case, where $ρ$ represents the speed of the underlying Markov chain converges to the stationary distribution. This implies that the iteration complexity of AdaTD(0) is no worse than that of TD(0) in the worst case. When the stochastic semi-gradients are sparse, we provide theoretical acceleration of AdaTD(0). Going beyond TD(0), we develop an adaptive variant of TD($λ$), which is referred to as AdaTD($λ$). Empirically, we evaluate the performance of AdaTD(0) and AdaTD($λ$) on several standard reinforcement learning tasks, which demonstrate the effectiveness of our new approaches.
Graph convolutional networks (GCNs) have recently enabled a popular class of algorithms for collaborative filtering (CF). Nevertheless, the theoretical underpinnings of their empirical successes remain elusive. In this paper, we endeavor to obtain a better understanding of GCN-based CF methods via the lens of graph signal processing. By identifying the critical role of smoothness, a key concept in graph signal processing, we develop a unified graph convolution-based framework for CF. We prove that many existing CF methods are special cases of this framework, including the neighborhood-based methods, low-rank matrix factorization, linear auto-encoders, and LightGCN, corresponding to different low-pass filters. Based on our framework, we then present a simple and computationally efficient CF baseline, which we shall refer to as Graph Filter based Collaborative Filtering (GF-CF). Given an implicit feedback matrix, GF-CF can be obtained in a closed form instead of expensive training with back-propagation. Experiments will show that GF-CF achieves competitive or better performance against deep learning-based methods on three well-known datasets, notably with a $70\%$ performance gain over LightGCN on the Amazon-book dataset.
Confidence calibration is of great importance to the reliability of decisions made by machine learning systems. However, discriminative classifiers based on deep neural networks are often criticized for producing overconfident predictions that fail to reflect the true correctness likelihood of classification accuracy. We argue that such an inability to model uncertainty is mainly caused by the closed-world nature in softmax: a model trained by the cross-entropy loss will be forced to classify input into one of $K$ pre-defined categories with high probability. To address this problem, we for the first time propose a novel $K$+1-way softmax formulation, which incorporates the modeling of open-world uncertainty as the extra dimension. To unify the learning of the original $K$-way classification task and the extra dimension that models uncertainty, we propose a novel energy-based objective function, and moreover, theoretically prove that optimizing such an objective essentially forces the extra dimension to capture the marginal data distribution. Extensive experiments show that our approach, Energy-based Open-World Softmax (EOW-Softmax), is superior to existing state-of-the-art methods in improving confidence calibration.
Recently, a new form of online shopping becomes more and more popular, which combines live streaming with E-Commerce activity. The streamers introduce products and interact with their audiences, and hence greatly improve the performance of selling products. Despite of the successful applications in industries, the live stream E-commerce has not been well studied in the data science community. To fill this gap, we investigate this brand-new scenario and collect a real-world Live Stream E-Commerce (LSEC) dataset. Different from conventional E-commerce activities, the streamers play a pivotal role in the LSEC events. Hence, the key is to make full use of rich interaction information among streamers, users, and products. We first conduct data analysis on the tripartite interaction data and quantify the streamer's influence on users' purchase behavior. Based on the analysis results, we model the tripartite information as a heterogeneous graph, which can be decomposed to multiple bipartite graphs in order to better capture the influence. We propose a novel Live Stream E-Commerce Graph Neural Network framework (LSEC-GNN) to learn the node representations of each bipartite graph, and further design a multi-task learning approach to improve product recommendation. Extensive experiments on two real-world datasets with different scales show that our method can significantly outperform various baseline approaches.