arXiv subjects
Publications and source records attributed to Wei Lin.
Applying Morse theory, we give a standard form for a class of surfaces which includes all the properly embedded incompressible surfaces in 3-dimensional handlebodies. We also give a necessary and sufficient condition to determine the incompressibility of such surfaces placed in our standard form. Our algorithm is practical. Several examples are given to test the algorithm.
In this paper, we propose Stochastic Knowledge Distillation (SKD) to obtain compact BERT-style language model dubbed SKDBERT. In each iteration, SKD samples a teacher model from a pre-defined teacher ensemble, which consists of multiple teacher models with multi-level capacities, to transfer knowledge into student model in an one-to-one manner. Sampling distribution plays an important role in SKD. We heuristically present three types of sampling distributions to assign appropriate probabilities for multi-level teacher models. SKD has two advantages: 1) it can preserve the diversities of multi-level teacher models via stochastically sampling single teacher model in each iteration, and 2) it can also improve the efficacy of knowledge distillation via multi-level teacher models when large capacity gap exists between the teacher model and the student model. Experimental results on GLUE benchmark show that SKDBERT reduces the size of a BERT$_{\rm BASE}$ model by 40% while retaining 99.5% performances of language understanding and being 100% faster.
We present a neural point cloud rendering pipeline through a novel multi-frequency-aware patch adversarial learning framework. The proposed approach aims to improve the rendering realness by minimizing the spectrum discrepancy between real and synthesized images, especially on the high-frequency localized sharpness information which causes image blur visually. Specifically, a patch multi-discriminator scheme is proposed for the adversarial learning, which combines both spectral domain (Fourier Transform and Discrete Wavelet Transform) discriminators as well as the spatial (RGB) domain discriminator to force the generator to capture global and local spectral distributions of the real images. The proposed multi-discriminator scheme not only helps to improve rendering realness, but also enhance the convergence speed and stability of adversarial learning. Moreover, we introduce a noise-resistant voxelisation approach by utilizing both the appearance distance and spatial distance to exclude the spatial outlier points caused by depth noise. Our entire architecture is fully differentiable and can be learned in an end-to-end fashion. Extensive experiments show that our method produces state-of-the-art results for neural point cloud rendering by a significant margin. Our source code will be made public at a later date.
This paper proposes DisCo, an automatic deep learning compilation module for data-parallel distributed training. Unlike most deep learning compilers that focus on training or inference on a single device, DisCo optimizes a DNN model for distributed training over multiple GPU machines. Existing single-device compilation strategies do not work well in distributed training, due mainly to communication inefficiency that they incur. DisCo generates optimized, joint computation operator and communication tensor fusion strategies to enable highly efficient distributed training. A GNN-based simulator is built to effectively estimate per-iteration training time achieved by operator/tensor fusion candidates. A backtracking search algorithm is driven by the simulator, navigating efficiently in the large strategy space to identify good operator/tensor fusion strategies that minimize distributed training time. We compare DisCo with existing DL fusion schemes and show that it achieves good training speed-up close to the ideal, full computation-communication overlap case.
Federated learning, where algorithms are trained across multiple decentralized devices without sharing local data, is increasingly popular in distributed machine learning practice. Typically, a graph structure $G$ exists behind local devices for communication. In this work, we consider parameter estimation in federated learning with data distribution and communication heterogeneity, as well as limited computational capacity of local devices. We encode the distribution heterogeneity by parametrizing distributions on local devices with a set of distinct $p$-dimensional vectors. We then propose to jointly estimate parameters of all devices under the $M$-estimation framework with the fused Lasso regularization, encouraging an equal estimate of parameters on connected devices in $G$. We provide a general result for our estimator depending on $G$, which can be further calibrated to obtain convergence rates for various specific problem setups. Surprisingly, our estimator attains the optimal rate under certain graph fidelity condition on $G$, as if we could aggregate all samples sharing the same distribution. If the graph fidelity condition is not met, we propose an edge selection procedure via multiple testing to ensure the optimality. To ease the burden of local computation, a decentralized stochastic version of ADMM is provided, with convergence rate $O(T^{-1}\log T)$ where $T$ denotes the number of iterations. We highlight that, our algorithm transmits only parameters along edges of $G$ at each iteration, without requiring a central machine, which preserves privacy. We further extend it to the case where devices are randomly inaccessible during the training process, with a similar algorithmic convergence guarantee. The computational and statistical efficiency of our method is evidenced by simulation experiments and the 2020 US presidential election data set.
Control problems are always challenging since they arise from the real-world systems where stochasticity and randomness are of ubiquitous presence. This naturally and urgently calls for developing efficient neural control policies for stabilizing not only the deterministic equations but the stochastic systems as well. Here, in order to meet this paramount call, we propose two types of controllers, viz., the exponential stabilizer (ES) based on the stochastic Lyapunov theory and the asymptotic stabilizer (AS) based on the stochastic asymptotic stability theory. The ES can render the controlled systems exponentially convergent but it requires a long computational time; conversely, the AS makes the training much faster but it can only assure the asymptotic (not the exponential) attractiveness of the control targets. These two stochastic controllers thus are complementary in applications. We also investigate rigorously the linear controller and the proposed neural stochastic controllers in both convergence time and energy cost and numerically compare them in these two indexes. More significantly, we use several representative physical systems to illustrate the usefulness of the proposed controllers in stabilization of dynamical systems.
Graph similarity learning refers to calculating the similarity score between two graphs, which is required in many realistic applications, such as visual tracking, graph classification, and collaborative filtering. As most of the existing graph neural networks yield effective graph representations of a single graph, little effort has been made for jointly learning two graph representations and calculating their similarity score. In addition, existing unsupervised graph similarity learning methods are mainly clustering-based, which ignores the valuable information embodied in graph pairs. To this end, we propose a contrastive graph matching network (CGMN) for self-supervised graph similarity learning in order to calculate the similarity between any two input graph objects. Specifically, we generate two augmented views for each graph in a pair respectively. Then, we employ two strategies, namely cross-view interaction and cross-graph interaction, for effective node representation learning. The former is resorted to strengthen the consistency of node representations in two views. The latter is utilized to identify node differences between different graphs. Finally, we transform node representations into graph-level representations via pooling operations for graph similarity computation. We have evaluated CGMN on eight real-world datasets, and the experiment results show that the proposed new approach is superior to the state-of-the-art methods in graph similarity learning downstream tasks.
Graph-Convolution-based methods have been successfully applied to representation learning on homophily graphs where nodes with the same label or similar attributes tend to connect with one another. Due to the homophily assumption of Graph Convolutional Networks (GCNs) that these methods use, they are not suitable for heterophily graphs where nodes with different labels or dissimilar attributes tend to be adjacent. Several methods have attempted to address this heterophily problem, but they do not change the fundamental aggregation mechanism of GCNs because they rely on summation operators to aggregate information from neighboring nodes, which is implicitly subject to the homophily assumption. Here, we introduce a novel aggregation mechanism and develop a RAndom Walk Aggregation-based Graph Neural Network (called RAW-GNN) method. The proposed approach integrates the random walk strategy with graph neural networks. The new method utilizes breadth-first random walk search to capture homophily information and depth-first search to collect heterophily information. It replaces the conventional neighborhoods with path-based neighborhoods and introduces a new path-based aggregator based on Recurrent Neural Networks. These designs make RAW-GNN suitable for both homophily and heterophily graphs. Extensive experimental results showed that the new method achieved state-of-the-art performance on a variety of homophily and heterophily graphs.
Graph database engines stand out in the era of big data for their efficiency of modeling and processing linked data. There is a strong need of testing graph database engines. However, random testing, the most practical way of automated test generation, faces the challenges of semantic validity, non-empty result, and behavior diversity to detect bugs in graph database engines. To address these challenges, in this paper, we propose GDsmith, the first black-box approach for testing graph database engines. It ensures that each randomly generated Cypher query satisfies the semantic requirements via skeleton generation and completion. GDsmith includes our technique to increase the probability of producing Cypher queries that return non-empty results by leveraging three types of structural mutation strategies. GDsmith also includes our technique to improve the behavior diversity of the generated Cypher queries by selecting property keys according to their previous frequencies when generating new queries. Our evaluation results demonstrate that GDsmith is effective and efficient for automated query generation and substantially outperforms the baseline. GDsmith successfully detects 27 previously unknown bugs on the released versions of three popular open-source graph database engines and receive positive feedback from their developers.
The scaling up of deep neural networks has been demonstrated to be effective in improving model quality, but also encompasses several training challenges in terms of training efficiency, programmability, and resource adaptability. We present Whale, a general and efficient distributed training framework for giant models. To support various parallel strategies and their hybrids, Whale generalizes the programming interface by defining two new primitives in the form of model annotations, allowing for incorporating user hints. The Whale runtime utilizes those annotations and performs graph optimizations to transform a local deep learning DAG graph for distributed multi-GPU execution. Whale further introduces a novel hardware-aware parallel strategy, which improves the performance of model training on heterogeneous GPUs in a balanced manner. Deployed in a production cluster with 512 GPUs, Whale successfully trains an industry-scale multimodal model with over ten trillion model parameters, named M6, demonstrating great scalability and efficiency.
Multi-view crowd counting has been previously proposed to utilize multi-cameras to extend the field-of-view of a single camera, capturing more people in the scene, and improve counting performance for occluded people or those in low resolution. However, the current multi-view paradigm trains and tests on the same single scene and camera-views, which limits its practical application. In this paper, we propose a cross-view cross-scene (CVCS) multi-view crowd counting paradigm, where the training and testing occur on different scenes with arbitrary camera layouts. To dynamically handle the challenge of optimal view fusion under scene and camera layout change and non-correspondence noise due to camera calibration errors or erroneous features, we propose a CVCS model that attentively selects and fuses multiple views together using camera layout geometry, and a noise view regularization method to train the model to handle non-correspondence errors. We also generate a large synthetic multi-camera crowd counting dataset with a large number of scenes and camera views to capture many possible variations, which avoids the difficulty of collecting and annotating such a large real dataset. We then test our trained CVCS model on real multi-view counting datasets, by using unsupervised domain transfer. The proposed CVCS model trained on synthetic data outperforms the same model trained only on real data, and achieves promising performance compared to fully supervised methods that train and test on the same single scene.
Distributed energy resources (DERs) in distribution networks can be aggregated as a virtual power plant (VPP) for transmission-level operations. A critical challenge for such coordination is the complexity of the AC-feasible power transfer region between a VPP and the transmission system at their point of common coupling. To overcome this challenge, this paper develops a characterization method for such regions. The proposed method constructs linear constraints to inner-approximate the AC-feasible power transfer regions. To guarantee AC-feasibility, the parameters in these constraints are determined by applying the Brouwer fixed point theorem to the second-order Taylor expansion of the nonlinear Dist-Flow equations. Based on the power transfer regions characterized with our method, a transmission-level operation problem with VPP participation is formulated and solved through big-M linearization. The proposed methods are verified by numerical experiments in the IEEE 33-bus and IEEE 136-bus test systems.
To train modern large DNN models, pipeline parallelism has recently emerged, which distributes the model across GPUs and enables different devices to process different microbatches in pipeline. Earlier pipeline designs allow multiple versions of model parameters to co-exist (similar to asynchronous training), and cannot ensure the same model convergence and accuracy performance as without pipelining. Synchronous pipelining has recently been proposed which ensures model performance by enforcing a synchronization barrier between training iterations. Nonetheless, the synchronization barrier requires waiting for gradient aggregation from all microbatches and thus delays the training progress. Optimized pipeline planning is needed to minimize such wait and hence the training time, which has not been well studied in the literature. This paper designs efficient, near-optimal algorithms for expediting synchronous pipeline-parallel training of modern large DNNs over arbitrary inter-GPU connectivity. Our algorithm framework comprises two components: a pipeline partition and device mapping algorithm, and a pipeline scheduler that decides processing order of microbatches over the partitions, which together minimize the per-iteration training time. We conduct thorough theoretical analysis, extensive testbed experiments and trace-driven simulation, and demonstrate our scheme can accelerate training up to 157% compared with state-of-the-art designs.
The development of personalized recommendation has significantly improved the accuracy of information matching and the revenue of e-commerce platforms. Recently, it has 2 trends: 1) recommender systems must be trained timely to cope with ever-growing new products and ever-changing user interests from online marketing and social network; 2) SOTA recommendation models introduce DNN modules to improve prediction accuracy. Traditional CPU-based recommender systems cannot meet these two trends, and GPU- centric training has become a trending approach. However, we observe that GPU devices in training recommender systems are underutilized, and they cannot attain an expected throughput improvement as what it has achieved in CV and NLP areas. This issue can be explained by two characteristics of these recommendation models: First, they contain up to a thousand input feature fields, introducing fragmentary and memory-intensive operations; Second, the multiple constituent feature interaction submodules introduce substantial small-sized compute kernels. To remove this roadblock to the development of recommender systems, we propose a novel framework named PICASSO to accelerate the training of recommendation models on commodity hardware. Specifically, we conduct a systematic analysis to reveal the bottlenecks encountered in training recommendation models. We leverage the model structure and data distribution to unleash the potential of hardware through our packing, interleaving, and caching optimization. Experiments show that PICASSO increases the hardware utilization by an order of magnitude on the basis of SOTA baselines and brings up to 6x throughput improvement for a variety of industrial recommendation models. Using the same hardware budget in production, PICASSO on average shortens the walltime of daily training tasks by 7 hours, significantly reducing the delay of continuous delivery.
Data based detection and quantification of causation in complex, nonlinear dynamical systems is of paramount importance to science, engineering and beyond. Inspired by the widely used methodology in recent years, the cross-map-based techniques, we develop a general framework to advance towards a comprehensive understanding of dynamical causal mechanisms, which is consistent with the natural interpretation of causality. In particular, instead of measuring the smoothness of the cross map as conventionally implemented, we define causation through measuring the {\it scaling law} for the continuity of the investigated dynamical system directly. The uncovered scaling law enables accurate, reliable, and efficient detection of causation and assessment of its strength in general complex dynamical systems, outperforming those existing representative methods. The continuity scaling based framework is rigorously established and demonstrated using datasets from model complex systems and the real world.
Menasco showed that a closed surface in the complement of a non-split prime alternating link in $S^3$ contains a circle isotopic in the link complement to a meridian of the links. This result is known as the meridian lemma for alternating links. We give a meridian lemma for the class of fully alternating links in the thickened orientable surfaces of positive genus.
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.
Tie-line power exchanges among regional power systems facilitate renewable accommodations. Power exchanges can be calculated via a tie-line security region that provides the feasible region of the coupling parameters among regional power systems. However, a tie-line security region is a high-dimension polytope due to multiple time periods and border buses inherently in power system operations, leading to the considerable computational burden. A fast calculation method for tie-line security regions in high dimension is studied in this paper. The high-dimension polytope across all the time periods is decomposed as a Cartesian production of lower-dimension polytopes at each time period by leveraging dispatch levels of generations. For each lower-dimension polytope, the computational burden brought by multiple border buses is alleviated by aggregating tie-line power. Also, minimum renewable curtailments are preserved by incorporating an additional dimension in the tie-line security region. For the coupling parameters located within our tie-line security region, a feasible decision of the regional power system exists. Finally, the tie-line security region is used to reduce renewable curtailments in an interconnected power system under a decentralized and non-iterative framework. The performance of the presented methods is corroborated in the IEEE 9-bus system, a 661-bus utility system and a five-region system.