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GreenLearning networks (GL) directly learn Green's function in physical space, making them an interpretable model for capturing unknown solution operators of partial differential equations (PDEs). For many PDEs, the corresponding Green's function exhibits asymptotic smoothness. In this paper, we propose a framework named Green Multigrid networks (GreenMGNet), an operator learning algorithm designed for a class of asymptotically smooth Green's functions. Compared with the pioneering GL, the new framework presents itself with better accuracy and efficiency, thereby achieving a significant improvement. GreenMGNet is composed of two technical novelties. First, Green's function is modeled as a piecewise function to take into account its singular behavior in some parts of the hyperplane. Such piecewise function is then approximated by a neural network with augmented output(AugNN) so that it can capture singularity accurately. Second, the asymptotic smoothness property of Green's function is used to leverage the Multi-Level Multi-Integration (MLMI) algorithm for both the training and inference stages. Several test cases of operator learning are presented to demonstrate the accuracy and effectiveness of the proposed method. On average, GreenMGNet achieves $3.8\%$ to $39.15\%$ accuracy improvement. To match the accuracy level of GL, GreenMGNet requires only about $10\%$ of the full grid data, resulting in a $55.9\%$ and $92.5\%$ reduction in training time and GPU memory cost for one-dimensional test problems, and a $37.7\%$ and $62.5\%$ reduction for two-dimensional test problems.

We present observations and timing analyses of 68 millisecond pulsars (MSPs) comprising the 15-year data set of the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). NANOGrav is a pulsar timing array (PTA) experiment that is sensitive to low-frequency gravitational waves. This is NANOGrav's fifth public data release, including both "narrowband" and "wideband" time-of-arrival (TOA) measurements and corresponding pulsar timing models. We have added 21 MSPs and extended our timing baselines by three years, now spanning nearly 16 years for some of our sources. The data were collected using the Arecibo Observatory, the Green Bank Telescope, and the Very Large Array between frequencies of 327 MHz and 3 GHz, with most sources observed approximately monthly. A number of notable methodological and procedural changes were made compared to our previous data sets. These improve the overall quality of the TOA data set and are part of the transition to new pulsar timing and PTA analysis software packages. For the first time, our data products are accompanied by a full suite of software to reproduce data reduction, analysis, and results. Our timing models include a variety of newly detected astrometric and binary pulsar parameters, including several significant improvements to pulsar mass constraints. We find that the time series of 23 pulsars contain detectable levels of red noise, 10 of which are new measurements. In this data set, we find evidence for a stochastic gravitational-wave background., Comment: 90 pages, 74 figures, 6 tables; published in Astrophysical Journal Letters as part of Focus on NANOGrav's 15-year Data Set and the Gravitational Wave Background. For questions or comments, please email comments@nanograv.org

Parameter sharing has proven to be a parameter-efficient approach. Previous work on Transformers has focused on sharing parameters in different layers, which can improve the performance of models with limited parameters by increasing model depth. In this paper, we study why this approach works from two perspectives. First, increasing model depth makes the model more complex, and we hypothesize that the reason is related to model complexity (referring to FLOPs). Secondly, since each shared parameter will participate in the network computation several times in forward propagation, its corresponding gradient will have a different range of values from the original model, which will affect the model convergence. Based on this, we hypothesize that training convergence may also be one of the reasons. Through further analysis, we show that the success of this approach can be largely attributed to better convergence, with only a small part due to the increased model complexity. Inspired by this, we tune the training hyperparameters related to model convergence in a targeted manner. Experiments on 8 machine translation tasks show that our model achieves competitive performance with only half the model complexity of parameter sharing models.

Deploying NMT models on mobile devices is essential for privacy, low latency, and offline scenarios. For high model capacity, NMT models are rather large. Running these models on devices is challenging with limited storage, memory, computation, and power consumption. Existing work either only focuses on a single metric such as FLOPs or general engine which is not good at auto-regressive decoding. In this paper, we present MobileNMT, a system that can translate in 15MB and 30ms on devices. We propose a series of principles for model compression when combined with quantization. Further, we implement an engine that is friendly to INT8 and decoding. With the co-design of model and engine, compared with the existing system, we speed up 47.0x and save 99.5% of memory with only 11.6% loss of BLEU. The code is publicly available at https://github.com/zjersey/Lightseq-ARM., Comment: accepted by ACL2023 Industry Track

For years the model performance in machine learning obeyed a power-law relationship with the model size. For the consideration of parameter efficiency, recent studies focus on increasing model depth rather than width to achieve better performance. In this paper, we study how model width affects the Transformer model through a parameter-efficient multi-path structure. To better fuse features extracted from different paths, we add three additional operations to each sublayer: a normalization at the end of each path, a cheap operation to produce more features, and a learnable weighted mechanism to fuse all features flexibly. Extensive experiments on 12 WMT machine translation tasks show that, with the same number of parameters, the shallower multi-path model can achieve similar or even better performance than the deeper model. It reveals that we should pay more attention to the multi-path structure, and there should be a balance between the model depth and width to train a better large-scale Transformer., Comment: accepted by EMNLP2022 Findings

This paper describes the submissions of the NiuTrans Team to the WNGT 2020 Efficiency Shared Task. We focus on the efficient implementation of deep Transformer models \cite{wang-etal-2019-learning, li-etal-2019-niutrans} using NiuTensor (https://github.com/NiuTrans/NiuTensor), a flexible toolkit for NLP tasks. We explored the combination of deep encoder and shallow decoder in Transformer models via model compression and knowledge distillation. The neural machine translation decoding also benefits from FP16 inference, attention caching, dynamic batching, and batch pruning. Our systems achieve promising results in both translation quality and efficiency, e.g., our fastest system can translate more than 40,000 tokens per second with an RTX 2080 Ti while maintaining 42.9 BLEU on \textit{newstest2018}. The code, models, and docker images are available at NiuTrans.NMT (https://github.com/NiuTrans/NiuTrans.NMT)., Comment: NiuTrans at the WNGT 2020 Translation Efficiency Task

This paper describes the NiuTrans system for the WMT21 translation efficiency task (http://statmt.org/wmt21/efficiency-task.html). Following last year's work, we explore various techniques to improve efficiency while maintaining translation quality. We investigate the combinations of lightweight Transformer architectures and knowledge distillation strategies. Also, we improve the translation efficiency with graph optimization, low precision, dynamic batching, and parallel pre/post-processing. Our system can translate 247,000 words per second on an NVIDIA A100, being 3$\times$ faster than last year's system. Our system is the fastest and has the lowest memory consumption on the GPU-throughput track. The code, model, and pipeline will be available at NiuTrans.NMT (https://github.com/NiuTrans/NiuTrans.NMT)., Comment: NiuTrans at the WMT21 Translation Efficiency Task

Improving Transformer efficiency has become increasingly attractive recently. A wide range of methods has been proposed, e.g., pruning, quantization, new architectures and etc. But these methods are either sophisticated in implementation or dependent on hardware. In this paper, we show that the efficiency of Transformer can be improved by combining some simple and hardware-agnostic methods, including tuning hyper-parameters, better design choices and training strategies. On the WMT news translation tasks, we improve the inference efficiency of a strong Transformer system by 3.80X on CPU and 2.52X on GPU. The code is publicly available at https://github.com/Lollipop321/mini-decoder-network., Comment: accepted by EMNLP (Findings) 2021

The large attention-based encoder-decoder network (Transformer) has become prevailing recently due to its effectiveness. But the high computation complexity of its decoder raises the inefficiency issue. By examining the mathematic formulation of the decoder, we show that under some mild conditions, the architecture could be simplified by compressing its sub-layers, the basic building block of Transformer, and achieves a higher parallelism. We thereby propose Compressed Attention Network, whose decoder layer consists of only one sub-layer instead of three. Extensive experiments on 14 WMT machine translation tasks show that our model is 1.42x faster with performance on par with a strong baseline. This strong baseline is already 2x faster than the widely used standard baseline without loss in performance., Comment: accepted by AAAI2021

Unsupervised Bilingual Dictionary Induction methods based on the initialization and the self-learning have achieved great success in similar language pairs, e.g., English-Spanish. But they still fail and have an accuracy of 0% in many distant language pairs, e.g., English-Japanese. In this work, we show that this failure results from the gap between the actual initialization performance and the minimum initialization performance for the self-learning to succeed. We propose Iterative Dimension Reduction to bridge this gap. Our experiments show that this simple method does not hamper the performance of similar language pairs and achieves an accuracy of 13.64~55.53% between English and four distant languages, i.e., Chinese, Japanese, Vietnamese and Thai., Comment: Accepted by COLING2020

Knowledge distillation has been proven to be effective in model acceleration and compression. It allows a small network to learn to generalize in the same way as a large network. Recent successes in pre-training suggest the effectiveness of transferring model parameters. Inspired by this, we investigate methods of model acceleration and compression in another line of research. We propose Weight Distillation to transfer the knowledge in the large network parameters through a parameter generator. Our experiments on WMT16 En-Ro, NIST12 Zh-En, and WMT14 En-De machine translation tasks show that weight distillation can train a small network that is 1.88~2.94x faster than the large network but with competitive performance. With the same sized small network, weight distillation can outperform knowledge distillation by 0.51~1.82 BLEU points., Comment: accepted by ACL2021

8-bit integer inference, as a promising direction in reducing both the latency and storage of deep neural networks, has made great progress recently. On the other hand, previous systems still rely on 32-bit floating point for certain functions in complex models (e.g., Softmax in Transformer), and make heavy use of quantization and de-quantization. In this work, we show that after a principled modification on the Transformer architecture, dubbed Integer Transformer, an (almost) fully 8-bit integer inference algorithm Scale Propagation could be derived. De-quantization is adopted when necessary, which makes the network more efficient. Our experiments on WMT16 En<->Ro, WMT14 En<->De and En->Fr translation tasks as well as the WikiText-103 language modelling task show that the fully 8-bit Transformer system achieves comparable performance with the floating point baseline but requires nearly 4x less memory footprint., Comment: accepted by IJCAI2020

In this paper, we report our recent practice at Tencent for user modeling based on mobile app usage. User behaviors on mobile app usage, including retention, installation, and uninstallation, can be a good indicator for both long-term and short-term interests of users. For example, if a user installs Snapseed recently, she might have a growing interest in photographing. Such information is valuable for numerous downstream applications, including advertising, recommendations, etc. Traditionally, user modeling from mobile app usage heavily relies on handcrafted feature engineering, which requires onerous human work for different downstream applications, and could be sub-optimal without domain experts. However, automatic user modeling based on mobile app usage faces unique challenges, including (1) retention, installation, and uninstallation are heterogeneous but need to be modeled collectively, (2) user behaviors are distributed unevenly over time, and (3) many long-tailed apps suffer from serious sparsity. In this paper, we present a tailored AutoEncoder-coupled Transformer Network (AETN), by which we overcome these challenges and achieve the goals of reducing manual efforts and boosting performance. We have deployed the model at Tencent, and both online/offline experiments from multiple domains of downstream applications have demonstrated the effectiveness of the output user embeddings., Comment: To be published in the KDD2020 proceedings as a full paper

Nowadays, news apps have taken over the popularity of paper-based media, providing a great opportunity for personalization. Recurrent Neural Network (RNN)-based sequential recommendation is a popular approach that utilizes users' recent browsing history to predict future items. This approach is limited that it does not consider the societal influences of news consumption, i.e., users may follow popular topics that are constantly changing, while certain hot topics might be spreading only among specific groups of people. Such societal impact is difficult to predict given only users' own reading histories. On the other hand, the traditional User-based Collaborative Filtering (UserCF) makes recommendations based on the interests of the "neighbors", which provides the possibility to supplement the weaknesses of RNN-based methods. However, conventional UserCF only uses a single similarity metric to model the relationships between users, which is too coarse-grained and thus limits the performance. In this paper, we propose a framework of deep neural networks to integrate the RNN-based sequential recommendations and the key ideas from UserCF, to develop Collaborative Sequential Recommendation Networks (CSRNs). Firstly, we build a directed co-reading network of users, to capture the fine-grained topic-specific similarities between users in a vector space. Then, the CSRN model encodes users with RNNs, and learns to attend to neighbors and summarize what news they are reading at the moment. Finally, news articles are recommended according to both the user's own state and the summarized state of the neighbors. Experiments on two public datasets show that the proposed model outperforms the state-of-the-art approaches significantly.

Single Particle Tracking (SPT) is a powerful class of tools for analyzing the dynamics of individual biological macromolecules moving inside living cells. The acquired data is typically in the form of a sequence of camera images that are then post-processed to reveal details about the motion. In this work, we develop an algorithm for jointly estimating both particle trajectory and motion model parameters from the data. Our approach uses Expectation Maximization (EM) combined with an Unscented Kalman filter (UKF) and an Unscented Rauch-Tung-Striebel smoother (URTSS), allowing us to use an accurate, nonlinear model of the observations acquired by the camera. Due to the shot noise characteristics of the photon generation process, this model uses a Poisson distribution to capture the measurement noise inherent in imaging. In order to apply a UKF, we first must transform the measurements into a model with additive Gaussian noise. We consider two approaches, one based on variance stabilizing transformations (where we compare the Anscombe and Freeman-Tukey transforms) and one on a Gaussian approximation to the Poisson distribution. Through simulations, we demonstrate efficacy of the approach and explore the differences among these measurement transformations., Comment: Accepted by 58th Conference on Decision and Control (CDC)

Unsupervised multi-domain image-to-image translation aims to synthesis images among multiple domains without labeled data, which is more general and complicated than one-to-one image mapping. However, existing methods mainly focus on reducing the large costs of modeling and do not pay enough attention to the quality of generated images. In some target domains, their translation results may not be expected or even it has model collapse. To improve the image quality, we propose an effective many-to-many mapping framework for unsupervised multi-domain image-to-image translation. There are two key aspects in our method. The first is a proposed many-to-many architecture with only one domain-shared encoder and several domain-specialized decoders to effectively and simultaneously translate images across multiple domains. The second is two proposed constraints extended from one-to-one mappings to further help improve the generation. All the evaluations demonstrate our framework is superior to existing methods and provides an effective solution for multi-domain image-to-image translation., Comment: 13 pages, 14 figures, 6 tables

Extreme events, such as wave-storms, need to be characterized for coastal infrastructure design purposes. Such description should contain information on both the univariate behaviour and the joint-dependence of storm-variables. These two aspects have been here addressed through generalized Pareto distributions and hierarchical Archimedean copulas. A non-stationary model has been used to highlight the relationship between these extreme events and non-stationary climate. It has been applied to a Representative Concentration Pathway 8.5 Climate-Change scenario, for a fetch-limited environment (Catalan Coast). In the non-stationary model, all considered variables decrease in time, except for storm-duration at the northern part of the Catalan Coast. The joint distribution of storm variables presents cyclical fluctuations, with a stronger influence of climate dynamics than of climate itself.

The development of high-energy and high-power density supercapacitors (SCs) is critical for enabling next-generation energy storage applications. Nanocarbons are excellent SC electrode materials due to their economic viability, high-surface area, and high stability. Although nanocarbons have high theoretical surface area and hence high double layer capacitance, the net amount of energy stored in nanocarbon-SCs is much below theoretical limits due to two inherent bottlenecks: i) their low quantum capacitance and ii) limited ion-accessible surface area. Here, we demonstrate that defects in graphene could be effectively used to mitigate these bottlenecks by drastically increasing the quantum capacitance and opening new channels to facilitate ion diffusion in otherwise closed interlayer spaces. Our results support the emergence of a new energy paradigm in SCs with 250% enhancement in double layer capacitance beyond the theoretical limit. Furthermore, we demonstrate prototype defect engineered bulk SC devices with energy densities 500% higher than state-of-the-art commercial SCs without compromising the power density., Comment: 15 pages, 5 figures, and 8 supplemental figures

We present a study of the environment of barred galaxies using a volume-limited sample of over 30,000 galaxies drawn from the Sloan Digital Sky Survey. We use four different statistics to quantify the environment: the projected two-point cross-correlation function, the background-subtracted number count of neighbor galaxies, the overdensity of the local environment, and the membership of our galaxies to galaxy groups to segregate central and satellite systems. For barred galaxies as a whole, we find a very weak difference in all the quantities compared to unbarred galaxies of the control sample. When we split our sample into early- and late-type galaxies, we see a weak but significant trend for early-type galaxies with a bar to be more strongly clustered on scales from a few 100 kpc to 1 Mpc when compared to unbarred early-type galaxies. This indicates that the presence of a bar in early-type galaxies depends on the location within their host dark matter halos. This is confirmed by the group catalog in the sense that for early-types, the fraction of central galaxies is smaller if they have a bar. For late-type galaxies, we find fewer neighbors within $\sim$50 kpc around the barred galaxies when compared to unbarred galaxies form the control sample, suggesting that tidal forces from close companions suppress the formation/growth of bars. Finally, we find no obvious correlation between overdensity and the bars in our sample, showing that galactic bars are not obviously linked to the large-scale structure of the universe., Comment: 11 pages, 8 figures. Accepted for publication in ApJ; minor changes and references updated