Label smoothing regularization (LSR) has a great success in training deep neural networks by stochastic algorithms such as stochastic gradient descent and its variants. However, the theoretical understanding of its power from the view of optimization is still rare. This study opens the door to a deep understanding of LSR by initiating the analysis. In this paper, we analyze the convergence behaviors of stochastic gradient descent with label smoothing regularization for solving non-convex problems and show that an appropriate LSR can help to speed up the convergence by reducing the variance. More interestingly, we proposed a simple yet effective strategy, namely Two-Stage LAbel smoothing algorithm (TSLA), that uses LSR in the early training epochs and drops it off in the later training epochs. We observe from the improved convergence result of TSLA that it benefits from LSR in the first stage and essentially converges faster in the second stage. To the best of our knowledge, this is the first work for understanding the power of LSR via establishing convergence complexity of stochastic methods with LSR in non-convex optimization. We empirically demonstrate the effectiveness of the proposed method in comparison with baselines on training ResNet models over benchmark data sets.

The study of deep networks (DNs) in the infinite-width limit, via the so-called Neural Tangent Kernel (NTK) approach, has provided new insights into the dynamics of learning, generalization, and the impact of initialization. One key DN architecture remains to be kernelized, namely, the Recurrent Neural Network (RNN). In this paper we introduce and study the Recurrent Neural Tangent Kernel (RNTK), which sheds new insights into the behavior of overparametrized RNNs, including how different time steps are weighted by the RNTK to form the output under different initialization parameters and nonlinearity choices, and how inputs of different lengths are treated. We demonstrate via a number of experiments that the RNTK offers significant performance gains over other kernels, including standard NTKs across a range of different data sets. A unique benefit of the RNTK is that it is agnostic to the length of the input, in stark contrast to other kernels.

The behavior of many dynamical systems follow complex, yet still unknown partial differential equations (PDEs). While several machine learning methods have been proposed to learn PDEs directly from data, previous methods are limited to discrete-time approximations or make the limiting assumption of the observations arriving at regular grids. We propose a general continuous-time differential model for dynamical systems whose governing equations are parameterized by message passing graph neural networks. The model admits arbitrary space and time discretizations, which removes constraints on the locations of observation points and time intervals between the observations. The model is trained with continuous-time adjoint method enabling efficient neural PDE inference. We demonstrate the model's ability to work with unstructured grids, arbitrary time steps, and noisy observations. We compare our method with existing approaches on several well-known physical systems that involve first and higher-order PDEs with state-of-the-art predictive performance.

In many important graph data processing applications the acquired information includes both node features and observations of the graph topology. Graph neural networks (GNNs) are designed to exploit both sources of evidence but they do not optimally tradeoff their utility and integrate them in a manner that is also universal. Here, universality refers to independence on homophily or heterophily graph assumptions. We address these issues by introducing a new Generalized PageRank (GPR) GNN architecture that adaptively learns the GPR weights so as to jointly optimize node feature and topological information extraction, regardless of the extent to which the node labels are homophilic or heterophilic. Learned GPR weights automatically adjust to the node label pattern, irrelevant on the type of initialization, and thereby guarantee excellent learning performance for label patterns that are usually hard to handle. Furthermore, they allow one to avoid feature over-smoothing, a process which renders feature information nondiscriminative, without requiring the network to be shallow. Our accompanying theoretical analysis of the GPR-GNN method is facilitated by novel synthetic benchmark datasets generated by the so-called contextual stochastic block model. We also compare the performance of our GNN architecture with that of several state-ofthe-art GNNs on the problem of node-classification, using well-known benchmark homophilic and heterophilic datasets. The results demonstrate that GPR-GNN offers significant performance improvement compared to existing techniques on both synthetic and benchmark data. Graph-centered machine learning has received significant interest in recent years due to the ubiquity of graph-structured data and its importance in solving numerous real-world problems such as semisupervised node classification and graph classification (Zhu, 2005; Shervashidze et al., 2011; Lü & Zhou, 2011). Usually, the data at hand contains two sources of information: Node features and graph topology.

Adaptive gradient methods are typically used for training over-parameterized models capable of exactly fitting the data; we thus study their convergence in this interpolation setting. Under an interpolation assumption, we prove that AMSGrad with a constant step-size and momentum can converge to the minimizer at the faster $O(1/T)$ rate for smooth, convex functions. Furthermore, in this setting, we show that AdaGrad can achieve an $O(1)$ regret in the online convex optimization framework. When interpolation is only approximately satisfied, we show that constant step-size AMSGrad converges to a neighbourhood of the solution. On the other hand, we prove that AdaGrad is robust to the violation of interpolation and converges to the minimizer at the optimal rate. However, we demonstrate that even for simple, convex problems satisfying interpolation, the empirical performance of these methods heavily depends on the step-size and requires tuning. We alleviate this problem by using stochastic line-search (SLS) and Polyak's step-sizes (SPS) to help these methods adapt to the function's local smoothness. By using these techniques, we prove that AdaGrad and AMSGrad do not require knowledge of problem-dependent constants and retain the convergence guarantees of their constant step-size counterparts. Experimentally, we show that these techniques help improve the convergence and generalization performance across tasks, from binary classification with kernel mappings to classification with deep neural networks.

From the statistical learning perspective, complexity control via explicit regularization is a necessity for improving the generalization of over-parameterized models, which deters the memorization of intricate patterns existing only in the training data. However, the impressive generalization performance of over-parameterized neural networks with only implicit regularization challenges the importance of explicit regularization. Furthermore, explicit regularization does not prevent neural networks from memorizing unnatural patterns, such as random labels. In this work, we revisit the role and importance of explicit regularization methods for generalization of the predictive probability, not just the generalization of the 0-1 loss. Specifically, we analyze the possible cause of the poor predictive probability and identify that regularization of predictive confidence is required during training. We then empirically show that explicit regularization significantly improves the reliability of the predictive probability, which enables better predictive uncertainty representation and prevents the overconfidence problem. Our findings present a new direction to improve the predictive probability quality of deterministic neural networks, which can be an efficient and scalable alternative to Bayesian neural networks and ensemble methods.

Learning continuous-time stochastic dynamics is a fundamental and essential problem in modeling sporadic time series, whose observations are irregular and sparse in both time and dimension. For a given system whose latent states and observed data are high-dimensional, it is generally impossible to derive a precise continuous-time stochastic process to describe the system behaviors. To solve the above problem, we apply Variational Bayesian method and propose a flexible continuous-time stochastic recurrent neural network named Variational Stochastic Differential Networks (VSDN), which embeds the complicated dynamics of the sporadic time series by neural Stochastic Differential Equations (SDE). VSDNs capture the stochastic dependency among latent states and observations by deep neural networks. We also incorporate two differential Evidence Lower Bounds to efficiently train the models. Through comprehensive experiments, we show that VSDNs outperform state-of-the-art continuous-time deep learning models and achieve remarkable performance on prediction and interpolation tasks for sporadic time series.

Current graph neural network (GNN) architectures naively average or sum node embeddings into an aggregated graph representation---potentially losing structural or semantic information. We here introduce OT-GNN, a model that computes graph embeddings using parametric prototypes that highlight key facets of different graph aspects. Towards this goal, we are (to our knowledge) the first to successfully combine optimal transport with parametric graph models. Graph representations are obtained from Wasserstein distances between the set of GNN node embeddings and "prototype" point clouds as free parameters. We theoretically prove that, unlike traditional sum aggregation, our function class on point clouds satisfies a fundamental universal approximation theorem. Empirically, we address an inherent collapse optimization issue by proposing a noise contrastive regularizer to steer the model towards truly exploiting the optimal transport geometry. Finally, we consistently report better generalization performance on several molecular property prediction tasks, while exhibiting smoother graph representations.

Learning disentangled representations is regarded as a fundamental task for improving the generalization, robustness, and interpretability of generative models. However, measuring disentanglement has been challenging and inconsistent, often dependent on an ad-hoc external model or specific to a certain dataset. To address this, we present a method for quantifying disentanglement that only uses the generative model, by measuring the topological similarity of conditional submanifolds in the learned representation. To illustrate the effectiveness and applicability of our method, we empirically evaluate several state-of-the-art models across multiple datasets. We find that our method ranks models similarly to existing methods. Figure 1: Factors in the dSprites dataset displaying topological similarity and semantic correspondence to respective latent dimensions in a disentangled generative model, as shown through Wasserstein RLT distributions of homology and latent interpolations along respective dimensions. Learning disentangled representations is important for a variety of tasks, including adversarial robustness, generalization to novel tasks, and interpretability (Stutz et al., 2019; Alemi et al., 2017; Ridgeway, 2016; Bengio et al., 2013). Recently, deep generative models have shown marked improvement in disentanglement across an increasing number of datasets and a variety of training objectives (Chen et al., 2016; Lin et al., 2020; Higgins et al., 2017; Kim and Mnih, 2018; Chen et al., 2018b; Burgess et al., 2018; Karras et al., 2019). Nevertheless, quantifying the extent of this disentanglement has remained challenging and inconsistent.

To apply deep CNNs to mobile terminals and portable devices, many scholars have recently worked on the compressing and accelerating deep convolutional neural networks. Based on this, we propose a novel uniform channel pruning (UCP) method to prune deep CNN, and the modified squeeze-and-excitation blocks (MSEB) is used to measure the importance of the channels in the convolutional layers. The unimportant channels, including convolutional kernels related to them, are pruned directly, which greatly reduces the storage cost and the number of calculations. There are two types of residual blocks in ResNet. For ResNet with bottlenecks, we use the pruning method with traditional CNN to trim the 3x3 convolutional layer in the middle of the blocks. For ResNet with basic residual blocks, we propose an approach to consistently prune all residual blocks in the same stage to ensure that the compact network structure is dimensionally correct. Considering that the network loses considerable information after pruning and that the larger the pruning amplitude is, the more information that will be lost, we do not choose fine-tuning but retrain from scratch to restore the accuracy of the network after pruning. Finally, we verified our method on CIFAR-10, CIFAR-100 and ILSVRC-2012 for image classification. The results indicate that the performance of the compact network after retraining from scratch, when the pruning rate is small, is better than the original network. Even when the pruning amplitude is large, the accuracy can be maintained or decreased slightly. On the CIFAR-100, when reducing the parameters and FLOPs up to 82% and 62% respectively, the accuracy of VGG-19 even improved by 0.54% after retraining.