Batch normalization (BN) has become a critical component across diverse deep neural networks. The network with BN is invariant to positively linear re-scale transformation, which makes there exist infinite functionally equivalent networks with different scales of weights. However, optimizing these equivalent networks with the first-order method such as stochastic gradient descent will obtain a series of iterates converging to different local optima owing to their different gradients across training. To obviate this, we propose a quotient manifold \emph{PSI manifold}, in which all the equivalent weights of the network with BN are regarded as the same element. Next, we construct gradient descent and stochastic gradient descent on the proposed PSI manifold to train the network with BN. The two algorithms guarantee that every group of equivalent weights (caused by positively re-scaling) converge to the equivalent optima. Besides that, we give convergence rates of the proposed algorithms on the PSI manifold. The results show that our methods accelerate training compared with the algorithms on the Euclidean weight space. Finally, empirical results verify that our algorithms consistently improve the existing methods in both convergence rate and generalization ability under various experimental settings.
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This work simultaneously considers the discriminability and transferability properties of deep representations in the typical supervised learning task, i.e., image classification. By a comprehensive temporal analysis, we observe a trade-off between these two properties. The discriminability keeps increasing with the training progressing while the transferability intensely diminishes in the later training period. From the perspective of information-bottleneck theory, we reveal that the incompatibility between discriminability and transferability is attributed to the over-compression of input information. More importantly, we investigate why and how the InfoNCE loss can alleviate the over-compression, and further present a learning framework, named contrastive temporal coding~(CTC), to counteract the over-compression and alleviate the incompatibility. Extensive experiments validate that CTC successfully mitigates the incompatibility, yielding discriminative and transferable representations. Noticeable improvements are achieved on the image classification task and challenging transfer learning tasks. We hope that this work will raise the significance of the transferability property in the conventional supervised learning setting. Code is available at //github.com/DTennant/dt-tradeoff.
The seminal paper by Mazumdar and Saha \cite{MS17a} introduced an extensive line of work on clustering with noisy queries. Yet, despite significant progress on the problem, the proposed methods depend crucially on knowing the exact probabilities of errors of the underlying fully-random oracle. In this work, we develop robust learning methods that tolerate general semi-random noise obtaining qualitatively the same guarantees as the best possible methods in the fully-random model. More specifically, given a set of $n$ points with an unknown underlying partition, we are allowed to query pairs of points $u,v$ to check if they are in the same cluster, but with probability $p$, the answer may be adversarially chosen. We show that information theoretically $O\left(\frac{nk \log n} {(1-2p)^2}\right)$ queries suffice to learn any cluster of sufficiently large size. Our main result is a computationally efficient algorithm that can identify large clusters with $O\left(\frac{nk \log n} {(1-2p)^2}\right) + \text{poly}\left(\log n, k, \frac{1}{1-2p} \right)$ queries, matching the guarantees of the best known algorithms in the fully-random model. As a corollary of our approach, we develop the first parameter-free algorithm for the fully-random model, answering an open question by \cite{MS17a}.
Generative Adversarial Networks (GANs) are the most popular image generation models that have achieved remarkable progress on various computer vision tasks. However, training instability is still one of the open problems for all GAN-based algorithms. Quite a number of methods have been proposed to stabilize the training of GANs, the focuses of which were respectively put on the loss functions, regularization and normalization technologies, training algorithms, and model architectures. Different from the above methods, in this paper, a new perspective on stabilizing GANs training is presented. It is found that sometimes the images produced by the generator act like adversarial examples of the discriminator during the training process, which may be part of the reason causing the unstable training of GANs. With this finding, we propose the Direct Adversarial Training (DAT) method to stabilize the training process of GANs. Furthermore, we prove that the DAT method is able to minimize the Lipschitz constant of the discriminator adaptively. The advanced performance of DAT is verified on multiple loss functions, network architectures, hyper-parameters, and datasets. Specifically, DAT achieves significant improvements of 11.5% FID on CIFAR-100 unconditional generation based on SSGAN, 10.5% FID on STL-10 unconditional generation based on SSGAN, and 13.2% FID on LSUN-Bedroom unconditional generation based on SSGAN. Code will be available at //github.com/iceli1007/DAT-GAN
Block stacking storage systems are highly adaptable warehouse systems with low investment costs. With multiple, deep lanes they can achieve high storage densities, but accessing some unit loads can be time-consuming. The unit-load pre-marshalling problem sorts the unit loads in a block stacking storage system in off-peak time periods to prepare for upcoming orders. The goal is to find a minimum number of unit-load moves needed to sequence a storage bay in ascending order based on the retrieval priority group of each unit load. In this paper, we present two solution approaches for determining the minimum number of unit-load moves. We show that for storage bays with one access direction, it is possible to adapt existing, optimal tree search procedures and lower bound heuristics from the container pre-marshalling problem. For multiple access directions, we develop a novel, two-step solution approach based on a network flow model and an A* algorithm with an adapted lower bound that is applicable in all scenarios. We further analyze the performance of the presented solutions in computational experiments for randomly generated problem instances and show that multiple access directions greatly reduce both the total access time of unit loads and the required sorting effort.
Neural networks are vulnerable to adversarial attacks: adding well-crafted, imperceptible perturbations to their input can modify their output. Adversarial training is one of the most effective approaches in training robust models against such attacks. However, it is much slower than vanilla training of neural networks since it needs to construct adversarial examples for the entire training data at every iteration, hampering its effectiveness. Recently, Fast Adversarial Training (FAT) was proposed that can obtain robust models efficiently. However, the reasons behind its success are not fully understood, and more importantly, it can only train robust models for $\ell_\infty$-bounded attacks as it uses FGSM during training. In this paper, by leveraging the theory of coreset selection, we show how selecting a small subset of training data provides a general, more principled approach toward reducing the time complexity of robust training. Unlike existing methods, our approach can be adapted to a wide variety of training objectives, including TRADES, $\ell_p$-PGD, and Perceptual Adversarial Training (PAT). Our experimental results indicate that our approach speeds up adversarial training by 2-3 times while experiencing a slight reduction in the clean and robust accuracy.
Normalization is known to help the optimization of deep neural networks. Curiously, different architectures require specialized normalization methods. In this paper, we study what normalization is effective for Graph Neural Networks (GNNs). First, we adapt and evaluate the existing methods from other domains to GNNs. Faster convergence is achieved with InstanceNorm compared to BatchNorm and LayerNorm. We provide an explanation by showing that InstanceNorm serves as a preconditioner for GNNs, but such preconditioning effect is weaker with BatchNorm due to the heavy batch noise in graph datasets. Second, we show that the shift operation in InstanceNorm results in an expressiveness degradation of GNNs for highly regular graphs. We address this issue by proposing GraphNorm with a learnable shift. Empirically, GNNs with GraphNorm converge faster compared to GNNs using other normalization. GraphNorm also improves the generalization of GNNs, achieving better performance on graph classification benchmarks.
Sampling methods (e.g., node-wise, layer-wise, or subgraph) has become an indispensable strategy to speed up training large-scale Graph Neural Networks (GNNs). However, existing sampling methods are mostly based on the graph structural information and ignore the dynamicity of optimization, which leads to high variance in estimating the stochastic gradients. The high variance issue can be very pronounced in extremely large graphs, where it results in slow convergence and poor generalization. In this paper, we theoretically analyze the variance of sampling methods and show that, due to the composite structure of empirical risk, the variance of any sampling method can be decomposed into \textit{embedding approximation variance} in the forward stage and \textit{stochastic gradient variance} in the backward stage that necessities mitigating both types of variance to obtain faster convergence rate. We propose a decoupled variance reduction strategy that employs (approximate) gradient information to adaptively sample nodes with minimal variance, and explicitly reduces the variance introduced by embedding approximation. We show theoretically and empirically that the proposed method, even with smaller mini-batch sizes, enjoys a faster convergence rate and entails a better generalization compared to the existing methods.
Modern neural network training relies heavily on data augmentation for improved generalization. After the initial success of label-preserving augmentations, there has been a recent surge of interest in label-perturbing approaches, which combine features and labels across training samples to smooth the learned decision surface. In this paper, we propose a new augmentation method that leverages the first and second moments extracted and re-injected by feature normalization. We replace the moments of the learned features of one training image by those of another, and also interpolate the target labels. As our approach is fast, operates entirely in feature space, and mixes different signals than prior methods, one can effectively combine it with existing augmentation methods. We demonstrate its efficacy across benchmark data sets in computer vision, speech, and natural language processing, where it consistently improves the generalization performance of highly competitive baseline networks.
With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.
Image segmentation is considered to be one of the critical tasks in hyperspectral remote sensing image processing. Recently, convolutional neural network (CNN) has established itself as a powerful model in segmentation and classification by demonstrating excellent performances. The use of a graphical model such as a conditional random field (CRF) contributes further in capturing contextual information and thus improving the segmentation performance. In this paper, we propose a method to segment hyperspectral images by considering both spectral and spatial information via a combined framework consisting of CNN and CRF. We use multiple spectral cubes to learn deep features using CNN, and then formulate deep CRF with CNN-based unary and pairwise potential functions to effectively extract the semantic correlations between patches consisting of three-dimensional data cubes. Effective piecewise training is applied in order to avoid the computationally expensive iterative CRF inference. Furthermore, we introduce a deep deconvolution network that improves the segmentation masks. We also introduce a new dataset and experimented our proposed method on it along with several widely adopted benchmark datasets to evaluate the effectiveness of our method. By comparing our results with those from several state-of-the-art models, we show the promising potential of our method.
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