Complexity Measures for Neural Networks with General Activation Functions Using Path-based Norms

A simple approach is proposed to obtain complexity controls for neural networks with general activation functions. The approach is motivated by approximating the general activation functions with one-dimensional ReLU networks, which reduces the problem to the complexity controls of ReLU networks. Specifically, we consider two-layer networks and deep residual networks, for which path-based norms are derived to control complexities. We also provide preliminary analyses of the function spaces induced by these norms and a priori estimates of the corresponding regularized estimators.

A Qualitative Study of the Dynamic Behavior of Adaptive Gradient Algorithms

The dynamic behavior of RMSprop and Adam algorithms is studied through a combination of careful numerical experiments and theoretical explanations. Three types of qualitative features are observed in the training loss curve: fast initial convergence, oscillations and large spikes. The sign gradient descent (signGD) algorithm, which is the limit of Adam when taking the learning rate to $0$ while keeping the momentum parameters fixed, is used to explain the fast initial convergence. For the late phase of Adam, three different types of qualitative patterns are observed depending on the choice of the hyper-parameters: oscillations, spikes and divergence. In particular, Adam converges faster and smoother when the values of the two momentum factors are close to each other.

Cross-Modality 3D Object Detection

In this paper, we focus on exploring the fusion of images and point clouds for 3D object detection in view of the complementary nature of the two modalities, i.e., images possess more semantic information while point clouds specialize in distance sensing. To this end, we present a novel two-stage multi-modal fusion network for 3D object detection, taking both binocular images and raw point clouds as input. The whole architecture facilitates two-stage fusion. The first stage aims at producing 3D proposals through sparse point-wise feature fusion. Within the first stage, we further exploit a joint anchor mechanism that enables the network to utilize 2D-3D classification and regression simultaneously for better proposal generation. The second stage works on the 2D and 3D proposal regions and fuses their dense features. In addition, we propose to use pseudo LiDAR points from stereo matching as a data augmentation method to densify the LiDAR points, as we observe that objects missed by the detection network mostly have too few points especially for far-away objects. Our experiments on the KITTI dataset show that the proposed multi-stage fusion helps the network to learn better representations.

The Slow Deterioration of the Generalization Error of the Random Feature Model

The random feature model exhibits a kind of resonance behavior when the number of parameters is close to the training sample size. This behavior is characterized by the appearance of large generalization gap, and is due to the occurrence of very small eigenvalues for the associated Gram matrix. In this paper, we examine the dynamic behavior of the gradient descent algorithm in this regime. We show, both theoretically and experimentally, that there is a dynamic self-correction mechanism at work: The larger the eventual generalization gap, the slower it develops, both because of the small eigenvalues. This gives us ample time to stop the training process and obtain solutions with good generalization property.

Rethinking Image Deraining via Rain Streaks and Vapors

Single image deraining regards an input image as a fusion of a background image, a transmission map, rain streaks, and atmosphere light. While advanced models are proposed for image restoration (i.e., background image generation), they regard rain streaks with the same properties as background rather than transmission medium. As vapors (i.e., rain streaks accumulation or fog-like rain) are conveyed in the transmission map to model the veiling effect, the fusion of rain streaks and vapors do not naturally reflect the rain image formation. In this work, we reformulate rain streaks as transmission medium together with vapors to model rain imaging. We propose an encoder-decoder CNN named as SNet to learn the transmission map of rain streaks. As rain streaks appear with various shapes and directions, we use ShuffleNet units within SNet to capture their anisotropic representations. As vapors are brought by rain streaks, we propose a VNet containing spatial pyramid pooling (SSP) to predict the transmission map of vapors in multi-scales based on that of rain streaks. Meanwhile, we use an encoder CNN named ANet to estimate atmosphere light. The SNet, VNet, and ANet are jointly trained to predict transmission maps and atmosphere light for rain image restoration. Extensive experiments on the benchmark datasets demonstrate the effectiveness of the proposed visual model to predict rain streaks and vapors. The proposed deraining method performs favorably against state-of-the-art deraining approaches.

Robust Tracking against Adversarial Attacks

While deep convolutional neural networks (CNNs) are vulnerable to adversarial attacks, considerably few efforts have been paid to construct robust deep tracking algorithms against adversarial attacks. Current studies on adversarial attack and defense mainly reside in a single image. In this work, we first attempt to generate adversarial examples on top of video sequences to improve the tracking robustness against adversarial attacks. To this end, we take temporal motion into consideration when generating lightweight perturbations over the estimated tracking results frame-by-frame. On one hand, we add the temporal perturbations into the original video sequences as adversarial examples to greatly degrade the tracking performance. On the other hand, we sequentially estimate the perturbations from input sequences and learn to eliminate their effect for performance restoration. We apply the proposed adversarial attack and defense approaches to state-of-the-art deep tracking algorithms. Extensive evaluations on the benchmark datasets demonstrate that our defense method not only eliminates the large performance drops caused by adversarial attacks, but also achieves additional performance gains when deep trackers are not under adversarial attacks.

Unsupervised Deep Representation Learning for Real-Time Tracking

The advancement of visual tracking has continuously been brought by deep learning models. Typically, supervised learning is employed to train these models with expensive labeled data. In order to reduce the workload of manual annotations and learn to track arbitrary objects, we propose an unsupervised learning method for visual tracking. The motivation of our unsupervised learning is that a robust tracker should be effective in bidirectional tracking. Specifically, the tracker is able to forward localize a target object in successive frames and backtrace to its initial position in the first frame. Based on such a motivation, in the training process, we measure the consistency between forward and backward trajectories to learn a robust tracker from scratch merely using unlabeled videos. We build our framework on a Siamese correlation filter network, and propose a multi-frame validation scheme and a cost-sensitive loss to facilitate unsupervised learning. Without bells and whistles, the proposed unsupervised tracker achieves the baseline accuracy as classic fully supervised trackers while achieving a real-time speed. Furthermore, our unsupervised framework exhibits a potential in leveraging more unlabeled or weakly labeled data to further improve the tracking accuracy.

Semantic Equivalent Adversarial Data Augmentation for Visual Question Answering

Visual Question Answering (VQA) has achieved great success thanks to the fast development of deep neural networks (DNN). On the other hand, the data augmentation, as one of the major tricks for DNN, has been widely used in many computer vision tasks. However, there are few works studying the data augmentation problem for VQA and none of the existing image based augmentation schemes (such as rotation and flipping) can be directly applied to VQA due to its semantic structure -- an $\langle image, question, answer\rangle$ triplet needs to be maintained correctly. For example, a direction related Question-Answer (QA) pair may not be true if the associated image is rotated or flipped. In this paper, instead of directly manipulating images and questions, we use generated adversarial examples for both images and questions as the augmented data. The augmented examples do not change the visual properties presented in the image as well as the \textbf{semantic} meaning of the question, the correctness of the $\langle image, question, answer\rangle$ is thus still maintained. We then use adversarial learning to train a classic VQA model (BUTD) with our augmented data. We find that we not only improve the overall performance on VQAv2, but also can withstand adversarial attack effectively, compared to the baseline model. The source code is available at https://github.com/zaynmi/seada-vqa.

The Quenching-Activation Behavior of the Gradient Descent Dynamics for Two-layer Neural Network Models

A numerical and phenomenological study of the gradient descent (GD) algorithm for training two-layer neural network models is carried out for different parameter regimes when the target function can be accurately approximated by a relatively small number of neurons. It is found that for Xavier-like initialization, there are two distinctive phases in the dynamic behavior of GD in the under-parametrized regime: An early phase in which the GD dynamics follows closely that of the corresponding random feature model and the neurons are effectively quenched, followed by a late phase in which the neurons are divided into two groups: a group of a few "activated" neurons that dominate the dynamics and a group of background (or "quenched") neurons that support the continued activation and deactivation process. This neural network-like behavior is continued into the mildly over-parametrized regime, where it undergoes a transition to a random feature-like behavior. The quenching-activation process seems to provide a clear mechanism for "implicit regularization". This is qualitatively different from the dynamics associated with the "mean-field" scaling where all neurons participate equally and there does not appear to be qualitative changes when the network parameters are changed.