Maximum-and-Concatenation Networks

While successful in many fields, deep neural networks (DNNs) still suffer from some open problems such as bad local minima and unsatisfactory generalization performance. In this work, we propose a novel architecture called Maximum-and-Concatenation Networks (MCN) to try eliminating bad local minima and improving generalization ability as well. Remarkably, we prove that MCN has a very nice property; that is, \emph{every local minimum of an $(l+1)$-layer MCN can be better than, at least as good as, the global minima of the network consisting of its first $l$ layers}. In other words, by increasing the network depth, MCN can autonomously improve its local minima's goodness, what is more, \emph{it is easy to plug MCN into an existing deep model to make it also have this property}. Finally, under mild conditions, we show that MCN can approximate certain continuous functions arbitrarily well with \emph{high efficiency}; that is, the covering number of MCN is much smaller than most existing DNNs such as deep ReLU. Based on this, we further provide a tight generalization bound to guarantee the inference ability of MCN when dealing with testing samples.

Classify and Generate Reciprocally: Simultaneous Positive-Unlabelled Learning and Conditional Generation with Extra Data

The scarcity of class-labeled data is a ubiquitous bottleneck in a wide range of machine learning problems. While abundant unlabeled data normally exist and provide a potential solution, it is extremely challenging to exploit them. In this paper, we address this problem by leveraging Positive-Unlabeled~(PU) classification and conditional generation with extra unlabeled data \emph{simultaneously}, both of which aim to make full use of agnostic unlabeled data to improve classification and generation performances. In particular, we present a novel training framework to jointly target both PU classification and conditional generation when exposing to extra data, especially out-of-distribution unlabeled data, by exploring the interplay between them: 1) enhancing the performance of PU classifiers with the assistance of a novel Conditional Generative Adversarial Network~(CGAN) that is robust to noisy labels, 2) leveraging extra data with predicted labels from a PU classifier to help the generation. Our key contribution is a Classifier-Noise-Invariant Conditional GAN~(CNI-CGAN) that can learn the clean data distribution from noisy labels predicted by a PU classifier. Theoretically, we proved the optimal condition of CNI-CGAN and experimentally, we conducted extensive evaluations on diverse datasets, verifying the simultaneous improvements on both classification and generation.

Invertible Image Rescaling

High-resolution digital images are usually downscaled to fit various display screens or save the cost of storage and bandwidth, meanwhile the post-upscaling is adpoted to recover the original resolutions or the details in the zoom-in images. However, typical image downscaling is a non-injective mapping due to the loss of high-frequency information, which leads to the ill-posed problem of the inverse upscaling procedure and poses great challenges for recovering details from the downscaled low-resolution images. Simply upscaling with image super-resolution methods results in unsatisfactory recovering performance. In this work, we propose to solve this problem by modeling the downscaling and upscaling processes from a new perspective, i.e. an invertible bijective transformation, which can largely mitigate the ill-posed nature of image upscaling. We develop an Invertible Rescaling Net (IRN) with deliberately designed framework and objectives to produce visually-pleasing low-resolution images and meanwhile capture the distribution of the lost information using a latent variable following a specified distribution in the downscaling process. In this way, upscaling is made tractable by inversely passing a randomly-drawn latent variable with the low-resolution image through the network. Experimental results demonstrate the significant improvement of our model over existing methods in terms of both quantitative and qualitative evaluations of image upscaling reconstruction from downscaled images.

Spatial Pyramid Based Graph Reasoning for Semantic Segmentation

The convolution operation suffers from a limited receptive filed, while global modeling is fundamental to dense prediction tasks, such as semantic segmentation. In this paper, we apply graph convolution into the semantic segmentation task and propose an improved Laplacian. The graph reasoning is directly performed in the original feature space organized as a spatial pyramid. Different from existing methods, our Laplacian is data-dependent and we introduce an attention diagonal matrix to learn a better distance metric. It gets rid of projecting and re-projecting processes, which makes our proposed method a light-weight module that can be easily plugged into current computer vision architectures. More importantly, performing graph reasoning directly in the feature space retains spatial relationships and makes spatial pyramid possible to explore multiple long-range contextual patterns from different scales. Experiments on Cityscapes, COCO Stuff, PASCAL Context and PASCAL VOC demonstrate the effectiveness of our proposed methods on semantic segmentation. We achieve comparable performance with advantages in computational and memory overhead.

Revisiting EXTRA for Smooth Distributed Optimization

EXTRA is a popular method for the dencentralized distributed optimization and has broad applications. This paper revisits the EXTRA. Firstly, we give a sharp complexity analysis for EXTRA with the improved $O\left(\left(\frac{L}{\mu}+\frac{1}{1-\sigma_2(W)}\right)\log\frac{1}{\epsilon(1-\sigma_2(W))}\right)$ communication and computation complexities for $\mu$-strongly convex and $L$-smooth problems, where $\sigma_2(W)$ is the second largest singular value of the weight matrix $W$. When the strong convexity is absent, we prove the $O\left(\left(\frac{L}{\epsilon}+\frac{1}{1-\sigma_2(W)}\right)\log\frac{1}{1-\sigma_2(W)}\right)$ complexities. Then, we use the Catalyst framework to accelerate EXTRA and obtain the $O\left(\sqrt{\frac{L}{\mu(1-\sigma_2(W))}}\log\frac{ L}{\mu(1-\sigma_2(W))}\log\frac{1}{\epsilon}\right)$ communication and computation complexities for strongly convex and smooth problems and the $O\left(\sqrt{\frac{L}{\epsilon(1-\sigma_2(W))}}\log\frac{1}{\epsilon(1-\sigma_2(W))}\right)$ complexities for non-strongly convex ones. Our communication complexities of the accelerated EXTRA are only worse by the factors of $\left(\log\frac{L}{\mu(1-\sigma_2(W))}\right)$ and $\left(\log\frac{1}{\epsilon(1-\sigma_2(W))}\right)$ from the lower complexity bounds for strongly convex and non-strongly convex problems, respectively.

Histogram Transform Ensembles for Large-scale Regression

We propose a novel algorithm for large-scale regression problems named histogram transform ensembles (HTE), composed of random rotations, stretchings, and translations. First of all, we investigate the theoretical properties of HTE when the regression function lies in the H\"{o}lder space $C^{k,\alpha}$, $k \in \mathbb{N}_0$, $\alpha \in (0,1]$. In the case that $k=0, 1$, we adopt the constant regressors and develop the na\"{i}ve histogram transforms (NHT). Within the space $C^{0,\alpha}$, although almost optimal convergence rates can be derived for both single and ensemble NHT, we fail to show the benefits of ensembles over single estimators theoretically. In contrast, in the subspace $C^{1,\alpha}$, we prove that if $d \geq 2(1+\alpha)/\alpha$, the lower bound of the convergence rates for single NHT turns out to be worse than the upper bound of the convergence rates for ensemble NHT. In the other case when $k \geq 2$, the NHT may no longer be appropriate in predicting smoother regression functions. Instead, we apply kernel histogram transforms (KHT) equipped with smoother regressors such as support vector machines (SVMs), and it turns out that both single and ensemble KHT enjoy almost optimal convergence rates. Then we validate the above theoretical results by numerical experiments. On the one hand, simulations are conducted to elucidate that ensemble NHT outperform single NHT. On the other hand, the effects of bin sizes on accuracy of both NHT and KHT also accord with theoretical analysis. Last but not least, in the real-data experiments, comparisons between the ensemble KHT, equipped with adaptive histogram transforms, and other state-of-the-art large-scale regression estimators verify the effectiveness and accuracy of our algorithm.

Tensor Q-Rank: A New Data Dependent Tensor Rank

Recently, the \textit{Tensor Nuclear Norm~(TNN)} regularization based on t-SVD has been widely used in various low tubal-rank tensor recovery tasks. However, these models usually require smooth change of data along the third dimension to ensure their low rank structures. In this paper, we propose a new definition of tensor rank named \textit{tensor Q-rank} by a column orthonormal matrix $\mathbf{Q}$, and further make $\mathbf{Q}$ data-dependent. We introduce an explainable selection method of $\mathbf{Q}$, under which the data tensor may have a more significant low tensor Q-rank structure than that of low tubal-rank structure. We also provide a corresponding envelope of our rank function and apply it to the low rank tensor completion problem. Then we give an effective algorithm and briefly analyze why our method works better than TNN based methods in the case of complex data with low sampling rate. Finally, experimental results on real-world datasets demonstrate the superiority of our proposed model in the tensor completion problem.

Dynamical System Inspired Adaptive Time Stepping Controller for Residual Network Families

The correspondence between residual networks and dynamical systems motivates researchers to unravel the physics of ResNets with well-developed tools in numeral methods of ODE systems. The Runge-Kutta-Fehlberg method is an adaptive time stepping that renders a good trade-off between the stability and efficiency. Can we also have an adaptive time stepping for ResNets to ensure both stability and performance? In this study, we analyze the effects of time stepping on the Euler method and ResNets. We establish a stability condition for ResNets with step sizes and weight parameters, and point out the effects of step sizes on the stability and performance. Inspired by our analyses, we develop an adaptive time stepping controller that is dependent on the parameters of the current step, and aware of previous steps. The controller is jointly optimized with the network training so that variable step sizes and evolution time can be adaptively adjusted. We conduct experiments on ImageNet and CIFAR to demonstrate the effectiveness. It is shown that our proposed method is able to improve both stability and accuracy without introducing additional overhead in inference phase.

Patch-level Neighborhood Interpolation: A General and Effective Graph-based Regularization Strategy

Regularization plays a crucial role in machine learning models, especially for deep neural networks. The existing regularization techniques mainly reply on the i.i.d. assumption and only employ the information of the current sample, without the leverage of neighboring information between samples. In this work, we propose a general regularizer called Patch-level Neighborhood Interpolation~(\textbf{Pani}) that fully exploits the relationship between samples. Furthermore, by explicitly constructing a patch-level graph in the different network layers and interpolating the neighborhood features to refine the representation of the current sample, our Patch-level Neighborhood Interpolation can then be applied to enhance two popular regularization strategies, namely Virtual Adversarial Training (VAT) and MixUp, yielding their neighborhood versions. The first derived \textbf{Pani VAT} presents a novel way to construct non-local adversarial smoothness by incorporating patch-level interpolated perturbations. In addition, the \textbf{Pani MixUp} method extends the original MixUp regularization to the patch level and then can be developed to MixMatch, achieving the state-of-the-art performance. Finally, extensive experiments are conducted to verify the effectiveness of the Patch-level Neighborhood Interpolation in both supervised and semi-supervised settings.

SOGNet: Scene Overlap Graph Network for Panoptic Segmentation

The panoptic segmentation task requires a unified result from semantic and instance segmentation outputs that may contain overlaps. However, current studies widely ignore modeling overlaps. In this study, we aim to model overlap relations among instances and resolve them for panoptic segmentation. Inspired by scene graph representation, we formulate the overlapping problem as a simplified case, named scene overlap graph. We leverage each object's category, geometry and appearance features to perform relational embedding, and output a relation matrix that encodes overlap relations. In order to overcome the lack of supervision, we introduce a differentiable module to resolve the overlap between any pair of instances. The mask logits after removing overlaps are fed into per-pixel instance \verb|id| classification, which leverages the panoptic supervision to assist in the modeling of overlap relations. Besides, we generate an approximate ground truth of overlap relations as the weak supervision, to quantify the accuracy of overlap relations predicted by our method. Experiments on COCO and Cityscapes demonstrate that our method is able to accurately predict overlap relations, and outperform the state-of-the-art performance for panoptic segmentation. Our method also won the Innovation Award in COCO 2019 challenge.