This paper presents OptNet, a network architecture that integrates optimization problems (here, specifically in the form of quadratic programs) as individual layers in larger end-to-end trainable deep networks. These layers encode constraints and complex dependencies between the hidden states that traditional convolutional and fully-connected layers often cannot capture. In this paper, we explore the foundations for such an architecture: we show how techniques from sensitivity analysis, bilevel optimization, and implicit differentiation can be used to exactly differentiate through these layers and with respect to layer parameters; we develop a highly efficient solver for these layers that exploits fast GPU-based batch solves within a primal-dual interior point method, and which provides backpropagation gradients with virtually no additional cost on top of the solve; and we highlight the application of these approaches in several problems. In one notable example, we show that the method is capable of learning to play mini-Sudoku (4x4) given just input and output games, with no a priori information about the rules of the game; this highlights the ability of our architecture to learn hard constraints better than other neural architectures.
In the machine learning setting, a wide array of applications consider optimization as a means to perform inference in learning. Among many other applications, these architectures are well-studied for generic classification and structured prediction tasks ; in vision for tasks such as denoising ; and uses unrolled optimization within a network to stabilize the convergence of generative adversarial networks @cite_10 . Indeed, the general idea of solving restricted classes of optimization problem using neural networks goes back many decades @cite_16 @cite_15 , but has seen a number of advances in recent years. These models are often trained by one of the following four methods.
@cite_15 @cite_16 @cite_10
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Model-based optimization methods and discriminative learning methods have been the two dominant strategies for solving various inverse problems in low-level vision. Typically, those two kinds of methods have their respective merits and drawbacks, e.g., model-based optimization methods are flexible for handling different inverse problems but are usually time-consuming with sophisticated priors for the purpose of good performance, in the meanwhile, discriminative learning methods have fast testing speed but their application range is greatly restricted by the specialized task. Recent works have revealed that, with the aid of variable splitting techniques, denoiser prior can be plugged in as a modular part of model-based optimization methods to solve other inverse problems (e.g., deblurring). Such an integration induces considerable advantage when the denoiser is obtained via discriminative learning. However, the study of integration with fast discriminative denoiser prior is still lacking. To this end, this paper aims to train a set of fast and effective CNN (convolutional neural network) denoisers and integrate them into model-based optimization method to solve other inverse problems. Experimental results demonstrate that the learned set of denoisers can not only achieve promising Gaussian denoising results but also can be used as prior to deliver good performance for various low-level vision applications. In recent years, we have witnessed the great success of deep learning on various problems both in low and high-level computer visions. The low-level vision problems, including inpainting, deblurring, denoising, super-resolution, and so on, are highly anticipated to occur in machine vision and image processing. Many deep learning based methods have been proposed to solve low-level vision problems. Most researches treat these problems independently; however, most of the time they appear concurrently. Motivated by the success of generative model in the field of image generation, we develop a deep cascade of neural networks to solve the inpainting, deblurring, denoising problems at the same time. Our model contains two networks: inpainting GAN and deblurring-denoising network. Inpainting GAN generates the coarse patches to fill the lost part in damaged image, and the deblurring-denoising network, stacked by a convolutional auto-encoder, will further refine them. Unlike other methods that handle each problem separately, our method jointly optimizes the two sub-networks. Because GAN training is not only unstable but also difficult, we adopt the Wasserstein distance as the loss function of the inpainting GAN and propose a gradual training strategy. Learning from the idea of residual learning, we utilize skip connections to pass image details from input to reconstruction layer. Experimental results have demonstrated that the proposed model can achieve state-of-the-art performance. Through the experiments, we also demonstrated the effectiveness of the cascade architecture. A citing sentence is one that appears in a scientific article and cites previous work. Citing sentences have been studied and used in many applications. For example, they have been used in scientific paper summarization, automatic survey generation, paraphrase identification, and citation function classification. Citing sentences that cite multiple papers are common in scientific writing. This observation should be taken into consideration when using citing sentences in applications. For instance, when a citing sentence is used in a summary of a scientific paper, only the fragments of the sentence that are relevant to the summarized paper should be included in the summary. In this paper, we present and compare three different approaches for identifying the fragments of a citing sentence that are related to a given target reference. Our methods are: word classification, sequence labeling, and segment classification. Our experiments show that segment classification achieves the best results. Machine learning models are frequently used to solve complex security problems, as well as to make decisions in sensitive situations like guiding autonomous vehicles or predicting financial market behaviors. Previous efforts have shown that numerous machine learning models are vulnerable to adversarial manipulations of their inputs taking the form of adversarial samples. Such inputs are crafted by adding carefully selected perturbations to legitimate inputs so as to force the machine learning model to misbehave, for instance by outputting a wrong class if the machine learning task of interest is classification. In fact, to the best of our knowledge, all previous work on adversarial samples crafting for neural networks considered models used to solve classification tasks, most frequently in computer vision applications. In this paper, we investigate adversarial input sequences for recurrent neural networks processing sequential data. We show that the classes of algorithms introduced previously to craft adversarial samples misclassified by feed-forward neural networks can be adapted to recurrent neural networks. In a experiment, we show that adversaries can craft adversarial sequences misleading both categorical and sequential recurrent neural networks. Neural network robustness has recently been highlighted by the existence of adversarial examples. Many previous works show that the learned networks do not perform well on perturbed test data, and significantly more labeled data is required to achieve adversarially robust generalization. In this paper, we theoretically and empirically show that with just more unlabeled data, we can learn a model with better adversarially robust generalization. The key insight of our results is based on a risk decomposition theorem, in which the expected robust risk is separated into two parts: the stability part which measures the prediction stability in the presence of perturbations, and the accuracy part which evaluates the standard classification accuracy. As the stability part does not depend on any label information, we can optimize this part using unlabeled data. We further prove that for a specific Gaussian mixture problem illustrated by schmidt2018adversarially , adversarially robust generalization can be almost as easy as the standard generalization in supervised learning if a sufficiently large amount of unlabeled data is provided. Inspired by the theoretical findings, we propose a new algorithm called PASS by leveraging unlabeled data during adversarial training. We show that in the transductive and semi-supervised settings, PASS achieves higher robust accuracy and defense success rate on the Cifar-10 task. Neural Networks are function approximators that have achieved state-of-the-art accuracy in numerous machine learning tasks. In spite of their great success in terms of accuracy, their large training time makes it difficult to use them for various tasks. In this paper, we explore the idea of learning weight evolution pattern from a simple network for accelerating training of novel neural networks. We use a neural network to learn the training pattern from MNIST classification and utilize it to accelerate training of neural networks used for CIFAR-10 and ImageNet classification. Our method has a low memory footprint and is computationally efficient. This method can also be used with other optimizers to give faster convergence. The results indicate a general trend in the weight evolution during training of neural networks. Prediction markets are economic mechanisms for aggregating information about future events through sequential interactions with traders. The pricing mechanisms in these markets are known to be related to optimization algorithms in machine learning and through these connections we have some understanding of how equilibrium market prices relate to the beliefs of the traders in a market. However, little is known about rates and guarantees for the convergence of these sequential mechanisms, and two recent papers cite this as an important open question. In this paper we show how some previously studied prediction market trading models can be understood as a natural generalization of randomized coordinate descent which we call randomized subspace descent (RSD). We establish convergence rates for RSD and leverage them to prove rates for the two prediction market models above, answering the open questions. Our results extend beyond standard centralized markets to arbitrary trade networks. In recent years, supervised learning with convolutional networks (CNNs) has seen huge adoption in computer vision applications. Comparatively, unsupervised learning with CNNs has received less attention. In this work we hope to help bridge the gap between the success of CNNs for supervised learning and unsupervised learning. We introduce a class of CNNs called deep convolutional generative adversarial networks (DCGANs), that have certain architectural constraints, and demonstrate that they are a strong candidate for unsupervised learning. Training on various image datasets, we show convincing evidence that our deep convolutional adversarial pair learns a hierarchy of representations from object parts to scenes in both the generator and discriminator. Additionally, we use the learned features for novel tasks - demonstrating their applicability as general image representations. We present a novel method to solve image analogy problems [3]: it allows to learn the relation between paired images present in training data, and then generalize and generate images that correspond to the relation, but were never seen in the training set. Therefore, we call the method Conditional Analogy Generative Adversarial Network (CAGAN), as it is based on adversarial training and employs deep convolutional neural networks. An especially interesting application of that technique is automatic swapping of clothing on fashion model photos. Our work has the following contributions. First, the definition of the end-to-end trainable CAGAN architecture, which implicitly learns segmentation masks without expensive supervised labeling data. Second, experimental results show plausible segmentation masks and often convincing swapped images, given the target article. Finally, we discuss the next steps for that technique: neural network architecture improvements and more advanced applications. Abstract: In recent years, supervised learning with convolutional networks (CNNs) has seen huge adoption in computer vision applications. Comparatively, unsupervised learning with CNNs has received less attention. In this work we hope to help bridge the gap between the success of CNNs for supervised learning and unsupervised learning. We introduce a class of CNNs called deep convolutional generative adversarial networks (DCGANs), that have certain architectural constraints, and demonstrate that they are a strong candidate for unsupervised learning. Training on various image datasets, we show convincing evidence that our deep convolutional adversarial pair learns a hierarchy of representations from object parts to scenes in both the generator and discriminator. Additionally, we use the learned features for novel tasks - demonstrating their applicability as general image representations. In recent years, Deep Reinforcement Learning has made impressive advances in solving several important benchmark problems for sequential decision making. Many control applications use a generic multilayer perceptron (MLP) for non-vision parts of the policy network. In this work, we propose a new neural network architecture for the policy network representation that is simple yet effective. The proposed Structured Control Net (SCN) splits the generic MLP into two separate sub-modules: a nonlinear control module and a linear control module. Intuitively, the nonlinear control is for forward-looking and global control, while the linear control stabilizes the local dynamics around the residual of global control. We hypothesize that this will bring together the benefits of both linear and nonlinear policies: improve training sample efficiency, final episodic reward, and generalization of learned policy, while requiring a smaller network and being generally applicable to different training methods. We validated our hypothesis with competitive results on simulations from OpenAI MuJoCo, Roboschool, Atari, and a custom 2D urban driving environment, with various ablation and generalization tests, trained with multiple black-box and policy gradient training methods. The proposed architecture has the potential to improve upon broader control tasks by incorporating problem specific priors into the architecture. As a case study, we demonstrate much improved performance for locomotion tasks by emulating the biological central pattern generators (CPGs) as the nonlinear part of the architecture. This paper presents a new approach to neural modeling based on the idea of using an automated method to optimize the parameters of a synaptic learning rule The synaptic modi cation rule is considered as a parametric function This function has local inputs and is the same in many neurons We can use standard optimization methods to select appropriate parameters for a given type of task We also present a theoretical analysis permitting to study the generalization property of such parametric learning rules By generalization we mean the possibility for the learning rule to learn to solve new tasks Experiments were performed on three types of problems a biologically inspired circuit for conditioning in Aplysia Boolean functions linearly separable as well as non linearly separable and classi cation tasks The neural network architecture as well as the form and initial parameter values of the synaptic learning function can be designed using a priori knowledge In a document network such as a citation network of scientific documents, web-logs, etc., the content produced by authors exhibits their interest in certain topics. In addition some authors influence other authors' interests. In this work, we propose to model the influence of cited authors along with the interests of citing authors. Moreover, we hypothesize that apart from the citations present in documents, the context surrounding the citation mention provides extra topical information about the cited authors. However, associating terms in the context to the cited authors remains an open problem. We propose novel document generation schemes that incorporate the context while simultaneously modeling the interests of citing authors and influence of the cited authors. Our experiments show significant improvements over baseline models for various evaluation criteria such as link prediction between document and cited author, and quantitatively explaining unseen text. Deep feedforward and recurrent networks have achieved impressive results in many perception and language processing applications. Recently, more complex architectures such as Neural Turing Machines and Memory Networks have been proposed for tasks including question answering and general computation, creating a new set of optimization challenges. In this paper, we explore the low-overhead and easy-to-implement optimization technique of adding annealed Gaussian noise to the gradient, which we find surprisingly effective when training these very deep architectures. Unlike classical weight noise, gradient noise injection is complementary to advanced stochastic optimization algorithms such as Adam and AdaGrad. The technique not only helps to avoid overfitting, but also can result in lower training loss. We see consistent improvements in performance across an array of complex models, including state-of-the-art deep networks for question answering and algorithm learning. We observe that this optimization strategy allows a fully-connected 20-layer deep network to escape a bad initialization with standard stochastic gradient descent. We encourage further application of this technique to additional modern neural architectures. The field of deep learning has seen significant advancement in recent years. However, much of the existing work has been focused on real-valued numbers. Recent work has shown that a deep learning system using the complex numbers can be deeper for a fixed parameter budget compared to its real-valued counterpart. In this work, we explore the benefits of generalizing one step further into the hyper-complex numbers, quaternions specifically, and provide the architecture components needed to build deep quaternion networks. We develop the theoretical basis by reviewing quaternion convolutions, developing a novel quaternion weight initialization scheme, and developing novel algorithms for quaternion batch-normalization. These pieces are tested in a classification model by end-to-end training on the CIFAR-10 and CIFAR-100 data sets and a segmentation model by end-to-end training on the KITTI Road Segmentation data set. These quaternion networks show improved convergence compared to real-valued and complex-valued networks, especially on the segmentation task, while having fewer parameters Classification, which involves finding rules that partition a given da.ta set into disjoint groups, is one class of data mining problems. Approaches proposed so far for mining classification rules for large databases are mainly decision tree based symbolic learning methods. The connectionist approach based on neura.l networks has been thought not well suited for data mining. One of the major reasons cited is that knowledge generated by neural networks is not explicitly represented in the form of rules suitable for verification or interpretation by humans. This paper examines this issue. With our newly developed algorithms, rules which are similar to, or more concise than those generated by the symbolic methods can be extracted from the neural networks. The data mining process using neural networks with the emphasis on rule extraction is described. ExperimenM results and comparison with previously published works are presented. We introduce a method to stabilize Generative Adversarial Networks (GANs) by defining the generator objective with respect to an unrolled optimization of the discriminator. This allows training to be adjusted between using the optimal discriminator in the generator's objective, which is ideal but infeasible in practice, and using the current value of the discriminator, which is often unstable and leads to poor solutions. We show how this technique solves the common problem of mode collapse, stabilizes training of GANs with complex recurrent generators, and increases diversity and coverage of the data distribution by the generator. Citation relationship between scientific publications has been successfully used for scholarly bibliometrics, information retrieval and data mining tasks, and citation-based recommendation algorithms are well documented. While previous studies investigated citation relations from various viewpoints, most of them share the same assumption that, if paper1 cites paper2 (or author1 cites author2), they are connected, regardless of citation importance, sentiment, reason, topic, or motivation. However, this assumption is oversimplified. In this study, we employ an innovative "context-rich heterogeneous network" approach, which paves a new way for citation recommendation task. In the network, we characterize 1) the importance of citation relationships between citing and cited papers, and 2) the topical citation motivation. Unlike earlier studies, the citation information, in this paper, is characterized by citation textual contexts extracted from the full-text citing paper. We also propose algorithm to cope with the situation when large portion of full-text missing information exists in the bibliographic repository. Evaluation results show that, context-rich heterogeneous network can significantly enhance the citation recommendation performance. Purpose – The purpose of this paper is to suggest an alternative to the widely used Times Cited criterion for analysing citation networks. The approach involves taking account of the natures of the papers that cite a given paper, so as to differentiate between papers that attract the same number of citations.Design methodology approach – ArticleRank is an algorithm that has been derived from Google's PageRank algorithm to measure the influence of journal articles. ArticleRank is applied to two datasets – a citation network based on an early paper on webometrics, and a self‐citation network based on the 19 most cited papers in the Journal of Documentation – using citation data taken from the Web of Knowledge database.Findings – ArticleRank values provide a different ranking of a set of papers from that provided by the corresponding Times Cited values, and overcomes the inability of the latter to differentiate between papers with the same numbers of citations. The difference in rankings between Times Cited ... Computer vision has become increasingly important and effective in recent years due to its wide-ranging applications in areas as diverse as smart surveillance and monitoring, health and medicine, sports and recreation, robotics, drones, and self-driving cars. Visual recognition tasks, such as image classification, localization, and detection, are the core building blocks of many of these applications, and recent developments in Convolutional Neural Networks (CNNs) have led to outstanding performance in these state-of-the-art visual recognition tasks and systems. As a result, CNNs now form the crux of deep learning algorithms in computer vision. is self-contained guide will benefit those who seek to both understand the theory be- hind CNNs and to gain hands-on experience on the application of CNNs in computer vision. It provides a comprehensive introduction to CNNs starting with the essential concepts behind neural networks: training, regularization, and optimization of CNNs. e book also discusses a wide range of loss functions, network layers, and popular CNN architectures, reviews the differ- ent techniques for the evaluation of CNNs, and presents some popular CNN tools and libraries that are commonly used in computer vision. Further, this text describes and discusses case stud- ies that are related to the application of CNN in computer vision, including image classification, object detection, semantic segmentation, scene understanding, and image generation. is book is ideal for undergraduate and graduate students, as no prior background knowl- edge in the field is required to follow the material, as well as new researchers, developers, engi- neers, and practitioners who are interested in gaining a quick understanding of CNN models.