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We characterize a rich class of valuated matroids, called R-minor valuated matroids that includes the indicator functions of matroids, and is closed under operations such as taking minors, duality, and induction by network. We exhibit a family of valuated matroids that are not R-minor based on sparse paving matroids. Valuated matroids are inherently related to gross substitute valuations in mathematical economics. By the same token we refute the Matroid Based Valuation Conjecture by Ostrovsky and Paes Leme (Theoretical Economics 2015) asserting that every gross substitute valuation arises from weighted matroid rank functions by repeated applications of merge and endowment operations. Our result also has implications in the context of Lorentzian polynomials: it reveals the limitations of known construction operations.

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While Reinforcement Learning (RL) achieves tremendous success in sequential decision-making problems of many domains, it still faces key challenges of data inefficiency and the lack of interpretability. Interestingly, many researchers have leveraged insights from the causality literature recently, bringing forth flourishing works to unify the merits of causality and address well the challenges from RL. As such, it is of great necessity and significance to collate these Causal Reinforcement Learning (CRL) works, offer a review of CRL methods, and investigate the potential functionality from causality toward RL. In particular, we divide existing CRL approaches into two categories according to whether their causality-based information is given in advance or not. We further analyze each category in terms of the formalization of different models, ranging from the Markov Decision Process (MDP), Partially Observed Markov Decision Process (POMDP), Multi-Arm Bandits (MAB), and Dynamic Treatment Regime (DTR). Moreover, we summarize the evaluation matrices and open sources while we discuss emerging applications, along with promising prospects for the future development of CRL.

Blockchain is an emerging decentralized data collection, sharing and storage technology, which have provided abundant transparent, secure, tamper-proof, secure and robust ledger services for various real-world use cases. Recent years have witnessed notable developments of blockchain technology itself as well as blockchain-adopting applications. Most existing surveys limit the scopes on several particular issues of blockchain or applications, which are hard to depict the general picture of current giant blockchain ecosystem. In this paper, we investigate recent advances of both blockchain technology and its most active research topics in real-world applications. We first review the recent developments of consensus mechanisms and storage mechanisms in general blockchain systems. Then extensive literature is conducted on blockchain enabled IoT, edge computing, federated learning and several emerging applications including healthcare, COVID-19 pandemic, social network and supply chain, where detailed specific research topics are discussed in each. Finally, we discuss the future directions, challenges and opportunities in both academia and industry.

Automated Driving Systems (ADS) have made great achievements in recent years thanks to the efforts from both academia and industry. A typical ADS is composed of multiple modules, including sensing, perception, planning and control, which brings together the latest advances in multiple domains. Despite these achievements, safety assurance of the systems is still of great significance, since the unsafe behavior of ADS can bring catastrophic consequences and unacceptable economic and social losses. Testing is an important approach to system validation for the deployment in practice; in the context of ADS, it is extremely challenging, due to the system complexity and multidisciplinarity. There has been a great deal of literature that focuses on the testing of ADS, and a number of surveys have also emerged to summarize the technical advances. However, most of these surveys focus on the system-level testing that is performed within software simulators, and thereby ignore the distinct features of individual modules. In this paper, we provide a comprehensive survey on the existing ADS testing literature, which takes into account both module-level and system-level testing. Specifically, we make the following contributions: (1) we build a threat model that reveals the potential safety threats for each module of an ADS; (2) we survey the module-level testing techniques for ADS and highlight the technical differences affected by the properties of the modules; (3) we also survey the system-level testing techniques, but we focus on empirical studies that take a bird's-eye view on the system, the problems due to the collaborations between modules, and the gaps between ADS testing in simulators and real world; (4) we identify the challenges and opportunities in ADS testing, which facilitates the future research in this field.

Since the 1950s, machine translation (MT) has become one of the important tasks of AI and development, and has experienced several different periods and stages of development, including rule-based methods, statistical methods, and recently proposed neural network-based learning methods. Accompanying these staged leaps is the evaluation research and development of MT, especially the important role of evaluation methods in statistical translation and neural translation research. The evaluation task of MT is not only to evaluate the quality of machine translation, but also to give timely feedback to machine translation researchers on the problems existing in machine translation itself, how to improve and how to optimise. In some practical application fields, such as in the absence of reference translations, the quality estimation of machine translation plays an important role as an indicator to reveal the credibility of automatically translated target languages. This report mainly includes the following contents: a brief history of machine translation evaluation (MTE), the classification of research methods on MTE, and the the cutting-edge progress, including human evaluation, automatic evaluation, and evaluation of evaluation methods (meta-evaluation). Manual evaluation and automatic evaluation include reference-translation based and reference-translation independent participation; automatic evaluation methods include traditional n-gram string matching, models applying syntax and semantics, and deep learning models; evaluation of evaluation methods includes estimating the credibility of human evaluations, the reliability of the automatic evaluation, the reliability of the test set, etc. Advances in cutting-edge evaluation methods include task-based evaluation, using pre-trained language models based on big data, and lightweight optimisation models using distillation techniques.

In 1954, Alston S. Householder published Principles of Numerical Analysis, one of the first modern treatments on matrix decomposition that favored a (block) LU decomposition-the factorization of a matrix into the product of lower and upper triangular matrices. And now, matrix decomposition has become a core technology in machine learning, largely due to the development of the back propagation algorithm in fitting a neural network. The sole aim of this survey is to give a self-contained introduction to concepts and mathematical tools in numerical linear algebra and matrix analysis in order to seamlessly introduce matrix decomposition techniques and their applications in subsequent sections. However, we clearly realize our inability to cover all the useful and interesting results concerning matrix decomposition and given the paucity of scope to present this discussion, e.g., the separated analysis of the Euclidean space, Hermitian space, Hilbert space, and things in the complex domain. We refer the reader to literature in the field of linear algebra for a more detailed introduction to the related fields.

As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.

This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.

Small data challenges have emerged in many learning problems, since the success of deep neural networks often relies on the availability of a huge amount of labeled data that is expensive to collect. To address it, many efforts have been made on training complex models with small data in an unsupervised and semi-supervised fashion. In this paper, we will review the recent progresses on these two major categories of methods. A wide spectrum of small data models will be categorized in a big picture, where we will show how they interplay with each other to motivate explorations of new ideas. We will review the criteria of learning the transformation equivariant, disentangled, self-supervised and semi-supervised representations, which underpin the foundations of recent developments. Many instantiations of unsupervised and semi-supervised generative models have been developed on the basis of these criteria, greatly expanding the territory of existing autoencoders, generative adversarial nets (GANs) and other deep networks by exploring the distribution of unlabeled data for more powerful representations. While we focus on the unsupervised and semi-supervised methods, we will also provide a broader review of other emerging topics, from unsupervised and semi-supervised domain adaptation to the fundamental roles of transformation equivariance and invariance in training a wide spectrum of deep networks. It is impossible for us to write an exclusive encyclopedia to include all related works. Instead, we aim at exploring the main ideas, principles and methods in this area to reveal where we are heading on the journey towards addressing the small data challenges in this big data era.

Graph convolutional networks (GCNs) have been successfully applied in node classification tasks of network mining. However, most of these models based on neighborhood aggregation are usually shallow and lack the "graph pooling" mechanism, which prevents the model from obtaining adequate global information. In order to increase the receptive field, we propose a novel deep Hierarchical Graph Convolutional Network (H-GCN) for semi-supervised node classification. H-GCN first repeatedly aggregates structurally similar nodes to hyper-nodes and then refines the coarsened graph to the original to restore the representation for each node. Instead of merely aggregating one- or two-hop neighborhood information, the proposed coarsening procedure enlarges the receptive field for each node, hence more global information can be learned. Comprehensive experiments conducted on public datasets demonstrate the effectiveness of the proposed method over the state-of-art methods. Notably, our model gains substantial improvements when only a few labeled samples are provided.

Many natural language processing tasks solely rely on sparse dependencies between a few tokens in a sentence. Soft attention mechanisms show promising performance in modeling local/global dependencies by soft probabilities between every two tokens, but they are not effective and efficient when applied to long sentences. By contrast, hard attention mechanisms directly select a subset of tokens but are difficult and inefficient to train due to their combinatorial nature. In this paper, we integrate both soft and hard attention into one context fusion model, "reinforced self-attention (ReSA)", for the mutual benefit of each other. In ReSA, a hard attention trims a sequence for a soft self-attention to process, while the soft attention feeds reward signals back to facilitate the training of the hard one. For this purpose, we develop a novel hard attention called "reinforced sequence sampling (RSS)", selecting tokens in parallel and trained via policy gradient. Using two RSS modules, ReSA efficiently extracts the sparse dependencies between each pair of selected tokens. We finally propose an RNN/CNN-free sentence-encoding model, "reinforced self-attention network (ReSAN)", solely based on ReSA. It achieves state-of-the-art performance on both Stanford Natural Language Inference (SNLI) and Sentences Involving Compositional Knowledge (SICK) datasets.

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