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Given a dataset of input states, measurements, and probabilities, is it possible to efficiently predict the measurement probabilities associated with a quantum circuit? Recent work of Caro and Datta (2020) studied the problem of PAC learning quantum circuits in an information theoretic sense, leaving open questions of computational efficiency. In particular, one candidate class of circuits for which an efficient learner might have been possible was that of Clifford circuits, since the corresponding set of states generated by such circuits, called stabilizer states, are known to be efficiently PAC learnable (Rocchetto 2018). Here we provide a negative result, showing that proper learning of CNOT circuits is hard for classical learners unless $\textsf{RP} = \textsf{NP}$. As the classical analogue and subset of Clifford circuits, this naturally leads to a hardness result for Clifford circuits as well. Additionally, we show that if $\textsf{RP} = \textsf{NP}$ then there would exist efficient proper learning algorithms for CNOT and Clifford circuits. By similar arguments, we also find that an efficient proper quantum learner for such circuits exists if and only if $\textsf{NP} \subseteq \textsf{RQP}$.

A wide variety of bidirectional data accessors, ranging from mixed optics to functor lenses, can be formalized within a unique framework--dependent optics. Starting from two indexed categories, which encode what maps are allowed in the forward and backward directions, we define a category of dependent optics and establish under what assumptions it has coproducts. Different choices of indexed categories correspond to different families of optics: we discuss dependent lenses and prisms, as well as closed dependent optics. We introduce the notion of Tambara representation and use it to classify contravariant functors from the category of optics, thus generalizing the profunctor encoding of optics to the dependent case.

Cities often lack up-to-date data analytics to evaluate and implement transport planning interventions to achieve sustainability goals, as traditional data sources are expensive, infrequent, and suffer from data latency. Mobile phone data provide an inexpensive source of geospatial information to capture human mobility at unprecedented geographic and temporal granularity. This paper proposes a method to estimate updated mode of transportation usage in a city, with novel usage of mobile phone application traces to infer previously hard to detect modes, such as bikes and ride-hailing/taxi. By using data fusion and matrix factorisation, we integrate socioeconomic and demographic attributes of the local resident population into the model. We tested the method in a case study of Santiago (Chile), and found that changes from 2012 to 2020 in mode of transportation inferred by the method are coherent with expectations from domain knowledge and the literature, such as ride-hailing trips replacing mass transport.

The interaction data used by recommender systems (RSs) inevitably include noises resulting from mistaken or exploratory clicks, especially under implicit feedbacks. Without proper denoising, RS models cannot effectively capture users' intrinsic preferences and the true interactions between users and items. To address such noises, existing methods mostly rely on auxiliary data which are not always available. In this work, we ground on Optimal Transport (OT) to globally match a user embedding space and an item embedding space, allowing both non-deep and deep RS models to discriminate intrinsic and noisy interactions without supervision. Specifically, we firstly leverage the OT framework via Sinkhorn distance to compute the continuous many-to-many user-item matching scores. Then, we relax the regularization in Sinkhorn distance to achieve a closed-form solution with a reduced time complexity. Finally, to consider individual user behaviors for denoising, we develop a partial OT framework to adaptively relabel user-item interactions through a personalized thresholding mechanism. Extensive experiments show that our framework can significantly boost the performances of existing RS models.

Recent decades, the emergence of numerous novel algorithms makes it a gimmick to propose an intelligent optimization system based on metaphor, and hinders researchers from exploring the essence of search behavior in algorithms. However, it is difficult to directly discuss the search behavior of an intelligent optimization algorithm, since there are so many kinds of intelligent schemes. To address this problem, an intelligent optimization system is regarded as a simulated physical optimization system in this paper. The dynamic search behavior of such a simplified physical optimization system are investigated with quantum theory. To achieve this goal, the Schroedinger equation is employed as the dynamics equation of the optimization algorithm, which is used to describe dynamic search behaviours in the evolution process with quantum theory. Moreover, to explore the basic behaviour of the optimization system, the optimization problem is assumed to be decomposed and approximated. Correspondingly, the basic search behaviour is derived, which constitutes the basic iterative process of a simple optimization system. The basic iterative process is compared with some classical bare-bones schemes to verify the similarity of search behavior under different metaphors. The search strategies of these bare bones algorithms are analyzed through experiments.

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.

Since deep neural networks were developed, they have made huge contributions to everyday lives. Machine learning provides more rational advice than humans are capable of in almost every aspect of daily life. However, despite this achievement, the design and training of neural networks are still challenging and unpredictable procedures. To lower the technical thresholds for common users, automated hyper-parameter optimization (HPO) has become a popular topic in both academic and industrial areas. This paper provides a review of the most essential topics on HPO. The first section introduces the key hyper-parameters related to model training and structure, and discusses their importance and methods to define the value range. Then, the research focuses on major optimization algorithms and their applicability, covering their efficiency and accuracy especially for deep learning networks. This study next reviews major services and toolkits for HPO, comparing their support for state-of-the-art searching algorithms, feasibility with major deep learning frameworks, and extensibility for new modules designed by users. The paper concludes with problems that exist when HPO is applied to deep learning, a comparison between optimization algorithms, and prominent approaches for model evaluation with limited computational resources.

Driven by the visions of Internet of Things and 5G communications, the edge computing systems integrate computing, storage and network resources at the edge of the network to provide computing infrastructure, enabling developers to quickly develop and deploy edge applications. Nowadays the edge computing systems have received widespread attention in both industry and academia. To explore new research opportunities and assist users in selecting suitable edge computing systems for specific applications, this survey paper provides a comprehensive overview of the existing edge computing systems and introduces representative projects. A comparison of open source tools is presented according to their applicability. Finally, we highlight energy efficiency and deep learning optimization of edge computing systems. Open issues for analyzing and designing an edge computing system are also studied in this survey.