Parametrized quantum circuits (PQCs) have been broadly used as a hybrid quantum-classical machine learning scheme to accomplish generative tasks. However, whether PQCs have better expressive power than classical generative neural networks, such as restricted or deep Boltzmann machines, remains an open issue. In this paper, we prove that PQCs with a simple structure already outperform any classical neural network for generative tasks, unless the polynomial hierarchy collapses. Our proof builds on known results from tensor networks and quantum circuits (in particular, instantaneous quantum polynomial circuits). In addition, PQCs equipped with ancillary qubits for postselection may possess expressive power stronger than that of those without postselection. We employ them as an application for Bayesian learning, since it is possible to learn prior probabilities rather than assuming they are known. We expect that it will find many more applications in semisupervised learning where prior distributions are normally assumed to be unknown. Lastly, we conduct several numerical experiments using the Rigetti Forest platform to demonstrate the performance of the proposed Bayesian quantum circuit.

Residual connections significantly boost the performance of deep neural networks. However, few theoretical results address the influence of residuals on the hypothesis complexity and the generalization ability of deep neural networks. This article studies the influence of residual connections on the hypothesis complexity of the neural network in terms of the covering number of its hypothesis space. We first present an upper bound of the covering number of networks with residual connections. This bound shares a similar structure with that of neural networks without residual connections. This result suggests that moving a weight matrix or nonlinear activation from the bone to a vine would not increase the hypothesis space. Afterward, an O(1/√N) margin-based multiclass generalization bound is obtained for ResNet, as an exemplary case of any deep neural network with residual connections. Generalization guarantees for similar state-of-the-art neural network architectures, such as DenseNet and ResNeXt, are straightforward. According to the obtained generalization bound, we should introduce regularization terms to control the magnitude of the norms of weight matrices not to increase too much, in practice, to ensure a good generalization ability, which justifies the technique of weight decay.

Existing MKC algorithms cannot efficiently address the situation where some rows and columns of base kernel matrices are absent. This paper proposes two simple yet effective algorithms to address this issue. Different from existing approaches where incomplete kernel matrices are firstly imputed and a standard MKC algorithm is applied to the imputed kernel matrices, our first algorithm integrates imputation and clustering into a unified learning procedure. Specifically, we perform multiple kernel clustering directly with the presence of incomplete kernel matrices, which are treated as auxiliary variables to be jointly optimized. Also, it adaptively imputes incomplete kernel matrices and combines them to best serve clustering. Moreover, we further improve this algorithm by encouraging these incomplete kernel matrices to mutually complete each other. The three-step iterative algorithm is designed to solve the resultant optimization problems. After that, we theoretically study the generalization bound of the proposed algorithms. Extensive experiments are conducted on 13 benchmark data sets to compare the proposed algorithms with existing imputation-based methods. Our algorithms consistently achieve superior performance and the improvement becomes more significant with increasing missing ratio, verifying the effectiveness and advantages of the proposed joint imputation and clustering.

Quantum computers are next-generation devices that hold promise to perform calculations beyond the reach of classical computers. A leading method towards achieving this goal is through quantum machine learning, especially quantum generative learning. Due to the intrinsic probabilistic nature of quantum mechanics, it is reasonable to postulate that quantum generative learning models (QGLMs) may surpass their classical counterparts. As such, QGLMs are receiving growing attention from the quantum physics and computer science communities, where various QGLMs that can be efficiently implemented on near-term quantum machines with potential computational advantages are proposed. In this paper, we review the current progress of QGLMs from the perspective of machine learning. Particularly, we interpret these QGLMs, covering quantum circuit Born machines, quantum generative adversarial networks, quantum Boltzmann machines, and quantum variational autoencoders, as the quantum extension of classical generative learning models. In this context, we explore their intrinsic relations and their fundamental differences. We further summarize the potential applications of QGLMs in both conventional machine learning tasks and quantum physics. Last, we discuss the challenges and further research directions for QGLMs.

Hashing plays a pivotal role in nearest-neighbor searching for large-scale image retrieval. Recently, deep learning-based hashing methods have achieved promising performance. However, most of these deep methods involve discriminative models, which require large-scale, labeled training datasets, thus hindering their real-world applications. In this paper, we propose a novel strategy to exploit the semantic similarity of the training data and design an efficient generative adversarial framework to learn binary hash codes in an unsupervised manner. Specifically, our model consists of three different neural networks: an encoder network to learn hash codes from images, a generative network to generate images from hash codes, and a discriminative network to distinguish between pairs of hash codes and images. By adversarially training these networks, we successfully learn mutually coherent encoder and generative networks, and can output efficient hash codes from the encoder network. We also propose a novel strategy, which utilizes both feature and neighbor similarities, to construct a semantic similarity matrix, then use this matrix to guide the hash code learning process. Integrating the supervision of this semantic similarity matrix into the adversarial learning framework can efficiently preserve the semantic information of training data in Hamming space. The experimental results on three widely used benchmarks show that our method not only significantly outperforms several state-of-the-art unsupervised hashing methods, but also achieves comparable performance with popular supervised hashing methods.

Domain adaptation, which transfers the knowledge from label-rich source domain to unlabeled target domains, is a challenging task in machine learning. The prior domain adaptation methods focus on pairwise adaptation assumption with a single source and a single target domain, while little work concerns the scenario of one source domain and multiple target domains. Applying pairwise adaptation methods to this setting may be suboptimal, as they fail to consider the semantic association among multiple target domains. In this work we propose a deep semantic information propagation approach in the novel context of multiple unlabeled target domains and one labeled source domain. Our model aims to learn a unified subspace common for all domains with a heterogeneous graph attention network, where the transductive ability of the graph attention network can conduct semantic propagation of the related samples among multiple domains. In particular, the attention mechanism is applied to optimize the relationships of multiple domain samples for better semantic transfer. Then, the pseudo labels of the target domains predicted by the graph attention network are utilized to learn domain-invariant representations by aligning labeled source centroid and pseudo-labeled target centroid. We test our approach on four challenging public datasets, and it outperforms several popular domain adaptation methods.