Quantum error correction requires the use of error syndromes derived from measurements that may be unreliable. Recently, quantum data-syndrome (QDS) codes have been proposed as a possible approach to protect against both data and syndrome errors, in which a set of linearly dependent stabilizer measurements are performed to increase redundancy. Motivated by wanting to reduce the total number of measurements performed, we introduce QDS subsystem codes, and show that they can outperform similar QDS stabilizer codes derived from them. We also give a construction of single-error-correcting QDS stabilizer codes from impure stabilizer codes, and show that any such code must satisfy a variant of the quantum Hamming bound for QDS codes. Finally, we use this bound to prove a new bound that applies to impure, but not pure, stabilizer codes that may be of independent interest.
相關內容
We develop domain theory in constructive and predicative univalent foundations (also known as homotopy type theory). That we work predicatively means that we do not assume Voevodsky's propositional resizing axioms. Our work is constructive in the sense that we do not rely on excluded middle or the axiom of (countable) choice. Domain theory studies so-called directed complete posets (dcpos) and Scott continuous maps between them and has applications in programming language semantics, higher-type computability and topology. A common approach to deal with size issues in a predicative foundation is to work with information systems, abstract bases or formal topologies rather than dcpos, and approximable relations rather than Scott continuous functions. In our type-theoretic approach, we instead accept that dcpos may be large and work with type universes to account for this. A priori one might expect that complex constructions of dcpos result in a need for ever-increasing universes and are predicatively impossible. We show that such constructions can be carried out in a predicative setting. We illustrate the development with applications in the semantics of programming languages: the soundness and computational adequacy of the Scott model of PCF and Scott's $D_\infty$ model of the untyped $\lambda$-calculus. We also give a predicative account of continuous and algebraic dcpos, and of the related notions of a small basis and its rounded ideal completion. The fact that nontrivial dcpos have large carriers is in fact unavoidable and characteristic of our predicative setting, as we explain in a complementary chapter on the constructive and predicative limitations of univalent foundations. Our account of domain theory in univalent foundations is fully formalised with only a few minor exceptions. The ability of the proof assistant Agda to infer universe levels has been invaluable for our purposes.
Training and Hyperparameter Optimization (HPO) of deep learning-based AI models are often compute resource intensive and calls for the use of large-scale distributed resources as well as scalable and resource efficient hyperparameter search algorithms. This work studies the potential of using model performance prediction to aid the HPO process carried out on High Performance Computing systems. In addition, a quantum annealer is used to train the performance predictor and a method is proposed to overcome some of the problems derived from the current limitations in quantum systems as well as to increase the stability of solutions. This allows for achieving results on a quantum machine comparable to those obtained on a classical machine, showing how quantum computers could be integrated within classical machine learning tuning pipelines. Furthermore, results are presented from the development of a containerized benchmark based on an AI-model for collision event reconstruction that allows us to compare and assess the suitability of different hardware accelerators for training deep neural networks.
The usage and impact of deep learning for cleaner production and sustainability purposes remain little explored. This work shows how deep learning can be harnessed to increase sustainability in production and product usage. Specifically, we utilize deep learning-based computer vision to determine the wear states of products. The resulting insights serve as a basis for novel product-service systems with improved integration and result orientation. Moreover, these insights are expected to facilitate product usage improvements and R&D innovations. We demonstrate our approach on two products: machining tools and rotating X-ray anodes. From a technical standpoint, we show that it is possible to recognize the wear state of these products using deep-learning-based computer vision. In particular, we detect wear through microscopic images of the two products. We utilize a U-Net for semantic segmentation to detect wear based on pixel granularity. The resulting mean dice coefficients of 0.631 and 0.603 demonstrate the feasibility of the proposed approach. Consequently, experts can now make better decisions, for example, to improve the machining process parameters. To assess the impact of the proposed approach on environmental sustainability, we perform life cycle assessments that show gains for both products. The results indicate that the emissions of CO2 equivalents are reduced by 12% for machining tools and by 44% for rotating anodes. This work can serve as a guideline and inspire researchers and practitioners to utilize computer vision in similar scenarios to develop sustainable smart product-service systems and enable cleaner production.
Curated knowledge graphs encode domain expertise and improve the performance of recommendation, segmentation, ad targeting, and other machine learning systems in several domains. As new concepts emerge in a domain, knowledge graphs must be expanded to preserve machine learning performance. Manually expanding knowledge graphs, however, is infeasible at scale. In this work, we propose a method for knowledge graph expansion with humans-in-the-loop. Concretely, given a knowledge graph, our method predicts the "parents" of new concepts to be added to this graph for further verification by human experts. We show that our method is both accurate and provably "human-friendly". Specifically, we prove that our method predicts parents that are "near" concepts' true parents in the knowledge graph, even when the predictions are incorrect. We then show, with a controlled experiment, that satisfying this property increases both the speed and the accuracy of the human-algorithm collaboration. We further evaluate our method on a knowledge graph from Pinterest and show that it outperforms competing methods on both accuracy and human-friendliness. Upon deployment in production at Pinterest, our method reduced the time needed for knowledge graph expansion by ~400% (compared to manual expansion), and contributed to a subsequent increase in ad revenue of 20%.
Recent advances in deep learning have led to increased interest in solving high-efficiency end-to-end transmission problems using methods that employ the nonlinear property of neural networks. These methods, we call semantic coding, extract semantic features of the source signal across space and time, and design source-channel coding methods to transmit these features over wireless channels. Rapid progress has led to numerous research papers, but a consolidation of the discovered knowledge has not yet emerged. In this article, we gather ideas to categorize the expansive aspects on semantic coding as two paradigms, i.e., explicit and implicit semantic coding. We first focus on those two paradigms of semantic coding by identifying their common and different components in building semantic communication systems. We then focus on the applications of semantic coding to different transmission tasks. Our article highlights the improved quality, flexibility, and capability brought by semantic coded transmission. Finally, we point out future directions.
Quantum Intermediate Representation (QIR) is a Microsoft-developed, LLVM-based intermediate representation for quantum program compilers. QIR aims to provide a general solution for quantum program compilers independent of front-end languages and back-end hardware, thus avoiding duplicate development of intermediate representations and compilers. Since it is still under development, QIR is described in natural language and lacks a formal definition, leading to ambiguity in its interpretation and a lack of rigor in implementing quantum functions. In this paper, we provide formal definitions for the data types and instruction sets of QIR, aiming to provide correctness and security guarantees for operations and intermediate code conversions in QIR. To validate our design, we show some samples of unsafe QIR code where errors can be detected by our formal approach.
We investigate the convergence and convergence rate of stochastic training algorithms for Neural Networks (NNs) that have been inspired by Dropout (Hinton et al., 2012). With the goal of avoiding overfitting during training of NNs, dropout algorithms consist in practice of multiplying the weight matrices of a NN componentwise by independently drawn random matrices with $\{0, 1 \}$-valued entries during each iteration of Stochastic Gradient Descent (SGD). This paper presents a probability theoretical proof that for fully-connected NNs with differentiable, polynomially bounded activation functions, if we project the weights onto a compact set when using a dropout algorithm, then the weights of the NN converge to a unique stationary point of a projected system of Ordinary Differential Equations (ODEs). After this general convergence guarantee, we go on to investigate the convergence rate of dropout. Firstly, we obtain generic sample complexity bounds for finding $\epsilon$-stationary points of smooth nonconvex functions using SGD with dropout that explicitly depend on the dropout probability. Secondly, we obtain an upper bound on the rate of convergence of Gradient Descent (GD) on the limiting ODEs of dropout algorithms for NNs with the shape of arborescences of arbitrary depth and with linear activation functions. The latter bound shows that for an algorithm such as Dropout or Dropconnect (Wan et al., 2013), the convergence rate can be impaired exponentially by the depth of the arborescence. In contrast, we experimentally observe no such dependence for wide NNs with just a few dropout layers. We also provide a heuristic argument for this observation. Our results suggest that there is a change of scale of the effect of the dropout probability in the convergence rate that depends on the relative size of the width of the NN compared to its depth.
We have developed efficient parameterized algorithms for the enumeration problems of graphs arising in chemistry. In particular, we have focused on the following problems: enumeration of Kekul\'e structures, computation of Hosoya index, computation of Merrifield-Simmons index, and computation of graph entropy based on matchings and independent sets. All these problems are known to be $\# P$-complete. We have developed FPT algorithms for bounded treewidth and bounded pathwidth for these problems with a better time complexity than the known state-of-the-art in the literature. We have also conducted experiments on the entire PubChem database of chemical compounds and tested our algorithms. We also provide a comparison with naive baseline algorithms for these problems, along with a distribution of treewidth for the chemical compounds available in the PubChem database.
A fundamental problem in quantum physics is to encode functions that are completely anti-symmetric under permutations of identical particles. The Barron space consists of high-dimensional functions that can be parameterized by infinite neural networks with one hidden layer. By explicitly encoding the anti-symmetric structure, we prove that the anti-symmetric functions which belong to the Barron space can be efficiently approximated with sums of determinants. This yields a factorial improvement in complexity compared to the standard representation in the Barron space and provides a theoretical explanation for the effectiveness of determinant-based architectures in ab-initio quantum chemistry.
The era of big data provides researchers with convenient access to copious data. However, people often have little knowledge about it. The increasing prevalence of big data is challenging the traditional methods of learning causality because they are developed for the cases with limited amount of data and solid prior causal knowledge. This survey aims to close the gap between big data and learning causality with a comprehensive and structured review of traditional and frontier methods and a discussion about some open problems of learning causality. We begin with preliminaries of learning causality. Then we categorize and revisit methods of learning causality for the typical problems and data types. After that, we discuss the connections between learning causality and machine learning. At the end, some open problems are presented to show the great potential of learning causality with data.
小貼士
登錄享
相關主題
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191