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Solving the time-dependent Schr\"odinger equation is an important application area for quantum algorithms. We consider Schr\"odinger's equation in the semi-classical regime. Here the solutions exhibit strong multiple-scale behavior due to a small parameter $\hbar$, in the sense that the dynamics of the quantum states and the induced observables can occur on different spatial and temporal scales. Such a Schr\"odinger equation finds many applications, including in Born-Oppenheimer molecular dynamics and Ehrenfest dynamics. This paper considers quantum analogues of pseudo-spectral (PS) methods on classical computers. Estimates on the gate counts in terms of $\hbar$ and the precision $\varepsilon$ are obtained. It is found that the number of required qubits, $m$, scales only logarithmically with respect to $\hbar$. When the solution has bounded derivatives up to order $\ell$, the symmetric Trotting method has gate complexity $\mathcal{O}\Big({ (\varepsilon \hbar)^{-\frac12} \mathrm{polylog}(\varepsilon^{-\frac{3}{2\ell}} \hbar^{-1-\frac{1}{2\ell}})}\Big),$ provided that the diagonal unitary operators in the pseudo-spectral methods can be implemented with $\mathrm{poly}(m)$ operations. When physical observables are the desired outcomes, however, the step size in the time integration can be chosen independently of $\hbar$. The gate complexity in this case is reduced to $\mathcal{O}\Big({\varepsilon^{-\frac12} \mathrm{polylog}( \varepsilon^{-\frac3{2\ell}} \hbar^{-1} )}\Big),$ with $\ell$ again indicating the smoothness of the solution.

We share our experience with the recently released WILDS benchmark, a collection of ten datasets dedicated to developing models and training strategies which are robust to domain shifts. Several experiments yield a couple of critical observations which we believe are of general interest for any future work on WILDS. Our study focuses on two datasets: iWildCam and FMoW. We show that (1) Conducting separate cross-validation for each evaluation metric is crucial for both datasets, (2) A weak correlation between validation and test performance might make model development difficult for iWildCam, (3) Minor changes in the training of hyper-parameters improve the baseline by a relatively large margin (mainly on FMoW), (4) There is a strong correlation between certain domains and certain target labels (mainly on iWildCam). To the best of our knowledge, no prior work on these datasets has reported these observations despite their obvious importance. Our code is public.

Production companies face problems when it comes to quickly adapting their production control to fluctuating demands or changing requirements. Control approaches aiming to encapsulate production functions in the sense of services have shown to be promising in order to increase flexibility of Cyber-Physical Production Systems. But an existing challenge of such approaches is finding production plans based on provided functionalities for a set of requirements, especially when there is no direct (i.e., syntactic) match between demanded and provided functions. In such cases it can become complicated to find those provided functions that can be arranged into a plan satisfying the demand. While there is a variety of different approaches to production planning, flexible production poses specific requirements that are not covered by existing research. In this contribution, we first capture these requirements for flexible production environments. Afterwards, an overview of current Artificial Intelligence approaches that can be utilized in order to overcome the aforementioned challenges is given. Approaches from both symbolic AI planning as well as approaches based on Machine Learning are discussed and eventually compared against the requirements. Based on this comparison, a research agenda is derived.

In this report, we present the system design, operational strategy, and results of coordinated multi-vehicle field demonstrations of autonomous marine robotic technologies in search-for-life missions within the Pacific shelf margin of Costa Rica and the Santorini-Kolumbo caldera complex, which serve as analogs to environments that may exist in oceans beyond Earth. This report focuses on the automation of ROV manipulator operations for targeted biological sample-collection-and-return from the seafloor. In the context of future extraterrestrial exploration missions to ocean worlds, an ROV is an analog to a planetary lander, which must be capable of high-level autonomy. Our field trials involve two underwater vehicles, the SuBastian ROV and the Nereid Under Ice (NUI) hybrid ROV for mixed initiative (i.e., teleoperated or autonomous) missions, both equipped 7-DoF hydraulic manipulators. We describe an adaptable, hardware-independent computer vision architecture that enables high-level automated manipulation. The vision system provides a 3D understanding of the workspace to inform manipulator motion planning in complex unstructured environments. We demonstrate the effectiveness of the vision system and control framework through field trials in increasingly challenging environments, including the automated collection and return of biological samples from within the active undersea volcano, Kolumbo. Based on our experiences in the field, we discuss the performance of our system and identify promising directions for future research.

Linear dynamical systems are canonical models for learning-based control of plants with uncertain dynamics. The setting consists of a stochastic differential equation that captures the state evolution of the plant understudy, while the true dynamics matrices are unknown and need to be learned from the observed data of state trajectory. An important issue is to ensure that the system is stabilized and destabilizing control actions due to model uncertainties are precluded as soon as possible. A reliable stabilization procedure for this purpose that can effectively learn from unstable data to stabilize the system in a finite time is not currently available. In this work, we propose a novel Bayesian learning algorithm that stabilizes unknown continuous-time stochastic linear systems. The presented algorithm is flexible and exposes effective stabilization performance after a remarkably short time period of interacting with the system.

Ciphertexts of an order-preserving encryption (OPE) scheme preserve the order of their corresponding plaintexts. However, OPEs are vulnerable to inference attacks that exploit this preserved order. At another end, differential privacy has become the de-facto standard for achieving data privacy. One of the most attractive properties of DP is that any post-processing (inferential) computation performed on the noisy output of a DP algorithm does not degrade its privacy guarantee. In this paper, we propose a novel differentially private order preserving encryption scheme, OP$\epsilon$. Under OP$\epsilon$, the leakage of order from the ciphertexts is differentially private. As a result, in the least, OP$\epsilon$ ensures a formal guarantee (specifically, a relaxed DP guarantee) even in the face of inference attacks. To the best of our knowledge, this is the first work to combine DP with a property-preserving encryption scheme. We demonstrate OP$\epsilon$'s practical utility in answering range queries via extensive empirical evaluation on four real-world datasets. For instance, OP$\epsilon$ misses only around $4$ in every $10K$ correct records on average for a dataset of size $\sim732K$ with an attribute of domain size $\sim18K$ and $\epsilon= 1$.

K-core decomposition is a commonly used metric to analyze graph structure or study the relative importance of nodes in complex graphs. Recent years have seen rapid growth in the scale of the graph, especially in industrial settings. For example, our industrial partner runs popular social applications with billions of users and is able to gather a rich set of user data. As a result, applying K-core decomposition on large graphs has attracted more and more attention from academics and the industry. A simple but effective method to deal with large graphs is to train them in the distributed settings, and some distributed K-core decomposition algorithms are also proposed. Despite their effectiveness, we experimentally and theoretically observe that these algorithms consume too many resources and become unstable on super-large-scale graphs, especially when the given resources are limited. In this paper, we deal with those super-large-scale graphs and propose a divide-and-conquer strategy on top of the distributed K-core decomposition algorithm. We evaluate our approach on three large graphs. The experimental results show that the consumption of resources can be significantly reduced, and the calculation on large-scale graphs becomes more stable than the existing methods. For example, the distributed K-core decomposition algorithm can scale to a large graph with 136 billion edges without losing correctness with our divide-and-conquer technique.

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.

Understanding latent user needs beneath shopping behaviors is critical to e-commercial applications. Without a proper definition of user needs in e-commerce, most industry solutions are not driven directly by user needs at current stage, which prevents them from further improving user satisfaction. Representing implicit user needs explicitly as nodes like "outdoor barbecue" or "keep warm for kids" in a knowledge graph, provides new imagination for various e- commerce applications. Backed by such an e-commerce knowledge graph, we propose a supervised learning algorithm to conceptualize user needs from their transaction history as "concept" nodes in the graph and infer those concepts for each user through a deep attentive model. Offline experiments demonstrate the effectiveness and stability of our model, and online industry strength tests show substantial advantages of such user needs understanding.

Many resource allocation problems in the cloud can be described as a basic Virtual Network Embedding Problem (VNEP): finding mappings of request graphs (describing the workloads) onto a substrate graph (describing the physical infrastructure). In the offline setting, the two natural objectives are profit maximization, i.e., embedding a maximal number of request graphs subject to the resource constraints, and cost minimization, i.e., embedding all requests at minimal overall cost. The VNEP can be seen as a generalization of classic routing and call admission problems, in which requests are arbitrary graphs whose communication endpoints are not fixed. Due to its applications, the problem has been studied intensively in the networking community. However, the underlying algorithmic problem is hardly understood. This paper presents the first fixed-parameter tractable approximation algorithms for the VNEP. Our algorithms are based on randomized rounding. Due to the flexible mapping options and the arbitrary request graph topologies, we show that a novel linear program formulation is required. Only using this novel formulation the computation of convex combinations of valid mappings is enabled, as the formulation needs to account for the structure of the request graphs. Accordingly, to capture the structure of request graphs, we introduce the graph-theoretic notion of extraction orders and extraction width and show that our algorithms have exponential runtime in the request graphs' maximal width. Hence, for request graphs of fixed extraction width, we obtain the first polynomial-time approximations. Studying the new notion of extraction orders we show that (i) computing extraction orders of minimal width is NP-hard and (ii) that computing decomposable LP solutions is in general NP-hard, even when restricting request graphs to planar ones.