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Fractional derivatives are a well-studied generalization of integer order derivatives. Naturally, for optimization, it is of interest to understand the convergence properties of gradient descent using fractional derivatives. Convergence analysis of fractional gradient descent is currently limited both in the methods analyzed and the settings analyzed. This paper aims to fill in these gaps by analyzing variations of fractional gradient descent in smooth and convex, smooth and strongly convex, and smooth and non-convex settings. First, novel bounds will be established bridging fractional and integer derivatives. Then, these bounds will be applied to the aforementioned settings to prove $O(1/T)$ convergence for smooth and convex functions and linear convergence for smooth and strongly convex functions. Additionally, we prove $O(1/T)$ convergence for smooth and non-convex functions using an extended notion of smoothness that is more natural for fractional derivatives. Finally, empirical results will be presented on the potential speed up of fractional gradient descent over standard gradient descent as well as the challenges of predicting which will be faster in general.

Data entry forms use completeness requirements to specify the fields that are required or optional to fill for collecting necessary information from different types of users. However, some required fields may not be applicable for certain types of users anymore. Nevertheless, they may still be incorrectly marked as required in the form; we call such fields obsolete required fields. Since obsolete required fields usually have not-null validation checks before submitting the form, users have to enter meaningless values in such fields in order to complete the form submission. These meaningless values threaten the quality of the filled data. To avoid users filling meaningless values, existing techniques usually rely on manually written rules to identify the obsolete required fields and relax their completeness requirements. However, these techniques are ineffective and costly. In this paper, we propose LACQUER, a learning-based automated approach for relaxing the completeness requirements of data entry forms. LACQUER builds Bayesian Network models to automatically learn conditions under which users had to fill meaningless values. To improve its learning ability, LACQUER identifies the cases where a required field is only applicable for a small group of users, and uses SMOTE, an oversampling technique, to generate more instances on such fields for effectively mining dependencies on them. Our experimental results show that LACQUER can accurately relax the completeness requirements of required fields in data entry forms with precision values ranging between 0.76 and 0.90 on different datasets. LACQUER can prevent users from filling 20% to 64% of meaningless values, with negative predictive values between 0.72 and 0.91. Furthermore, LACQUER is efficient; it takes at most 839 ms to predict the completeness requirement of an instance.

Achievability in information theory refers to demonstrating a coding strategy that accomplishes a prescribed performance benchmark for the underlying task. In quantum information theory, the crafted Hayashi-Nagaoka operator inequality is an essential technique in proving a wealth of one-shot achievability bounds since it effectively resembles a union bound in various problems. In this work, we show that the pretty-good measurement naturally plays a role as the union bound as well. A judicious application of it considerably simplifies the derivation of one-shot achievability for classical-quantum (c-q) channel coding via an elegant three-line proof. The proposed analysis enjoys the following favorable features. (i) The established one-shot bound admits a closed-form expression as in the celebrated Holevo-Helstrom Theorem. Namely, the error probability of sending $M$ messages through a c-q channel is upper bounded by the minimum error of distinguishing the joint channel input-output state against $(M-1)$ decoupled products states. (ii) Our bound directly yields asymptotic results in the large deviation, small deviation, and moderate deviation regimes in a unified manner. (iii) The coefficients incurred in applying the Hayashi-Nagaoka operator inequality are no longer needed. Hence, the derived one-shot bound sharpens existing results relying on the Hayashi-Nagaoka operator inequality. In particular, we obtain the tightest achievable $\epsilon$-one-shot capacity for c-q channel coding heretofore, improving the third-order coding rate in the asymptotic scenario. (iv) Our result holds for infinite-dimensional Hilbert space. (v) The proposed method applies to deriving one-shot achievability for classical data compression with quantum side information, entanglement-assisted classical communication over quantum channels, and various quantum network information-processing protocols.

Although robust statistical estimators are less affected by outlying observations, their computation is usually more challenging. This is particularly the case in high-dimensional sparse settings. The availability of new optimization procedures, mainly developed in the computer science domain, offers new possibilities for the field of robust statistics. This paper investigates how such procedures can be used for robust sparse association estimators. The problem can be split into a robust estimation step followed by an optimization for the remaining decoupled, (bi-)convex problem. A combination of the augmented Lagrangian algorithm and adaptive gradient descent is implemented to also include suitable constraints for inducing sparsity. We provide results concerning the precision of the algorithm and show the advantages over existing algorithms in this context. High-dimensional empirical examples underline the usefulness of this procedure. Extensions to other robust sparse estimators are possible.

Previously, non-autoregressive models were widely perceived as being superior in generation efficiency but inferior in generation quality due to the difficulties of modeling multiple target modalities. To enhance the multi-modality modeling ability, we propose the diffusion glancing transformer, which employs a modality diffusion process and residual glancing sampling. The modality diffusion process is a discrete process that interpolates the multi-modal distribution along the decoding steps, and the residual glancing sampling approach guides the model to continuously learn the remaining modalities across the layers. Experimental results on various machine translation and text generation benchmarks demonstrate that DIFFGLAT achieves better generation accuracy while maintaining fast decoding speed compared with both autoregressive and non-autoregressive models.

State inference and parameter learning in sequential models can be successfully performed with approximation techniques that maximize the evidence lower bound to the marginal log-likelihood of the data distribution. These methods may be referred to as Dynamical Variational Autoencoders, and our specific focus lies on the deep Kalman filter. It has been shown that the ELBO objective can oversimplify data representations, potentially compromising estimation quality. Tighter Monte Carlo objectives have been proposed in the literature to enhance generative modeling performance. For instance, the IWAE objective uses importance weights to reduce the variance of marginal log-likelihood estimates. In this paper, importance sampling is applied to the DKF framework for learning deep Markov models, resulting in the IW-DKF, which shows an improvement in terms of log-likelihood estimates and KL divergence between the variational distribution and the transition model. The framework using the sampled DKF update rule is also accommodated to address sequential state and parameter estimation when working with highly non-linear physics-based models. An experiment with the 3-space Lorenz attractor shows an enhanced generative modeling performance and also a decrease in RMSE when estimating the model parameters and latent states, indicating that tighter MCOs lead to improved state inference performance.

Asteroid restructuring uses robotics, self replication, and mechanical automatons to autonomously restructure an asteroid into a large rotating space station. The restructuring process makes structures from asteroid oxide materials; uses productive self-replication to make replicators, helpers, and products; and creates a multiple floor station to support a large population. In an example simulation, it takes 12 years to autonomously restructure a large asteroid into the space station. This is accomplished with a single rocket launch. The single payload contains a base station, 4 robots (spiders), and a modest set of supplies. Our simulation creates 3000 spiders and over 23,500 other pieces of equipment. Only the base station and spiders (replicators) have advanced microprocessors and algorithms. These represent 21st century technologies created and trans-ported from Earth. The equipment and tools are built using in-situ materials and represent 18th or 19th century technologies. The equipment and tools (helpers) have simple mechanical programs to perform repetitive tasks. The resulting example station would be a rotating framework almost 5 kilometers in diameter. Once completed, it could support a population of over 700,000 people. Many researchers identify the high launch costs, the harsh space environment, and the lack of gravity as the key obstacles hindering the development of space stations. The single probe addresses the high launch cost. The autonomous construction eliminates the harsh space environment for construction crews. The completed rotating station provides radiation protection and centripetal gravity for the first work crews and colonists.

Causality can be described in terms of a structural causal model (SCM) that carries information on the variables of interest and their mechanistic relations. For most processes of interest the underlying SCM will only be partially observable, thus causal inference tries to leverage any exposed information. Graph neural networks (GNN) as universal approximators on structured input pose a viable candidate for causal learning, suggesting a tighter integration with SCM. To this effect we present a theoretical analysis from first principles that establishes a novel connection between GNN and SCM while providing an extended view on general neural-causal models. We then establish a new model class for GNN-based causal inference that is necessary and sufficient for causal effect identification. Our empirical illustration on simulations and standard benchmarks validate our theoretical proofs.

Deep neural networks have revolutionized many machine learning tasks in power systems, ranging from pattern recognition to signal processing. The data in these tasks is typically represented in Euclidean domains. Nevertheless, there is an increasing number of applications in power systems, where data are collected from non-Euclidean domains and represented as the graph-structured data with high dimensional features and interdependency among nodes. The complexity of graph-structured data has brought significant challenges to the existing deep neural networks defined in Euclidean domains. Recently, many studies on extending deep neural networks for graph-structured data in power systems have emerged. In this paper, a comprehensive overview of graph neural networks (GNNs) in power systems is proposed. Specifically, several classical paradigms of GNNs structures (e.g., graph convolutional networks, graph recurrent neural networks, graph attention networks, graph generative networks, spatial-temporal graph convolutional networks, and hybrid forms of GNNs) are summarized, and key applications in power systems such as fault diagnosis, power prediction, power flow calculation, and data generation are reviewed in detail. Furthermore, main issues and some research trends about the applications of GNNs in power systems are discussed.

Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.