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Quantum computing holds immense potential for solving classically intractable problems by leveraging the unique properties of quantum mechanics. The scalability of quantum architectures remains a significant challenge. Multi-core quantum architectures are proposed to solve the scalability problem, arising a new set of challenges in hardware, communications and compilation, among others. One of these challenges is to adapt a quantum algorithm to fit within the different cores of the quantum computer. This paper presents a novel approach for circuit partitioning using Deep Reinforcement Learning, contributing to the advancement of both quantum computing and graph partitioning. This work is the first step in integrating Deep Reinforcement Learning techniques into Quantum Circuit Mapping, opening the door to a new paradigm of solutions to such problems.

The self-random number generation (SRNG) problem is considered for general setting. In the literature, the optimum SRNG rate with respect to the variational distance has been discussed. In this paper, we first try to characterize the optimum SRNG rate with respect to a subclass of $f$-divergences. The subclass of $f$-divergences considered in this paper includes typical distance measures such as the variational distance, the KL divergence, the Hellinger distance and so on. Hence our result can be considered as a generalization of the previous result with respect to the variational distance. Next, we consider the obtained optimum SRNG rate from several viewpoints. The $\varepsilon$-source coding problem is one of related problems with the SRNG problem. Our results reveal how the SRNG problem with the $f$-divergence relate to the $\varepsilon$-fixed-length source coding problem. We also apply our results to the rate distortion perception (RDP) function. As a result, we can establish a lower bound for the RDP function with respect to $f$-divergences using our findings. Finally, we discuss the representation of the optimum SRNG rate using the smooth R\'enyi entropy.

We consider (stochastic) subgradient methods for strongly convex but potentially nonsmooth non-Lipschitz optimization. We provide new equivalent dual descriptions (in the style of dual averaging) for the classic subgradient method, the proximal subgradient method, and the switching subgradient method. These equivalences enable $O(1/T)$ convergence guarantees in terms of both their classic primal gap and a not previously analyzed dual gap for strongly convex optimization. Consequently, our theory provides these classic methods with simple, optimal stopping criteria and optimality certificates at no added computational cost. Our results apply to a wide range of stepsize selections and of non-Lipschitz ill-conditioned problems where the early iterations of the subgradient method may diverge exponentially quickly (a phenomenon which, to the best of our knowledge, no prior works address). Even in the presence of such undesirable behaviors, our theory still ensures and bounds eventual convergence.

The growing computing power over the years has enabled simulations to become more complex and accurate. While immensely valuable for scientific discovery and problem-solving, however, high-fidelity simulations come with significant computational demands. As a result, it is common to run a low-fidelity model with a subgrid-scale model to reduce the computational cost, but selecting the appropriate subgrid-scale models and tuning them are challenging. We propose a novel method for learning the subgrid-scale model effects when simulating partial differential equations augmented by neural ordinary differential operators in the context of discontinuous Galerkin (DG) spatial discretization. Our approach learns the missing scales of the low-order DG solver at a continuous level and hence improves the accuracy of the low-order DG approximations as well as accelerates the filtered high-order DG simulations with a certain degree of precision. We demonstrate the performance of our approach through multidimensional Taylor-Green vortex examples at different Reynolds numbers and times, which cover laminar, transitional, and turbulent regimes. The proposed method not only reconstructs the subgrid-scale from the low-order (1st-order) approximation but also speeds up the filtered high-order DG (6th-order) simulation by two orders of magnitude.

Sequential neural posterior estimation (SNPE) techniques have been recently proposed for dealing with simulation-based models with intractable likelihoods. They are devoted to learning the posterior from adaptively proposed simulations using neural network-based conditional density estimators. As a SNPE technique, the automatic posterior transformation (APT) method proposed by Greenberg et al. (2019) performs notably and scales to high dimensional data. However, the APT method bears the computation of an expectation of the logarithm of an intractable normalizing constant, i.e., a nested expectation. Although atomic APT was proposed to solve this by discretizing the normalizing constant, it remains challenging to analyze the convergence of learning. In this paper, we propose a nested APT method to estimate the involved nested expectation instead. This facilitates establishing the convergence analysis. Since the nested estimators for the loss function and its gradient are biased, we make use of unbiased multi-level Monte Carlo (MLMC) estimators for debiasing. To further reduce the excessive variance of the unbiased estimators, this paper also develops some truncated MLMC estimators by taking account of the trade-off between the bias and the average cost. Numerical experiments for approximating complex posteriors with multimodal in moderate dimensions are provided.

The loss function plays an important role in optimizing the performance of a learning system. A crucial aspect of the loss function is the assignment of sample weights within a mini-batch during loss computation. In the context of continual learning (CL), most existing strategies uniformly treat samples when calculating the loss value, thereby assigning equal weights to each sample. While this approach can be effective in certain standard benchmarks, its optimal effectiveness, particularly in more complex scenarios, remains underexplored. This is particularly pertinent in training "in the wild," such as with self-training, where labeling is automated using a reference model. This paper introduces the Online Meta-learning for Sample Importance (OMSI) strategy that approximates sample weights for a mini-batch in an online CL stream using an inner- and meta-update mechanism. This is done by first estimating sample weight parameters for each sample in the mini-batch, then, updating the model with the adapted sample weights. We evaluate OMSI in two distinct experimental settings. First, we show that OMSI enhances both learning and retained accuracy in a controlled noisy-labeled data stream. Then, we test the strategy in three standard benchmarks and compare it with other popular replay-based strategies. This research aims to foster the ongoing exploration in the area of self-adaptive CL.

Calibrating simulation models that take large quantities of multi-dimensional data as input is a hard simulation optimization problem. Existing adaptive sampling strategies offer a methodological solution. However, they may not sufficiently reduce the computational cost for estimation and solution algorithm's progress within a limited budget due to extreme noise levels and heteroskedasticity of system responses. We propose integrating stratification with adaptive sampling for the purpose of efficiency in optimization. Stratification can exploit local dependence in the simulation inputs and outputs. Yet, the state-of-the-art does not provide a full capability to adaptively stratify the data as different solution alternatives are evaluated. We devise two procedures for data-driven calibration problems that involve a large dataset with multiple covariates to calibrate models within a fixed overall simulation budget. The first approach dynamically stratifies the input data using binary trees, while the second approach uses closed-form solutions based on linearity assumptions between the objective function and concomitant variables. We find that dynamical adjustment of stratification structure accelerates optimization and reduces run-to-run variability in generated solutions. Our case study for calibrating a wind power simulation model, widely used in the wind industry, using the proposed stratified adaptive sampling, shows better-calibrated parameters under a limited budget.

Discrepancies between the true Martian atmospheric density and the onboard density model can significantly impair the performance of spacecraft entry navigation filters. This work introduces a new approach to online filtering for Martian entry by using a neural network to estimate atmospheric density and employing a consider analysis to account for the uncertainty in the estimate. The network is trained on an exponential atmospheric density model, and its parameters are dynamically adapted in real time to account for any mismatches between the true and estimated densities. The adaptation of the network is formulated as a maximum likelihood problem, leveraging the measurement innovations of the filter to identify optimal network parameters. The incorporation of a neural network enables the use of stochastic optimizers known for their efficiency in the machine learning domain within the context of the maximum likelihood approach. Performance comparisons against previous approaches are conducted in various realistic Mars entry navigation scenarios, resulting in superior estimation accuracy and precise alignment of the estimated density with a broad selection of realistic Martian atmospheres sampled from perturbed Mars-GRAM data.

Knowledge graph completion aims to predict missing relations between entities in a knowledge graph. While many different methods have been proposed, there is a lack of a unifying framework that would lead to state-of-the-art results. Here we develop PathCon, a knowledge graph completion method that harnesses four novel insights to outperform existing methods. PathCon predicts relations between a pair of entities by: (1) Considering the Relational Context of each entity by capturing the relation types adjacent to the entity and modeled through a novel edge-based message passing scheme; (2) Considering the Relational Paths capturing all paths between the two entities; And, (3) adaptively integrating the Relational Context and Relational Path through a learnable attention mechanism. Importantly, (4) in contrast to conventional node-based representations, PathCon represents context and path only using the relation types, which makes it applicable in an inductive setting. Experimental results on knowledge graph benchmarks as well as our newly proposed dataset show that PathCon outperforms state-of-the-art knowledge graph completion methods by a large margin. Finally, PathCon is able to provide interpretable explanations by identifying relations that provide the context and paths that are important for a given predicted relation.

Recently, deep learning has achieved very promising results in visual object tracking. Deep neural networks in existing tracking methods require a lot of training data to learn a large number of parameters. However, training data is not sufficient for visual object tracking as annotations of a target object are only available in the first frame of a test sequence. In this paper, we propose to learn hierarchical features for visual object tracking by using tree structure based Recursive Neural Networks (RNN), which have fewer parameters than other deep neural networks, e.g. Convolutional Neural Networks (CNN). First, we learn RNN parameters to discriminate between the target object and background in the first frame of a test sequence. Tree structure over local patches of an exemplar region is randomly generated by using a bottom-up greedy search strategy. Given the learned RNN parameters, we create two dictionaries regarding target regions and corresponding local patches based on the learned hierarchical features from both top and leaf nodes of multiple random trees. In each of the subsequent frames, we conduct sparse dictionary coding on all candidates to select the best candidate as the new target location. In addition, we online update two dictionaries to handle appearance changes of target objects. Experimental results demonstrate that our feature learning algorithm can significantly improve tracking performance on benchmark datasets.