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Subset-Sum is an NP-complete problem where one must decide if a multiset of $n$ integers contains a subset whose elements sum to a target value $m$. The best-known classical and quantum algorithms run in time $\tilde{O}(2^{n/2})$ and $\tilde{O}(2^{n/3})$, respectively, based on the well-known meet-in-the-middle technique. Here we introduce a novel classical dynamic-programming-based data structure with applications to Subset-Sum and a number of variants, including Equal-Sums (where one seeks two disjoint subsets with the same sum), 2-Subset-Sum (a relaxed version of Subset-Sum where each item in the input set can be used twice in the summation), and Shifted-Sums, a generalization of both of these variants, where one seeks two disjoint subsets whose sums differ by some specified value. Given any modulus $p$, our data structure can be constructed in time $O(n^2p)$, after which queries can be made in time $O(n^2)$ to the lists of subsets summing to any value modulo $p$. We use this data structure in combination with variable-time amplitude amplification and a new quantum pair finding algorithm, extending the quantum claw finding algorithm to the multiple solutions case, to give an $O(2^{0.504n})$ quantum algorithm for Shifted-Sums, an improvement on the best-known $O(2^{0.773n})$ classical running time. Incidentally, we obtain new $\tilde{O}(2^{n/2})$ and $\tilde{O}(2^{n/3})$ classical and quantum algorithms for Subset-Sum, not based on the seminal meet-in-the-middle method. We also study Pigeonhole Equal-Sums and Pigeonhole Modular Equal-Sums, where the existence of a solution is guaranteed by the pigeonhole principle. For the former problem, we give faster classical and quantum algorithms with running time $\tilde{O}(2^{n/2})$ and $\tilde{O}(2^{2n/5})$, respectively. For the more general modular problem, we give a classical algorithm that also runs in time $\tilde{O}(2^{n/2})$.

In this paper, we study a sequential decision making problem faced by e-commerce carriers related to when to send out a vehicle from the central depot to serve customer requests, and in which order to provide the service, under the assumption that the time at which parcels arrive at the depot is stochastic and dynamic. The objective is to maximize the number of parcels that can be delivered during the service hours. We propose two reinforcement learning approaches for solving this problem, one based on a policy function approximation (PFA) and the second on a value function approximation (VFA). Both methods are combined with a look-ahead strategy, in which future release dates are sampled in a Monte-Carlo fashion and a tailored batch approach is used to approximate the value of future states. Our PFA and VFA make a good use of branch-and-cut-based exact methods to improve the quality of decisions. We also establish sufficient conditions for partial characterization of optimal policy and integrate them into PFA/VFA. In an empirical study based on 720 benchmark instances, we conduct a competitive analysis using upper bounds with perfect information and we show that PFA and VFA greatly outperform two alternative myopic approaches. Overall, PFA provides best solutions, while VFA (which benefits from a two-stage stochastic optimization model) achieves a better tradeoff between solution quality and computing time.

Quantum Search Algorithm made a big impact by being able to solve the search problem for a set with $N$ elements using only $O(\sqrt{N})$ steps. Unfortunately, it is impossible to reduce the order of the complexity of this problem, however, it is possible to make improvements by a constant factor. In this paper we pursued such improvements for search problem in sets with known probability distributions. We have shown that by using a modified version of quantum search algorithm, it is possible to decrease the expected number of iterations for such sets.

Differentiable renderers provide a direct mathematical link between an object's 3D representation and images of that object. In this work, we develop an approximate differentiable renderer for a compact, interpretable representation, which we call Fuzzy Metaballs. Our approximate renderer focuses on rendering shapes via depth maps and silhouettes. It sacrifices fidelity for utility, producing fast runtimes and high-quality gradient information that can be used to solve vision tasks. Compared to mesh-based differentiable renderers, our method has forward passes that are 5x faster and backwards passes that are 30x faster. The depth maps and silhouette images generated by our method are smooth and defined everywhere. In our evaluation of differentiable renderers for pose estimation, we show that our method is the only one comparable to classic techniques. In shape from silhouette, our method performs well using only gradient descent and a per-pixel loss, without any surrogate losses or regularization. These reconstructions work well even on natural video sequences with segmentation artifacts. Project page: //leonidk.github.io/fuzzy-metaballs

Lighting is a determining factor in photography that affects the style, expression of emotion, and even quality of images. Creating or finding satisfying lighting conditions, in reality, is laborious and time-consuming, so it is of great value to develop a technology to manipulate illumination in an image as post-processing. Although previous works have explored techniques based on the physical viewpoint for relighting images, extensive supervisions and prior knowledge are necessary to generate reasonable images, restricting the generalization ability of these works. In contrast, we take the viewpoint of image-to-image translation and implicitly merge ideas of the conventional physical viewpoint. In this paper, we present an Illumination-Aware Network (IAN) which follows the guidance from hierarchical sampling to progressively relight a scene from a single image with high efficiency. In addition, an Illumination-Aware Residual Block (IARB) is designed to approximate the physical rendering process and to extract precise descriptors of light sources for further manipulations. We also introduce a depth-guided geometry encoder for acquiring valuable geometry- and structure-related representations once the depth information is available. Experimental results show that our proposed method produces better quantitative and qualitative relighting results than previous state-of-the-art methods. The code and models are publicly available on //github.com/NK-CS-ZZL/IAN.

It has been rightfully emphasized that the use of AI for clinical decision making could amplify health disparities. An algorithm may encode protected characteristics, and then use this information for making predictions due to undesirable correlations in the (historical) training data. It remains unclear how we can establish whether such information is actually used. Besides the scarcity of data from underserved populations, very little is known about how dataset biases manifest in predictive models and how this may result in disparate performance. This article aims to shed some light on these issues by exploring new methodology for subgroup analysis in image-based disease detection models. We utilize two publicly available chest X-ray datasets, CheXpert and MIMIC-CXR, to study performance disparities across race and biological sex in deep learning models. We explore test set resampling, transfer learning, multitask learning, and model inspection to assess the relationship between the encoding of protected characteristics and disease detection performance across subgroups. We confirm subgroup disparities in terms of shifted true and false positive rates which are partially removed after correcting for population and prevalence shifts in the test sets. We further find a previously used transfer learning method to be insufficient for establishing whether specific patient information is used for making predictions. The proposed combination of test-set resampling, multitask learning, and model inspection reveals valuable new insights about the way protected characteristics are encoded in the feature representations of deep neural networks.

Teleoperation is a widely adopted strategy to control robotic manipulators executing complex tasks that require highly dexterous movements and critical high-level intelligence. Classical teleoperation schemes are based on either joystick control, or on more intuitive interfaces which map directly the user arm motions into one robot arm's motions. These approaches have limits when the execution of a given task requires reconfigurable multiple robotic arm systems. Indeed, the simultaneous teleoperation of two or more robot arms could extend the workspace of the manipulation cell, or increase its total payload, or afford other advantages. In different phases of a reconfigurable multi-arm system, each robot could act as an independent arm, or as one of a pair of cooperating arms, or as one of the fingers of a virtual, large robot hand. This manuscript proposes a novel telemanipulation framework that enables both the individual and combined control of any number of robotic arms. Thanks to the designed control architecture, the human operator can intuitively choose the proposed control modalities and the manipulators that make the task convenient to execute through the user interface. Moreover, through the tele-impedance paradigm, the system can address complex tasks that require physical interaction by letting the robot mimic the arm impedance and position references of the human operator. The proposed framework is validated with 8 subjects controlling 4 Franka Emika Panda robots with 7-DoFs to execute a telemanipulation task. Qualitative results of the experiments show us the promising applicability of our framework.

Coded caching is an effective technique to decongest the amount of traffic in the backhaul link. In such a scheme, each file hosted in the server is divided into a number of packets to pursue a low transmission rate based on the delicate design of contents cached into users and broadcast messages. However, the implementation complexity of this scheme increases with the number of packets. It is desirable to design a scheme with a small subpacketization level and a relatively low transmission rate. Recently, placement delivery array (PDA) was proposed to address the subpacketization bottleneck of coded caching. This paper investigates the design PDA from a new perspective, i.e., the injective arc coloring of regular digraphs. It is shown that the injective arc coloring of a regular digraph can yield a PDA with the same number of rows and columns. Based on this, a new class of regular digraphs are defined and the upper bounds on the injective chromatic index of such digraphs are derived. Consequently, some new coded caching schemes with a linear subpacketization level and a small transmission rate are proposed, one of which generalizes the existing scheme for the scenario with a more flexible number of users.

Density peaks clustering has become a nova of clustering algorithm because of its simplicity and practicality. However, there is one main drawback: it is time-consuming due to its high computational complexity. Herein, a density peaks clustering algorithm with sparse search and K-d tree is developed to solve this problem. Firstly, a sparse distance matrix is calculated by using K-d tree to replace the original full rank distance matrix, so as to accelerate the calculation of local density. Secondly, a sparse search strategy is proposed to accelerate the computation of relative-separation with the intersection between the set of $k$ nearest neighbors and the set consisting of the data points with larger local density for any data point. Furthermore, a second-order difference method for decision values is adopted to determine the cluster centers adaptively. Finally, experiments are carried out on datasets with different distribution characteristics, by comparing with other six state-of-the-art clustering algorithms. It is proved that the algorithm can effectively reduce the computational complexity of the original DPC from $O(n^2K)$ to $O(n(n^{1-1/K}+k))$. Especially for larger datasets, the efficiency is elevated more remarkably. Moreover, the clustering accuracy is also improved to a certain extent. Therefore, it can be concluded that the overall performance of the newly proposed algorithm is excellent.

When learning tasks over time, artificial neural networks suffer from a problem known as Catastrophic Forgetting (CF). This happens when the weights of a network are overwritten during the training of a new task causing forgetting of old information. To address this issue, we propose MetA Reusable Knowledge or MARK, a new method that fosters weight reusability instead of overwriting when learning a new task. Specifically, MARK keeps a set of shared weights among tasks. We envision these shared weights as a common Knowledge Base (KB) that is not only used to learn new tasks, but also enriched with new knowledge as the model learns new tasks. Key components behind MARK are two-fold. On the one hand, a metalearning approach provides the key mechanism to incrementally enrich the KB with new knowledge and to foster weight reusability among tasks. On the other hand, a set of trainable masks provides the key mechanism to selectively choose from the KB relevant weights to solve each task. By using MARK, we achieve state of the art results in several popular benchmarks, surpassing the best performing methods in terms of average accuracy by over 10% on the 20-Split-MiniImageNet dataset, while achieving almost zero forgetfulness using 55% of the number of parameters. Furthermore, an ablation study provides evidence that, indeed, MARK is learning reusable knowledge that is selectively used by each task.