We introduce algebraic machine reasoning, a new reasoning framework that is well-suited for abstract reasoning. Effectively, algebraic machine reasoning reduces the difficult process of novel problem-solving to routine algebraic computation. The fundamental algebraic objects of interest are the ideals of some suitably initialized polynomial ring. We shall explain how solving Raven's Progressive Matrices (RPMs) can be realized as computational problems in algebra, which combine various well-known algebraic subroutines that include: Computing the Gr\"obner basis of an ideal, checking for ideal containment, etc. Crucially, the additional algebraic structure satisfied by ideals allows for more operations on ideals beyond set-theoretic operations. Our algebraic machine reasoning framework is not only able to select the correct answer from a given answer set, but also able to generate the correct answer with only the question matrix given. Experiments on the I-RAVEN dataset yield an overall $93.2\%$ accuracy, which significantly outperforms the current state-of-the-art accuracy of $77.0\%$ and exceeds human performance at $84.4\%$ accuracy.
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Polynomial based approaches, such as the Mat-Dot and entangled polynomial codes (EPC) have been used extensively within coded matrix computations to obtain schemes with good recovery thresholds. However, these schemes are well-recognized to suffer from poor numerical stability in decoding. Moreover, the encoding process in these schemes involves linearly combining a large number of input submatrices, i.e., the encoding weight is high. For the practically relevant case of sparse input matrices, this can have the undesirable effect of significantly increasing the worker node computation time. In this work, we propose a generalization of the EPC scheme by combining the idea of gradient coding along with the basic EPC encoding. Our technique allows us to reduce the weight of the encoding and arrive at schemes that exhibit much better numerical stability; this is achieved at the expense of a worse threshold. By appropriately setting parameters in our scheme, we recover several well-known schemes in the literature. Simulation results show that our scheme provides excellent numerical stability and fast computation speed (for sparse input matrices) as compared to EPC and Mat-Dot codes.
It is realized that existing powerful tests of goodness-of-fit are all based on sorted uniforms and, consequently, can suffer from the confounded effect of different locations and various signal frequencies in the deviations of the distributions under the alternative hypothesis from those under the null. This paper proposes circularly symmetric tests that are obtained by circularizing reweighted Anderson-Darling tests, with the focus on the circularized versions of Anderson-Darling and Zhang test statistics. Two specific types of circularization are considered, one is obtained by taking the average of the corresponding so-called scan test statistics and the other by using the maximum. To a certain extent, this circularization technique effectively eliminates the location effect and allows the weights to focus on the various signal frequencies. A limited but arguably convincing simulation study on finite-sample performance demonstrates that the circularized Zhang method outperforms the circularized Anderson-Darling and that the circularized tests outperform their parent methods. Large-sample theoretical results are also obtained for the average type of circularization. The results show that both the circularized Anderson-Darling and circularized Zhang have asymptotic distributions that are a weighted sum of an infinite number of independent squared standard normal random variables. In addition, the kernel matrices and functions are circulant. As a result, asymptotic approximations are computationally efficient via the fast Fourier transform.
The estimation of large covariance matrices has a high dimensional bias. Correcting for this bias can be reformulated via the tool of Free Probability Theory as a free deconvolution. The goal of this work is a computational and statistical resolution of this problem. Our approach is based on complex-analytic methods methods to invert $S$-transforms. In particular, one needs a theoretical understanding of the Riemann surfaces where multivalued $S$ transforms live and an efficient computational scheme.
Several task and motion planning algorithms have been proposed recently to design paths for mobile robot teams with collaborative high-level missions specified using formal languages, such as Linear Temporal Logic (LTL). However, the designed paths often lack reactivity to failures of robot capabilities (e.g., sensing, mobility, or manipulation) that can occur due to unanticipated events (e.g., human intervention or system malfunctioning) which in turn may compromise mission performance. To address this novel challenge, in this paper, we propose a new resilient mission planning algorithm for teams of heterogeneous robots with collaborative LTL missions. The robots are heterogeneous with respect to their capabilities while the mission requires applications of these skills at certain areas in the environment in a temporal/logical order. The proposed method designs paths that can adapt to unexpected failures of robot capabilities. This is accomplished by re-allocating sub-tasks to the robots based on their currently functioning skills while minimally disrupting the existing team motion plans. We provide experiments and theoretical guarantees demonstrating the efficiency and resiliency of the proposed algorithm.
The trade algorithm, which includes the curveball and fastball implementations, is the state-of-the-art for uniformly sampling r x c binary matrices with fixed row and column sums. The mixing time of the trade algorithm is currently unknown, although 5r is currently used as a heuristic. We propose a distribution-based approach to estimating the mixing time, but which also can return a sample of matrices that are nearly guaranteed to be uniformly randomly sampled. In numerical experiments on matrices that vary by size, fill, and row and column sum distributions, we find that the upper bound on mixing time is at least 10r, and that it increases as a function of both c and the fraction of cells containing a 1.
Artificial Intelligence (AI) and its applications have sparked extraordinary interest in recent years. This achievement can be ascribed in part to advances in AI subfields including Machine Learning (ML), Computer Vision (CV), and Natural Language Processing (NLP). Deep learning, a sub-field of machine learning that employs artificial neural network concepts, has enabled the most rapid growth in these domains. The integration of vision and language has sparked a lot of attention as a result of this. The tasks have been created in such a way that they properly exemplify the concepts of deep learning. In this review paper, we provide a thorough and an extensive review of the state of the arts approaches, key models design principles and discuss existing datasets, methods, their problem formulation and evaluation measures for VQA and Visual reasoning tasks to understand vision and language representation learning. We also present some potential future paths in this field of research, with the hope that our study may generate new ideas and novel approaches to handle existing difficulties and develop new applications.
With the rapid development of facial forgery techniques, forgery detection has attracted more and more attention due to security concerns. Existing approaches attempt to use frequency information to mine subtle artifacts under high-quality forged faces. However, the exploitation of frequency information is coarse-grained, and more importantly, their vanilla learning process struggles to extract fine-grained forgery traces. To address this issue, we propose a progressive enhancement learning framework to exploit both the RGB and fine-grained frequency clues. Specifically, we perform a fine-grained decomposition of RGB images to completely decouple the real and fake traces in the frequency space. Subsequently, we propose a progressive enhancement learning framework based on a two-branch network, combined with self-enhancement and mutual-enhancement modules. The self-enhancement module captures the traces in different input spaces based on spatial noise enhancement and channel attention. The Mutual-enhancement module concurrently enhances RGB and frequency features by communicating in the shared spatial dimension. The progressive enhancement process facilitates the learning of discriminative features with fine-grained face forgery clues. Extensive experiments on several datasets show that our method outperforms the state-of-the-art face forgery detection methods.
This work aims to provide an engagement decision support tool for Beyond Visual Range (BVR) air combat in the context of Defensive Counter Air (DCA) missions. In BVR air combat, engagement decision refers to the choice of the moment the pilot engages a target by assuming an offensive stance and executing corresponding maneuvers. To model this decision, we use the Brazilian Air Force's Aerospace Simulation Environment (\textit{Ambiente de Simula\c{c}\~ao Aeroespacial - ASA} in Portuguese), which generated 3,729 constructive simulations lasting 12 minutes each and a total of 10,316 engagements. We analyzed all samples by an operational metric called the DCA index, which represents, based on the experience of subject matter experts, the degree of success in this type of mission. This metric considers the distances of the aircraft of the same team and the opposite team, the point of Combat Air Patrol, and the number of missiles used. By defining the engagement status right before it starts and the average of the DCA index throughout the engagement, we create a supervised learning model to determine the quality of a new engagement. An algorithm based on decision trees, working with the XGBoost library, provides a regression model to predict the DCA index with a coefficient of determination close to 0.8 and a Root Mean Square Error of 0.05 that can furnish parameters to the BVR pilot to decide whether or not to engage. Thus, using data obtained through simulations, this work contributes by building a decision support system based on machine learning for BVR air combat.
With the rise of knowledge graph (KG), question answering over knowledge base (KBQA) has attracted increasing attention in recent years. Despite much research has been conducted on this topic, it is still challenging to apply KBQA technology in industry because business knowledge and real-world questions can be rather complicated. In this paper, we present AliMe-KBQA, a bold attempt to apply KBQA in the E-commerce customer service field. To handle real knowledge and questions, we extend the classic "subject-predicate-object (SPO)" structure with property hierarchy, key-value structure and compound value type (CVT), and enhance traditional KBQA with constraints recognition and reasoning ability. We launch AliMe-KBQA in the Marketing Promotion scenario for merchants during the "Double 11" period in 2018 and other such promotional events afterwards. Online results suggest that AliMe-KBQA is not only able to gain better resolution and improve customer satisfaction, but also becomes the preferred knowledge management method by business knowledge staffs since it offers a more convenient and efficient management experience.
The present paper surveys neural approaches to conversational AI that have been developed in the last few years. We group conversational systems into three categories: (1) question answering agents, (2) task-oriented dialogue agents, and (3) chatbots. For each category, we present a review of state-of-the-art neural approaches, draw the connection between them and traditional approaches, and discuss the progress that has been made and challenges still being faced, using specific systems and models as case studies.
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