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The Kalman filter (KF) is a state estimation algorithm that optimally combines system knowledge and measurements to minimize the mean squared error of the estimated states. While KF was initially designed for linear systems, numerous extensions of it, such as extended Kalman filter (EKF), unscented Kalman filter (UKF), cubature Kalman filter (CKF), etc., have been proposed for nonlinear systems. Although different types of nonlinear KFs have different pros and cons, they all use the same framework of linear KF, which, according to what we found in this paper, tends to give overconfident and less accurate state estimations when the measurement functions are nonlinear. Therefore, in this study, we designed a new framework for nonlinear KFs and showed theoretically and empirically that the new framework estimates the states and covariance matrix more accurately than the old one. The new framework was tested on four different nonlinear KFs and five different tasks, showcasing its ability to reduce the estimation errors by several orders of magnitude in low-measurement-noise conditions, with only about a 10 to 90% increase in computational time. All types of nonlinear KFs can benefit from the new framework, and the benefit will increase as the sensors become more and more accurate in the future. As an example, EKF, the simplest nonlinear KF that was previously believed to work poorly for strongly nonlinear systems, can now provide fast and fairly accurate state estimations with the help of the new framework. The codes are available at //github.com/Shida-Jiang/A-new-framework-for-nonlinear-Kalman-filters.

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Recently, Bessa et al. (PODS 2023) showed that sketches based on coordinated weighted sampling theoretically and empirically outperform popular linear sketching methods like Johnson-Lindentrauss projection and CountSketch for the ubiquitous problem of inner product estimation. We further develop this finding by introducing and analyzing two alternative sampling-based methods. In contrast to the computationally expensive algorithm in Bessa et al., our methods run in linear time (to compute the sketch) and perform better in practice, significantly beating linear sketching on a variety of tasks. For example, they provide state-of-the-art results for estimating the correlation between columns in unjoined tables, a problem that we show how to reduce to inner product estimation in a black-box way. While based on known sampling techniques (threshold and priority sampling) we introduce significant new theoretical analysis to prove approximation guarantees for our methods.

In the realm of human activity recognition (HAR), the integration of explainable Artificial Intelligence (XAI) emerges as a critical necessity to elucidate the decision-making processes of complex models, fostering transparency and trust. Traditional explanatory methods like Class Activation Mapping (CAM) and attention mechanisms, although effective in highlighting regions vital for decisions in various contexts, prove inadequate for HAR. This inadequacy stems from the inherently abstract nature of HAR data, rendering these explanations obscure. In contrast, state-of-th-art post-hoc interpretation techniques for time series can explain the model from other perspectives. However, this requires extra effort. It usually takes 10 to 20 seconds to generate an explanation. To overcome these challenges, we proposes a novel, model-agnostic framework that enhances both the interpretability and efficacy of HAR models through the strategic use of competitive data augmentation. This innovative approach does not rely on any particular model architecture, thereby broadening its applicability across various HAR models. By implementing competitive data augmentation, our framework provides intuitive and accessible explanations of model decisions, thereby significantly advancing the interpretability of HAR systems without compromising on performance.

Facial expression recognition (FER) is vital for human-computer interaction and emotion analysis, yet recognizing expressions in low-resolution images remains challenging. This paper introduces a practical method called Dynamic Resolution Guidance for Facial Expression Recognition (DRGFER) to effectively recognize facial expressions in images with varying resolutions without compromising FER model accuracy. Our framework comprises two main components: the Resolution Recognition Network (RRN) and the Multi-Resolution Adaptation Facial Expression Recognition Network (MRAFER). The RRN determines image resolution, outputs a binary vector, and the MRAFER assigns images to suitable facial expression recognition networks based on resolution. We evaluated DRGFER on widely-used datasets RAFDB and FERPlus, demonstrating that our method retains optimal model performance at each resolution and outperforms alternative resolution approaches. The proposed framework exhibits robustness against resolution variations and facial expressions, offering a promising solution for real-world applications.

Characterizing graph neural networks (GNNs) is essential for identifying performance bottlenecks and facilitating their deployment. Despite substantial work in this area, a comprehensive survey on GNN characterization is lacking. This work presents a comprehensive survey, proposing a triple-level classification method to categorize, summarize, and compare existing efforts. In addition, we identify promising future directions for GNN characterization. Our survey aims to help scholars systematically understand GNN performance bottlenecks and patterns from a computer architecture perspective, contributing to more efficient GNN execution.

Modern manipulators are acclaimed for their precision but often struggle to operate in confined spaces. This limitation has driven the development of hyper-redundant and continuum robots. While these present unique advantages, they face challenges in, for instance, weight, mechanical complexity, modeling and costs. The Minimally Actuated Serial Robot (MASR) has been proposed as a light-weight, low-cost and simpler alternative where passive joints are actuated with a Mobile Actuator (MA) moving along the arm. Yet, Inverse Kinematics (IK) and a general motion planning algorithm for the MASR have not be addressed. In this letter, we propose the MASR-RRT* motion planning algorithm specifically developed for the unique kinematics of MASR. The main component of the algorithm is a data-based model for solving the IK problem while considering minimal traverse of the MA. The model is trained solely using the forward kinematics of the MASR and does not require real data. With the model as a local-connection mechanism, MASR-RRT* minimizes a cost function expressing the action time. In a comprehensive analysis, we show that MASR-RRT* is superior in performance to the straight-forward implementation of the standard RRT*. Experiments on a real robot in different environments with obstacles validate the proposed algorithm.

Quantum relative entropy programs are convex optimization problems which minimize a linear functional over an affine section of the epigraph of the quantum relative entropy function. Recently, the self-concordance of a natural barrier function was proved for this set. This has opened up the opportunity to use interior-point methods for nonsymmetric cone programs to solve these optimization problems. In this paper, we show how common structures arising from applications in quantum information theory can be exploited to improve the efficiency of solving quantum relative entropy programs using interior-point methods. First, we show that the natural barrier function for the epigraph of the quantum relative entropy composed with positive linear operators is optimally self-concordant, even when these linear operators map to singular matrices. Compared to modelling problems using the full quantum relative entropy cone, this allows us to remove redundant log determinant expressions from the barrier function and reduce the overall barrier parameter. Second, we show how certain slices of the quantum relative entropy cone exhibit useful properties which should be exploited whenever possible to perform certain key steps of interior-point methods more efficiently. We demonstrate how these methods can be applied to applications in quantum information theory, including quantifying quantum key rates, quantum rate-distortion functions, quantum channel capacities, and the ground state energy of Hamiltonians. Our numerical results show that these techniques improve computation times by up to several orders of magnitude, and allow previously intractable problems to be solved.

Motivated by the growing theoretical understanding of neural networks that employ the Rectified Linear Unit (ReLU) as their activation function, we revisit the use of ReLU activation functions for learning implicit neural representations (INRs). Inspired by second order B-spline wavelets, we incorporate a set of simple constraints to the ReLU neurons in each layer of a deep neural network (DNN) to remedy the spectral bias. This in turn enables its use for various INR tasks. Empirically, we demonstrate that, contrary to popular belief, one can learn state-of-the-art INRs based on a DNN composed of only ReLU neurons. Next, by leveraging recent theoretical works which characterize the kinds of functions ReLU neural networks learn, we provide a way to quantify the regularity of the learned function. This offers a principled approach to selecting the hyperparameters in INR architectures. We substantiate our claims through experiments in signal representation, super resolution, and computed tomography, demonstrating the versatility and effectiveness of our method. The code for all experiments can be found at //github.com/joeshenouda/relu-inrs.

Embedding entities and relations into a continuous multi-dimensional vector space have become the dominant method for knowledge graph embedding in representation learning. However, most existing models ignore to represent hierarchical knowledge, such as the similarities and dissimilarities of entities in one domain. We proposed to learn a Domain Representations over existing knowledge graph embedding models, such that entities that have similar attributes are organized into the same domain. Such hierarchical knowledge of domains can give further evidence in link prediction. Experimental results show that domain embeddings give a significant improvement over the most recent state-of-art baseline knowledge graph embedding models.

Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.

Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis.

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