The beamforming performance of the uniform circular array (UCA) in near-field wideband communication systems is investigated. Compared to uniform linear array (ULA), UCA exhibits uniform effective array aperture in all directions, thus enabling more users to benefit from near-field communications. In this paper, the unique beam squint effect in near-field wideband UCA systems is comprehensively analyzed in both the distance and angular domains. It is rigorously demonstrated that the beam focal point only exists at a specific frequency in wideband UCA systems, resulting in significant beamforming loss. To alleviate this unique beam squint effect, the true-time delay (TTD)-based beamforming architecture is exploited. In particular, two wideband beamforming optimization approaches leveraging TTD units are proposed. 1) Analytical approach: In this approach, the phase shifters (PSs) and the time delay of TTD units are designed based on the analytical formula for beamforming gain. Following this design, the minimum number of TTD units required to achieve a predetermined beamforming gain is quantified. 2) Joint-optimization approach: In this method, the PSs and the TTD units are jointly optimized under practical maximum delay constraints to approximate the optimal unconstrained analog beamformer. Specifically, an efficient alternating optimization algorithm is proposed, where the PSs and the TTD units are alternately updated using either the closed-form solution or the low-complexity linear search approach. Extensive numerical results demonstrate that 1) the proposed beamforming schemes effectively mitigate the beam squint effect, and 2) the joint-optimization approach outperforms the analytical approach in terms of array gain and achievable spectral efficiency.
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We explore the minimax optimality of goodness-of-fit tests on general domains using the kernelized Stein discrepancy (KSD). The KSD framework offers a flexible approach for goodness-of-fit testing, avoiding strong distributional assumptions, accommodating diverse data structures beyond Euclidean spaces, and relying only on partial knowledge of the reference distribution, while maintaining computational efficiency. We establish a general framework and an operator-theoretic representation of the KSD, encompassing many existing KSD tests in the literature, which vary depending on the domain. We reveal the characteristics and limitations of KSD and demonstrate its non-optimality under a certain alternative space, defined over general domains when considering $\chi^2$-divergence as the separation metric. To address this issue of non-optimality, we propose a modified, minimax optimal test by incorporating a spectral regularizer, thereby overcoming the shortcomings of standard KSD tests. Our results are established under a weak moment condition on the Stein kernel, which relaxes the bounded kernel assumption required by prior work in the analysis of kernel-based hypothesis testing. Additionally, we introduce an adaptive test capable of achieving minimax optimality up to a logarithmic factor by adapting to unknown parameters. Through numerical experiments, we illustrate the superior performance of our proposed tests across various domains compared to their unregularized counterparts.
Safe control of neural network dynamic models (NNDMs) is important to robotics and many applications. However, it remains challenging to compute an optimal safe control in real time for NNDM. To enable real-time computation, we propose to use a sound approximation of the NNDM in the control synthesis. In particular, we propose Bernstein over-approximated neural dynamics (BOND) based on the Bernstein polynomial over-approximation (BPO) of ReLU activation functions in NNDM. To mitigate the errors introduced by the approximation and to ensure persistent feasibility of the safe control problems, we synthesize a worst-case safety index using the most unsafe approximated state within the BPO relaxation of NNDM offline. For the online real-time optimization, we formulate the first-order Taylor approximation of the nonlinear worst-case safety constraint as an additional linear layer of NNDM with the l2 bounded bias term for the higher-order remainder. Comprehensive experiments with different neural dynamics and safety constraints show that with safety guaranteed, our NNDMs with sound approximation are 10-100 times faster than the safe control baseline that uses mixed integer programming (MIP), validating the effectiveness of the worst-case safety index and scalability of the proposed BOND in real-time large-scale settings. The code is available at //github.com/intelligent-control-lab/BOND.
Graph Neural Networks (GNNs) have emerged as potent tools for predicting outcomes in graph-structured data. Despite their efficacy, a significant drawback of GNNs lies in their limited ability to provide robust uncertainty estimates, posing challenges to their reliability in contexts where errors carry significant consequences. Moreover, GNNs typically excel in in-distribution settings, assuming that training and test data follow identical distributions: a condition often unmet in real-world graph data scenarios. In this article, we leverage conformal prediction, a widely recognized statistical technique for quantifying uncertainty by transforming predictive model outputs into prediction sets, to address uncertainty quantification in GNN predictions amidst conditional shift \footnote{Representing the change in conditional probability distribution $P(label |input)$ from source domain to target domain.} in graph-based semi-supervised learning (SSL). Additionally, we propose a novel loss function aimed at refining model predictions by minimizing conditional shift in latent stages. Termed Conditional Shift Robust (CondSR) conformal prediction for GNNs, our approach CondSR is model-agnostic and adaptable to various classification models. We validate the effectiveness of our method on standard graph benchmark datasets, integrating it with state-of-the-art GNNs in node classification tasks. The code implementation is publicly available for further exploration and experimentation.
Deep equilibrium models (DEQs), as a typical implicit neural network, have demonstrated remarkable success on various tasks. There is, however, a lack of theoretical understanding of the connections and differences between implicit DEQs and explicit neural network models. In this paper, leveraging recent advances in random matrix theory (RMT), we perform an in-depth analysis on the eigenspectra of the conjugate kernel (CK) and neural tangent kernel (NTK) matrices for implicit DEQs, when the input data are drawn from a high-dimensional Gaussian mixture. We prove, in this setting, that the spectral behavior of these Implicit-CKs and NTKs depend on the DEQ activation function and initial weight variances, but only via a system of four nonlinear equations. As a direct consequence of this theoretical result, we demonstrate that a shallow explicit network can be carefully designed to produce the same CK or NTK as a given DEQ. Despite derived here for Gaussian mixture data, empirical results show the proposed theory and design principle also apply to popular real-world datasets.
Neural Networks (NNs) have been successfully employed to represent the state evolution of complex dynamical systems. Such models, referred to as NN dynamic models (NNDMs), use iterative noisy predictions of NN to estimate a distribution of system trajectories over time. Despite their accuracy, safety analysis of NNDMs is known to be a challenging problem and remains largely unexplored. To address this issue, in this paper, we introduce a method of providing safety guarantees for NNDMs. Our approach is based on stochastic barrier functions, whose relation with safety are analogous to that of Lyapunov functions with stability. We first show a method of synthesizing stochastic barrier functions for NNDMs via a convex optimization problem, which in turn provides a lower bound on the system's safety probability. A key step in our method is the employment of the recent convex approximation results for NNs to find piece-wise linear bounds, which allow the formulation of the barrier function synthesis problem as a sum-of-squares optimization program. If the obtained safety probability is above the desired threshold, the system is certified. Otherwise, we introduce a method of generating controls for the system that robustly maximizes the safety probability in a minimally-invasive manner. We exploit the convexity property of the barrier function to formulate the optimal control synthesis problem as a linear program. Experimental results illustrate the efficacy of the method. Namely, they show that the method can scale to multi-dimensional NNDMs with multiple layers and hundreds of neurons per layer, and that the controller can significantly improve the safety probability.
As image recognition models become more prevalent, scalable coding methods for machines and humans gain more importance. Applications of image recognition models include traffic monitoring and farm management. In these use cases, the scalable coding method proves effective because the tasks require occasional image checking by humans. Existing image compression methods for humans and machines meet these requirements to some extent. However, these compression methods are effective solely for specific image recognition models. We propose a learning-based scalable image coding method for humans and machines that is compatible with numerous image recognition models. We combine an image compression model for machines with a compression model, providing additional information to facilitate image decoding for humans. The features in these compression models are fused using a feature fusion network to achieve efficient image compression. Our method's additional information compression model is adjusted to reduce the number of parameters by enabling combinations of features of different sizes in the feature fusion network. Our approach confirms that the feature fusion network efficiently combines image compression models while reducing the number of parameters. Furthermore, we demonstrate the effectiveness of the proposed scalable coding method by evaluating the image compression performance in terms of decoded image quality and bitrate.
Generative adversarial networks (GANs) have achieved remarkable progress in the natural image field. However, when applying GANs in the remote sensing (RS) image generation task, an extraordinary phenomenon is observed: the GAN model is more sensitive to the size of training data for RS image generation than for natural image generation. In other words, the generation quality of RS images will change significantly with the number of training categories or samples per category. In this paper, we first analyze this phenomenon from two kinds of toy experiments and conclude that the amount of feature information contained in the GAN model decreases with reduced training data. Then we establish a structural causal model (SCM) of the data generation process and interpret the generated data as the counterfactuals. Based on this SCM, we theoretically prove that the quality of generated images is positively correlated with the amount of feature information. This provides insights for enriching the feature information learned by the GAN model during training. Consequently, we propose two innovative adjustment schemes, namely Uniformity Regularization (UR) and Entropy Regularization (ER), to increase the information learned by the GAN model at the distributional and sample levels, respectively. We theoretically and empirically demonstrate the effectiveness and versatility of our methods. Extensive experiments on three RS datasets and two natural datasets show that our methods outperform the well-established models on RS image generation tasks. The source code is available at //github.com/rootSue/Causal-RSGAN.
This study focuses on the analysis of signals containing multiple components with crossover instantaneous frequencies (IF). This problem was initially solved with the chirplet transform (CT). Also, it can be sharpened by adding the synchrosqueezing step, which is called the synchrosqueezed chirplet transform (SCT). However, we found that the SCT goes wrong with the high chirp modulation signal due to the wrong estimation of the IF. In this paper, we present the improvement of the post-transformation of the CT. The main goal of this paper is to amend the estimation introduced in the SCT and carry out the high-order synchrosqueezed chirplet transform. The proposed method reduces the wrong estimation when facing a stronger variety of chirp-modulated multi-component signals. The theoretical analysis of the new reassignment ingredient is provided. Numerical experiments on some synthetic signals are presented to verify the effectiveness of the proposed high-order SCT.
Recent artificial intelligence (AI) systems have reached milestones in "grand challenges" ranging from Go to protein-folding. The capability to retrieve medical knowledge, reason over it, and answer medical questions comparably to physicians has long been viewed as one such grand challenge. Large language models (LLMs) have catalyzed significant progress in medical question answering; Med-PaLM was the first model to exceed a "passing" score in US Medical Licensing Examination (USMLE) style questions with a score of 67.2% on the MedQA dataset. However, this and other prior work suggested significant room for improvement, especially when models' answers were compared to clinicians' answers. Here we present Med-PaLM 2, which bridges these gaps by leveraging a combination of base LLM improvements (PaLM 2), medical domain finetuning, and prompting strategies including a novel ensemble refinement approach. Med-PaLM 2 scored up to 86.5% on the MedQA dataset, improving upon Med-PaLM by over 19% and setting a new state-of-the-art. We also observed performance approaching or exceeding state-of-the-art across MedMCQA, PubMedQA, and MMLU clinical topics datasets. We performed detailed human evaluations on long-form questions along multiple axes relevant to clinical applications. In pairwise comparative ranking of 1066 consumer medical questions, physicians preferred Med-PaLM 2 answers to those produced by physicians on eight of nine axes pertaining to clinical utility (p < 0.001). We also observed significant improvements compared to Med-PaLM on every evaluation axis (p < 0.001) on newly introduced datasets of 240 long-form "adversarial" questions to probe LLM limitations. While further studies are necessary to validate the efficacy of these models in real-world settings, these results highlight rapid progress towards physician-level performance in medical question answering.
Translational distance-based knowledge graph embedding has shown progressive improvements on the link prediction task, from TransE to the latest state-of-the-art RotatE. However, N-1, 1-N and N-N predictions still remain challenging. In this work, we propose a novel translational distance-based approach for knowledge graph link prediction. The proposed method includes two-folds, first we extend the RotatE from 2D complex domain to high dimension space with orthogonal transforms to model relations for better modeling capacity. Second, the graph context is explicitly modeled via two directed context representations. These context representations are used as part of the distance scoring function to measure the plausibility of the triples during training and inference. The proposed approach effectively improves prediction accuracy on the difficult N-1, 1-N and N-N cases for knowledge graph link prediction task. The experimental results show that it achieves better performance on two benchmark data sets compared to the baseline RotatE, especially on data set (FB15k-237) with many high in-degree connection nodes.
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