Heterogeneous Bayesian decentralized data fusion captures the set of problems in which two robots must combine two probability density functions over non-equal, but overlapping sets of random variables. In the context of multi-robot dynamic systems, this enables robots to take a "divide and conquer" approach to reason and share data over complementary tasks instead of over the full joint state space. For example, in a target tracking application, this allows robots to track different subsets of targets and share data on only common targets. This paper presents a framework by which robots can each use a local factor graph to represent relevant partitions of a complex global joint probability distribution, thus allowing them to avoid reasoning over the entirety of a more complex model and saving communication as well as computation costs. From a theoretical point of view, this paper makes contributions by casting the heterogeneous decentralized fusion problem in terms of a factor graph, analyzing the challenges that arise due to dynamic filtering, and then developing a new conservative filtering algorithm that ensures statistical correctness. From a practical point of view, we show how this framework can be used to represent different multi-robot applications and then test it with simulations and hardware experiments to validate and demonstrate its statistical conservativeness, applicability, and robustness to real-world challenges.
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Large language model (LLM) has achieved promising performance in multilingual machine translation tasks through zero/few-shot prompts or prompt-tuning. However, due to the mixture of multilingual data during the pre-training of LLM, the LLM-based translation models face the off-target issue in both prompt-based methods, including a series of phenomena, namely instruction misunderstanding, translation with wrong language and over-generation. For this issue, this paper introduces an \textbf{\underline{A}}uto-\textbf{\underline{C}}onstriction \textbf{\underline{T}}urning mechanism for \textbf{\underline{M}}ultilingual \textbf{\underline{N}}eural \textbf{\underline{M}}achine \textbf{\underline{T}}ranslation (\model), which is a novel supervised fine-tuning mechanism and orthogonal to the traditional prompt-based methods. In this method, \model automatically constructs a constrained template in the target side by adding trigger tokens ahead of the ground truth. Furthermore, trigger tokens can be arranged and combined freely to represent different task semantics, and they can be iteratively updated to maximize the label likelihood. Experiments are performed on WMT test sets with multiple metrics, and the experimental results demonstrate that \model achieves substantially improved performance across multiple translation directions and reduce the off-target phenomena in the translation.
We propose a zero-shot approach to image harmonization, aiming to overcome the reliance on large amounts of synthetic composite images in existing methods. These methods, while showing promising results, involve significant training expenses and often struggle with generalization to unseen images. To this end, we introduce a fully modularized framework inspired by human behavior. Leveraging the reasoning capabilities of recent foundation models in language and vision, our approach comprises three main stages. Initially, we employ a pretrained vision-language model (VLM) to generate descriptions for the composite image. Subsequently, these descriptions guide the foreground harmonization direction of a text-to-image generative model (T2I). We refine text embeddings for enhanced representation of imaging conditions and employ self-attention and edge maps for structure preservation. Following each harmonization iteration, an evaluator determines whether to conclude or modify the harmonization direction. The resulting framework, mirroring human behavior, achieves harmonious results without the need for extensive training. We present compelling visual results across diverse scenes and objects, along with a user study validating the effectiveness of our approach.
Both dual-functional radar-communication (DFRC) and massive multiple-input multiple-output (MIMO) have been recognized as enabling technologies for 6G wireless networks. This paper considers the advanced waveform design for hardware-efficient massive MIMO DFRC systems. Specifically, the transmit waveform is imposed with the quantized constant-envelope (QCE) constraint, which facilitates the employment of low-resolution digital-to-analog converters (DACs) and power-efficient amplifiers. The waveform design problem is formulated as the minimization of the mean square error (MSE) between the designed and desired beampatterns subject to the constructive interference (CI)-based communication quality of service (QoS) constraints and the QCE constraint. To solve the formulated problem, we first utilize the penalty technique to transform the discrete problem into an equivalent continuous penalty model. Then, we propose an inexact augmented Lagrangian method (ALM) algorithm for solving the penalty model. In particular, the ALM subproblem at each iteration is solved by a custom-built block successive upper-bound minimization (BSUM) algorithm, which admits closed-form updates, making the proposed inexact ALM algorithm computationally efficient. Simulation results demonstrate the superiority of the proposed approach over existing state-of-the-art ones. In addition, extensive simulations are conducted to examine the impact of various system parameters on the trade-off between communication and radar performances.
We present a randomized, inverse-free algorithm for producing an approximate diagonalization of any $n \times n$ matrix pencil $(A,B)$. The bulk of the algorithm rests on a randomized divide-and-conquer eigensolver for the generalized eigenvalue problem originally proposed by Ballard, Demmel, and Dumitriu [Technical Report 2010]. We demonstrate that this divide-and-conquer approach can be formulated to succeed with high probability provided the input pencil is sufficiently well-behaved, which is accomplished by generalizing the recent pseudospectral shattering work of Banks, Garza-Vargas, Kulkarni, and Srivastava [Foundations of Computational Mathematics 2022]. In particular, we show that perturbing and scaling $(A,B)$ regularizes its pseudospectra, allowing divide-and-conquer to run over a simple random grid and in turn producing an accurate diagonalization of $(A,B)$ in the backward error sense. The main result of the paper states the existence of a randomized algorithm that with high probability (and in exact arithmetic) produces invertible $S,T$ and diagonal $D$ such that $||A - SDT^{-1}||_2 \leq \varepsilon$ and $||B - ST^{-1}||_2 \leq \varepsilon$ in at most $O \left(\log^2 \left( \frac{n}{\varepsilon} \right) T_{\text{MM}}(n) \right)$ operations, where $T_{\text{MM}}(n)$ is the asymptotic complexity of matrix multiplication. This not only provides a new set of guarantees for highly parallel generalized eigenvalue solvers but also establishes nearly matrix multiplication time as an upper bound on the complexity of inverse-free, exact arithmetic matrix pencil diagonalization.
We propose a new method for cloth digitalization. Deviating from existing methods which learn from data captured under relatively casual settings, we propose to learn from data captured in strictly tested measuring protocols, and find plausible physical parameters of the cloths. However, such data is currently absent, so we first propose a new dataset with accurate cloth measurements. Further, the data size is considerably smaller than the ones in current deep learning, due to the nature of the data capture process. To learn from small data, we propose a new Bayesian differentiable cloth model to estimate the complex material heterogeneity of real cloths. It can provide highly accurate digitalization from very limited data samples. Through exhaustive evaluation and comparison, we show our method is accurate in cloth digitalization, efficient in learning from limited data samples, and general in capturing material variations. Code and data are available //github.com/realcrane/Bayesian-Differentiable-Physics-for-Cloth-Digitalization
We examine the linear regression problem in a challenging high-dimensional setting with correlated predictors where the vector of coefficients can vary from sparse to dense. In this setting, we propose a combination of probabilistic variable screening with random projection tools as a viable approach. More specifically, we introduce a new data-driven random projection tailored to the problem at hand and derive a theoretical bound on the gain in expected prediction error over conventional random projections. The variables to enter the projection are screened by accounting for predictor correlation. To reduce the dependence on fine-tuning choices, we aggregate over an ensemble of linear models. A thresholding parameter is introduced to obtain a higher degree of sparsity. Both this parameter and the number of models in the ensemble can be chosen by cross-validation. In extensive simulations, we compare the proposed method with other random projection tools and with classical sparse and dense methods and show that it is competitive in terms of prediction across a variety of scenarios with different sparsity and predictor covariance settings. We also show that the method with cross-validation is able to rank the variables satisfactorily. Finally, we showcase the method on two real data applications.
We propose a PnP algorithm for a camera constrained to two-dimensional motion (applicable, for instance, to many wheeled robotics platforms). Leveraging this assumption allows accuracy and performance improvements over 3D PnP algorithms due to the reduction in search space dimensionality. It also reduces the incidence of ambiguous pose estimates (as, in most cases, the spurious solutions fall outside the plane of movement). Our algorithm finds an approximate solution by solving a polynomial system and refines its prediction iteratively to minimize the reprojection error. The algorithm compares favorably to existing 3D PnP algorithms in terms of accuracy, performance, and robustness to noise.
We consider the differentially private (DP) facility location problem in the so called super-set output setting proposed by Gupta et al. [SODA 2010]. The current best known expected approximation ratio for an $\epsilon$-DP algorithm is $O\left(\frac{\log n}{\sqrt{\epsilon}}\right)$ due to Cohen-Addad et al. [AISTATS 2022] where $n$ denote the size of the metric space, meanwhile the best known lower bound is $\Omega(1/\sqrt{\epsilon})$ [NeurIPS 2019]. In this short note, we give a lower bound of $\tilde{\Omega}\left(\min\left\{\log n, \sqrt{\frac{\log n}{\epsilon}}\right\}\right)$ on the expected approximation ratio of any $\epsilon$-DP algorithm, which is the first evidence that the approximation ratio has to grow with the size of the metric space.
We consider estimating a matrix from noisy observations coming from an arbitrary additive bi- rotational invariant perturbation. We propose an estimator which is optimal among the class of rectangular rotational invariant estimators and can be applied irrespective of the prior on the signal. For the particular case of Gaussian noise, we prove the optimality of the proposed estimator, and we find an explicit expression for the MMSE in terms of the limiting singular value distribution of the observation matrix. Moreover, we prove a formula linking the asymptotic mutual information and the limit of a log-spherical integral of rectangular matrices. We also provide numerical checks for our results for general bi-rotational invariant noise, as well as Gaussian noise, which match our theoretical predictions.
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, thereby allowing manual manipulation in predicting the final answer.
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