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This paper introduces a novel Transformed Primal-Dual with variable-metric/preconditioner (TPDv) algorithm, designed to efficiently solve affine constrained optimization problems common in nonlinear partial differential equations (PDEs). Diverging from traditional methods, TPDv iteratively updates time-evolving preconditioning operators, enhancing adaptability. The algorithm is derived and analyzed, demonstrating global linear convergence rates under mild assumptions. Numerical experiments on challenging nonlinear PDEs, including the Darcy-Forchheimer model and a nonlinear electromagnetic problem, showcase the algorithm's superiority over existing methods in terms of iteration numbers and computational efficiency. The paper concludes with a comprehensive convergence analysis.

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This paper introduces a novel approach to leverage the generalizability capability of Diffusion Models for Source-Free Domain Adaptation (DM-SFDA). Our proposed DM-SFDA method involves fine-tuning a pre-trained text-to-image diffusion model to generate source domain images using features from the target images to guide the diffusion process. Specifically, the pre-trained diffusion model is fine-tuned to generate source samples that minimize entropy and maximize confidence for the pre-trained source model. We then apply established unsupervised domain adaptation techniques to align the generated source images with target domain data. We validate our approach through comprehensive experiments across a range of datasets, including Office-31, Office-Home, and VisDA. The results highlight significant improvements in SFDA performance, showcasing the potential of diffusion models in generating contextually relevant, domain-specific images.

This paper introduces a novel unsupervised technique that utilizes large language models (LLMs) to determine the most suitable dense retriever for a specific test(target) corpus. Selecting the appropriate dense retriever is vital for numerous IR applications that employ these retrievers, trained on public datasets, to encode or conduct searches within a new private target corpus. The effectiveness of a dense retriever can significantly diminish when applied to a target corpus that diverges in domain or task from the original training set. The problem becomes more pronounced in cases where the target corpus is unlabeled, e.g. in zero-shot scenarios, rendering direct evaluation of the model's effectiveness on the target corpus unattainable. Therefore, the unsupervised selection of an optimally pre-trained dense retriever, especially under conditions of domain shift, emerges as a critical challenge. Existing methodologies for ranking dense retrievers fall short in addressing these domain shift scenarios. To tackle this, our method capitalizes on LLMs to create pseudo-relevant queries, labels, and reference lists by analyzing a subset of documents from the target corpus. This allows for the ranking of dense retrievers based on their performance with these pseudo-relevant signals. Significantly, this strategy is the first to depend exclusively on the target corpus data, removing the necessity for training data and test labels. We assessed the effectiveness of our approach by compiling a comprehensive pool of cutting-edge dense retrievers and comparing our method against traditional dense retriever selection benchmarks. The findings reveal that our proposed solution surpasses the existing benchmarks in both the selection and ranking of dense retrievers.

This paper introduces a novel decision-making framework that promotes consistency among decisions made by diverse models while utilizing external knowledge. Leveraging the Integer Linear Programming (ILP) framework, we map predictions from various models into globally normalized and comparable values by incorporating information about decisions' prior probability, confidence (uncertainty), and the models' expected accuracy. Our empirical study demonstrates the superiority of our approach over conventional baselines on multiple datasets.

This paper introduces a new approach to address the issue of class imbalance in graph neural networks (GNNs) for learning on graph-structured data. Our approach integrates imbalanced node classification and Bias-Variance Decomposition, establishing a theoretical framework that closely relates data imbalance to model variance. We also leverage graph augmentation technique to estimate the variance, and design a regularization term to alleviate the impact of imbalance. Exhaustive tests are conducted on multiple benchmarks, including naturally imbalanced datasets and public-split class-imbalanced datasets, demonstrating that our approach outperforms state-of-the-art methods in various imbalanced scenarios. This work provides a novel theoretical perspective for addressing the problem of imbalanced node classification in GNNs.

This paper introduces AutoGCN, a generic Neural Architecture Search (NAS) algorithm for Human Activity Recognition (HAR) using Graph Convolution Networks (GCNs). HAR has gained attention due to advances in deep learning, increased data availability, and enhanced computational capabilities. At the same time, GCNs have shown promising results in modeling relationships between body key points in a skeletal graph. While domain experts often craft dataset-specific GCN-based methods, their applicability beyond this specific context is severely limited. AutoGCN seeks to address this limitation by simultaneously searching for the ideal hyperparameters and architecture combination within a versatile search space using a reinforcement controller while balancing optimal exploration and exploitation behavior with a knowledge reservoir during the search process. We conduct extensive experiments on two large-scale datasets focused on skeleton-based action recognition to assess the proposed algorithm's performance. Our experimental results underscore the effectiveness of AutoGCN in constructing optimal GCN architectures for HAR, outperforming conventional NAS and GCN methods, as well as random search. These findings highlight the significance of a diverse search space and an expressive input representation to enhance the network performance and generalizability.

This paper introduces a novel numerical approach to achieving smooth lane-change trajectories in autonomous driving scenarios. Our trajectory generation approach leverages particle swarm optimization (PSO) techniques, incorporating Neural Network (NN) predictions for trajectory refinement. The generation of smooth and dynamically feasible trajectories for the lane change maneuver is facilitated by combining polynomial curve fitting with particle propagation, which can account for vehicle dynamics. The proposed planning algorithm is capable of determining feasible trajectories with real-time computation capability. We conduct comparative analyses with two baseline methods for lane changing, involving analytic solutions and heuristic techniques in numerical simulations. The simulation results validate the efficacy and effectiveness of our proposed approach.

This paper introduces $K$-Tensors, a novel self-consistent clustering algorithm designed to cluster positive semi-definite (PSD) matrices by their eigenstructures. Clustering PSD matrices is crucial across various fields, including computer and biomedical sciences. Traditional clustering methods, which often involve matrix vectorization, tend to overlook the inherent PSD characteristics, thereby discarding valuable shape and eigenstructural information. To preserve this essential shape and eigenstructral information, our approach incorporates a unique distance metric that respects the PSD nature of the data. We demonstrate that $K$-Tensors is not only self-consistent but also reliably converges to a local optimum. Through numerical studies, we further validate the algorithm's effectiveness and explore its properties in detail.

In this paper, we propose a novel Feature Decomposition and Reconstruction Learning (FDRL) method for effective facial expression recognition. We view the expression information as the combination of the shared information (expression similarities) across different expressions and the unique information (expression-specific variations) for each expression. More specifically, FDRL mainly consists of two crucial networks: a Feature Decomposition Network (FDN) and a Feature Reconstruction Network (FRN). In particular, FDN first decomposes the basic features extracted from a backbone network into a set of facial action-aware latent features to model expression similarities. Then, FRN captures the intra-feature and inter-feature relationships for latent features to characterize expression-specific variations, and reconstructs the expression feature. To this end, two modules including an intra-feature relation modeling module and an inter-feature relation modeling module are developed in FRN. Experimental results on both the in-the-lab databases (including CK+, MMI, and Oulu-CASIA) and the in-the-wild databases (including RAF-DB and SFEW) show that the proposed FDRL method consistently achieves higher recognition accuracy than several state-of-the-art methods. This clearly highlights the benefit of feature decomposition and reconstruction for classifying expressions.

Non-IID data present a tough challenge for federated learning. In this paper, we explore a novel idea of facilitating pairwise collaborations between clients with similar data. We propose FedAMP, a new method employing federated attentive message passing to facilitate similar clients to collaborate more. We establish the convergence of FedAMP for both convex and non-convex models, and propose a heuristic method to further improve the performance of FedAMP when clients adopt deep neural networks as personalized models. Our extensive experiments on benchmark data sets demonstrate the superior performance of the proposed methods.

In this paper, we proposed to apply meta learning approach for low-resource automatic speech recognition (ASR). We formulated ASR for different languages as different tasks, and meta-learned the initialization parameters from many pretraining languages to achieve fast adaptation on unseen target language, via recently proposed model-agnostic meta learning algorithm (MAML). We evaluated the proposed approach using six languages as pretraining tasks and four languages as target tasks. Preliminary results showed that the proposed method, MetaASR, significantly outperforms the state-of-the-art multitask pretraining approach on all target languages with different combinations of pretraining languages. In addition, since MAML's model-agnostic property, this paper also opens new research direction of applying meta learning to more speech-related applications.

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