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Content-addressable memories such as Modern Hopfield Networks (MHN) have been studied as mathematical models of auto-association and storage/retrieval in the human declarative memory, yet their practical use for large-scale content storage faces challenges. Chief among them is the occurrence of meta-stable states, particularly when handling large amounts of high dimensional content. This paper introduces Hopfield Encoding Networks (HEN), a framework that integrates encoded neural representations into MHNs to improve pattern separability and reduce meta-stable states. We show that HEN can also be used for retrieval in the context of hetero association of images with natural language queries, thus removing the limitation of requiring access to partial content in the same domain. Experimental results demonstrate substantial reduction in meta-stable states and increased storage capacity while still enabling perfect recall of a significantly larger number of inputs advancing the practical utility of associative memory networks for real-world tasks., Comment: 17 pages, 8 figures, accepted as a workshop paper at UniReps @ Neurips 2024

Modern Cardinality Estimators struggle with data updates. This research tackles this challenge within single-table. We introduce ICE, an Index-based Cardinality Estimator, the first data-driven estimator that enables instant, tuple-leveled updates. ICE has learned two key lessons from the multidimensional index and applied them to solve cardinality estimation in dynamic scenarios: (1) Index possesses the capability for swift training and seamless updating amidst vast multidimensional data. (2) Index offers precise data distribution, staying synchronized with the latest database version. These insights endow the index with the ability to be a highly accurate, data-driven model that rapidly adapts to data updates and is resilient to out-of-distribution challenges during query testing. To make a solitary index support cardinality estimation, we have crafted sophisticated algorithms for training, updating, and estimating, analyzing unbiasedness and variance. Extensive experiments demonstrate the superiority of ICE. ICE offers precise estimations and fast updates/construction across diverse workloads. Compared to state-of-the-art real-time query-driven models, ICE boasts superior accuracy (2-3 orders of magnitude more precise), faster updates (4.7-6.9 times faster), and significantly reduced training time (up to 1-3 orders of magnitude faster).

The Maximum Minimal Cut Problem (MMCP), a NP-hard combinatorial optimization (CO) problem, has not received much attention due to the demanding and challenging bi-connectivity constraint. Moreover, as a CO problem, it is also a daunting task for machine learning, especially without labeled instances. To deal with these problems, this work proposes an unsupervised learning framework combined with heuristics for MMCP that can provide valid and high-quality solutions. As far as we know, this is the first work that explores machine learning and heuristics to solve MMCP. The unsupervised solver is inspired by a relaxation-plus-rounding approach, the relaxed solution is parameterized by graph neural networks, and the cost and penalty of MMCP are explicitly written out, which can train the model end-to-end. A crucial observation is that each solution corresponds to at least one spanning tree. Based on this finding, a heuristic solver that implements tree transformations by adding vertices is utilized to repair and improve the solution quality of the unsupervised solver. Alternatively, the graph is simplified while guaranteeing solution consistency, which reduces the running time. We conduct extensive experiments to evaluate our framework and give a specific application. The results demonstrate the superiority of our method against two techniques designed.

The knob tuning aims to optimize database performance by searching for the most effective knob configuration under a certain workload. Existing works suffer two significant problems. On the one hand, there exist multiple similar even useless evaluations of knob tuning even with the diverse searching methods because of the different sensitivities of knobs on a certain workload. On the other hand, the single evaluation of knob configurations may bring overestimation or underestimation because of the query uncertainty performance. To solve the above problems, we propose a decoupled query uncertainty-aware knob classifier, called KnobCF, to enhance the knob tuning. Our method has three significant contributions: (1) We propose a novel concept of the uncertainty-aware knob configuration estimation to enhance the knob tuning process. (2) We provide an effective few-shot uncertainty knob estimator without extra time consumption in training data collection, which has a high time efficiency in practical tuning tasks. (3) Our method provides a general framework that could be easily deployed in any knob tuning task because we make no changes to the knob tuners and the database management system. Our experiments on four open-source benchmarks demonstrate that our method effectively reduces useless evaluations and improves the tuning results. Especially in TPCC, our method achieves competitive tuning results with only 60% to 70% time consumption compared to the full workload evaluations.

The Spiking Neural Networks (SNNs), renowned for their bio-inspired operational mechanism and energy efficiency, mirror the human brain's neural activity. Yet, SNNs face challenges in balancing energy efficiency with the computational demands of advanced tasks. Our research introduces the RTFormer, a novel architecture that embeds Re-parameterized Temporal Sliding Batch Normalization (TSBN) within the Spiking Transformer framework. This innovation optimizes energy usage during inference while ensuring robust computational performance. The crux of RTFormer lies in its integration of reparameterized convolutions and TSBN, achieving an equilibrium between computational prowess and energy conservation.

Recently, there has been a growing availability of pre-trained text models on various model repositories. These models greatly reduce the cost of training new models from scratch as they can be fine-tuned for specific tasks or trained on large datasets. However, these datasets may not be publicly accessible due to the privacy, security, or intellectual property issues. In this paper, we aim to develop a lightweight student network that can learn from multiple teacher models without accessing their original training data. Hence, we investigate Data-Free Knowledge Amalgamation (DFKA), a knowledge-transfer task that combines insights from multiple pre-trained teacher models and transfers them effectively to a compact student network. To accomplish this, we propose STRATANET, a modeling framework comprising: (a) a steerable data generator that produces text data tailored to each teacher and (b) an amalgamation module that implements a self-regulative strategy using confidence estimates from the teachers' different layers to selectively integrate their knowledge and train a versatile student. We evaluate our method on three benchmark text classification datasets with varying labels or domains. Empirically, we demonstrate that the student model learned using our STRATANET outperforms several baselines significantly under data-driven and data-free constraints., Comment: 12 pages, 5 Figures, Proceedings of NAACL 2024

The process of database knob tuning has always been a challenging task. Recently, database knob tuning methods has emerged as a promising solution to mitigate these issues. However, these methods still face certain limitations.On one hand, when applying knob tuning algorithms to optimize databases in practice, it either requires frequent updates to the database or necessitates acquiring database workload and optimizing through workload replay. The former approach involves constant exploration and updating of database configurations, inevitably leading to a decline in database performance during optimization. The latter, on the other hand, requires the acquisition of workload data, which could lead to data leakage issues. Moreover, the hyperparameter configuration space for database knobs is vast, making it challenging for optimizers to converge. These factors significantly hinder the practical implementation of database tuning. To address these concerns, we proposes an efficient and micro-invasive knob tuning method. This method relies on workload synthesis on cloned databases to simulate the workload that needs tuning, thus minimizing the intrusion on the database. And we utilizing a configuration replacement strategy to filter configuration candidates that perform well under the synthesized workload to find best configuration. And during the tuning process, we employ a knowledge transfer method to extract a common high-performance space, to boost the convergence of the optimizer.

Graph Neural Networks (GNNs) have shown great performance in various tasks, with the core idea of learning from data labels and aggregating messages within the neighborhood of nodes. However, the common challenges in graphs are twofold: insufficient accurate (high-quality) labels and limited neighbors for nodes, resulting in weak GNNs. Existing graph augmentation methods typically address only one of these challenges, often adding training costs or relying on oversimplified or knowledge-intensive strategies, limiting their generalization. To simultaneously address both challenges faced by graphs in a generalized way, we propose an elegant method called IntraMix. Considering the incompatibility of vanilla Mixup with the complex topology of graphs, IntraMix innovatively employs Mixup among inaccurate labeled data of the same class, generating high-quality labeled data at minimal cost. Additionally, it finds data with high confidence of being clustered into the same group as the generated data to serve as their neighbors, thereby enriching the neighborhoods of graphs. IntraMix efficiently tackles both issues faced by graphs and challenges the prior notion of the limited effectiveness of Mixup in node classification. IntraMix is a theoretically grounded plug-in-play method that can be readily applied to all GNNs. Extensive experiments demonstrate the effectiveness of IntraMix across various GNNs and datasets. Our code is available at: https://github.com/Zhengsh123/IntraMix., Comment: Accepted by NeurIPS2024

Unsupervised (a.k.a. Self-supervised) representation learning (URL) has emerged as a new paradigm for time series analysis, because it has the ability to learn generalizable time series representation beneficial for many downstream tasks without using labels that are usually difficult to obtain. Considering that existing approaches have limitations in the design of the representation encoder and the learning objective, we have proposed Contrastive Shapelet Learning (CSL), the first URL method that learns the general-purpose shapelet-based representation through unsupervised contrastive learning, and shown its superior performance in several analysis tasks, such as time series classification, clustering, and anomaly detection. In this paper, we develop TimeCSL, an end-to-end system that makes full use of the general and interpretable shapelets learned by CSL to achieve explorable time series analysis in a unified pipeline. We introduce the system components and demonstrate how users interact with TimeCSL to solve different analysis tasks in the unified pipeline, and gain insight into their time series by exploring the learned shapelets and representation.

Conjugated polymer fibers can be used to manufacture various soft fibrous optoelectronic devices, significantly advancing wearable devices and smart textiles. Recently, conjugated polymer-based fibrous electronic devices have been widely used in energy conversion, electrochemical sensing, and human-machine interaction. However, the insufficient mechanical properties of conjugated polymer fibers, the difficulty in solution processing semiconductors with rigid main chains, and the challenges in large-scale continuous production have limited their further development in the wearable field. We regulated the pi - pi stacking interactions in conjugated polymer molecules below their critical liquid crystal concentration by applying fluid shear stress. We implemented secondary orientation, leading to the continuous fabrication of anisotropic semiconductor fibers. This strategy enables conjugated polymers with rigid backbones to synergistically enhance the mechanical and semiconductor properties of fibers through liquid crystal spinning. Furthermore, conjugated polymer fibers, exhibiting excellent electrochemical performance and high mechanical strength (600 MPa) that essentially meet the requirements for industrialized preparation, maintain stability under extreme temperatures, radiation, and chemical reagents. Lastly, we have demonstrated logic circuits using semiconductor fiber organic electrochemical transistors, showcasing its application potential in the field of wearable fabric-style logic processing. These findings confirm the importance of the liquid crystalline state and solution control in optimizing the performance of conjugated polymer fibers, thus paving the way for developing a new generation of soft fiber semiconductor devices.

In recent times, the field of unsupervised representation learning (URL) for time series data has garnered significant interest due to its remarkable adaptability across diverse downstream applications. Unsupervised learning goals differ from downstream tasks, making it tricky to ensure downstream task utility by focusing only on temporal feature characterization. Researchers have proposed multiple transformations to extract discriminative patterns implied in informative time series, trying to fill the gap. Despite the introduction of a variety of feature engineering techniques, e.g. spectral domain, wavelet transformed features, features in image form and symbolic features etc. the utilization of intricate feature fusion methods and dependence on heterogeneous features during inference hampers the scalability of the solutions. To address this, our study introduces an innovative approach that focuses on aligning and binding time series representations encoded from different modalities, inspired by spectral graph theory, thereby guiding the neural encoder to uncover latent pattern associations among these multi-modal features. In contrast to conventional methods that fuse features from multiple modalities, our proposed approach simplifies the neural architecture by retaining a single time series encoder, consequently leading to preserved scalability. We further demonstrate and prove mechanisms for the encoder to maintain better inductive bias. In our experimental evaluation, we validated the proposed method on a diverse set of time series datasets from various domains. Our approach outperforms existing state-of-the-art URL methods across diverse downstream tasks.

Soil organic carbon (SOC) sequestration is the transfer and storage of atmospheric carbon dioxide in soils, which plays an important role in climate change mitigation. SOC concentration can be improved by proper land use, thus it is beneficial if SOC can be estimated at a regional or global scale. As multispectral satellite data can provide SOC-related information such as vegetation and soil properties at a global scale, estimation of SOC through satellite data has been explored as an alternative to manual soil sampling. Although existing studies show promising results, they are mainly based on pixel-based approaches with traditional machine learning methods, and convolutional neural networks (CNNs) are uncommon. To study the use of CNNs on SOC remote sensing, here we propose the FNO-DenseNet based on the Fourier neural operator (FNO). By combining the advantages of the FNO and DenseNet, the FNO-DenseNet outperformed the FNO in our experiments with hundreds of times fewer parameters. The FNO-DenseNet also outperformed a pixel-based random forest by 18% in the mean absolute percentage error., Comment: This paper was accepted by the 2023 IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2023)

With the introduction of Transformers, different attention-based models have been proposed for image segmentation with promising results. Although self-attention allows capturing of long-range dependencies, it suffers from a quadratic complexity in the image size especially in 3D. To avoid the out-of-memory error during training, input size reduction is usually required for 3D segmentation, but the accuracy can be suboptimal when the trained models are applied on the original image size. To address this limitation, inspired by the Fourier neural operator (FNO), we introduce the HartleyMHA model which is robust to training image resolution with efficient self-attention. FNO is a deep learning framework for learning mappings between functions in partial differential equations, which has the appealing properties of zero-shot super-resolution and global receptive field. We modify the FNO by using the Hartley transform with shared parameters to reduce the model size by orders of magnitude, and this allows us to further apply self-attention in the frequency domain for more expressive high-order feature combination with improved efficiency. When tested on the BraTS'19 dataset, it achieved superior robustness to training image resolution than other tested models with less than 1% of their model parameters., Comment: This paper was accepted by the International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI 2023). arXiv admin note: text overlap with arXiv:2310.03872

Due to the computational complexity of 3D medical image segmentation, training with downsampled images is a common remedy for out-of-memory errors in deep learning. Nevertheless, as standard spatial convolution is sensitive to variations in image resolution, the accuracy of a convolutional neural network trained with downsampled images can be suboptimal when applied on the original resolution. To address this limitation, we introduce FNOSeg3D, a 3D segmentation model robust to training image resolution based on the Fourier neural operator (FNO). The FNO is a deep learning framework for learning mappings between functions in partial differential equations, which has the appealing properties of zero-shot super-resolution and global receptive field. We improve the FNO by reducing its parameter requirement and enhancing its learning capability through residual connections and deep supervision, and these result in our FNOSeg3D model which is parameter efficient and resolution robust. When tested on the BraTS'19 dataset, it achieved superior robustness to training image resolution than other tested models with less than 1% of their model parameters., Comment: This paper was accepted by the IEEE International Symposium on Biomedical Imaging (ISBI) 2023

Query cost estimation is a classical task for database management. Recently, researchers apply the AI-driven model to implement query cost estimation for achieving high accuracy. However, two defects of feature design lead to poor cost estimation accuracy-time efficiency. On the one hand, existing works only encode the query plan and data statistics while ignoring some other important variables, like storage structure, hardware, database knobs, etc. These variables also have significant impact on the query cost. On the other hand, due to the straightforward encoding design, existing works suffer heavy representation learning burden on ineffective dimensions of input. To meet the above two problems, we first propose an efficient feature engineering for query cost estimation, called QCFE. Specifically, we design a novel feature called feature snapshot to efficiently integrate the influences of the ignored variables. Further, we propose a difference-propagation feature reduction method for query cost estimation to filter the useless features. The experimental results demonstrate our QCFE could largely improve the time-accuracy efficiency on extensive benchmarks.

The knobs of modern database management systems have significant impact on the performance of the systems. With the development of cloud databases, an estimation service for knobs is urgently needed to improve the performance of database. Unfortunately, few attentions have been paid to estimate the performance of certain knob configurations. To fill this gap, we propose IWEK, an interpretable & transferable what-if estimator for database knobs. To achieve interpretable estimation, we propose linear estimator based on the random forest for database knobs for the explicit and trustable evaluation results. Due to its interpretability, our estimator capture the direct relationships between knob configuration and its performance, to guarantee the high availability of database. We design a two-stage transfer algorithm to leverage historical experiences to efficiently build the knob estimator for new scenarios. Due to its lightweight design, our method can largely reduce the overhead of collecting training data and could achieve cold start knob estimation for new scenarios. Extensive experiments on YCSB and TPCC show that our method performs well in interpretable and transferable knob estimation with limited training data. Further, our method could achieve efficient estimator transfer with only 10 samples in TPCC and YSCB.

Learned cardinality estimation methods have achieved high precision compared to traditional methods. Among learned methods, query-driven approaches have faced the workload drift problem for a long time. Although both data-driven and hybrid methods are proposed to avoid this problem, most of them suffer from high training and estimation costs, limited scalability, instability, and long-tail distribution problems on high-dimensional tables, which seriously affects the practical application of learned cardinality estimators. In this paper, we prove that most of these problems are directly caused by the widely used progressive sampling. We solve this problem by introducing predicate information into the autoregressive model and propose Duet, a stable, efficient, and scalable hybrid method to estimate cardinality directly without sampling or any non-differentiable process, which can not only reduce the inference complexity from $O(n)$ to $O(1)$ compared to Naru and UAE but also achieve higher accuracy on high cardinality and high-dimensional tables. Experimental results show that Duet can achieve all the design goals above and be much more practical. Besides, Duet even has a lower inference cost on CPU than that of most learned methods on GPU.

With the emergence of multimodal electronic health records, the evidence for an outcome may be captured across multiple modalities ranging from clinical to imaging and genomic data. Predicting outcomes effectively requires fusion frameworks capable of modeling fine-grained and multi-faceted complex interactions between modality features within and across patients. We develop an innovative fusion approach called MaxCorr MGNN that models non-linear modality correlations within and across patients through Hirschfeld-Gebelein-Renyi maximal correlation (MaxCorr) embeddings, resulting in a multi-layered graph that preserves the identities of the modalities and patients. We then design, for the first time, a generalized multi-layered graph neural network (MGNN) for task-informed reasoning in multi-layered graphs, that learns the parameters defining patient-modality graph connectivity and message passing in an end-to-end fashion. We evaluate our model an outcome prediction task on a Tuberculosis (TB) dataset consistently outperforming several state-of-the-art neural, graph-based and traditional fusion techniques., Comment: To appear in ML4MHD workshop at ICML 2023

Recent studies have shown great promise in unsupervised representation learning (URL) for multivariate time series, because URL has the capability in learning generalizable representation for many downstream tasks without using inaccessible labels. However, existing approaches usually adopt the models originally designed for other domains (e.g., computer vision) to encode the time series data and {rely on strong assumptions to design learning objectives, which limits their ability to perform well}. To deal with these problems, we propose a novel URL framework for multivariate time series by learning time-series-specific shapelet-based representation through a popular contrasting learning paradigm. To the best of our knowledge, this is the first work that explores the shapelet-based embedding in the unsupervised general-purpose representation learning. A unified shapelet-based encoder and a novel learning objective with multi-grained contrasting and multi-scale alignment are particularly designed to achieve our goal, and a data augmentation library is employed to improve the generalization. We conduct extensive experiments using tens of real-world datasets to assess the representation quality on many downstream tasks, including classification, clustering, and anomaly detection. The results demonstrate the superiority of our method against not only URL competitors, but also techniques specially designed for downstream tasks. Our code has been made publicly available at https://github.com/real2fish/CSL., Comment: Accepted by VLDB 2024, 14 pages

Innovative learning based structures have recently been proposed to tackle index and cardinality estimation tasks, specifically learned indexes and data driven cardinality estimators. These structures exhibit excellent performance in capturing data distribution, making them promising for integration into AI driven database kernels. However, accurate estimation for corner case queries requires a large number of network parameters, resulting in higher computing resources on expensive GPUs and more storage overhead. Additionally, the separate implementation for CE and learned index result in a redundancy waste by storage of single table distribution twice. These present challenges for designing AI driven database kernels. As in real database scenarios, a compact kernel is necessary to process queries within a limited storage and time budget. Directly integrating these two AI approaches would result in a heavy and complex kernel due to a large number of network parameters and repeated storage of data distribution parameters. Our proposed CardIndex structure effectively killed two birds with one stone. It is a fast multidim learned index that also serves as a lightweight cardinality estimator with parameters scaled at the KB level. Due to its special structure and small parameter size, it can obtain both CDF and PDF information for tuples with an incredibly low latency of 1 to 10 microseconds. For tasks with low selectivity estimation, we did not increase the model's parameters to obtain fine grained point density. Instead, we fully utilized our structure's characteristics and proposed a hybrid estimation algorithm in providing fast and exact results.

Multivariate time series classification (MTSC) is an important data mining task, which can be effectively solved by popular deep learning technology. Unfortunately, the existing deep learning-based methods neglect the hidden dependencies in different dimensions and also rarely consider the unique dynamic features of time series, which lack sufficient feature extraction capability to obtain satisfactory classification accuracy. To address this problem, we propose a novel temporal dynamic graph neural network (TodyNet) that can extract hidden spatio-temporal dependencies without undefined graph structure. It enables information flow among isolated but implicit interdependent variables and captures the associations between different time slots by dynamic graph mechanism, which further improves the classification performance of the model. Meanwhile, the hierarchical representations of graphs cannot be learned due to the limitation of GNNs. Thus, we also design a temporal graph pooling layer to obtain a global graph-level representation for graph learning with learnable temporal parameters. The dynamic graph, graph information propagation, and temporal convolution are jointly learned in an end-to-end framework. The experiments on 26 UEA benchmark datasets illustrate that the proposed TodyNet outperforms existing deep learning-based methods in the MTSC tasks.

Machine learning has emerged as a powerful tool for time series analysis. Existing methods are usually customized for different analysis tasks and face challenges in tackling practical problems such as partial labeling and domain shift. To improve the performance and address the practical problems universally, we develop UniTS, a novel framework that incorporates self-supervised representation learning (or pre-training). The components of UniTS are designed using sklearn-like APIs to allow flexible extensions. We demonstrate how users can easily perform an analysis task using the user-friendly GUIs, and show the superior performance of UniTS over the traditional task-specific methods without self-supervised pre-training on five mainstream tasks and two practical settings., Comment: Accepted by SIGMOD 24

Neural predictors have shown great potential in the evaluation process of neural architecture search (NAS). However, current predictor-based approaches overlook the fact that training a predictor necessitates a considerable number of trained neural networks as the labeled training set, which is costly to obtain. Therefore, the critical issue in utilizing predictors for NAS is to train a high-performance predictor using as few trained neural networks as possible. Although some methods attempt to address this problem through unsupervised learning, they often result in inaccurate predictions. We argue that the unsupervised tasks intended for the common graph data are too challenging for neural networks, causing unsupervised training to be susceptible to performance crashes in NAS. To address this issue, we propose a Curricumum-guided Contrastive Learning framework for neural Predictor (DCLP). Our method simplifies the contrastive task by designing a novel curriculum to enhance the stability of unlabeled training data distribution during contrastive training. Specifically, we propose a scheduler that ranks the training data according to the contrastive difficulty of each data and then inputs them to the contrastive learner in order. This approach concentrates the training data distribution and makes contrastive training more efficient. By using our method, the contrastive learner incrementally learns feature representations via unsupervised data on a smooth learning curve, avoiding performance crashes that may occur with excessively variable training data distributions. We experimentally demonstrate that DCLP has high accuracy and efficiency compared with existing predictors, and shows promising potential to discover superior architectures in various search spaces when combined with search strategies. Our code is available at: https://github.com/Zhengsh123/DCLP., Comment: Accepted by AAAI24

Hierarchical data storage is crucial for cloud-edge-end time-series database. Efficient hierarchical storage will directly reduce the storage space of local databases at each side and improve the access hit rate of data. However, no effective hierarchical data management strategy for cloud-edge-end time-series database has been proposed. To solve this problem, this paper proposes TS-Cabinet, a hierarchical storage scheduler for cloud-edge-end time-series database based on workload forecasting. To the best of our knowledge, it is the first work for hierarchical storage of cloud-edge-end time-series database. By building a temperature model, we calculate the current temperature for the timeseries data, and use the workload forecasting model to predict the data's future temperature. Finally, we perform hierarchical storage according to the data migration policy. We validate it on a public dataset, and the experimental results show that our method can achieve about 94% hit rate for data access on the cloud side and edge side, which is 12% better than the existing methods. TS-Cabinet can help cloud-edge-end time-series database avoid the storage overhead caused by storing the full amount of data at all three sides, and greatly reduce the data transfer overhead between each side when collaborative query processing.

This paper explores how to build a shapelet-based time series classification (TSC) model in the federated learning (FL) scenario, that is, using more data from multiple owners without actually sharing the data. We propose FedST, a novel federated TSC framework extended from a centralized shapelet transformation method. We recognize the federated shapelet search step as the kernel of FedST. Thus, we design a basic protocol for the FedST kernel that we prove to be secure and accurate. However, we identify that the basic protocol suffers from efficiency bottlenecks and the centralized acceleration techniques lose their efficacy due to the security issues. To speed up the federated protocol with security guarantee, we propose several optimizations tailored for the FL setting. Our theoretical analysis shows that the proposed methods are secure and more efficient. We conduct extensive experiments using both synthetic and real-world datasets. Empirical results show that our FedST solution is effective in terms of TSC accuracy, and the proposed optimizations can achieve three orders of magnitude of speedup.