An Unsupervised Learning Framework Combined with Heuristics for the Maximum Minimal Cut Problem

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.

Unsupervised Multi-modal Feature Alignment for Time Series Representation Learning

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.

Duet: efficient and scalable hybriD neUral rElation undersTanding

Learned cardinality estimation methods have achieved high precision compared to traditional methods. Among learned methods, query-driven approaches face the data and workload drift problem for a long time. Although both query-driven and hybrid methods are proposed to avoid this problem, even the state-of-the-art of them suffer from high training and estimation costs, limited scalability, instability, and long-tailed distribution problem on high cardinality and 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 predicates 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 reduces 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 and even has a lower inference cost on CPU than that of most learned methods on GPU.

TodyNet: Temporal Dynamic Graph Neural Network for Multivariate Time Series Classification

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.