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Predicting multivariate time series is crucial, demanding precise modeling of intricate patterns, including inter-series dependencies and intra-series variations. Distinctive trend characteristics in each time series pose challenges, and existing methods, relying on basic moving average kernels, may struggle with the non-linear structure and complex trends in real-world data. Given that, we introduce a learnable decomposition strategy to capture dynamic trend information more reasonably. Additionally, we propose a dual attention module tailored to capture inter-series dependencies and intra-series variations simultaneously for better time series forecasting, which is implemented by channel-wise self-attention and autoregressive self-attention. To evaluate the effectiveness of our method, we conducted experiments across eight open-source datasets and compared it with the state-of-the-art methods. Through the comparison results, our Leddam (LEarnable Decomposition and Dual Attention Module) not only demonstrates significant advancements in predictive performance, but also the proposed decomposition strategy can be plugged into other methods with a large performance-boosting, from 11.87% to 48.56% MSE error degradation.

Amidst task-specific learning-based control synthesis frameworks that achieve impressive empirical results, a unified framework that systematically constructs an optimal policy for sufficiently solving a general notion of a task is absent. Hence, we propose a theoretical framework for a task-centered control synthesis leveraging two critical ideas: 1) oracle-guided policy optimization for the non-limiting integration of sub-optimal task-based priors to guide the policy optimization and 2) task-vital multimodality to break down solving a task into executing a sequence of behavioral modes. The proposed approach results in highly agile parkour and diving on a 16-DoF dynamic bipedal robot. The obtained policy advances indefinitely on a track, performing leaps and jumps of varying lengths and heights for the parkour task. Corresponding to the dive task, the policy demonstrates front, back, and side flips from various initial heights. Finally, we introduce a novel latent mode space reachability analysis to study our policies' versatility and generalization by computing a feasible mode set function through which we certify a set of failure-free modes for our policy to perform at any given state.

Recently, promptable segmentation models, such as the Segment Anything Model (SAM), have demonstrated robust zero-shot generalization capabilities on static images. These promptable models exhibit denoising abilities for imprecise prompt inputs, such as imprecise bounding boxes. In this paper, we explore the potential of applying SAM to track and segment objects in videos where we recognize the tracking task as a prompt denoising task. Specifically, we iteratively propagate the bounding box of each object's mask in the preceding frame as the prompt for the next frame. Furthermore, to enhance SAM's denoising capability against position and size variations, we propose a multi-prompt strategy where we provide multiple jittered and scaled box prompts for each object and preserve the mask prediction with the highest semantic similarity to the template mask. We also introduce a point-based refinement stage to handle occlusions and reduce cumulative errors. Without involving tracking modules, our approach demonstrates comparable performance in video object/instance segmentation tasks on three datasets: DAVIS2017, YouTubeVOS2018, and UVO, serving as a concise baseline and endowing SAM-based downstream applications with tracking capabilities.

We reformulate the Lanczos tau method for the discretization of time-delay systems in terms of a pencil of operators, allowing for new insights into this approach. As a first main result, we show that, for the choice of a shifted Legendre basis, this method is equivalent to Pad\'e approximation in the frequency domain. We illustrate that Lanczos tau methods straightforwardly give rise to sparse, self nesting discretizations. Equivalence is also demonstrated with pseudospectral collocation, where the non-zero collocation points are chosen as the zeroes of orthogonal polynomials. The importance of such a choice manifests itself in the approximation of the $H^2$-norm, where, under mild conditions, super-geometric convergence is observed and, for a special case, super convergence is proved; both significantly faster than the algebraic convergence reported in previous work.

We introduce CrossNet, a complex spectral mapping approach to speaker separation and enhancement in reverberant and noisy conditions. The proposed architecture comprises an encoder layer, a global multi-head self-attention module, a cross-band module, a narrow-band module, and an output layer. CrossNet captures global, cross-band, and narrow-band correlations in the time-frequency domain. To address performance degradation in long utterances, we introduce a random chunk positional encoding. Experimental results on multiple datasets demonstrate the effectiveness and robustness of CrossNet, achieving state-of-the-art performance in tasks including reverberant and noisy-reverberant speaker separation. Furthermore, CrossNet exhibits faster and more stable training in comparison to recent baselines. Additionally, CrossNet's high performance extends to multi-microphone conditions, demonstrating its versatility in various acoustic scenarios.

We present AlloyInEcore, a tool for specifying metamodels with their static semantics to facilitate automated, formal reasoning on models. Software development projects require that software systems be specified in various models (e.g., requirements models, architecture models, test models, and source code). It is crucial to reason about those models to ensure the correct and complete system specifications. AlloyInEcore allows the user to specify metamodels with their static semantics, while, using the semantics, it automatically detects inconsistent models, and completes partial models. It has been evaluated on three industrial case studies in the automotive domain (//modelwriter.github.io/AlloyInEcore/).

Addressing the intricate challenge of modeling and re-rendering dynamic scenes, most recent approaches have sought to simplify these complexities using plane-based explicit representations, overcoming the slow training time issues associated with methods like Neural Radiance Fields (NeRF) and implicit representations. However, the straightforward decomposition of 4D dynamic scenes into multiple 2D plane-based representations proves insufficient for re-rendering high-fidelity scenes with complex motions. In response, we present a novel direction-aware representation (DaRe) approach that captures scene dynamics from six different directions. This learned representation undergoes an inverse dual-tree complex wavelet transformation (DTCWT) to recover plane-based information. DaReNeRF computes features for each space-time point by fusing vectors from these recovered planes. Combining DaReNeRF with a tiny MLP for color regression and leveraging volume rendering in training yield state-of-the-art performance in novel view synthesis for complex dynamic scenes. Notably, to address redundancy introduced by the six real and six imaginary direction-aware wavelet coefficients, we introduce a trainable masking approach, mitigating storage issues without significant performance decline. Moreover, DaReNeRF maintains a 2x reduction in training time compared to prior art while delivering superior performance.

The curse-of-dimensionality taxes computational resources heavily with exponentially increasing computational cost as the dimension increases. This poses great challenges in solving high-dimensional PDEs, as Richard E. Bellman first pointed out over 60 years ago. While there has been some recent success in solving numerically partial differential equations (PDEs) in high dimensions, such computations are prohibitively expensive, and true scaling of general nonlinear PDEs to high dimensions has never been achieved. We develop a new method of scaling up physics-informed neural networks (PINNs) to solve arbitrary high-dimensional PDEs. The new method, called Stochastic Dimension Gradient Descent (SDGD), decomposes a gradient of PDEs into pieces corresponding to different dimensions and randomly samples a subset of these dimensional pieces in each iteration of training PINNs. We prove theoretically the convergence and other desired properties of the proposed method. We demonstrate in various diverse tests that the proposed method can solve many notoriously hard high-dimensional PDEs, including the Hamilton-Jacobi-Bellman (HJB) and the Schr\"{o}dinger equations in tens of thousands of dimensions very fast on a single GPU using the PINNs mesh-free approach. Notably, we solve nonlinear PDEs with nontrivial, anisotropic, and inseparable solutions in 100,000 effective dimensions in 12 hours on a single GPU using SDGD with PINNs. Since SDGD is a general training methodology of PINNs, it can be applied to any current and future variants of PINNs to scale them up for arbitrary high-dimensional PDEs.

With the exponential surge in diverse multi-modal data, traditional uni-modal retrieval methods struggle to meet the needs of users demanding access to data from various modalities. To address this, cross-modal retrieval has emerged, enabling interaction across modalities, facilitating semantic matching, and leveraging complementarity and consistency between different modal data. Although prior literature undertook a review of the cross-modal retrieval field, it exhibits numerous deficiencies pertaining to timeliness, taxonomy, and comprehensiveness. This paper conducts a comprehensive review of cross-modal retrieval's evolution, spanning from shallow statistical analysis techniques to vision-language pre-training models. Commencing with a comprehensive taxonomy grounded in machine learning paradigms, mechanisms, and models, the paper then delves deeply into the principles and architectures underpinning existing cross-modal retrieval methods. Furthermore, it offers an overview of widely used benchmarks, metrics, and performances. Lastly, the paper probes the prospects and challenges that confront contemporary cross-modal retrieval, while engaging in a discourse on potential directions for further progress in the field. To facilitate the research on cross-modal retrieval, we develop an open-source code repository at //github.com/BMC-SDNU/Cross-Modal-Retrieval.

Graphs are used widely to model complex systems, and detecting anomalies in a graph is an important task in the analysis of complex systems. Graph anomalies are patterns in a graph that do not conform to normal patterns expected of the attributes and/or structures of the graph. In recent years, graph neural networks (GNNs) have been studied extensively and have successfully performed difficult machine learning tasks in node classification, link prediction, and graph classification thanks to the highly expressive capability via message passing in effectively learning graph representations. To solve the graph anomaly detection problem, GNN-based methods leverage information about the graph attributes (or features) and/or structures to learn to score anomalies appropriately. In this survey, we review the recent advances made in detecting graph anomalies using GNN models. Specifically, we summarize GNN-based methods according to the graph type (i.e., static and dynamic), the anomaly type (i.e., node, edge, subgraph, and whole graph), and the network architecture (e.g., graph autoencoder, graph convolutional network). To the best of our knowledge, this survey is the first comprehensive review of graph anomaly detection methods based on GNNs.