To address the above issues, we propose CrossGNN, a linear complexity GNN model to refine the cross-scale and cross-variable interaction for MTS. To deal with the unexpected noise in time dimension, an adaptive multi-scale identifier (AMSI) is leveraged to construct multi-scale time series with reduced noise.

Recent advancements in satellite technology have enabled granular insight into the evolution of human activity onthe planet'ssurface.

Tensor-based multimodal fusion techniques have exhibited great predictive performance.

This paper proposes a new embedding structure for the output of nonlinear dimensionality reduction (NLDR). It borrows the space-time concept from physics and shows that the new structure can encode (or represent) more information than conventional Euclidean space. The idea is pioneering and wonderful. It goes beyond all conventional embedding structures and has theoretical guarantee to accommodate more symmetry in the input space. It brings much flexibility to the NLDR problem.

We propose a class of trainable deep learning-based geometries called Neural Spacetimes (NSTs), which can universally represent nodes in weighted directed acyclic graphs (DAGs) as events in a spacetime manifold. While most works in the literature focus on undirected graph representation learning or causality embedding separately, our differentiable geometry can encode both graph edge weights in its spatial dimensions and causality in the form of edge directionality in its temporal dimensions. We use a product manifold that combines a quasi-metric (for space) and a partial order (for time). NSTs are implemented as three neural networks trained in an end-to-end manner: an embedding network, which learns to optimize the location of nodes as events in the spacetime manifold, and two other networks that optimize the space and time geometries in parallel, which we call a neural (quasi-)metric and a neural partial order, respectively. The latter two networks leverage recent ideas at the intersection of fractal geometry and deep learning to shape the geometry of the representation space in a data-driven fashion, unlike other works in the literature that use fixed spacetime manifolds such as Minkowski space or De Sitter space to embed DAGs. Our main theoretical guarantee is a universal embedding theorem, showing that any $k$-point DAG can be embedded into an NST with $1+\mathcal{O}(\log(k))$ distortion while exactly preserving its causal structure. The total number of parameters defining the NST is sub-cubic in $k$ and linear in the width of the DAG. If the DAG has a planar Hasse diagram, this is improved to $\mathcal{O}(\log(k)) + 2)$ spatial and 2 temporal dimensions. We validate our framework computationally with synthetic weighted DAGs and real-world network embeddings; in both cases, the NSTs achieve lower embedding distortions than their counterparts using fixed spacetime geometries.

Video prediction aims to predict future frames from a video's previous content. Existing methods mainly process video data where the time dimension mingles with the space and channel dimensions from three distinct angles: as a sequence of individual frames, as a 3D volume in spatiotemporal coordinates, or as a stacked image where frames are treated as separate channels. Most of them generally focus on one of these perspectives and may fail to fully exploit the relationships across different dimensions. To address this issue, this paper introduces a convolutional mixer for video prediction, termed ViP-Mixer, to model the spatiotemporal evolution in the latent space of an autoencoder. The ViP-Mixers are stacked sequentially and interleave feature mixing at three levels: frames, channels, and locations. Extensive experiments demonstrate that our proposed method achieves new state-of-the-art prediction performance on three benchmark video datasets covering both synthetic and real-world scenarios.

Recent progress in long sequence time-series forecasting (LSTF) has been led by either transformers with sparse attention ([16] and references therein) or attention in combination with signal preprocessing such as seasonal-trend decomposition [17] or adopting auto-correlation to account for periodicity in the data [13]. On the other hand, Fourier transform has been proposed as an alternative mixing tool in lieu of standard attention [12] to speed up prediction in natural language processing (NLP) tasks (FNet, [2]). Though Fourier transform is meant to mimic the mixing functions of multilayer perceptron(MLP,[11]), it is not well-understood why it works and when assistance from attention layers remain necessary to maintain performance. In computer vision (CV), Fourier transform is also used as a filtering step in early stages of transformer (GFNet,[8]) to enhance a fully attention-based architecture. A recent advance in CV is to adopt window attention to reduce quadratic complexity of full attention [12].