Modeling Point-to-Point Dependency for High-Dimensional Long-Term Series Forecasting

The strategic planning and reliability of modern web services, from cloud infrastructures to e-commerce platforms, increasingly hinge on accurate long-term forecasting of high-dimensional time series. A fundamental challenge within this task is modeling the intricate point-to-point dependencies that span across both time and variable dimensions. However, many existing methods face restricted direction modeling and computational inefficiency due to their reliance on localized paradigms and Transformer architectures. To address these, we propose replacing Self-Attention with autocorrelation, achieving two key innovations: 1) We propose calculating autocorrelation across both variable and time dimensions, which is a global paradigm, to model point-to-point dependencies. 2) Our proposed Spectral Product Mechanism (SPM) optimizes traditional autocorrelation into a data-driven form suitable for deep learning. Moreover, SPM reformulates autocorrelation as spectral product and reduces the complexity from O(N2) to O(NlogN), while its Hadamard product-based correlation score matrix further reduces core computation to O(N) compared to Self-Attention's O(N2) matrix multiplication. We further propose a Generalized Spectral Product Mechanism (GSPM), which extends traditional autocorrelation by mapping input into distinct feature representations, enabling modeling of complex dependencies through cross-feature correlations. SPM and GSPM surpass current state-of-the-art (SOTA) methods on 14 authoritative benchmarks, collectively securing the top rank on 22 out of 28 metrics, while ranking 1st in time, 2nd in memory, and 2nd in parameter overhead. Source code is available at: https://github.com/lxy-PhD2022/SPM.