Shared-Memory Axis Inversion for Long-term Time Series Forecasting

Multivariate long-term series forecasting (LTSF) involves both temporal and variate axes, whereas efficient sequence models typically model only one axis explicitly. We characterize the resulting resolution–efficiency trade-off in terms of native-step alignment and cross-axis coupling cost, and formulate Step-indexed Completion (SInC) as a design criterion. To realize SInC, we propose DAMIE, which models the two axes sequentially: it first builds shared temporal memory indexed by native time steps, then uses Flip Attention to form a variate-to-time alignment distribution for each target variate and read out its representation from the memory. Across 11 datasets from five benchmark families, DAMIE achieves strong forecasting performance and a favorable accuracy–efficiency trade-off, particularly in settings with many variates. Further analyses indicate that step-indexed cross-axis readout helps target variates select relevant historical information and connect temporal and variate representations.