Crossformer: Cross-Dimension Dependency Transformer for Multivariate Time Series Forecasting

Crossformer is a Transformer-based architecture for multivariate time series forecasting, introduced by Yunhao Zhang and Junchi Yan at ICLR 2023. Unlike earlier Transformer variants that treat each variate independently, Crossformer explicitly models cross-dimension dependencies alongside temporal patterns. It achieves this through a two-stage attention design — cross-time and cross-dimension — applied over segment-level embeddings organized in a hierarchical encoder, enabling the model to capture both intra-variate dynamics and inter-variate correlations simultaneously.