Linear Transformers as VAR Models: Aligning Autoregressive Attention Mechanisms with Autoregressive Forecasting
This work addresses the problem of effective and interpretable time series forecasting for researchers and practitioners in the field of multivariate time series forecasting.
The authors tackled the problem of aligning autoregressive attention mechanisms with autoregressive forecasting in time series forecasting, resulting in improved performance, interpretability, and computational efficiency with their proposed model, SAMoVAR. SAMoVAR delivers improved results compared to state-of-the-art TSF models.
Autoregressive attention-based time series forecasting (TSF) has drawn increasing interest, with mechanisms like linear attention sometimes outperforming vanilla attention. However, deeper Transformer architectures frequently misalign with autoregressive objectives, obscuring the underlying VAR structure embedded within linear attention and hindering their ability to capture the data generative processes in TSF. In this work, we first show that a single linear attention layer can be interpreted as a dynamic vector autoregressive (VAR) structure. We then explain that existing multi-layer Transformers have structural mismatches with the autoregressive forecasting objective, which impair interpretability and generalization ability. To address this, we show that by rearranging the MLP, attention, and input-output flow, multi-layer linear attention can also be aligned as a VAR model. Then, we propose Structural Aligned Mixture of VAR (SAMoVAR), a linear Transformer variant that integrates interpretable dynamic VAR weights for multivariate TSF. By aligning the Transformer architecture with autoregressive objectives, SAMoVAR delivers improved performance, interpretability, and computational efficiency, comparing to SOTA TSF models.