First De-Trend then Attend: Rethinking Attention for Time-Series Forecasting

TL;DR

This paper investigates the relationships between attention mechanisms in different domains for time-series forecasting, revealing their equivalence under linear conditions, and proposes TDformer, a model that combines trend decomposition with domain-specific attention for improved accuracy.

Contribution

It provides a theoretical and empirical analysis of attention models across domains and introduces TDformer, a novel approach that enhances forecasting by integrating trend decomposition with domain-specific attention.

Findings

TDformer outperforms existing models on benchmark datasets.

Attention models in different domains are equivalent under linear conditions.

Decomposition-based attention improves long-term forecasting accuracy.

Abstract

Transformer-based models have gained large popularity and demonstrated promising results in long-term time-series forecasting in recent years. In addition to learning attention in time domain, recent works also explore learning attention in frequency domains (e.g., Fourier domain, wavelet domain), given that seasonal patterns can be better captured in these domains. In this work, we seek to understand the relationships between attention models in different time and frequency domains. Theoretically, we show that attention models in different domains are equivalent under linear conditions (i.e., linear kernel to attention scores). Empirically, we analyze how attention models of different domains show different behaviors through various synthetic experiments with seasonality, trend and noise, with emphasis on the role of softmax operation therein. Both these theoretical and empirical analyses motivate us to propose a new method: TDformer (Trend Decomposition Transformer), that first applies seasonal-trend decomposition, and then additively combines an MLP which predicts the trend component with Fourier attention which predicts the seasonal component to obtain the final prediction. Extensive experiments on benchmark time-series forecasting datasets demonstrate that TDformer achieves state-of-the-art performance against existing attention-based models.