TEAFormers: TEnsor-Augmented Transformers for Multi-Dimensional Time Series Forecasting (2410.20439v1)

Abstract: Multi-dimensional time series data, such as matrix and tensor-variate time series, are increasingly prevalent in fields such as economics, finance, and climate science. Traditional Transformer models, though adept with sequential data, do not effectively preserve these multi-dimensional structures, as their internal operations in effect flatten multi-dimensional observations into vectors, thereby losing critical multi-dimensional relationships and patterns. To address this, we introduce the Tensor-Augmented Transformer (TEAFormer), a novel method that incorporates tensor expansion and compression within the Transformer framework to maintain and leverage the inherent multi-dimensional structures, thus reducing computational costs and improving prediction accuracy. The core feature of the TEAFormer, the Tensor-Augmentation (TEA) module, utilizes tensor expansion to enhance multi-view feature learning and tensor compression for efficient information aggregation and reduced computational load. The TEA module is not just a specific model architecture but a versatile component that is highly compatible with the attention mechanism and the encoder-decoder structure of Transformers, making it adaptable to existing Transformer architectures. Our comprehensive experiments, which integrate the TEA module into three popular time series Transformer models across three real-world benchmarks, show significant performance enhancements, highlighting the potential of TEAFormers for cutting-edge time series forecasting.

• The paper introduces the TEAFormer, which integrates tensor expansion and compression within Transformer models to preserve multi-dimensional data while reducing computational overhead.
• It employs a dedicated tensor-augmentation module to enable effective multi-view feature learning and aggregation from complex time series data.
• Empirical results across models such as Transformer, Informer, and Autoformer show significant improvements in forecasting accuracy, as evidenced by lower MAE and MSE metrics.

Tensor-Augmented Transformers for Multi-Dimensional Time Series Forecasting

The paper introduces a novel approach termed the Tensor-Augmented Transformer (TEAFormer) for enhancing the prediction capabilities of traditional Transformer models when dealing with multi-dimensional time series data. This advancement is particularly relevant given the increasing prevalence of matrix and tensor-valued time series found in various fields, such as economics, finance, and climate science. The paper addresses the limitations of existing Transformer architectures, which tend to flatten multi-dimensional observations, thereby losing critical structural relationships inherent in such data types.

Key Contributions

1. Tensor-Augmented Transformer (TEAFormer): The central innovation of this research is the TEAFormer, designed to integrate tensor expansion and compression techniques within the standard Transformer model. This integration not only maintains the multi-dimensional structure of the data but also reduces computational overheads while improving accuracy.
2. Tensor-Augmentation Module: The authors developed a versatile Tensor-Augmentation (TEA) module. This module performs tensor expansion and compression, enabling the model to effectively conduct multi-view feature learning and information aggregation. The TEA module can seamlessly work with existing Transformer frameworks due to its compatibility with their encoder-decoder structure.
3. Empirical Validation: The research integrates the TEA module into three established time series forecasting models: Transformer, Informer, and Autoformer. Through extensive experiments on diverse datasets, the TEAFormer shows significant performance improvements, as demonstrated by enhanced Mean Absolute Error (MAE) and Mean Squared Error (MSE) metrics across real-world benchmarks.

Theoretical and Practical Implications

Theoretically, the integration of tensor operations within the Transformer framework represents a significant step forward in preserving the dimensionality and intrinsic structure of data throughout the end-to-end modeling process. By expanding the capabilities of Transformers to handle multi-dimensional time series, the TEAFormer enables the model to better capture complex dependencies and interactions within the data.

Practically, the TEAFormer’s potential lies in its applicability to various fields where multi-dimensional data is prevalent. The ability to maintain and leverage data structures can lead to more accurate forecasts, which are crucial for decision-making in economics, finance, climate science, and other domains. Additionally, by reducing computational complexity through operations on compressed tensor representations, the model becomes feasible for deployment in scenarios with limited computational resources.

Future Directions

Several future research avenues emerge from this work. Firstly, refining the tensor compression strategy could further improve the model’s efficiency and forecasting prowess. Furthermore, extending the TEA module to support more complex data types beyond the current focus could broaden its applicability. Investigating the role of TEAFormers in handling data with non-linear relationships, which often occur in language and textual applications, also presents a promising direction for research.

The introduction of the TEAFormer provides valuable insights and a robust approach to multi-dimensional time series forecasting, laying the groundwork for future advancements in AI-driven predictions. As multi-dimensional data continues to proliferate across various industries, methods like the TEAFormer will be instrumental in harnessing and interpreting such complex information efficiently.