[Paper Review] Ada-MSHyper: Adaptive Multi-Scale Hypergraph Transformer for Time Series Forecasting

Zongjiang Shang, Ling Chen+2 more|arXiv (Cornell University)|Oct 31, 2024

Time Series Analysis and Forecasting4 citations

TL;DR

Ada-MSHyper proposes an adaptive multi-scale hypergraph transformer for time series forecasting that addresses semantic sparsity and temporal variation entanglement by modeling group-wise interactions through an adaptive hypergraph structure and a node-hyperedge constraint mechanism. It achieves state-of-the-art performance, reducing MSE by up to 10.38% on short-range forecasting across 11 real-world datasets.

ABSTRACT

Although transformer-based methods have achieved great success in multi-scale temporal pattern interaction modeling, two key challenges limit their further development: (1) Individual time points contain less semantic information, and leveraging attention to model pair-wise interactions may cause the information utilization bottleneck. (2) Multiple inherent temporal variations (e.g., rising, falling, and fluctuating) entangled in temporal patterns. To this end, we propose Adaptive Multi-Scale Hypergraph Transformer (Ada-MSHyper) for time series forecasting. Specifically, an adaptive hypergraph learning module is designed to provide foundations for modeling group-wise interactions, then a multi-scale interaction module is introduced to promote more comprehensive pattern interactions at different scales. In addition, a node and hyperedge constraint mechanism is introduced to cluster nodes with similar semantic information and differentiate the temporal variations within each scales. Extensive experiments on 11 real-world datasets demonstrate that Ada-MSHyper achieves state-of-the-art performance, reducing prediction errors by an average of 4.56%, 10.38%, and 4.97% in MSE for long-range, short-range, and ultra-long-range time series forecasting, respectively. Code is available at https://github.com/shangzongjiang/Ada-MSHyper.

Motivation & Objective

• To address semantic information sparsity in time series, where individual time points carry limited meaning, by modeling group-wise interactions instead of relying solely on pair-wise attention.
• To resolve temporal variation entanglement, where multiple patterns like rising, falling, and fluctuating coexist and overlap across scales.
• To enable transformers to effectively capture multi-scale temporal patterns by introducing an adaptive hypergraph structure that learns implicit group interactions.
• To improve model robustness and representation by differentiating temporal variations within each scale using semantic and distance-based constraints.
• To achieve state-of-the-art performance in long-range, short-range, and ultra-long-range time series forecasting.

Proposed method

• An adaptive hypergraph learning (AHL) module constructs dynamic hypergraphs from multi-scale feature representations, enabling discovery of implicit group-wise interactions across different temporal scales.
• A multi-scale interaction module applies hypergraph convolution with self-attention to aggregate information across nodes and hyperedges, enhancing pattern representation at multiple scales.
• A node and hyperedge constraint (NHC) mechanism enforces semantic similarity to cluster nodes with similar meaning and distance similarity to differentiate distinct temporal variations within each scale.
• The NHC mechanism uses node-level constraints to group semantically similar time points and hyperedge-level constraints to separate different temporal dynamics such as trends and fluctuations.
• The model is trained end-to-end with standard regression loss, and the hypergraph structure is dynamically updated during training based on feature similarity.
• The framework is evaluated on 11 real-world time series datasets, including electricity, traffic, and weather data, under long-, short-, and ultra-long-range forecasting settings.

Experimental results

Research questions

• RQ1 Can adaptive hypergraph learning effectively model group-wise interactions in time series, reducing the limitations of pair-wise attention in low-semantic contexts?
• RQ2 How can temporal variations such as rising, falling, and fluctuating patterns be disentangled within each scale to improve forecasting accuracy?
• RQ3 To what extent does incorporating node and hyperedge constraints enhance the model’s ability to cluster semantically similar time points and differentiate dynamic patterns?
• RQ4 Does the proposed Ada-MSHyper framework outperform existing SOTA methods in multi-scale time series forecasting across diverse real-world datasets?
• RQ5 Can the model generalize across different forecasting horizons, including long-range, short-range, and ultra-long-range tasks?

Key findings

• Ada-MSHyper achieves state-of-the-art performance on 11 real-world time series datasets, outperforming existing SOTA methods in all evaluation settings.
• The model reduces mean squared error (MSE) by an average of 4.56% on long-range forecasting tasks compared to the best baseline.
• On short-range forecasting, Ada-MSHyper achieves a 10.38% average reduction in MSE, demonstrating strong performance on fine-grained temporal patterns.
• For ultra-long-range forecasting, the model reduces MSE by 4.97% on average, indicating robustness in capturing distant dependencies.
• Ablation studies confirm that both node and hyperedge constraints are essential, with the full NHC mechanism significantly improving noise robustness and pattern disentanglement.
• Visualization results show that the model successfully clusters semantically similar nodes and isolates distinct temporal variations, such as trends and oscillations, into separate hyperedges.