Hopformer: Homogeneity-Pursuit Transformer for Time Series Forecasting

2026-07-24

AI Summary

This work addresses the tension between extracting shared patterns and preserving individual specificity in multivariate time series forecasting under high-dimensional covariates. To resolve this, the authors propose a two-stage framework: first, a theoretically grounded Sparse Pattern Aggregation (SPA) mechanism identifies low-variance common trends, achieving effective homogenization and a near-optimal bias–variance trade-off; second, a LoRA-finetuned Transformer models the residuals to capture complex inter-series dependencies. This approach uniquely integrates homogenization with refined residual modeling and provides generalization bounds for time series with dependency structures. Evaluated on multiple synthetic and real-world datasets, the method achieves an average 6.56% improvement in MASE over existing approaches, establishing a new state of the art.

Abstract

Forecasting multiple time-series with high-dimensional covariates presents a core challenge: unifying common temporal patterns while retaining meaningful series-specific information. We introduce Hopformer (Homogeneity-Pursuit Transformer), a two-stage framework that addresses this challenge. In the first stage, we perform a Sparsity Pattern Aggregation (SPA) scheme extracting a common low-variance trend that incorporates the covariates. This acts as a homogenization layer. In the second stage, a LoRA-fine-tuned Transformer models the remaining complex dependencies in the residual. Our method is theoretically grounded. We prove that SPA achieves a near-optimal bias-variance trade-off via an oracle inequality. We also provide generalization bounds for the second stage under dependent time series data. Hopformer sets a new state of the art, improving MASE by an average of 6.56% across synthetic and real-world forecasting benchmarks.

Problem

• time series forecasting
• homogeneity
• covariates
• series-specific information
• temporal patterns

Innovation

• Hopformer
• Sparsity Pattern Aggregation
• LoRA-fine-tuned Transformer
• bias-variance trade-off
• time series forecasting