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Hopformer introduces a novel two-stage framework for time series forecasting by combining sparsity pattern aggregation with LoRA-fine-tuned Transformers, offering theoretical guarantees on bias-variance trade-offs alongside improved accuracy over existing benchmarks. This research advances the field of machine learning by addressing high-dimensional covariate challenges while maintaining distinct series-specific information through rigorous mathematical proofs and generalization bounds.
Hopformer: Homogeneity-Pursuit Transformer for Time Series Forecasting
arXiv:2607.22299v1 Announce Type: cross 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.
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.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2607.22299 [stat.ML]
(or arXiv:2607.22299v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2607.22299 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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