LagNet: Lag-Structured Operators for Long-Term Time Series Forecasting

arXiv:2610.23735v1 Announce Type: new Abstract: Long-term time series forecasting maps a finite history window to an extended future horizon. Many existing models focus primarily on the design of input representations and model structures, while paying less attention to the structural form of the history-to-future forecasting operator itself. We examine this operator directly and find that, across model families, sensitivity matrices exhibit recurring diagonal patterns whose diagonals correspond to relative temporal lags. Motivated by this observation, we develop a framework for direct multi-step forecasting based on lag-structured temporal operators. Its basic building block, LagLayer, constructs a Toeplitz matrix by tying history-to-future connections with the same relative lag and incorporates horizon-wise and history-wise scaling coefficients to relax exact sharing. This design enables LagLayer to serve as an effective replacement for temporal linear layers in existing forecasting models. Stacking LagLayer modules with activations and multiple feature maps yields LagNet. Experiments on long-term time series forecasting benchmarks show that our method is competitive with strong baselines, while sensitivity matrix diagnostics and limited-data experiments demonstrate that LagLayer provides an effective and sample-efficient alternative to a linear layer.

Abstract:Long-term time series forecasting maps a finite history window to an extended future horizon. Many existing models focus primarily on the design of input representations and model structures, while paying less attention to the structural form of the history-to-future forecasting operator itself. We examine this operator directly and find that, across model families, sensitivity matrices exhibit recurring diagonal patterns whose diagonals correspond to relative temporal lags. Motivated by this observation, we develop a framework for direct multi-step forecasting based on lag-structured temporal operators. Its basic building block, LagLayer, constructs a Toeplitz matrix by tying history-to-future connections with the same relative lag and incorporates horizon-wise and history-wise scaling coefficients to relax exact sharing. This design enables LagLayer to serve as an effective replacement for temporal linear layers in existing forecasting models. Stacking LagLayer modules with activations and multiple feature maps yields LagNet. Experiments on long-term time series forecasting benchmarks show that our method is competitive with strong baselines, while sensitivity matrix diagnostics and limited-data experiments demonstrate that LagLayer provides an effective and sample-efficient alternative to a linear layer.

Machine Learning (cs.LG)

arXiv:2610.23735 [cs.LG]

(or arXiv:2610.23735v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.23735 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

aiqbench analysis

LagNet: Lag-Structured Operators for Long-Term Time Series Forecasting

Related coverage