Value Lifting for Multivariate Time-Series Classification: From Fourier-Taylor Structure to Trainable High-Order Representations

Existing multivariate time-series classification (MTSC) models mainly improve temporal dependency modeling and cross-variable interaction, but they leave underexplored whether the scalar values these encoders produce benefit from an explicit, trainable transformation before classification. Here, we study this question through value lifting and instantiate it with Fourier-Taylor High-Order Lifting (FT-Lift), which converts intermediate values into a structured collection of odd- and even-order responses and learns how to combine them. Specifically, after coefficient relaxation, the Fourier-Taylor derivation provides a structured route to the high-order representation. The results show that FT-Lift improves the complete MTSC system, transfers to conventional MTSC backbones with architecture-dependent gains, achieves the best average rank among the compared lifting formulations, and provides task-dependent benefits from high-order value transformation. Overall, the evidence supports FT-Lift as a useful trainable value-lifting component for MTSC rather than a uniquely Fourier-specific function family.