SPAR: SPARSE PHASE-AWARE ADAPTATION OF REPRESENTATIONS FOR TIME SERIES FORECASTING WITH EXOGENOUS VARIABLES

Exogenous variables provide complementary information for time series forecasting, but redundant or unstable cross-variable dependencies can impair predictions. Existing methods primarily model or select these dependencies, with limited ability to directly regulate their predictive effects in learned representations. Using sparse autoencoders (SAEs), we find that representation shifts induced by incorporating exogenous variables concentrate in a small set of sparse features, and that intervening on these features can substantially alter forecasting behavior. Motivated by this observation, we propose Sparse Phase-aware Adaptation of Representations (SPAR), a plug-in that leverages sparse adaptation shifts as an intervention interface to selectively regulate the predictive effects of exogenous variables. SPAR learns phase-aware corrections from forecasting error, enabling beneficial cross-variable effects to be preserved while mitigating harmful ones. Experiments on four backbones demonstrate consistent improvements, with average relative MSE reductions of 5.78%, 8.02%, 6.84%, and 5.74%, respectively, across seven datasets, highlighting SPAR's strong generalizability across diverse backbones and datasets. Code is available at: https://anonymous.4open.science/r/spar-Wzcc-Xzcz.