CGHead: A Conservative Gated Prediction Head for iTransformer-Based Long-Term Multivariate Time Series Forecasting

Long-term multivariate time-series forecasting is important in intelligent transportation, electricity-load analysis, environmental monitoring, and industrial operations. This study investigates whether a constrained, shared temporal mapping can provide an output-side correction with a small additional parameter count while retaining the iTransformer representation and encoder. We propose CGHead, a two-branch output-head adapter that places a shared direct linear branch in parallel with the original projection and fuses their outputs using a conservatively initialized, learned scalar coefficient. Under the frozen paired protocol, CGHead reduced Traffic MSE by 0.0010–0.0019 (0.19–0.44%) across four forecasting horizons and improved performance for all 10 paired seeds. Direct 10-seed head-to-head tests on Traffic, Electricity, and Weather found no universal CGHead advantage over FixedGate or MLPHead. On Traffic, FixedGate’s Holm-significant gains over CGHead were numerically tiny (MSE difference −0.000003; MAE difference −0.000002), whereas MLPHead’s gains were larger (MSE difference −0.009118; MAE difference −0.004821); no head-to-head difference was detected after Holm correction for Electricity or Weather. In a prospectively specified 10-seed Solar-Energy 720-step validation, iTransformer had MSE 0.264680 ± 0.002217 versus 0.266215 ± 0.001834 for CGHead; the paired difference was −0.001535 (95% CI [−0.003264, 0.000195], two-sided p = 0.075706), providing no evidence of CGHead improvement on the primary metric. The MAE secondary metric also favored iTransformer on average (difference −0.001499, p = 0.042556 uncorrected). The evidence supports a modest, dataset-dependent correction on selected Traffic conditions rather than universal superiority or a demonstrated runtime advantage.