Simple Temperature Scaling of Channel Graphs Is Enough for Multivariate Time Series Forecasting

In multivariate time series forecasting, modeling channels independently can miss useful dependencies, whereas jointly modeling them may introduce irrelevant or noisy interactions, with the appropriate interaction scope varying across datasets. How to continuously control and theoretically characterize this scope within a unified framework spanning Channel Independence (CI), Channel Partiality (CP), and Channel Dependence (CD) remains an open question. We view CI, CP, and CD as different concentration regimes of a common channel interaction distribution. Building on this view, we propose $\tau$former, a temporal Transformer that continuously regulates interaction scope through temperature scaling of a learned channel graph. Learned channel embeddings determine relative channel preferences, while temperature controls how strongly these preferences are expressed in the propagation weights. We derive temperature-dependent propagation bounds and introduce two complementary graph metrics to characterize the resulting channel interaction patterns. Extensive experiments on nine benchmark datasets across four prediction horizons demonstrate the competitive forecasting performance of $\tau$former. Further analyses validate its ability to accommodate different channel interaction requirements and its robustness under input corruption. Our code is available at https://anonymous.4open.science/r/Tauformer-2F29/.