Not All Frequencies Are Harmonious: Conflict-Aware Multi-Task Spectral Training for Time-Series Forecasting

Time-series forecasts can improve in some frequency bands while becoming less accurate in others. Aggregate error can conceal these trade-offs. Band loss values alone do not reveal how reducing one band's error affects the others during training. We therefore formulate time-series forecasting as a spectral multi-objective problem and propose Dyadic Spectral Alignment and Coordination (DySAC), a model-agnostic training framework. DySAC partitions the forecasting residual into non-overlapping dyadic bands. Each band defines a separate prediction objective for the same time series. It coordinates their gradients to seek compatible updates to the shared forecasting model. The resulting band coefficients reflect gradient directions, not just loss values or gradient norms. The aim is to distribute forecasting gains across frequencies rather than concentrate them in a few bands. The forecasting backbone and inference procedure remain unchanged. We evaluate prediction errors on the same bands to assess this balance. Across seven datasets and four backbones, DySAC yields a mean task-wise improvement of +3.85% over MSE training, with positive mean improvement in every dataset–backbone setting. The results support more balanced spectral performance, although individual tasks can still regress. Measured training-step times are 2.52-3.30 × MSE in a four-setting timing benchmark, with no change to inference.