Insight Precedes Action: A Geometric Rethinking of Time Series Forecasting

Time series forecasting has advanced rapidly, yet most approaches rely on end-to-end optimization to discover predictive structure in the training data, leaving its potential as an explicit prior underexplored. Meanwhile, attention-based models typically determine cross-channel interaction through query–key similarity, without directly considering the value representations being aggregated. These considerations lead to two key questions: (i) how can predictive structure be extracted directly from the training data and provided to the model as prior knowledge, and (ii) should the information being aggregated also contribute to determining cross-channel interaction strength? To address these questions, we introduce Navigator, which integrates Foreseer and BendingFormer to rethink forecasting through two complementary geometric structures. A Predictability Basis is first constructed from past–future statistical relationships in the training data by identifying linear directions in the historical observation space with strong predictive relevance. Foreseer then uses this basis to re-express historical observations in a predictability-oriented coordinate system for subsequent modeling. BendingFormer introduces Geometric Bending Attention (GBA), which measures the directional alignment between query-to-key and key-to-value transitions, allowing value representations to directly inform cross-channel interaction strength. Together, these components embody the principle that insight precedes action: predictive structure extracted before training guides temporal representation, while the joint query–key–value geometry guides information aggregation. Extensive experiments on twelve real-world datasets demonstrate state-of-the-art forecasting performance with consistent results across random seeds, while comprehensive analyses support the effectiveness of its two core designs.