Title: Attribution Scores are Redundant: Explaining Feature Contribution By Trajectories. Abstract: Opening black boxes and revealing the inner mechanism of deep models is vital in applying them to real-world tasks. As one of the most intuitive and straightforward explanations for deep models, attributive explanation methods have been extensively studied. Existing attribution methods typically assign attribution scores to each individual feature as an explanation. However, when we use or evaluate the explanations in practice, what really matters is not the attribution scores, but the rank order of features (e.g., identifying the top-contributing features, or checking for changes in the model output by masking features in order). In other words, achieving attribution scores is a redundant step in achieving explanations. To address this, we propose a novel framework TRAjectory importanCE (TRACE) which directly provides feature ranking explanations. Our method introduces several improvements. First, TRACE greatly reduces the set of feasible explanations, allowing us to actually solve for the best explanation. Second, TRACE is able to achieve the theoretically-grounded best possible explanation in commonly used deletion evaluations. Third, we provide extensive experiments to validate that TRACE outperforms attribution methods with a significant margin.