A universal measure of how complex any model really is

Most complexity measures are either vague rules of thumb or computationally expensive. This work proposes a mathematically rigorous measure based on how much model predictions change across different inputs, applicable to any parametric or kernel-based model. The measure unifies existing complexity concepts (polynomial degree, kernel length scales, tree depth) and reveals new insights into double descent—the counterintuitive phenomenon where test error drops after initially rising as models get larger.