Minimum Norm Interpolation via The Local Theory of Banach Spaces: The Role of $2$-Uniform Convexity

ArXi:2603.28956v1 Announce Type: cross The minimum-norm interpolator (MNI) framework has recently attracted considerable attention as a tool for understanding generalization in overparameterized models, such as neural networks. In this work, we study the MNI under a $2$-uniform convexity assumption, which is weaker than requiring the norm to be induced by an inner product, and it typically does not admit a closed-form solution. At a high level, we show that this condition yields an upper bound on the MNI bias in both linear and nonlinear models.