New research explores minimum norm interpolation in Banach spaces

Researchers have published a paper exploring the minimum-norm interpolator (MNI) framework within the context of Banach spaces, specifically focusing on the role of 2-uniform convexity. This assumption is less restrictive than requiring the norm to be induced by an inner product, which typically means the MNI does not have a closed-form solution. The study establishes an upper bound for the MNI bias in both linear and nonlinear models under this condition. The paper demonstrates that this bound is sharp for overparameterized linear regression with specific covariate distributions and also proves sharp generalization bounds for the $\ell_p$-MNI when $p$ is within a certain range and covariates are non-Gaussian. AI

IMPACT Provides theoretical insights into generalization bounds for overparameterized models, potentially influencing future model development.

RANK_REASON Academic paper on a theoretical machine learning framework. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.LG →

• 2-uniform convexity
• linear regression
• Minimum Norm Interpolator
• neural networks

• paper
• other

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