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从最小范数插值理解延迟泛化AI 解读

Grokking shows that fitting the training data and learning the underlying signal can occur at very different stages. However, existing theories offer limited quantitative insight into how this delayed generalization depends on inductive bias and signal structure. Our work addresses the gap by developing a statistical theory that characterizes how regularization geometry and signal sparsity govern generalization near interpolation. In particular, we focus on the prototypical…

最小范数插值的局部Banach空间理论：高斯性的作用AI 解读

We study minimum-norm interpolation (MNI) in overparameterized linear regression with isotropic Gaussian covariates, in settings where the MNI has no closed-form formula. Whereas most prior work relied on Gaussian comparison tools such as the convex Gaussian min--max theorem (CGMT), our approach uses tools from high-dimensional geometry and probability. First, when the norm is in isotropic position, we obtain an ``offset'' bound that controls the amount by which the MNI…

高斯线性回归中早停的精确风险界AI 解读

We study early-stopped mirror descent (ESMD) for high-dimensional Gaussian linear regression over arbitrary convex bodies and design matrices, where the task is to minimize the in-sample mean squared error. Our main result shows that some of the sharpest risk bounds for the least squares estimator (LSE), based on the local Gaussian width, extend to ESMD. We derive sufficient conditions on the potential, expressed via the Minkowski functional, under which our result holds.…