Inflating the min-norm interpolator by a factor >1 reduces generalization error in linear regression with anisotropic covariances when d/n diverges to infinity.
Hanson-wright inequality and sub-gaussian concentra- tion
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abstract
In this expository note, we give a modern proof of Hanson-Wright inequality for quadratic forms in sub-gaussian random variables. We deduce a useful concentration inequality for sub-gaussian random vectors. Two examples are given to illustrate these results: a concentration of distances between random vectors and subspaces, and a bound on the norms of products of random and deterministic matrices.
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Riemannian gradient descent on rank-r Gram matrices for EDMC achieves linear convergence with high probability for sampling probability p ≥ O(ν² r² log(n)/n) and a hard-thresholding initialization under a weaker rate.
Muon achieves dimension-free saddle-point escape through non-linear spectral shaping, resolvent calculus, and structural incoherence, yielding an algebraically dimension-free escape bound.
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Shrinkage to Infinity: Reducing Test Error by Inflating the Minimum Norm Interpolator in Linear Models
Inflating the min-norm interpolator by a factor >1 reduces generalization error in linear regression with anisotropic covariances when d/n diverges to infinity.
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Provable Non-Convex Euclidean Distance Matrix Completion: Geometry, Reconstruction, and Robustness
Riemannian gradient descent on rank-r Gram matrices for EDMC achieves linear convergence with high probability for sampling probability p ≥ O(ν² r² log(n)/n) and a hard-thresholding initialization under a weaker rate.
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Dimension-Free Saddle-Point Escape in Muon
Muon achieves dimension-free saddle-point escape through non-linear spectral shaping, resolvent calculus, and structural incoherence, yielding an algebraically dimension-free escape bound.