ℓ₂-Boosting exhibits benign overfitting with logarithmic excess variance decay Θ(σ²/log(p/n)) under isotropic noise due to ℓ₁ bias, and a subdifferential early stopping rule recovers minimax-optimal ℓ₁ rates.
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Semi-discrete Flow Matching produces terminal assignment regions that are topologically simple (open, simply connected, homeomorphic to the ball under assumption) yet geometrically distinct from optimal transport Laguerre cells, as they can be non-convex with curved boundaries.
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When Does $\ell_2$-Boosting Overfit Benignly? High-Dimensional Risk Asymptotics and the $\ell_1$ Implicit Bias
ℓ₂-Boosting exhibits benign overfitting with logarithmic excess variance decay Θ(σ²/log(p/n)) under isotropic noise due to ℓ₁ bias, and a subdifferential early stopping rule recovers minimax-optimal ℓ₁ rates.
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Tessellations of Semi-Discrete Flow Matching
Semi-discrete Flow Matching produces terminal assignment regions that are topologically simple (open, simply connected, homeomorphic to the ball under assumption) yet geometrically distinct from optimal transport Laguerre cells, as they can be non-convex with curved boundaries.