In separable multiclass classification, the risk of gradient descent scales as k^{2/p} for losses with ℓ_p-smooth templates, giving logarithmic k-dependence for p=∞ and linear k-dependence for p=2 (provably unavoidable).
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Multiclass Loss Geometry Matters for Generalization of Gradient Descent in Separable Classification
In separable multiclass classification, the risk of gradient descent scales as k^{2/p} for losses with ℓ_p-smooth templates, giving logarithmic k-dependence for p=∞ and linear k-dependence for p=2 (provably unavoidable).