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Via an overparameterized linear model with Gaussian features, we provideconditions for good generalization for multiclass classification ofminimum-norm interpolating solutions in an asymptotic setting where both thenumber of underlying features and the number of classes scale with the numberof training points. The survival/contamination analysis framework forunderstanding the behavior of overparameterized learning problems is adapted tothis setting, revealing that multiclass classification qualitatively behaveslike binary classification in that, as long as there are not too many classes(made precise in the paper), it is possible to generalize well even in somesettings where the corresponding regression tasks would not generalize. Besidesvarious technical challenges, it turns out that the key difference from thebinary classification setting is that there are relatively fewer positivetraining examples of each class in the multiclass setting as the number ofclasses increases, making the multiclass problem "harder" than the binary one.

Generalization for multiclass classification with overparameterized linear models