  Neural collapse is a highly symmetric geometric pattern of neural networks
that emerges during the terminal phase of training, with profound implications
on the generalization performance and robustness of the trained networks. To
understand how the last-layer features and classifiers exhibit this recently
discovered implicit bias, in this paper, we introduce a surrogate model called
the unconstrained layer-peeled model (ULPM). We prove that gradient flow on
this model converges to critical points of a minimum-norm separation problem
exhibiting neural collapse in its global minimizer. Moreover, we show that the
ULPM with the cross-entropy loss has a benign global landscape for its loss
function, which allows us to prove that all the critical points are strict
saddle points except the global minimizers that exhibit the neural collapse
phenomenon. Empirically, we show that our results also hold during the training
of neural networks in real-world tasks when explicit regularization or weight
decay is not used.
