For quadratic loss wells, the paper derives an orientation-resolved formula predicting the random-subspace dimension where training succeeds, and shows it tracks measured transitions.
Exact expressions for double descent and implicit regularization via surrogate random design
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Predicting When Random Low-Dimensional Reparameterizations Train Neural Networks
For quadratic loss wells, the paper derives an orientation-resolved formula predicting the random-subspace dimension where training succeeds, and shows it tracks measured transitions.