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Structure and Gradient Dynamics Near Global Minima of Two-layer Neural Networks
Under mild assumptions, we investigate the structure of loss landscape of two-layer neural networks near global minima, determine the set of parameters which give perfect generalization, and fully characterize the gradient flows around it.
Optimistic Estimate Uncovers the Potential of Nonlinear Models
We propose an optimistic estimate to evaluate the best possible fitting performance of nonlinear models.
Linear Stability Hypothesis and Rank Stratification for Nonlinear Models
By these results, model rank of a target function predicts a minimal training data size for its successful recovery.
Limitation of Characterizing Implicit Regularization by Data-independent Functions
In recent years, understanding the implicit regularization of neural networks (NNs) has become a central task in deep learning theory.
