The Generalization Error of the Minimum-norm Solutions for Over-parameterized Neural Networks
This provides theoretical guarantees for generalization in over-parameterized settings, addressing a key problem in machine learning theory for researchers and practitioners.
The paper tackles the generalization error of minimum-norm solutions in over-parameterized neural networks, proving that for random feature, two-layer, and residual network models, the error scales comparably to the Monte Carlo rate with logarithmic terms when models are sufficiently over-parameterized.
We study the generalization properties of minimum-norm solutions for three over-parametrized machine learning models including the random feature model, the two-layer neural network model and the residual network model. We proved that for all three models, the generalization error for the minimum-norm solution is comparable to the Monte Carlo rate, up to some logarithmic terms, as long as the models are sufficiently over-parametrized.