Timezone: »

Memorization and Optimization in Deep Neural Networks with Minimum Over-parameterization
Simone Bombari · Mohammad Hossein Amani · Marco Mondelli

Thu Dec 01 02:00 PM -- 04:00 PM (PST) @ Hall J #810
The Neural Tangent Kernel (NTK) has emerged as a powerful tool to provide memorization, optimization and generalization guarantees in deep neural networks. A line of work has studied the NTK spectrum for two-layer and deep networks with at least a layer with $\Omega(N)$ neurons, $N$ being the number of training samples. Furthermore, there is increasing evidence suggesting that deep networks with sub-linear layer widths are powerful memorizers and optimizers, as long as the number of parameters exceeds the number of samples. Thus, a natural open question is whether the NTK is well conditioned in such a challenging sub-linear setup. In this paper, we answer this question in the affirmative. Our key technical contribution is a lower bound on the smallest NTK eigenvalue for deep networks with the minimum possible over-parameterization: up to logarithmic factors, the number of parameters is $\Omega(N)$ and, hence, the number of neurons is as little as $\Omega(\sqrt{N})$. To showcase the applicability of our NTK bounds, we provide two results concerning memorization capacity and optimization guarantees for gradient descent training.

Author Information

Simone Bombari (IST Austria)
Mohammad Hossein Amani (Institute of Science and Technology Austria)
Marco Mondelli (IST Austria)

More from the Same Authors