Which Minimizer Does My Neural Network Converge To?

TL;DR

This paper investigates how different training procedures and hyperparameters influence the specific minima a neural network converges to, highlighting the effects of initialization size, adaptive optimizers, and overparameterization.

Contribution

It clarifies how initialization, adaptive optimization, and overparameterization affect the converged minimizer, and proposes strategies to mitigate negative impacts.

Findings

Initialization size impacts test performance.

Adaptive optimizers like AdaGrad lead to different minima than GD.

Overparameterization introduces unique sources of error.

Abstract

The loss surface of an overparameterized neural network (NN) possesses many global minima of zero training error. We explain how common variants of the standard NN training procedure change the minimizer obtained. First, we make explicit how the size of the initialization of a strongly overparameterized NN affects the minimizer and can deteriorate its final test performance. We propose a strategy to limit this effect. Then, we demonstrate that for adaptive optimization such as AdaGrad, the obtained minimizer generally differs from the gradient descent (GD) minimizer. This adaptive minimizer is changed further by stochastic mini-batch training, even though in the non-adaptive case, GD and stochastic GD result in essentially the same minimizer. Lastly, we explain that these effects remain relevant for less overparameterized NNs. While overparameterization has its benefits, our work highlights that it induces sources of error absent from underparameterized models.