arXiv:1412.6544cs.NE
Qualitatively characterizing neural network optimization problems
Abstract
Training neural networks involves solving large-scale non-convex optimization problems. This task has long been believed to be extremely difficult, with fear of local minima and other obstacles motivating a variety of schemes to improve optimization, such as unsupervised pretraining. However, modern neural networks are able to achieve negligible training error on complex tasks, using only direct training with stochastic gradient descent. We introduce a simple analysis technique to look for evidence that such networks are overcoming local optima. We find that, in fact, on a straight path from initialization to solution, a variety of state of the art neural networks never encounter any significant obstacles.
In very high dimensional spaces (like trying to optimize a neural network with billions of parameters), to be "in a valley", you must be in a valley with respect to every one of the billions of dimensions. It turns out that in many practical settings, loss landscapes are pretty…
ImnimoView on HNParent context