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Training neural networks involves solving large-scale non-convex optimizationproblems. This task has long been believed to be extremely difficult, with fearof local minima and other obstacles motivating a variety of schemes to improveoptimization, such as unsupervised pretraining. However, modern neural networksare able to achieve negligible training error on complex tasks, using onlydirect training with stochastic gradient descent. We introduce a simpleanalysis technique to look for evidence that such networks are overcoming localoptima. We find that, in fact, on a straight path from initialization tosolution, a variety of state of the art neural networks never encounter anysignificant obstacles.

Qualitatively characterizing neural network optimization problems