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Training neural networks involves finding minima of a high-dimensionalnon-convex loss function. Knowledge of the structure of this energy landscapeis sparse. Relaxing from linear interpolations, we construct continuous pathsbetween minima of recent neural network architectures on CIFAR10 and CIFAR100.Surprisingly, the paths are essentially flat in both the training and testlandscapes. This implies that neural networks have enough capacity forstructural changes, or that these changes are small between minima. Also, eachminimum has at least one vanishing Hessian eigenvalue in addition to thoseresulting from trivial invariance.

Essentially No Barriers in Neural Network Energy Landscape