The loss functions of deep neural networks are complex and their geometric properties are not well understood. We show that the optima of these complex loss functions are in fact connected by simple curves, over which training and test accuracy are nearly constant. We introduce a training procedure to discover these high-accuracy pathways between modes. Inspired by this new geometric insight, we also propose a new ensembling method entitled Fast Geometric Ensembling (FGE). Using FGE we can train high-performing ensembles in the time required to train a single model. We achieve improved performance compared to the recent state-of-the-art Snapshot Ensembles, on CIFAR-10, CIFAR-100, and ImageNet.

The loss functions of deep neural networks are complex and their geometric properties are not well understood. We show that the optima of these complex loss functions are in fact connected by simple curves, over which training and test accuracy are nearly constant. We introduce a training procedure to discover these high-accuracy pathways between modes. Inspired by this new geometric insight, we also propose a new ensembling method entitled Fast Geometric Ensembling (FGE). Using FGE we can train high-performing ensembles in the time required to train a single model.

Update after author response: Thank you for the response. Additional details that the curves between the local optima are not unique would be also interesting to see. Summary: This paper first shows a very interesting finding on the loss surfaces of deep neural nets, and then presents a new ensembling method called Fast Geometric Ensembling (FGE). Given two already well trained deep neural nets (with no limitations on their architectures, apparently), we have two sets of weight vectors w1 and w2 (in a very high-dimensional space). This paper states a (surprising) fact that for given two weights w1 and w2, we can (always?) Figure 1 demonstrates this, and Left is the training accuracy plot on the 2D subspace passing independent weights w1, w2, w3 of ResNet-164 (from different random starts); whereas Middle and Right are the 2D subspace passing independent weights w1, w2 and one bend point w3 on the curve (Middle: Bezier, Right: Polygonal chain).

The loss functions of deep neural networks are complex and their geometric properties are not well understood. We show that the optima of these complex loss functions are in fact connected by simple curves, over which training and test accuracy are nearly constant. We introduce a training procedure to discover these high-accuracy pathways between modes. Inspired by this new geometric insight, we also propose a new ensembling method entitled Fast Geometric Ensembling (FGE). Using FGE we can train high-performing ensembles in the time required to train a single model.

The loss functions of deep neural networks are complex and their geometric properties are not well understood. We show that the optima of these complex loss functions are in fact connected by a simple polygonal chain with only one bend, over which training and test accuracy are nearly constant. We introduce a training procedure to discover these high-accuracy pathways between modes. Inspired by this new geometric insight, we propose a new ensembling method entitled Fast Geometric Ensembling (FGE). Using FGE we can train high-performing ensembles in the time required to train a single model. We achieve improved performance compared to the recent state-of-the-art Snapshot Ensembles, on CIFAR-10 and CIFAR-100, using state-of-the-art deep residual networks. On ImageNet we improve the top-1 error-rate of a pre-trained ResNet by 0.56% by running FGE for just 5 epochs.