Essentially No Barriers in Neural Network Energy Landscape
This provides insights into the optimization challenges in deep learning, though it is incremental as it builds on prior work on loss landscape analysis.
The study investigated the structure of neural network loss landscapes by constructing continuous paths between minima on CIFAR10 and CIFAR100, finding that these paths are essentially flat in both training and test landscapes, indicating minimal barriers between minima.
Training neural networks involves finding minima of a high-dimensional non-convex loss function. Knowledge of the structure of this energy landscape is sparse. Relaxing from linear interpolations, we construct continuous paths between minima of recent neural network architectures on CIFAR10 and CIFAR100. Surprisingly, the paths are essentially flat in both the training and test landscapes. This implies that neural networks have enough capacity for structural changes, or that these changes are small between minima. Also, each minimum has at least one vanishing Hessian eigenvalue in addition to those resulting from trivial invariance.