Spectrally-normalized margin bounds for neural networks
This provides a theoretical tool for understanding generalization in neural networks, but it is incremental as it builds on existing margin and complexity theories.
The paper tackles the problem of deriving generalization bounds for neural networks by introducing a margin-based multiclass bound that scales with spectral complexity, and empirically shows that this bound correlates with Lipschitz constants and excess risks on MNIST and CIFAR-10 datasets, indicating SGD selects predictors with complexity matching task difficulty.
This paper presents a margin-based multiclass generalization bound for neural networks that scales with their margin-normalized "spectral complexity": their Lipschitz constant, meaning the product of the spectral norms of the weight matrices, times a certain correction factor. This bound is empirically investigated for a standard AlexNet network trained with SGD on the mnist and cifar10 datasets, with both original and random labels; the bound, the Lipschitz constants, and the excess risks are all in direct correlation, suggesting both that SGD selects predictors whose complexity scales with the difficulty of the learning task, and secondly that the presented bound is sensitive to this complexity.