Norm-based Generalization Bounds for Compositionally Sparse Neural Networks
This work addresses generalization guarantees for deep learning models, particularly sparse networks, but it is incremental as it builds on existing norm-based bounds with a new focus on compositional sparsity.
The paper tackles the problem of generalization in deep sparse neural networks by proving new Rademacher complexity bounds based on convolutional filter norms, which are theoretically orders of magnitude better than standard bounds and empirically nearly non-vacuous in simple classification tasks.
In this paper, we investigate the Rademacher complexity of deep sparse neural networks, where each neuron receives a small number of inputs. We prove generalization bounds for multilayered sparse ReLU neural networks, including convolutional neural networks. These bounds differ from previous ones, as they consider the norms of the convolutional filters instead of the norms of the associated Toeplitz matrices, independently of weight sharing between neurons. As we show theoretically, these bounds may be orders of magnitude better than standard norm-based generalization bounds and empirically, they are almost non-vacuous in estimating generalization in various simple classification problems. Taken together, these results suggest that compositional sparsity of the underlying target function is critical to the success of deep neural networks.