Generalization Bounds for Rank-sparse Neural Networks

The paper titled 'Generalization Bounds for Rank-sparse Neural Networks' explores the observed phenomenon of the bottleneck rank property in neural networks, where deeper architectures tend to have low rank in their activations and weights. This characteristic is significant as it allows for the establishment of generalization bounds that can enhance our understanding of neural network performance. By proving that these bounds can exploit the low rank structure of weight matrices, the authors provide a framework for analyzing sample complexity, which is defined as \widetilde{O}(WrL^2), where W is the width, L is the depth, and r is the rank of the network. This research aligns with previous findings that regularizing linear networks with weight decay is equivalent to minimizing the Schatten p quasi norm, further emphasizing the importance of understanding the mathematical properties of neural networks in improving their efficiency and effectiveness.