Bulk-boundary decomposition of neural networks
Researchers have introduced the bulk-boundary decomposition, a novel framework for analyzing the training dynamics of deep neural networks. This approach separates the network's Lagrangian into a data-independent bulk term and a data-dependent boundary term. The bulk term characterizes the inherent dynamics influenced by network architecture and activation functions, while the boundary term reflects the stochastic interactions arising from training samples at the input and output layers. This decomposition reveals the local and homogeneous structure within deep networks, leading to the derivation of an energy continuity equation. AI
IMPACT Introduces a new theoretical lens for understanding and potentially optimizing neural network training processes.