A Two-Scale Complexity Measure for Deep Learning Models
This provides a theoretical tool for analyzing generalization in deep learning, though it appears incremental as an extension of effective dimension concepts.
The authors introduced a new capacity measure called 2sED for deep learning models, which provably bounds generalization error and correlates well with training error in simulations on standard datasets and architectures.
We introduce a novel capacity measure 2sED for statistical models based on the effective dimension. The new quantity provably bounds the generalization error under mild assumptions on the model. Furthermore, simulations on standard data sets and popular model architectures show that 2sED correlates well with the training error. For Markovian models, we show how to efficiently approximate 2sED from below through a layerwise iterative approach, which allows us to tackle deep learning models with a large number of parameters. Simulation results suggest that the approximation is good for different prominent models and data sets.