On information captured by neural networks: connections with
  memorization and generalization
Hrayr Harutyunyan
Despite the popularity and success of deep learning, there is limited
understanding of when, how, and why neural networks generalize to unseen
examples. Since learning can be seen as extracting information from data, we
formally study information captured by neural networks during training.
Specifically, we start with viewing learning in presence of noisy labels from
an information-theoretic perspective and derive a learning algorithm that
limits label noise information in weights. We then define a notion of unique
information that an individual sample provides to the training of a deep
network, shedding some light on the behavior of neural networks on examples
that are atypical, ambiguous, or belong to underrepresented subpopulations. We
relate example informativeness to generalization by deriving nonvacuous
generalization gap bounds. Finally, by studying knowledge distillation, we
highlight the important role of data and label complexity in generalization.
Overall, our findings contribute to a deeper understanding of the mechanisms
underlying neural network generalization.