# On information captured by neural networks: connections with memorization and generalization

arXiv: https://arxiv.org/abs/2306.15918 · HTML: https://mlsanity.com/paper/2306.15918/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 223 references that are in the map.
- First posted on arXiv 28 Jun 2023.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [Extracting Training Data from Diffusion Models](https://mlsanity.com/paper/2301.13188/) (2023)
- [Opening the Black Box of Deep Neural Networks via Information](https://mlsanity.com/paper/1703.00810/) (2017)
- [Unsupervised Label Noise Modeling and Loss Correction](https://mlsanity.com/paper/1904.11238/) (2019)
- [Training Deep Neural Networks on Noisy Labels with Bootstrapping](https://mlsanity.com/paper/1412.6596/) (2014)
- [User-friendly introduction to PAC-Bayes bounds](https://mlsanity.com/paper/2110.11216/) (2021)
- [Adding Gradient Noise Improves Learning for Very Deep Networks](https://mlsanity.com/paper/1511.06807/) (2015)
- [Understanding and Improving Knowledge Distillation](https://mlsanity.com/paper/2002.03532/) (2020)
- [Where is the Information in a Deep Neural Network?](https://mlsanity.com/paper/1905.12213/) (2019)
- [A linearized framework and a new benchmark for model selection for fine-tuning](https://mlsanity.com/paper/2102.00084/) (2021)
- [Subclass Distillation](https://mlsanity.com/paper/2002.03936/) (2020)
- [iCassava 2019 Fine-Grained Visual Categorization Challenge](https://mlsanity.com/paper/1908.02900/) (2019)
- [DNN or k-NN: That is the Generalize vs. Memorize Question](https://mlsanity.com/paper/1805.06822/) (2018)
- [Leveraging Random Label Memorization for Unsupervised Pre-Training](https://mlsanity.com/paper/1811.01640/) (2018)

## Abstract (arXiv)

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.