# The Deep Bootstrap Framework: Good Online Learners are Good Offline Generalizers

arXiv: https://arxiv.org/abs/2010.08127 · HTML: https://mlsanity.com/paper/2010.08127/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Oct 2020.

## Built on by (most cited first, 11 of 11)

- [Generative Models as a Data Source for Multiview Representation Learning](https://mlsanity.com/paper/2106.05258/) (2021)
- [Exploring the Limits of Large Scale Pre-training](https://mlsanity.com/paper/2110.02095/) (2021)
- [The Evolution of Out-of-Distribution Robustness Throughout Fine-Tuning](https://mlsanity.com/paper/2106.15831/) (2021)
- [Open-set Label Noise Can Improve Robustness Against Inherent Label Noise](https://mlsanity.com/paper/2106.10891/) (2021)
- [RATT: Leveraging Unlabeled Data to Guarantee Generalization](https://mlsanity.com/paper/2105.00303/) (2021)
- [Deconstructing Distributions: A Pointwise Framework of Learning](https://mlsanity.com/paper/2202.09931/) (2022)
- [Evaluating Distributional Distortion in Neural Language Modeling](https://mlsanity.com/paper/2203.12788/) (2022)
- [Knowledge Distillation: Bad Models Can Be Good Role Models](https://mlsanity.com/paper/2203.14649/) (2022)
- [Towards Understanding Generalization via Decomposing Excess Risk Dynamics](https://mlsanity.com/paper/2106.06153/) (2021)
- [Exploration of Dark Chemical Genomics Space via Portal Learning: Applied to Targeting the Undruggable Genome and COVID-19 Anti-Infective Polypharmacology](https://mlsanity.com/paper/2111.14283/) (2021)
- [A Solvable Model of Adaptive Learning Rate Rescaling: Acceleration, Stability & Scaling](https://mlsanity.com/paper/2610.06701/) (2026)

## Abstract (arXiv)

We propose a new framework for reasoning about generalization in deep learning. The core idea is to couple the Real World, where optimizers take stochastic gradient steps on the empirical loss, to an Ideal World, where optimizers take steps on the population loss. This leads to an alternate decomposition of test error into: (1) the Ideal World test error plus (2) the gap between the two worlds. If the gap (2) is universally small, this reduces the problem of generalization in offline learning to the problem of optimization in online learning. We then give empirical evidence that this gap between worlds can be small in realistic deep learning settings, in particular supervised image classification. For example, CNNs generalize better than MLPs on image distributions in the Real World, but this is "because" they optimize faster on the population loss in the Ideal World. This suggests our framework is a useful tool for understanding generalization in deep learning, and lays a foundation for future research in the area.