# A practical generalization metric for deep networks benchmarking

arXiv: https://arxiv.org/abs/2409.01498 · HTML: https://mlsanity.com/paper/2409.01498/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 47 references that are in the map.
- First posted on arXiv 2 Sep 2024.

## Builds on (most cited first, 30 of 31)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [Fantastic Generalization Measures and Where to Find Them](https://mlsanity.com/paper/1912.02178/) (2019)
- [A PAC-Bayesian Approach to Spectrally-Normalized Margin Bounds for Neural Networks](https://mlsanity.com/paper/1707.09564/) (2017)
- [Size-Independent Sample Complexity of Neural Networks](https://mlsanity.com/paper/1712.06541/) (2017)
- [On the Optimization of Deep Networks: Implicit Acceleration by Overparameterization](https://mlsanity.com/paper/1802.06509/) (2018)
- [Generalization Bounds of Stochastic Gradient Descent for Wide and Deep Neural Networks](https://mlsanity.com/paper/1905.13210/) (2019)
- [Deep learning generalizes because the parameter-function map is biased towards simple functions](https://mlsanity.com/paper/1805.08522/) (2018)
- [A Universal Law of Robustness via Isoperimetry](https://mlsanity.com/paper/2105.12806/) (2021)
- [Towards Understanding the Role of Over-Parametrization in Generalization of Neural Networks](https://mlsanity.com/paper/1805.12076/) (2018)
- [Non-Vacuous Generalization Bounds at the ImageNet Scale: A PAC-Bayesian Compression Approach](https://mlsanity.com/paper/1804.05862/) (2018)
- [Generalization Bounds of SGLD for Non-convex Learning: Two Theoretical Viewpoints](https://mlsanity.com/paper/1707.05947/) (2017)
- [SGD Learns Over-parameterized Networks that Provably Generalize on Linearly Separable Data](https://mlsanity.com/paper/1710.10174/) (2017)
- [In Search of Robust Measures of Generalization](https://mlsanity.com/paper/2010.11924/) (2020)
- [PAC-Bayes Compression Bounds So Tight That They Can Explain Generalization](https://mlsanity.com/paper/2211.13609/) (2022)
- [Non-Vacuous Generalization Bounds for Large Language Models](https://mlsanity.com/paper/2312.17173/) (2023)
- [NeurIPS 2020 Competition: Predicting Generalization in Deep Learning](https://mlsanity.com/paper/2012.07976/) (2020)
- [Towards Certifying L-infinity Robustness using Neural Networks with L-inf-dist Neurons](https://mlsanity.com/paper/2102.05363/) (2021)
- [Generalization bounds for deep learning](https://mlsanity.com/paper/2012.04115/) (2020)
- [Representation Based Complexity Measures for Predicting Generalization in Deep Learning](https://mlsanity.com/paper/2012.02775/) (2020)
- [Why Robust Generalization in Deep Learning is Difficult: Perspective of Expressive Power](https://mlsanity.com/paper/2205.13863/) (2022)
- [Robustness and Generalization via Generative Adversarial Training](https://mlsanity.com/paper/2109.02765/) (2021)
- [Complexity, Statistical Risk, and Metric Entropy of Deep Nets Using Total Path Variation](https://mlsanity.com/paper/1902.00800/) (2019)
- [Generalization Bounds with Data-dependent Fractal Dimensions](https://mlsanity.com/paper/2302.02766/) (2023)
- [When Representations Align: Universality in Representation Learning Dynamics](https://mlsanity.com/paper/2402.09142/) (2024)
- [It Is All About Data: A Survey on the Effects of Data on Adversarial Robustness](https://mlsanity.com/paper/2303.09767/) (2023)

## Built on by (most cited first, 1 of 1)

- [Failure Modes for Deep Learning-Based Online Mapping: How to Measure and Address Them](https://mlsanity.com/paper/2603.19852/) (2026)

## Abstract (arXiv)

There is an ongoing and dedicated effort to estimate bounds on the generalization error of deep learning models, coupled with an increasing interest with practical metrics that can be used to experimentally evaluate a model's ability to generalize. This interest is not only driven by practical considerations but is also vital for theoretical research, as theoretical estimations require practical validation. However, there is currently a lack of research on benchmarking the generalization capacity of various deep networks and verifying these theoretical estimations. This paper aims to introduce a practical generalization metric for benchmarking different deep networks and proposes a novel testbed for the verification of theoretical estimations. Our findings indicate that a deep network's generalization capacity in classification tasks is contingent upon both classification accuracy and the diversity of unseen data. The proposed metric system is capable of quantifying the accuracy of deep learning models and the diversity of data, providing an intuitive and quantitative evaluation method, a trade-off point. Furthermore, we compare our practical metric with existing generalization theoretical estimations using our benchmarking testbed. It is discouraging to note that most of the available generalization estimations do not correlate with the practical measurements obtained using our proposed practical metric. On the other hand, this finding is significant as it exposes the shortcomings of theoretical estimations and inspires new exploration.