# The Randomness of Input Data Spaces is an A Priori Predictor for Generalization

arXiv: https://arxiv.org/abs/2106.04181 · HTML: https://mlsanity.com/paper/2106.04181/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 52 references that are in the map.
- First posted on arXiv 8 Jun 2021.

## Builds on (most cited first, 23 of 23)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [A Closer Look at Memorization in Deep Networks](https://mlsanity.com/paper/1706.05394/) (2017)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [The Implicit Bias of Gradient Descent on Separable Data](https://mlsanity.com/paper/1710.10345/) (2017)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks](https://mlsanity.com/paper/1901.08584/) (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)
- [Implicit Regularization in Deep Matrix Factorization](https://mlsanity.com/paper/1905.13655/) (2019)
- [A PAC-Bayesian Approach to Spectrally-Normalized Margin Bounds for Neural Networks](https://mlsanity.com/paper/1707.09564/) (2017)
- [Stronger generalization bounds for deep nets via a compression approach](https://mlsanity.com/paper/1802.05296/) (2018)
- [Norm-Based Capacity Control in Neural Networks](https://mlsanity.com/paper/1503.00036/) (2015)
- [Size-Independent Sample Complexity of Neural Networks](https://mlsanity.com/paper/1712.06541/) (2017)
- [Uniform convergence may be unable to explain generalization in deep learning](https://mlsanity.com/paper/1902.04742/) (2019)
- [Generalization in Deep Learning](https://mlsanity.com/paper/1710.05468/) (2017)
- [A Bayesian Perspective on Generalization and Stochastic Gradient Descent](https://mlsanity.com/paper/1710.06451/) (2017)
- [Non-Vacuous Generalization Bounds at the ImageNet Scale: A PAC-Bayesian Compression Approach](https://mlsanity.com/paper/1804.05862/) (2018)
- [Fisher-Rao Metric, Geometry, and Complexity of Neural Networks](https://mlsanity.com/paper/1711.01530/) (2017)
- [A Priori Estimates of the Population Risk for Two-layer Neural Networks](https://mlsanity.com/paper/1810.06397/) (2018)
- [Deep Neural Networks Learn Non-Smooth Functions Effectively](https://mlsanity.com/paper/1802.04474/) (2018)

## Abstract (arXiv)

Over-parameterized models can perfectly learn various types of data distributions, however, generalization error is usually lower for real data in comparison to artificial data. This suggests that the properties of data distributions have an impact on generalization capability. This work focuses on the search space defined by the input data and assumes that the correlation between labels of neighboring input values influences generalization. If correlation is low, the randomness of the input data space is high leading to high generalization error. We suggest to measure the randomness of an input data space using Maurer's universal. Results for synthetic classification tasks and common image classification benchmarks (MNIST, CIFAR10, and Microsoft's cats vs. dogs data set) find a high correlation between the randomness of input data spaces and the generalization error of deep neural networks for binary classification problems.