# Predicting the generalization gap in neural networks using topological data analysis

arXiv: https://arxiv.org/abs/2203.12330 · HTML: https://mlsanity.com/paper/2203.12330/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 77 references that are in the map.
- First posted on arXiv 23 Mar 2022.

## Builds on (most cited first, 30 of 39)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [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)
- [Size-Independent Sample Complexity of Neural Networks](https://mlsanity.com/paper/1712.06541/) (2017)
- [The Marginal Value of Adaptive Gradient Methods in Machine Learning](https://mlsanity.com/paper/1705.08292/) (2017)
- [Why do deep convolutional networks generalize so poorly to small image transformations?](https://mlsanity.com/paper/1805.12177/) (2018)
- [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)
- [Predicting the Generalization Gap in Deep Networks with Margin Distributions](https://mlsanity.com/paper/1810.00113/) (2018)
- [Stochastic gradient descent performs variational inference, converges to limit cycles for deep networks](https://mlsanity.com/paper/1710.11029/) (2017)
- [Fisher-Rao Metric, Geometry, and Complexity of Neural Networks](https://mlsanity.com/paper/1711.01530/) (2017)
- [Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topology](https://mlsanity.com/paper/1812.09764/) (2018)
- [Intrinsic Dimension, Persistent Homology and Generalization in Neural Networks](https://mlsanity.com/paper/2111.13171/) (2021)
- [Hausdorff Dimension, Heavy Tails, and Generalization in Neural Networks](https://mlsanity.com/paper/2006.09313/) (2020)
- [Geometry Score: A Method For Comparing Generative Adversarial Networks](https://mlsanity.com/paper/1802.02664/) (2018)
- [giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Exploration](https://mlsanity.com/paper/2004.02551/) (2020)
- [Computing the Testing Error without a Testing Set](https://mlsanity.com/paper/2005.00450/) (2020)
- [Generalization in Deep Networks: The Role of Distance from Initialization](https://mlsanity.com/paper/1901.01672/) (2019)
- [NeurIPS 2020 Competition: Predicting Generalization in Deep Learning](https://mlsanity.com/paper/2012.07976/) (2020)
- [Adaptive Hierarchical Down-Sampling for Point Cloud Classification](https://mlsanity.com/paper/1904.08506/) (2019)
- [On Characterizing the Capacity of Neural Networks using Algebraic Topology](https://mlsanity.com/paper/1802.04443/) (2018)
- [Topological Approaches to Deep Learning](https://mlsanity.com/paper/1811.01122/) (2018)
- [A Framework for Differential Calculus on Persistence Barcodes](https://mlsanity.com/paper/1910.00960/) (2019)
- [Representation Based Complexity Measures for Predicting Generalization in Deep Learning](https://mlsanity.com/paper/2012.02775/) (2020)
- [Exposition and Interpretation of the Topology of Neural Networks](https://mlsanity.com/paper/1810.03234/) (2018)
- [Evaluating the Disentanglement of Deep Generative Models through Manifold Topology](https://mlsanity.com/paper/2006.03680/) (2020)

## Built on by (most cited first, 9 of 9)

- [Topological Data Analysis for Neural Network Analysis: A Comprehensive Survey](https://mlsanity.com/paper/2312.05840/) (2023)
- [Importance attribution in neural networks by means of persistence landscapes of time series](https://mlsanity.com/paper/2302.03132/) (2023)
- [One Period to Rule Them All: Identifying Critical Learning Periods in Deep Networks](https://mlsanity.com/paper/2506.15954/) (2025)
- [HOLE: Homological Observation of Latent Embeddings for Neural Network Interpretability](https://mlsanity.com/paper/2512.07988/) (2025)
- [TopoGeoScore: A Self-Supervised Source-Only Geometric Framework for OOD Checkpoint Selection](https://mlsanity.com/paper/2605.08870/) (2026)
- [Deciphering Two Training Clocks in Grokking via Deep Linear Network Theory with Conditional ReLU Reduction](https://mlsanity.com/paper/2606.05863/) (2026)
- [Is Supervised Learning Really That Different from Unsupervised?](https://mlsanity.com/paper/2505.11006/) (2025)
- [Upper Bounds on the Generalization Error of Deep Learning Models via Local Robustness and Stability](https://mlsanity.com/paper/2606.16883/) (2026)
- [BettiSplit: Topology-Guided Privacy-Aware Split Learning Against Feature Inversion and Gradient Leakage](https://mlsanity.com/paper/2607.24556/) (2026)

## Abstract (arXiv)

Understanding how neural networks generalize on unseen data is crucial for designing more robust and reliable models. In this paper, we study the generalization gap of neural networks using methods from topological data analysis. For this purpose, we compute homological persistence diagrams of weighted graphs constructed from neuron activation correlations after a training phase, aiming to capture patterns that are linked to the generalization capacity of the network. We compare the usefulness of different numerical summaries from persistence diagrams and show that a combination of some of them can accurately predict and partially explain the generalization gap without the need of a test set. Evaluation on two computer vision recognition tasks (CIFAR10 and SVHN) shows competitive generalization gap prediction when compared against state-of-the-art methods.