# Towards understanding deep learning with the natural clustering prior

arXiv: https://arxiv.org/abs/2203.08174 · HTML: https://mlsanity.com/paper/2203.08174/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 81 of its 158 references that are in the map.
- First posted on arXiv 15 Mar 2022.

## Builds on (most cited first, 30 of 81)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Improved Regularization of Convolutional Neural Networks with Cutout](https://mlsanity.com/paper/1708.04552/) (2017)
- [Do ImageNet Classifiers Generalize to ImageNet?](https://mlsanity.com/paper/1902.10811/) (2019)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness](https://mlsanity.com/paper/1811.12231/) (2018)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [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)
- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [AutoAugment: Learning Augmentation Policies from Data](https://mlsanity.com/paper/1805.09501/) (2018)
- [Network Dissection: Quantifying Interpretability of Deep Visual Representations](https://mlsanity.com/paper/1704.05796/) (2017)
- [Speech Recognition with Deep Recurrent Neural Networks](https://mlsanity.com/paper/1303.5778/) (2013)
- [Recognition in Terra Incognita](https://mlsanity.com/paper/1807.04975/) (2018)
- [Linear Mode Connectivity and the Lottery Ticket Hypothesis](https://mlsanity.com/paper/1912.05671/) (2019)

## Abstract (arXiv)

The prior knowledge (a.k.a. priors) integrated into the design of a machine learning system strongly influences its generalization abilities. In the specific context of deep learning, some of these priors are poorly understood as they implicitly emerge from the successful heuristics and tentative approximations of biological brains involved in deep learning design. Through the lens of supervised image classification problems, this thesis investigates the implicit integration of a natural clustering prior composed of three statements: (i) natural images exhibit a rich clustered structure, (ii) image classes are composed of multiple clusters and (iii) each cluster contains examples from a single class. The decomposition of classes into multiple clusters implies that supervised deep learning systems could benefit from unsupervised clustering to define appropriate decision boundaries. Hence, this thesis attempts to identify implicit clustering abilities, mechanisms and hyperparameters in deep learning systems and evaluate their relevance for explaining the generalization abilities of these systems. We do so through an extensive empirical study of the training dynamics as well as the neuron- and layer-level representations of deep neural networks. The resulting collection of experiments provides preliminary evidence for the relevance of the natural clustering prior for understanding deep learning.