Towards understanding deep learning with the natural clustering prior

TL;DR

This paper investigates how the natural clustering prior, reflecting the inherent clustered structure of natural images, influences deep learning generalization by analyzing training dynamics and representations.

Contribution

It provides empirical evidence on the implicit clustering abilities and mechanisms in deep neural networks, linking natural image structure to generalization.

Findings

Deep networks exhibit implicit clustering behaviors.

Clustering prior impacts decision boundary formation.

Training dynamics reveal clustering-related representations.

Abstract

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.