# Towards Understanding the Generalization Bias of Two Layer Convolutional Linear Classifiers with Gradient Descent

arXiv: https://arxiv.org/abs/1802.04420 · HTML: https://mlsanity.com/paper/1802.04420/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2018.

## Built on by (most cited first, 2 of 2)

- [Which Features are Learnt by Contrastive Learning? On the Role of Simplicity Bias in Class Collapse and Feature Suppression](https://mlsanity.com/paper/2305.16536/) (2023)
- [Principal Components Bias in Over-parameterized Linear Models, and its Manifestation in Deep Neural Networks](https://mlsanity.com/paper/2105.05553/) (2021)

## Abstract (arXiv)

A major challenge in understanding the generalization of deep learning is to explain why (stochastic) gradient descent can exploit the network architecture to find solutions that have good generalization performance when using high capacity models. We find simple but realistic examples showing that this phenomenon exists even when learning linear classifiers --- between two linear networks with the same capacity, the one with a convolutional layer can generalize better than the other when the data distribution has some underlying spatial structure. We argue that this difference results from a combination of the convolution architecture, data distribution and gradient descent, all of which are necessary to be included in a meaningful analysis. We provide a general analysis of the generalization performance as a function of data distribution and convolutional filter size, given gradient descent as the optimization algorithm, then interpret the results using concrete examples. Experimental results show that our analysis is able to explain what happens in our introduced examples.