[Paper Review] Quantifying Translation-Invariance in Convolutional Neural Networks

Eric Kauderer-Abrams|arXiv (Cornell University)|Dec 10, 2017

Advanced Neural Network Applications8 references81 citations

TL;DR

The paper introduces translation-sensitivity maps to quantify translation-invariance in CNNs and shows data augmentation is the primary driver of invariance, with architecture playing a secondary role.

ABSTRACT

A fundamental problem in object recognition is the development of image representations that are invariant to common transformations such as translation, rotation, and small deformations. There are multiple hypotheses regarding the source of translation invariance in CNNs. One idea is that translation invariance is due to the increasing receptive field size of neurons in successive convolution layers. Another possibility is that invariance is due to the pooling operation. We develop a simple a tool, the translation-sensitivity map, which we use to visualize and quantify the translation-invariance of various architectures. We obtain the surprising result that architectural choices such as the number of pooling layers and the convolution filter size have only a secondary effect on the translation-invariance of a network. Our analysis identifies training data augmentation as the most important factor in obtaining translation-invariant representations of images using convolutional neural networks.

Motivation & Objective

• Develop a tool to visualize and quantify translation-invariance in CNNs.
• Evaluate how architectural choices (depth, pooling, filter size) affect translation-invariance.
• Assess the impact of training data augmentation on translation-invariance.
• Provide quantitative measures to compare different CNN architectures on translation invariance.

Proposed method

• Introduce translation-sensitivity maps to visualize output changes under input translations.
• Define a normalized distance in score space between base and translated inputs.
• Compute a radial translation-sensitivity function as a one-dimensional summary.
• Train multiple CNN architectures on MNIST with and without data augmentation.
• Use Adam optimization and cross-entropy loss to train networks and evaluate on test data.
• Compare networks by translation-invariance using averaged translation-sensitivity maps.

Experimental results

Research questions

• RQ1 To what extent are CNN representations translation-invariant?
• RQ2 Which features of CNNs (architecture vs. training data) predominantly determine translation-invariance?
• RQ3 How do different amounts of convolutional/pooling layers affect translation-invariance?
• RQ4 Does input translation augmentation during training enhance translation-invariance more than architectural changes?

Key findings

• Data augmentation is the most important factor in achieving translation-invariant representations.
• Networks trained with augmented data are significantly more translation-invariant than those trained without augmentation.
• Architectural features (number of convolution/pooling layers, filter size) play a secondary role compared to augmentation.
• Deeper networks and larger filter sizes can improve invariance, but this benefit relies on augmented training data.
• Translation-invariance is not inherent to CNN architecture but can be learned from data variations.