[Paper Review] Why do deep convolutional networks generalize so poorly to small image transformations?

Aharon Azulay, Yair Weiss|arXiv (Cornell University)|May 30, 2018

Domain Adaptation and Few-Shot LearningComputer Science299 citations

TL;DR

The paper quantifies how modern CNNs are brittle to tiny image transformations like one-pixel translations or scaling, and analyzes why convolutional architecture and data augmentation fail to guarantee invariance, offering partial solutions like antialiasing and more augmentation.

ABSTRACT

Convolutional Neural Networks (CNNs) are commonly assumed to be invariant to small image transformations: either because of the convolutional architecture or because they were trained using data augmentation. Recently, several authors have shown that this is not the case: small translations or rescalings of the input image can drastically change the network's prediction. In this paper, we quantify this phenomena and ask why neither the convolutional architecture nor data augmentation are sufficient to achieve the desired invariance. Specifically, we show that the convolutional architecture does not give invariance since architectures ignore the classical sampling theorem, and data augmentation does not give invariance because the CNNs learn to be invariant to transformations only for images that are very similar to typical images from the training set. We discuss two possible solutions to this problem: (1) antialiasing the intermediate representations and (2) increasing data augmentation and show that they provide only a partial solution at best. Taken together, our results indicate that the problem of insuring invariance to small image transformations in neural networks while preserving high accuracy remains unsolved.

Motivation & Objective

• Quantify the lack of invariance of modern CNNs to small image deformations.
• Investigate how architectural choices (convolution, subsampling) and data augmentation contribute to brittleness.
• Explain why shift-invariance is not guaranteed by current CNN designs or training practices.
• Evaluate proposed remedies such as antialiasing and increased data augmentation and assess their effectiveness.

Proposed method

• Tested four perturbation protocols that create one-pixel differences (crop, embedding with black background, embedding with inpainting, embedding with size change) on 1000 ImageNet validation images.
• Measured two invariants: (i) P(Top-1 change) and (ii) mean absolute change (MAC) in the top class probability.
• Compared six pretrained CNNs (three from Keras: VGG16, ResNet50, InceptionResNetV2; three from PyTorch: VGG16, ResNet50, DenseNet121).
• Analyzed the impact of layer depth on shiftability by training readout classifiers on intermediate layers and evaluating one-pixel shift effects.
• Presented theoretical discussion on sampling, shiftability, and the Shannon-Nyquist theorem as it applies to CNN subsampling and nonlinearities.
• Evaluated proposed solutions: antialiasing of internal representations and expanded data augmentation.

Experimental results

Research questions

• RQ1 How often do small image transformations cause CNN predictions to change, and how does this vary across architectures and perturbation protocols?
• RQ2 Why do convolutional architectures and data augmentation fail to guarantee invariance under small translations or rescalings?
• RQ3 What is the role of subsampling (strides) and the sampling theorem in yielding or breaking shift invariance in CNNs?
• RQ4 Do antialiasing and increased data augmentation meaningfully improve invariance, and to what extent?
• RQ5 How does the typicality of an image with respect to training data affect a CNN’s vulnerability to small transformations?

Key findings

• A one-pixel perturbation can change a CNN’s top-1 prediction with probability up to about 30%.
• The lack of invariance is observed across multiple architectures and both Keras and PyTorch pretrained models.
• Translation invariance is not guaranteed because subsampling (stride) breaks literal shiftability; a shift-invariant global pool requires shiftable feature maps and proper sampling according to nyquist criteria.
• CNNs learn invariance only for images very similar to training data; when images deviate from photographer biases, sensitivity to small transformations increases.
• Antialiasing of intermediate representations provides only a partial improvement; increased data augmentation helps but does not fully solve the problem, especially for atypical images.
• Deeper layers become less shiftable due to cumulative subsampling and nonlinearities, leading to greater susceptibility to small translations as depth increases.