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Many of our core assumptions about how neural networks operate remainempirically untested. One common assumption is that convolutional neuralnetworks need to be stable to small translations and deformations to solveimage recognition tasks. For many years, this stability was baked into CNNarchitectures by incorporating interleaved pooling layers. Recently, however,interleaved pooling has largely been abandoned. This raises a number ofquestions: Are our intuitions about deformation stability right at all? Is itimportant? Is pooling necessary for deformation invariance? If not, how isdeformation invariance achieved in its absence? In this work, we rigorouslytest these questions, and find that deformation stability in convolutionalnetworks is more nuanced than it first appears: (1) Deformation invariance isnot a binary property, but rather that different tasks require differentdegrees of deformation stability at different layers. (2) Deformation stabilityis not a fixed property of a network and is heavily adjusted over the course oftraining, largely through the smoothness of the convolutional filters. (3)Interleaved pooling layers are neither necessary nor sufficient for achievingthe optimal form of deformation stability for natural image classification. (4)Pooling confers too much deformation stability for image classification atinitialization, and during training, networks have to learn to counteract thisinductive bias. Together, these findings provide new insights into the role ofinterleaved pooling and deformation invariance in CNNs, and demonstrate theimportance of rigorous empirical testing of even our most basic assumptionsabout the working of neural networks.

Pooling is neither necessary nor sufficient for appropriate deformation stability in CNNs