2019-ICLR-Pooling Is Neither Necessary nor Sufficient for Approp
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Under review as a conference paper at ICLR 2019
POOLING IS NEITHER NECESSARY NOR SUFFICIENT
FOR APPROPRIATE DEFORMATION STABILITY IN CNNS
Anonymous authors
Paper under double-blind review
ABSTRACT
Many of our core assumptions about how neural networks operate remain empiri-
cally untested. One common assumption is that convolutional neural networks need
to be stable to small translations and deformations to solve image recognition tasks.
For many years, this stability was baked into CNN architectures by incorporating
interleaved pooling layers. Recently, however, interleaved pooling has largely been
abandoned. This raises a number of questions: Are our intuitions about deforma-
tion stability right at all? Is it important? Is pooling necessary for deformation
invariance? If not, how is deformation invariance achieved in its absence? In this
work, we rigorously test these questions, and find that deformation stability in
convolutional networks is more nuanced than it first appears: (1) Deformation
invariance is not a binary property, but rather that different tasks require different
degrees of deformation stability at different layers. (2) Deformation stability is
not a fixed property of a network and is heavily adjusted over the course of train-
ing, largely through the smoothness of the convolutional filters. (3) Interleaved
pooling layers are neither necessary nor sufficient for achieving the optimal form
of deformation stability for natural image classification. (4) Pooling confers too
much deformation stability for image classification at initialization, and during
training, networks have to learn to counteract this inductive bias. Together, these
findings provide new insights into the role of interleaved pooling and deformation
invariance in CNNs, and demonstrate the importance of rigorous empirical testing
of even our most basic assumptions about the working of neural networks.
1 INTRODUCTION
Within deep learning, a variety of intuitions have been assumed to be common knowledge without
empirical verification, leading to recent active debate (Rahimi & Recht, 2017; LeCun, 2017; Sculley
et al., 2015; 2018). Nevertheless, many of these core ideas have informed the structure of broad
classes of models, with little attempt to rigorously test these assumptions.
In this paper, we seek to address this issue by undertaking a careful, empirical study of one of the
foundational intuitions informing convolutional neural networks (CNNs) for visual object recognition:
the need to make these models stable to small translations and deformations in the input images. This
intuition runs as follows: much of the variability in the visual domain comes from slight changes in
view, object position, rotation, size, and non-rigid deformations of (e.g.) organic objects; represen-
tations which are invariant to such transformations would (presumably) lead to better performance.
This idea is arguably one of the core principles initially responsible for the architectural choices of
convolutional filters and interleaved pooling LeCun et al. (1998; 2015), as well as the deployment
of parametric data augmentation strategies during training Simard et al. (2003). Yet, despite the
widespread impact of this idea, the relationship between visual object recognition and deformation
stability has not been thoroughly tested, and we do not actually know how modern CNNs realize
deformation stability, if they even do at all.
Moreover, for many years, the very success of CNNs on visual object recognition tasks was thought
to depend on the interleaved pooling layers that purportedly rendered these models insensitive to
small translations and deformations. However, despite this reasoning, recent models have largely
abandoned interleaved pooling layers, achieving similar or greater success without them Springenberg
et al. (2014); He et al. (2016).
1
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