Implicit Equivariance in Convolutional Networks
Convolutional Neural Networks(CNN) are inherently equivariant under translations, however, they do not have an equivalent embedded mechanism to handle other transformations such as rotations and change in scale. Several approaches exist that make CNNs equivariant under other transformation groups by...
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Main Authors | , , , |
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Format | Journal Article |
Language | English |
Published |
28.11.2021
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Subjects | |
Online Access | Get full text |
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Summary: | Convolutional Neural Networks(CNN) are inherently equivariant under
translations, however, they do not have an equivalent embedded mechanism to
handle other transformations such as rotations and change in scale. Several
approaches exist that make CNNs equivariant under other transformation groups
by design. Among these, steerable CNNs have been especially effective. However,
these approaches require redesigning standard networks with filters mapped from
combinations of predefined basis involving complex analytical functions. We
experimentally demonstrate that these restrictions in the choice of basis can
lead to model weights that are sub-optimal for the primary deep learning task
(e.g. classification). Moreover, such hard-baked explicit formulations make it
difficult to design composite networks comprising heterogeneous feature groups.
To circumvent such issues, we propose Implicitly Equivariant Networks (IEN)
which induce equivariance in the different layers of a standard CNN model by
optimizing a multi-objective loss function that combines the primary loss with
an equivariance loss term. Through experiments with VGG and ResNet models on
Rot-MNIST , Rot-TinyImageNet, Scale-MNIST and STL-10 datasets, we show that
IEN, even with its simple formulation, performs better than steerable networks.
Also, IEN facilitates construction of heterogeneous filter groups allowing
reduction in number of channels in CNNs by a factor of over 30% while
maintaining performance on par with baselines. The efficacy of IEN is further
validated on the hard problem of visual object tracking. We show that IEN
outperforms the state-of-the-art rotation equivariant tracking method while
providing faster inference speed. |
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DOI: | 10.48550/arxiv.2111.14157 |