We study the effect of injecting local scale equivariance into Convolutional Neural Networks. This is done by applying each convolutional filter at multiple scales. The output is a vector field encoding for the maximally activating scale and the scale itself, which is further processed by the following convolutional layers. This allows all the intermediate representations to be locally scale equivariant. We show that this improves the performance of the model by over 20 in the scale equivariant task of regressing the scaling factor applied to randomly scaled MNIST digits. Furthermore, we find it also useful for scale invariant tasks, such as the actual classification of randomly scaled digits. This highlights the usefulness of allowing for a compact representation that can also learn relationships between different local scales by keeping internal scale equivariance.
The modified convolution operator presented by @cite_11 is locally scale invariant and consists of all the elements shown in Fig. , except that the output consists only of the magnitude map. If we apply it to an image and look at the value at a single location of the output, small variations in scale of the underlying local object will have no effect on this value (see Fig. middle). This is precisely the sought behavior. However, if these scale variations contained information useful for the task at hand but were discarded, we would be hampering the model's performance. For instance, in histology and cytology, the sizes of cells and organelles can provide hints about their functionality, while in scene understanding, apparent object sizes implicitly encode distance from the camera and can be valuable information for scene segmentation @cite_3 .
@cite_3 @cite_11
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Many existing scene parsing methods adopt Convolutional Neural Networks with fixed-size receptive fields, which frequently result in inconsistent predictions of large objects and invisibility of small objects. To tackle this issue, we propose a scale-adaptive convolution to acquire flexiblesize receptive fields during scene parsing. Through adding a new scale regression layer, we can dynamically infer the position-adaptive scale coefficients which are adopted to resize the convolutional patches. Consequently, the receptive fields can be adjusted automatically according to the various sizes of the objects in scene images. Thus, the problems of invisible small objects and inconsistent large-object predictions can be alleviated. Furthermore, our proposed scale-adaptive convolutions are not only differentiable to learn the convolutional parameters and scale coefficients in an end-to-end way, but also of high parallelizability for the convenience of GPU implementation. Additionally, since the new scale regression layers are learned implicitly, any extra training supervision of object sizes is unnecessary. Extensive experiments on Cityscapes and ADE20K datasets well demonstrate the effectiveness of the proposed scaleadaptive convolutions. Convolutional Neural Networks (ConvNets) have shown excellent results on many visual classification tasks. With the exception of ImageNet, these datasets are carefully crafted such that objects are well-aligned at similar scales. Naturally, the feature learning problem gets more challenging as the amount of variation in the data increases, as the models have to learn to be invariant to certain changes in appearance. Recent results on the ImageNet dataset show that given enough data, ConvNets can learn such invariances producing very discriminative features [1]. But could we do more: use less parameters, less data, learn more discriminative features, if certain invariances were built into the learning process? In this paper we present a simple model that allows ConvNets to learn features in a locally scale-invariant manner without increasing the number of model parameters. We show on a modified MNIST dataset that when faced with scale variation, building in scale-invariance allows ConvNets to learn more discriminative features with reduced chances of over-fitting.