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Abstract

Despite the approximate invariance to scale learned in deep Convolutional Neural Networks (CNNs) trained on natural images, intermediate layers have been shown to contain information of scale while the invariance is only obtained in the final layers. In this paper, we experimentally analyze how this scale information is encoded in the hidden layers. Linear regression of scale is used to (i) evaluate whether scale information can be encoded, at a given layer, by individual response maps or a combination of many of them is necessary; (ii) evaluate whether the encoding of scale is shared among classes. If we can find a direction representative of scale variations in the hidden space, is this consistent across the data manifold? Or is it rather encoded locally within class-specific neighborhoods? We observe that scale information is encoded as a combination of a few response maps (around 3%) and that the encoding is relatively consistent across classes, with some amount of class-specific encoding.

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