2018
DOI: 10.1007/s11263-018-1098-y
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Understanding Image Representations by Measuring Their Equivariance and Equivalence

Abstract: Despite the importance of image representations such as histograms of oriented gradients and deep Convolutional Neural Networks (CNN), our theoretical understanding of them remains limited. Aimed at filling this gap, we investigate two key mathematical properties of representations: equivariance and equivalence. Equivariance studies how transformations of the input image are encoded by the representation, invariance being a special case where a transformation has no effect. Equivalence studies whether two repr… Show more

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Cited by 58 publications
(20 citation statements)
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“…Further, “efference copy” signals (Colby et al, 1992; Crapse and Sommer 2007), which signal the magnitude and direction of movements between samples, might also lead to predictable shifts in the embedding space. This intrinsic information about the sampling process could enable the system to learn representations that are “equivariant”, as opposed to “invariant”, over identity-preserving transformations (c.f., Lenc and Vedaldi, 2015; Bouchacourt et al, 2021).…”
Section: Discussionmentioning
confidence: 99%
“…Further, “efference copy” signals (Colby et al, 1992; Crapse and Sommer 2007), which signal the magnitude and direction of movements between samples, might also lead to predictable shifts in the embedding space. This intrinsic information about the sampling process could enable the system to learn representations that are “equivariant”, as opposed to “invariant”, over identity-preserving transformations (c.f., Lenc and Vedaldi, 2015; Bouchacourt et al, 2021).…”
Section: Discussionmentioning
confidence: 99%
“…To handle such ambiguity, the image generation in RSL-Net [39] is conditional on both a satellite image and a live radar image, where the exact appearance of the synthetic image is dictated by the live radar image, and the synthetic image is pixel-wise aligned to the satellite image. In particular, as CNNs are non-equivariant 2 to rotation [26], RSL-Net seeks to infer the rotation offset prior to image generation:…”
Section: B Image Generation Vs Point Learningmentioning
confidence: 99%
“…In an attempt to better understand the properties of a CNN, some recent vision works have focused on analyzing their internal representations (Szegedy et al 2014;Yosinski et al 2014;Lenc and Vedaldi 2015;Mahendran and Vedaldi 2015;Zeiler and Fergus 2014;Simonyan et al 2014;Agrawal et al 2014;Zhou et al 2015;Eigen et al 2013). Some of these investigated properties of the network, like stability (Szegedy et al 2014), feature transferability (Yosinski et al 2014), equivariance, invariance and equivalence (Lenc and Vedaldi 2015), the ability to reconstruct the input (Mahendran and Vedaldi 2015) and how the number of layers, filters and parameters affects the network performance (Agrawal et al 2014;Eigen et al 2013). Zeiler and Fergus (2014) use deconvolutional networks to visualize locally optimal visual inputs for individual filters.…”
Section: Related Workmentioning
confidence: 99%