Christine Allen-Blanchette

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In this paper, we explore the exponential map and its inverse, the logarithm map, for the group SIM(n) of similarity transformations in &#x211D;<sup>n</sup> which are the composition of a rotation, a translation and a uniform scaling. We give a formula for the exponential map and we prove that it is surjective. We give an explicit formula for the case of n(More)
Convolutional neural networks (CNNs) are equivariant with respect to translation; a translation in the input causes a translation in the output. Attempts to generalize equivariance have concentrated on rotations. In this paper, we combine the idea of the spatial transformer, and the canonical coordinate representations of groups (polar transform) to realize(More)
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