Orientation independent Möbius CNNs
MobiusCNNs
This repository implements and evaluates convolutional networks on the Möbius strip as toy model instantiations of Coordinate Independent Convolutional Networks.
Background (tl;dr)
All derivations and a detailed description of the models are found in Section 5 of our paper. What follows is an informal tl;dr, summarizing the central aspects of Möbius CNNs.
Feature fields on the Möbius strip: A key characteristic of the Möbius strip is its topological twist, making it a non-orientable manifold. Convolutional weight sharing on the Möbius strip is therefore only well defined up to a reflection of kernels. To account for the ambiguity of kernel orientations, one needs to demand that the kernel responses (feature vectors) transform in a predictable way when different orientations are chosen. Mathematically, this transformation is specified by a