Visible to the public On the Geometry of Rectifier Convolutional Neural Networks

TitleOn the Geometry of Rectifier Convolutional Neural Networks
Publication TypeConference Paper
Year of Publication2019
AuthorsGamba, Matteo, Azizpour, Hossein, Carlsson, Stefan, Björkman, Mårten
Conference Name2019 IEEE/CVF International Conference on Computer Vision Workshop (ICCVW)
Date PublishedOct. 2019
ISBN Number 978-1-7281-5023-9
KeywordsComplexity theory, compositionality, Computer vision, Computing Theory and Compositionality, convolution, Convolutional codes, convolutional layers, convolutional networks, convolutional neural nets, convolutional neural networks, Deep Learning, Geometry, gradient descent, Human Behavior, human factors, inductive bias, Kernel, learning (artificial intelligence), natural data, preactivation space, preimage, pubcrawl, rectifier convolutional neural networks, Tensile stress, trained rectifier networks, understanding

While recent studies have shed light on the expressivity, complexity and compositionality of convolutional networks, the real inductive bias of the family of functions reachable by gradient descent on natural data is still unknown. By exploiting symmetries in the preactivation space of convolutional layers, we present preliminary empirical evidence of regularities in the preimage of trained rectifier networks, in terms of arrangements of polytopes, and relate it to the nonlinear transformations applied by the network to its input.

Citation Keygamba_geometry_2019