Deep Quaternion Networks

The field of deep learning has seen significant advancement in recent years. However, much of the existing work has been focused on real-valued numbers. Recent work has shown that a deep learning system using the complex numbers can be deeper for a fixed parameter budget compared to its real-valued counterpart. In this work, we explore the benefits of generalizing one step further into the hyper-complex numbers, quaternions specifically, and provide the architecture components needed to build deep quaternion networks. We develop the theoretical basis by reviewing quaternion convolutions, developing a novel quaternion weight initialization scheme, and developing novel algorithms for quaternion batch-normalization. These pieces are tested in a classification model by end-to-end training on the CIFAR-10 and CIFAR-100 data sets and a segmentation model by end-to-end training on the KITTI Road Segmentation data set. These quaternion networks show improved convergence compared to real-valued and complex-valued networks, especially on the segmentation task, while having fewer parametersComment: IJCNN 2018, 8 pages, 1 figur

Avant-Garde, Kitsch and Law

Fifty years ago, in the Fall, 1939, issue of Partisan Review, Clement Greenberg published an essay entitles, Avant-Garde and Kitsch

Confronting the Politics and Law Behind Battles over the ICC’s Bashir Indictment

Nesrine Malik points in the wrong direction in arguing that charges of genocide embarrass the ICC more than they do Omar al-Bashir. The embarrassment here should come from those, such as Malik, who snidely downplay the level of war crimes committed in Darfur, who discuss genocide as if it is a cultural rather than political matter (does Malik seriously think genocide ever has anything to do with a country’s cultural traditions, as she says in defending Sudan?), or who naively give credence to predictable political push-back from Sudan and its allies. The ICC faces serious legal and political obstacles, some of its own making. These obstacles, however, must be faced and overcome, not used as an excuse to cripple the ICC