We investigate a recently proposed family of positive-definite kernels that mimic the computation in large neural networks. We examine the properties of these kernels using tools from differential geometry; specifically, we analyze the geometry of surfaces in Hilbert space that are induced by these kernels. When this geometry is described by a Riemannian manifold, we derive results for the metric, curvature, and volume element. Interestingly, though, we find that the simplest kernel in this family does not admit such an interpretation. We explore two variations of these kernels that mimic computation in neural networks with different activation functions. We experiment with these new kernels on several data sets and highlight their general trends in performance for classification.
The authors of these documents have submitted their reports to this technical report series for the purpose of non-commercial dissemination of scientific work. The reports are copyrighted by the authors, and their existence in electronic format does not imply that the authors have relinquished any rights. You may copy a report for scholarly, non-commercial purposes, such as research or instruction, provided that you agree to respect the author's copyright. For information concerning the use of this document for other than research or instructional purposes, contact the authors. Other information concerning this technical report series can be obtained from the Computer Science and Engineering Department at the University of California at San Diego, email@example.com.
[ Search ]