Marissa Pastor, Juyong Song, Danh-Tai Hoang, Junghyo Jo
Feedforward neural networks have been investigated to understand learning and memory, as well as applied to numerous practical problems in pattern classification. It is a rule of thumb that more complex tasks require larger networks. However, the design of optimal network architectures for specific tasks is still an unsolved fundamental problem. In this study, we consider three-layered neural networks for memorizing binary patterns. We developed a new complexity measure of binary patterns, and estimated the minimal network size for memorizing them as a function of their complexity. We formulated the minimal network size for regular, random, and complex patterns. In particular, the minimal size for complex patterns, which are neither ordered nor disordered, was predicted by measuring their Hamming distances from known ordered patterns. Our predictions agree with simulations based on the back-propagation algorithm. © 2016 Elsevier B.V.
Asia Pacific Center for Theoretical Physics, Pohang, South Korea; Department of Physics, University of San Carlos Talamban, Cebu, Philippines; Department of Physics, Pohang University of Science and Technology, Pohang, South Korea; Department of Natural Sciences, Quang Binh University, Dong Hoi, Viet Nam
