Reviews: A graph-theoretic approach to multitasking

The authors lay an ambitious groundwork for studying the multitasking capability of general neural network architectures. They prove a variety of theorems concerning behavior of their defined criteria--the multitasking capacity \alpha--and how it relates to graph connectivity and size via graph matchings and degree. Pros: The problem being studied is quite clearly motivated, and the authors present a genuinely novel new measure for attempting to understand the multitasking capability of networks. The authors fairly systematically calculate bounds on their parameter in a variety of different graph-theoretic scenarios. Cons: It's unclear how practically useful the parameter \alpha will be for real networks currently in use.