Develop new tools for improving the transparency of AI systems to inspection.

Extend techniques for designing complex systems to be readily verified.

I wonder if sheaf theory could be useful for this. The basic idea of sheaf theory is that you can prove things about a global structure by looking at local structures, and how you 'glue' them together to get the global structure. Michael Robinson has been doing lots of interesting work using sheaf theory to understand networks. For example, here's a presentation of an application of sheaf cohomology to asynchronous computation design.