Highly-nonlinear continuous functions have become a
pervasive model of computation. Despite newsworthy progress, the
practical success of “intelligent” computing is still restricted by
our ability to answer questions regarding their reliability and
quality: How do we rigorously know that a system will do exactly what
we want it to do and nothing else? For traditional software and
hardware systems that primarily use rule-based designs, automated
reasoning has provided the fundamental principles and widely-used
tools for ensuring their quality. However, the rigid symbolic
formulations of typical automated reasoning methods often make them
unsuitable for dealing with computation units that are driven by
numerical and data-driven approaches. I will overview some of our
attempts in bridging this gap. I will highlight how the core challenge
of NP-hardness is shared across discrete and continuous domains, and
how it motivates us to seek the unification of symbolic, numerical,
and statistical methods towards better understanding and handling of
the curse of dimensionality.
4/10/2023