Page 264 - Artificial Intelligence for the Internet of Everything

242 Artificial Intelligence for the Internet of Everything

the law, we need (warranted) confidence that these systems will perform as
we expect them to. Traditionally we have relied on extensive testing to
identify defects in engineered systems, but this is insufficient for hybrid com-
putational physical systems.
First, AI systems often continue to learn and improve while in operation,
so performance tomorrow may not be the same as it is today. Second, the
space of input parameters for even a moderately complex IoT system is
unworkably large, and the environmental interactions that lead to prob-
lems may be rare and unexpected. Worst of all, as we have seen with
the Volkswagen emissions scandal (EPA United States Environmental
Protection Agency, 2017), a combination of AI and IoT can support
systems that actively evade testing measures.
One possible avenue for avoiding this problem is to import some of the
formal methods of validation and verification (V&V) from computer sci-
ence. Although this field has its own problems, as evidenced by a never-
ending stream of vulnerabilities and malware, it also offers concrete
approaches for dealing with some of the problems outlined above. Further-
more, failures in computer systems’ V&V often turn on physical consider-
ations, such as timing, suggesting that better integration between logical and
physical analyses are needed on both sides.
We believe that formal methods from a branch of mathematics called cat-
egory theory (CT) can help to bridge this divide. One reason is that CT
methods have already been applied extensively to both computational sys-
tems (Barr & Wells, 1990; Fong, Spivak, & Tuy eras, 2017; Spivak, 2012)
and physical ones (Baez & Fong, 2015; Baez & Pollard, 2017; Vagner,
Spivak, & Lerman, 2015). Moreover, CT has demonstrated particular suc-
cess in linking physical and computational analyses in the field of quantum
computing (Coecke & Kissinger, 2017; Selinger, 2004). More generally,
CT provides a generic theory of open and interconnected systems (Fong,
Soboci nski, & Rapisarda, 2016), offering a common conceptual space for
mixing AI, IoT, and traditional processes.
The central feature of categorical structures is compositionality, the abil-
ity to build up complex systems by linking together simpler components.
Given the range in the systems of interest we must understand
“component” in the broadest sense, to include humans (as both subjects
and actors) as well as physical entities and algorithms. Some components like
IoT sensors and actuators require description at both levels, and humans also
incorporate both physical and logical (and stochastic) behaviors. Further-
more, compositional methods lend themselves to a systems-of-systems