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Compositional Models for Complex Systems 263

semantic theory is a substantial project, beyond the scope of this chapter. At
least in part this is because designs are multimodal: at a minimum they must
incorporate both geometry and composition for physical components,
code, and protocols for logical components, and assembly and installation
procedures for both. Nonetheless, a formalization of the design process
using algebras and operads sets the stage and clarifies the requirements
for such an undertaking.

13.7 ARCHITECTURES FOR LEARNING

In this section we sketch an example of how the formalization of system rep-
resentation through compositional architectures can provide a platform for
both the application and the management of AI techniques.
The bread and butter of contemporary AI is the automation of specific
information-processing tasks, such as image classification or voice transcrip-
tion. There are already many successful applications of such methods, and
these will only continue to improve with new methods and more powerful
devices.
However, the application of these methods in complex systems is still
relatively inflexible. Training data for the problem must be collected and
wrangled into a form appropriate for AI algorithms. The information pro-
cessing that connects AI to applications is usually done by hand on an ad hoc
basis. What is required here is not new learning methods per se, but rather
methods for more easily and efficiently specifying learning problems and
integrating their results.
System architectures can help with this by explicitly representing the
state parameters of the system and clustering them in component decompo-
sitions. Properly implemented, this could allow for the automatic generation
of learning problem specifications based on available parameters. For exam-
ple, the state space and the loss function for the control process in Fig. 13.1B
can be easily extracted from the parameters of the settings, measured tem-
perature, and activity of the heater and AC, and the stream of historical data
can be organized along the same lines.
This is an object-level application: we want to use AI to solve a problem
inside our system. Architectures also offer up new possibilities for metalevel
applications: using AI to solve problems about our system.
Ad hoc system design and provisioning is a good example. In net-
worked systems like the IoT, we expect to have an infrastructure of
devices, data, services, and human and organizational actors available for
commission; we must assemble a system from these pieces to achieve a