  This work investigates the framework and performance issues of the composite
neural network, which is composed of a collection of pre-trained and
non-instantiated neural network models connected as a rooted directed acyclic
graph for solving complicated applications. A pre-trained neural network model
is generally well trained, targeted to approximate a specific function. Despite
a general belief that a composite neural network may perform better than a
single component, the overall performance characteristics are not clear. In
this work, we construct the framework of a composite network, and prove that a
composite neural network performs better than any of its pre-trained components
with a high probability bound. In addition, if an extra pre-trained component
is added to a composite network, with high probability, the overall performance
will not be degraded. In the study, we explore a complicated application --
PM2.5 prediction -- to illustrate the correctness of the proposed composite
network theory. In the empirical evaluations of PM2.5 prediction, the
constructed composite neural network models support the proposed theory and
perform better than other machine learning models, demonstrate the advantages
of the proposed framework.
