  The quest for successful variational quantum machine learning (QML) relies on
the design of suitable parametrized quantum circuits (PQCs), as analogues to
neural networks in classical machine learning. Successful QML models must
fulfill the properties of trainability and non-dequantization, among others.
Recent works have highlighted an intricate interplay between trainability and
dequantization of such models, which is still unresolved. In this work we
contribute to this debate from the perspective of machine learning, proving a
number of results identifying, among others when trainability and
non-dequantization are not mutually exclusive. We begin by providing a number
of new somewhat broader definitions of the relevant concepts, compared to what
is found in other literature, which are operationally motivated, and consistent
with prior art. With these precise definitions given and motivated, we then
study the relation between trainability and dequantization of variational QML.
Next, we also discuss the degrees of "variationalness" of QML models, where we
distinguish between models like the hardware efficient ansatz and quantum
kernel methods. Finally, we introduce recipes for building PQC-based QML models
which are both trainable and nondequantizable, and corresponding to different
degrees of variationalness. We do not address the practical utility for such
models. Our work however does point toward a way forward for finding more
general constructions, for which finding applications may become feasible.
