  Generalisation in machine learning often relies on the ability to encode
structures present in data into an inductive bias of the model class. To
understand the power of quantum machine learning, it is therefore crucial to
identify the types of data structures that lend themselves naturally to quantum
models. In this work we look to quantum contextuality -- a form of
nonclassicality with links to computational advantage -- for answers to this
question. We introduce a framework for studying contextuality in machine
learning, which leads us to a definition of what it means for a learning model
to be contextual. From this, we connect a central concept of contextuality,
called operational equivalence, to the ability of a model to encode a linearly
conserved quantity in its label space. A consequence of this connection is that
contextuality is tied to expressivity: contextual model classes that encode the
inductive bias are generally more expressive than their noncontextual
counterparts. To demonstrate this, we construct an explicit toy learning
problem -- based on learning the payoff behaviour of a zero-sum game -- for
which this is the case. By leveraging tools from geometric quantum machine
learning, we then describe how to construct quantum learning models with the
associated inductive bias, and show through our toy problem that they
outperform their corresponding classical surrogate models. This suggests that
understanding learning problems of this form may lead to useful insights about
the power of quantum machine learning.
