  Convex piecewise quadratic (PWQ) functions frequently appear in control and
elsewhere. For instance, it is well-known that the optimal value function (OVF)
as well as Q-functions for linear MPC are convex PWQ functions. Now, in
learning-based control, these functions are often represented with the help of
artificial neural networks (NN). In this context, a recurring question is how
to choose the topology of the NN in terms of depth, width, and activations in
order to enable efficient learning. An elegant answer to that question could be
a topology that, in principle, allows to exactly describe the function to be
learned. Such solutions are already available for related problems. In fact,
suitable topologies are known for piecewise affine (PWA) functions that can,
for example, reflect the optimal control law in linear MPC. Following this
direction, we show in this paper that convex PWQ functions can be exactly
described by max-out-NN with only one hidden layer and two neurons.
