I am reading Goodfellow et al Deeplearning Book. I found it difficult to understand the difference between the definition of the hypothesis space and representation capacity of a model.
In Chapter 5, it is written about hypothesis space:
One way to control the capacity of a learning algorithm is by choosing its hypothesis space, the set of functions that the learning algorithm is allowed to select as being the solution.
And about representational capacity:
The model speciﬁes which family of functions the learning algorithm can choose from when varying the parameters in order to reduce a training objective. This is called the representational capacity of the model.
If we take the linear regression model as an example and allow our output $y$ to takes polynomial inputs, I understand the hypothesis space as the ensemble of quadratic functions taking input $x$, i.e $y = a_0 + a_1x + a_2x^2$.
How is it different from the definition of the representational capacity, where parameters are $a_0$, $a_1$ and $a_2$?