If we consider a supervised model as a set of parameterized functions, we can define representational capacity as the intrinsic ability of a certain generic function to map a relatively large number of data distributions. To understand this concept, let's consider a function f(x) that admits infinite derivatives, and rewrite it as a Taylor expansion:
We can decide to take only the first n terms, so to have an n-degree polynomial function. Consider a simple bi-dimensional scenario with six functions (starting from a linear one); we can observe the different behavior with a small set of data points:
Different behavior produced ...
