This postmodifier is an adjective phrase headed by "based" .The whole part after "based" is an adjective complement which is in this case obligatory since the adjective "based" and the following preposition "on" form one lexical unit. Precisely,adjective and its complementing preposition are inseparable since you will automatically add "on" after saying "based" in such contexts.( I suppose you will
).Of course, the bond between the adjective and its complement need not to be so strong and obligatory like it is in the case of "based on". So, "on the linguistic input" is an adjective complement by its function and a prepositional phrase by its form.