There is a familiar ambiguity in the usage of the term "subject". Sometimes, we speak of the subject of a verb, sometimes of the subject of a predicate (a VP) or a sentence. Let us assume the second sense of the term "subject". Then it is the VP that determines the θ-role of the subject, compositionally. The subject is not governed by the verb as the complements of the verb are governed by it [...] it is natural to regard the subject as "subject-of-VP" or "subject-of-S" rather than "subject-of-verb".
- Chomsky (1993), a pag.103-104

[…] let us introduce the term "SUBJECT" having the following sense: the subject of an infinitive, an NP or a small clause [...] is a SUBJECT [...] The notion SUBJECT accords with the idea that the subject is the "most prominent nominal element" in some sense, taking INFL to be the head of S.
- Chomsky (1993), a pag.209