Here are some more details about the difference between "declining revenues" and "identifying grammatical errors".
In "declining revenues", the word "declining" is a participle: a verb form that is serving as an adjective. The word which it is modifying, "revenues" is the word that would have been the subject if "declining" were an actual verb ("decline") instead of a participle. "Revenues" is the subject with which the actual verb of the sentence ("are", which comes much later) must agree.
In "identifying grammatical errors", "identifying" is a gerund: a verb form that is serving as a noun. So in this case, "identifying" is itself the subject of a sentence. A gerund is always singular, and so the verb for which it is the subject must be singular.
This difference between a participle and a gerund is famous in linguistics, because Noam Chomsky used it to prove that the grammar of English cannot be expressed using a Markov or "finite state" process. Chomsky pointed out that the sentence "Flying planes can be dangerous" means two different things, depending on whether "flying planes" is interpreted as "planes which fly" (where "flying" is a participle) or "the activity of flying planes" (where "flying" is a gerund). For reasons which I don't quite understand, a Markov process cannot express this kind of difference.
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