It's pretty much a linear growth, but with some complexities. Basically, the number of ships goes up in a linear fashion based on the AI Progress. The exact number of ships added per AIP depend on the difficulty level you are playing on, the types of AI, etc. Suffice it to say, the number of ships in a wave (or a reinforcement event) are based on a variety of multipliers, and AIP is one of them -- perhaps the most significant one.
Then, however, the AIP also affects the tech level of the AI, as I'm sure you know. When the tech level goes up, there is a corresponding drop in the number of ships it can then build. That is based off the same number of how many fewer percent ships you can build of higher-mark ships as a human player, also. So when the AI suddenly jumps up to Mark III from Mark II, or so, the size of the waves drop a bit even though their composition is tougher. Then as the AIP increases from there, you get progressively harder in the new tech level, too.
By the time you pass something like 1000 AIP, you wind up with all Mark IV ships, and their numbers just keep climbing after that. If you're able to survive up to 4000+ AIP, most likely it's not going to get much harder in that particular game -- generally by then all of the planets are filled with 4000+ Mark IV/V ships, the AI is sending hugely brutal waves and CPAs, and so forth. A few players are able to get to that point when trying to (for instance) take all the planets in a large map, but it's a challenging scenario for a lot of reasons, and generally those players are on difficulty 5 or 6 for one thing, as well as having a certain style of turtling tactic that is letting them withstand those crazy waves at key defensive locations or similar.
Anyway, those are the extreme cases, which is not what you really asked about, but I think it helps answer your question. In general, the AIP is pretty linear.