Well they provided the environment for you to think, but that gives them the right to own your thoughts? It's possible, and even common in universities for the organization to have the right to use but not own your discoveries. If that makes a business non-viable, it's really not our problem.
If I pay you to invent something, and you invent it, I expect to get it. I'm not paying you for the privilege of inviting you to my office. I'm paying you for the output of specific thoughts you have.
This is incorrect both de facto and de jure. Anything you invent while employed at a university or a company like IBM or Microsoft will belong to them forever, without exception.
The cardinal rule is that, if you do not want your invention to belong to your employer, don't work for them.
All of the sour grapes about these arrangements are indictments of working for someone else, and I wholeheartedly agree! If you have the least bit of cojones, make something people want and sell it yourself. But, if you prefer the golden yoke, the owner of the farm gets all the fruits.
That can be the case, but depends on circumstances. The point I was making is likely to hold up in court even without a specific contract clause in place to address it.
Where do you draw the line, is the context as generic as "AI" or "ML", implying that anything AI related, even if not directly comparable to your employers product is owned by the employer?
I mean I would personally say it's anything directly in the employer's lines of business with a fairly limited scope. But as personal advice I wouldn't recommend others to do anything with AI on the side, with the intention to own it, if they work in AI as a career.