Here's the thing about AI: you get what you optimize for. If you optimize for a specific skill, like chess or StarCraft, your final system will possess this skill and nothing else. It won't generalize to any other task.

To generalize, you must optimize for generality itself.
To be clear, optimizing for task-specific skill can be valuable. It gets you somewhere. But now, we're at a stage in the development of AI where generalization has become, inevitably, the bottleneck to skill acquisition.
Of course, if you can amass a sufficiently dense sampling of situations within a sufficiently narrow domain, you can always train a machine model -- but it will break down as soon as it encounters anything it has never seen before.

That's modern deep learning.
And for many high-value real-world tasks, that's just about every day. Consider self-driving cars, or domestic robotics. You can't enumerate the set of possible situations a driver might ever encounter -- billions of miles are not nearly enough.
You can't even enumerate the set of possible kitchens a robot might operate in. If you want to ever be able to deploy a L5 self-driven system or a human-level domestic robot, you have to figure out how to implement broad cognitive abilities -- beyond task-specific skills.
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