If saved tags / training worked on the global feed, it would be a great way of finding stories and people with similar interests! Just a thought. Maybe they could just work when you went into the feed itself (rather than displaying all the time, which might be distracting).
I think there is a stronger case to be made for discovery specific features, which have been planned since day one and are behind four major features that are launching this year (notifications, newsletters, dark theme, native oauth for sending services).
However, saved stories are private, so you wouldn't be able to share them. Public tags are not something I've ever thought of as an idea, but that would be a reasonable feature.
The new features sound great! Based on experience, I'd say if you think it's cool, I'm probably going to as well. Looking forward to hearing more.
I think I probably should have focused on intelligence training in my suggestion. What I have in mind is more of a view that would filter from the global share feed things I've given thumbs-down to (I don't create many of my own tags, so I guess those are tags that come directly from the blogs themselves?) or show me how many things with tags I've given thumbs-up to are in the global shared feed. I guess that would in a sense reveal others' choices and preferences, which I hadn't thought about as a privacy issue but can see now that you mention it.
Finally, just a shoutout as ever--the service rocks. I was inspired by the podcast where you said you get lots of ideas from the forums, so I thought I'd throw one out there. Thanks!