Remove carriage bolts from concrete

To totally remove them you have to break some of the concrete as the head is much larger than the protruding threaded portion. I'd just cut them off flush.

The head is actually what’s exposed. Is there a good way to extract it?

If there are no nuts on it below the concrete I'd put a pipe wrench on it and see if it will turn and either screw or pull out.

There may be a nut down there and you can unscrew it but if they just bent the end of the bolt, welded it to rebar or whatever, you are chipping it out or cutting it off.

Doesn't it have a square section just below the round head?

If you don't have one, buy, borrow or rent a Sawzall. Or a cutting torch.

You don't generally need that.

When I worked in a factory we removed bolts sticking out of the floor constantly. We'd have a machine bolted down then change to some different technology and the bolts had to go. They were usually in a drilled hole and anchored, with threads up so you could put the plate down and crank a nut down to hold them, so it's not quite the same as having the bolt head out, but the same method would work.

Whack them with a big hammer. They break off flush. If you use a sawzall you're going to have to follow up with an angle grinder to get the little edge off.

Must be one big hammer...

As was stated, there are two outcomes. Cut it off and leave flush with wall or unscrew if possible and fill the opening. Otherwise, it'll be twist, yank, tug, pull or anything that will break the concrete then you'll have to repair.

No. I would guess (it's been a while) a 3 pound hammer, 1/2 to 5/8 inch bolts.

You'd be surprised how brittle they are. Hit them fairly hard and they snap instead of bending. Never had to grind one down like you would if you used a cutoff saw.