This is interesting to me, and I had not known that such research has been done.
I've heard that there's a consistent problem in machine learning of people overtraining their algorithms to particular data sets. The diversity of examples in the paper appears to be impressive, but it could be that the algorithm would break if given images that would appear to us to be qualitatively similar to the ones displayed.
I think that Gromov may not have expressed himself very clearly, and his remarks may not have been intended to be taken literally. Consider the many starfish in this picture. By looking at the photo, one can infer that any given star-fish has five-fold symmetry with high probability, even though some of the ones in the distance wouldn't look like they had five-fold symmetry (or even look like star-fish at all) if they were viewed in isolation. I don't think that existing AI has the capacity to make these sorts of inferences at a high level of generality.
I think #3 is the real issue. Most of the starfishes in that picture aren't 5-fold symmetric, but a person who had never seen starfish before would first notice "those all look like variations of a general form" and then "that general form is 5-fold symmetric". I don't know of any learning algorithms that do this, but I also don't know what to search for.
So you're probably right that it's an issue of "pattern recognition ability", but it's not as bad as you originally said.
In a recent comment thread I expressed skepticism as to whether there's been meaningful progress on general artificial intelligence.
I hedged because of my lack of subject matter knowledge, but thinking it over, I realized that I do have relevant subject matter knowledge, coming from my background in pure math.
In a blog post from April 2013, Fields Medalist Timothy Gowers wrote:
I don't know of any computer programs that have been able to prove theorems outside of the class "very routine and not requiring any ideas," without human assistance (and without being heavily specialized to an individual theorem). I think that if such projects existed, Gowers would be aware of them and would likely have commented on them within his post.
It's easy to give an algorithm that generates a proof of a mathematical theorem that's provable: choose a formal language with definitions and axioms, and for successive values of n, enumerate all sequences of mathematical deductions of length n, halting if the final line of a sequence is the statement of the the desired theorem. But the running time of this algorithm is exponential in the length of the proof, and the algorithm is infeasible to implement except for theorems with very short proofs.
It appears that the situation is not "there are computer programs that are able to prove mathematical theorems, just not as yet as efficiently as humans," but rather "computer programs are unable to prove any nontrivial theorems."
I'll highlight the Sylow theorems from group theory as examples of nontrivial theorems. Their statements are simple, and their proofs are not very long, but they're ingenious, and involve substantive ideas. If somebody was able to write a program that's able to find proofs of the Sylow theorems, I would consider that to be strong evidence that there's been meaningful progress on general artificial intelligence. In absence of such examples, I have a strong prior against there having been meaningful progress on general artificial intelligence.
I will update my views if I learn of the existence of such programs, or of programs that are capable of comparably impressive original research in domains outside of math.