The idea that humans are the most intelligent animals on Earth appears patently obvious to a lot of people. And to a large extent, I agree with this intuition. Humans clearly dominate the world in technological innovation, control, communication, and coordination.

However, more recently I have been acquainted with some evidence that the proposition is not actually true, or at the very least is non-obvious. The conundrum arises when we distinguish raw innovative capability, from the ability to efficiently process culture. I'll explain the basic case here.

Robin Hanson has sometimes pointed to the accumulation of culture as the relevant separation between humans and other animals. Under this view, the reason why humans are able to dominate the world with technology has less to due with our raw innovation abilities, and more to do with the fact that we can efficiently process accumulated cultural information and build on it.

If the reason for our technological dominance is due to raw innovative ability, we might expect a more discontinuous jump in capabilities for AI, since there was a sharp change between "unable to innovate" and "able to innovate" during evolutionary history, which might have been due to some key architectural tweak. We might therefore expect that our AIs will experience the same jump after receiving the same tweak.

If the reason for our technological dominance is due to our ability to process culture, however, then the case for a discontinuous jump in capabilities is weaker. This is because our AI systems can already process culture somewhat efficiently right now (see GPT-2) and there doesn't seem like a hard separation between "being able to process culture inefficiently" and "able to process culture efficiently" other than the initial jump from not being able to do it at all, which we have already passed. Therefore, our current systems are currently bottlenecked on some metric which is more continuous.

The evidence for the cultural accumulation view comes from a few lines of inquiry, such as

Feral children lack an innovating culture to learn from, and are correspondingly 'unintelligent' from our point of view. This is despite the fact that feral children hold more-or-less the exact same raw innovative capabilities as normal humans. For Genie, one feral child, "Doctors found it extremely difficult to test or estimate Genie's mental age or any of her cognitive abilities, but on two attempts they found Genie scored at the level of a 13-month-old."
Books like The Secret of Our Success document remarkable instances of raw innovative capability being much less useful than ability to use culture. See the SlateStarCodex review here.
Evolutionarily, increases in raw innovative capability may universally aid reproductive capability for any animal, whereas increases in ability to efficiently process culture would only help in a species that developed culture to begin with. It's no suprise therefore, that after humans developed language, we quickly developed the capability to process cultural information, whereas other animals can't learn much from our civilization. However, this doesn't necessarily mean they are less innovative in general.

Under the view that our dominance is due to cultural accumulation, we would expect that there are some animals that are more intelligent than humans in the sense of raw innovative ability. The reason is that it would be surprising a priori for us to be the most intelligent, unless we had reason to believe so anthropically. However, if culture is the reason why we dominate, then the anthropic argument here is weaker.

We do see some initial signs that humans might not be the most intelligent species on Earth in the innovative sense. For instance,

Although humans have the highest encephalization quotient, we don't have the most neurons, or even the most neurons in our forebrain.
Some animals have easily measurable cognitive capabilities which surpass ours. One example is the chimpanzee, which may have better working memory. Edit: Now I'm not sure whether this fact is correct. See comments below for more discussion.

If humans are the most intelligent in the sense of having the best raw innovative abilities, this hypothesis should be testable by administering a battery of cognitive tests to animals. However, this is made difficult due to a number of factors.

First, most intelligence tests that humans take rely on their ability to process language, disqualifying other animals from the start.

Second, humans might be biased towards administering tests about things that we are good at, since we might not even be aware of the type of cognitive abilities we score poorly on. This may have the effect of proving that humans are superior in intelligence, but only on the limited subset of tests that we used.

Third, if we use current human intelligence tests (or anything like them), the following argument arises. Computers can already outperform humans at some tasks that intelligence tests measure, such as memory, but this doesn't mean that computers already have a better ability innovate. We would need to test something that we felt confident accurately indicated innovative ability.

Since I'm mostly interested in this question because of its implications for AI takeoff speeds, I'd want to know what type of things are most useful for developing technology, and see if we can see the same abilities in animals sans cultural accumulation modules.