Some thoughts:

Progress is not like a liquid, that increases continually with research. Progress is an unknown function, composed of huge number of discrete "discoveries". Each discovery is hidden behind research of variable level of difficulty. Each discovery, may or may not enable more discoveries. The reality may have either a finite or infinite amount of discoveries waiting to be made. We don't know for sure. This universe could have a finite amount of discoveries. But it is possible that we may find a way to travel to infinite other universes, and these may have infinite discoveries waiting to be made.

The shape of the technical progress function, depends on these unknown factors. So it is wrong to assume that it is an exponential. Although an exponential seems like a good approximation around the local point in which we currently are. The population have been growing, and the economy have been growing. These two factors have enabled an increased amount of resources dedicated to research. The more research being done, increases the probability of discovering the available discoveries that exist at the current technological level. The speed of progress depends on the amount of research, and the number of latent discoveries hidden in our reality.

We are approximating the point, in which we can build artificial general intelligence. This will be a machine similar to a human mind, but capable of dramatically faster reasoning. Its internal dialogue will be millions of times faster than a human mind. Because it will move at electrical speeds, instead of biological speeds. Also it will have practically perfect and unlimited memory (compared to human capabilities). And will have almost instantaneous capability to resolve mathematical calculations of reasonable level. With these improvements, it can be expected that it will be much more effective at making discoveries than a human. Additionally these machines will be industrially replicable. So it will be possible to put a large amount of them at work on problems. It is reasonable to expect that these machines will resolve the chain of discoveries available to be made faster than humans.

These artificial machines will maximize discoveries, from the chain of discoveries available. What this is going to mean, depends on the actual unknown amount discoveries available in this universe. If things like nanotechnology, molecular machines, biological machines, etc, are actually possible, these intelligent machines are well equipped to discover them dramatically faster than we humans. If there is new physic available to be discovered, these machines have much better chance than humans at discovering it.

Will machine superintelligence actually create a singularity? maybe, or maybe not. Depends on the amount of discoveries to be made, contained in this universe, and their level of difficulty. It could be the case that our universe is running out of hidden discoveries. So any prediction on the shape of the curve of progress, is pure speculation. For example, we could have already run out of exploitable significant discoveries in physics. Or we could be on the verge of discovering faster-than-light/instantaneous communications, and lots of other things.

In my opinion the invention of artificial general intelligence, and superintelligence is imminent. A matter of years. I base this on introspective observation of the thinking process of my mind. And in comparison of it with the operation of artificial neural networks. They show similarities. The thinking process of the mind is entirely reproducible with deep learning networks, assembled in the right structure. An interesting topic is, who is doing this research. Obviously, the big tech corporations are working on it. But are states organizations also working on it? Who is doing the biggest investment? Who has the best odds of inventing it? What will happen when someone gets it? Are they going to immediately announce it?