I was one of the people that was super excited after reading the Chris Olah blogpost from 2014, and over the past decade I've seen the insight go exactly nowhere. It's neat but it hasn't driven any interesting results, though Ayasdi did some interesting stuff with TDA and Gunnar Carlson has been playing around with neural nets recently.
I think it's incorrect that the insight has gone nowhere. See, for eg, contrastive loss / clip, or vqgan image generation. Arguably also diffusion models.
More generally, in my experience as an AI researcher, understandings of the geometry of data leads directly to changes in model architecture. Though people disparage that as "trial and error" it is far more directed than people on the outside give credit for.
The geometric intuition is solid, but actually applying topology has been less fruitful in spite of a lot of people trying their best, as Chris Olah himself has said elsewhere in this thread.
Ayasdi immediately came to mind too seeing this post. I haven't thought of them in a long time, looks like they got bought out in 2019, prepandemic too which was probably best since mid pandemic had a lot of poor valuations
I would expect model/algorithm improvements from using topological concepts to analyze the manifolds in question or concrete results in model interpretability. Gunnar has studied some toy examples, but they were barely a step up from the ones Olah constructed for the sake of explanation and they haven't borne any further fruit.
You can say any advance or insight is just lying dormant, it doesn't mean anything unless you can specifically articulate why it still has potential. I haven't made any claims on the future of the intersection of deep learning and topology, I was pointing out that it's been anything but dormant given the interest in it but it hasn't lead anywhere.
