I think this question might interest @KordingLab, @xaqlab, @benlansdell, @antoniocbscosta, @rbhar90, @Aras121, @a_tschantz, @NoahGuzman14

This might also interest @KaiUeltzhoeffer, @DaltonSakthi, @marceljuengling

@NatashaMhatre I think this is also related to our previous discussion on the controllability and stability of complex dynamical systems. Instead of framing the question in the abstract I think we can connect it to an existing hypothesis in machine learning. :)

I haven't seen this question properly formulated anywhere so this represents my attempt. From my discussions with an applied topologist it has yet to be properly addressed. I also highly doubt that this is one of those problems where there will be a single ‘eureka’ moment. ;)

Finally, we are all on Twitter to exchange ideas and not one-up each other so I hope everyone feels free to share their perspective. :)

Perhaps there’s some minimum lower dimension for any data which preserves its most relevant characteristics. “Empirically, this is observed to be true for many kinds of data including text data and natural images.” Does there generally exist some latent structure or intrinsic...

... dynamics in some data which are important & the rest can be reduced away? Mean field modelling comes to mind — captures processes by coarse graining essential shape of data, w/o having all underlying parameters. I’m not confident this is the answer, but an interesting theory