There’s plenty, including a line of work by Carina Curto, Katrin Hess and others that is taken seriously by a number of mathematically inclined neuroscience people (Tom Burns if he’s reading can comment further). As far as I know this kind of work is the closest to breaking through into the mainstream. At some level you can think of homology as a natural way of preserving information in noisy systems, for reasons similar to why (co)homology of tori was a useful way for Kitaev to formulate his surface code. Whether or not real brains/NNs have some emergent computation that makes use of this is a separate question, I’m not aware of really compelling evidence.
There is more speculative but definitely interesting work by Matilde Marcolli. I believe Manin has thought about this (because he’s thought about everything) and if you have twenty years to acquire the prerequisites (gamma spaces!) you can gaze into deep pools by reading that too.
There’s plenty, including a line of work by Carina Curto, Katrin Hess and others that is taken seriously by a number of mathematically inclined neuroscience people (Tom Burns if he’s reading can comment further). As far as I know this kind of work is the closest to breaking through into the mainstream. At some level you can think of homology as a natural way of preserving information in noisy systems, for reasons similar to why (co)homology of tori was a useful way for Kitaev to formulate his surface code. Whether or not real brains/NNs have some emergent computation that makes use of this is a separate question, I’m not aware of really compelling evidence.
There is more speculative but definitely interesting work by Matilde Marcolli. I believe Manin has thought about this (because he’s thought about everything) and if you have twenty years to acquire the prerequisites (gamma spaces!) you can gaze into deep pools by reading that too.