> Similarly, there are, right now, efforts in order to really check if the “H” in the HNSWs is really needed, and if instead a flat data structure with just one layer would perform more or less the same (I hope I’ll cover more about this in the future: my feeling is that the truth is in the middle, and that it makes sense to modify the level selection function to just have levels greater than a given threshold).
Small world networks have been my obsession for almost a decade, from a biological and sociological evolution angle. Love this stuff.
This is the paper he's referring to, which I was just reading again yesterday :)
As someone also interested in not just repair of the social fabric, but the evolution of gendered social dynamics in social species (biologically and culturally), it's interesting to me that there might be some property of networks that:
1. Makes any random point as close as possible to any other random point (all solutions are equally likely to be close to the unknown solution somewhere in the network)
2. Minimally edges must be maintained (valuable in social networks, where edges are relationships that have maintenance cost)
3. Involves some negotiation between hierarchy (aka entrepreneurial networks, with opportunity for value extraction thru rent-seeking traffic) and hubness (which dissolve capture points in networks via "weaving" them out of existence). All the short paths in a small-world pass through hubs, which necessarily maintain many more weaker connections in a much more "gossip" comms protocols
Am working on this stuff related to collective intelligence and democracy work, if anyone wants to be in touch https://linkedin.com/in/patcon-
Small world networks have been my obsession for almost a decade, from a biological and sociological evolution angle. Love this stuff.
This is the paper he's referring to, which I was just reading again yesterday :)
Down with the Hierarchy: The 'H' in HNSW Stands for "Hubs" (2025) https://arxiv.org/abs/2412.01940
Also:
Hubs in Space: Popular Nearest Neighbors in High-Dimensional Data (2010) https://www.jmlr.org/papers/v11/radovanovic10a.html
As someone also interested in not just repair of the social fabric, but the evolution of gendered social dynamics in social species (biologically and culturally), it's interesting to me that there might be some property of networks that:
1. Makes any random point as close as possible to any other random point (all solutions are equally likely to be close to the unknown solution somewhere in the network)
2. Minimally edges must be maintained (valuable in social networks, where edges are relationships that have maintenance cost)
3. Involves some negotiation between hierarchy (aka entrepreneurial networks, with opportunity for value extraction thru rent-seeking traffic) and hubness (which dissolve capture points in networks via "weaving" them out of existence). All the short paths in a small-world pass through hubs, which necessarily maintain many more weaker connections in a much more "gossip" comms protocols
Am working on this stuff related to collective intelligence and democracy work, if anyone wants to be in touch https://linkedin.com/in/patcon-