I think the √8lnm may be in there because JL is putting an upper bound on the interference, rather than describing the typical interference of two features. As you increase m (more features), it becomes more difficult to choose feature embeddings such that no features have high interference with any other features.
So its not really the ‘typical’ noise between any two given features, but it might be the relevant bound for the noise anyway? Not sure right now which one matters more for practical purposes.
I think the √8lnm may be in there because JL is putting an upper bound on the interference, rather than describing the typical interference of two features. As you increase m (more features), it becomes more difficult to choose feature embeddings such that no features have high interference with any other features.
So its not really the ‘typical’ noise between any two given features, but it might be the relevant bound for the noise anyway? Not sure right now which one matters more for practical purposes.