Good point on the rotational symmetry, that makes sense now.
I still think that this assumption is fairly realistic because in practice, most pairs of unrelated features would co-occur only very rarely, and I expect the winner-take-all dynamic to dominate most of the time. But I agree that it would be nice to quantify this and test it out.
Agreed that’s a plausible hypothesis. I mostly wish that in this toy model you had a hyperparameter for the frequency of co-occurrence of features, and identified how it affects the rate of incidental polysemanticity.
Good point on the rotational symmetry, that makes sense now.
Agreed that’s a plausible hypothesis. I mostly wish that in this toy model you had a hyperparameter for the frequency of co-occurrence of features, and identified how it affects the rate of incidental polysemanticity.