I don’t know of specific examples, but this is the image I have in my head when thinking about why untied weights are more free than tied weights:
I think more generally this is why I think studying SAEs in the TMS setup can be a bit challenging, because there’s often too much symmetry and not enough complexity for untied weights to be useful, meaning just forcing your weights to be tied can fix a lot of problems! (We include it in ARENA mostly for illustration of key concepts, not because it gets you many super informative results). But I’m keen for more work like this trying to understand feature absorption better in more tractible cases
I don’t know of specific examples, but this is the image I have in my head when thinking about why untied weights are more free than tied weights:
I think more generally this is why I think studying SAEs in the TMS setup can be a bit challenging, because there’s often too much symmetry and not enough complexity for untied weights to be useful, meaning just forcing your weights to be tied can fix a lot of problems! (We include it in ARENA mostly for illustration of key concepts, not because it gets you many super informative results). But I’m keen for more work like this trying to understand feature absorption better in more tractible cases