UPDATE: we’ve corrected equations 9 and 10 in the paper (screenshot of the draft below) and also added a footnote that hopefully helps clarify the derivation. I’ve also attached a revised figure 6, showing that this doesn’t change the overall story (for the mathematical reasons I mentioned in my previous comment). These will go up on arXiv, along with some other minor changes (like remembering to mention SAEs’ widths), likely some point next week. Thanks again Sam for pointing this out!
Updated equations (draft):
Updated figure 6 (shrinkage comparison for GELU-1L):
On bmag, it’s unclear what a “natural” choice would be for setting this parameter in order to simplify the architecture further. One natural reference point is to set it to ermag⊙bgate, but this corresponds to getting rid of the discontinuity in the Jump ReLU (turning the magnitude encoder into a ReLU on multiplicatively rescaled gate encoder preactivations). Effectively (removing the now unnecessary auxiliary task), this would give results similar to the “baseline + rescale & shift” benchmark in section 5.2 of the paper, although probably worse, as we wouldn’t have the shift.