Introduction

Soon after we released Not All Language Model Features Are One-Dimensionally Linear, I started working with @Logan Riggs and @Jannik Brinkmann on a natural followup to the paper: could we build a variant of SAEs that could find multi-dimensional features directly, instead of needing to cluster SAE latents post-hoc like we did in the paper.

We worked on this for a few months last summer and tried a bunch of things. Unfortunately, none of our results were that compelling, and eventually our interest in the project died down and we didn’t publish our (mostly negative) results. Recently, multiple people (@Noa Nabeshima , @chanind, Goncalo Paulo) said they were interested in working on SAEs that could find multi-dimensional features, so I decided I would write up what we tried.