The Linear Representation Hypothesis Needs a Group Action

The paper argues that “linear representations” cannot be evaluated coherently without first defining equivalence between representations.

Different equivalence choices preserve different structures, so a metric, probe, or intervention may be testing a different claim than it appears to. The authors frame the issue with group actions, tying the representation object, the procedure that produces it, and the asserted property together. They use the framework to audit common representation quantities and recent interpretability analyses. HF Daily Papers' note