The Linear Representation Hypothesis Needs a Group Action
Quick summary
arXiv:2609.27158v1 Announce Type: cross Abstract: To make claims about representations that generalize beyond a particular trained model, we need to specify when two representations should count as equivalent. The Linear Representation Hypothesis is often discussed without making this equivalence explicit. Different notions of equivalence preserve different structures, so metrics, probes, and interventions that appear to study the same representation may in fact correspond to different hypotheses. We therefore argue that the Linear Representation Hypothesis is not one hypothesis but a family o
Key takeaways
- arXiv:2609.27158v1 Announce Type: cross Abstract: To make claims about representations that generalize beyond a particular trained model, we need to specify when two representations should count as equivalent.
- The Linear Representation Hypothesis is often discussed without making this equivalence explicit.
- Different notions of equivalence preserve different structures, so metrics, probes, and interventions that appear to study the same representation may in fact correspond to different hypotheses.
Why it matters
The value of this work lies as much in how it was tested as in the claim itself. Sample design, baselines, uncertainty and replication help separate a laboratory result from real-world impact.
Member comments