Which linear directions are compositional?

by Ari Holtzmanabout 1 month ago

1

One of the things I don't really buy about so-called linear representations in the residual stream of Transformer LLMs: that they form a linear space where you can compose directions. However, I bet related vectors (e.g. the vector for red and the vector for blue) do compose naturally. Can we trawl through the linear directions we've found and map out which ones are coherent linear subspaces and which ones are singular directions that are probably not really linear so much as approximately linear in the places where we've tested?

llms linear representations compositionality Implemented:https://github.com/Hypogenic-AI/compositional-directions-17d5-claude Implemented:https://github.com/Hypogenic-AI/compositional-directions-fe75-codex Implemented:https://github.com/Hypogenic-AI/compositional-directions-cf35-gemini

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If you are inspired by this idea, you can reach out to the authors for collaboration or cite it:

@misc{holtzman-which-linear-directions-2026,
  author = {Holtzman, Ari},
  title = {Which linear directions are compositional?},
  year = {2026},
  url = {https://hypogenic.ai/ideahub/idea/DQvf9rozqmC2H3nxft7J}
}

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