Assuming linear representations enables identifying the location of certain variables in a DNN, but many insights fail to generalise when more powerful non-linear maps are used

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

• Linear representation hypothesis: neural networks represent meaningful concepts as directions in their activation spaces.hypothesis0.815
  Foundation for interpreting features as linear directions.
• The fact that ϕ_lin tracks DNN performance more closely than ϕ_nonlin throughout training may support the linear representation hypothesis for IOI task featureshypothesis0.802
  Authors' tentative hypothesis from Fig. 4 but they acknowledge they cannot formalise this intuition
• Non-linear ϕ_nonlin achieves near-perfect IIA on distributive law task for both And-Or and And-Or-And algorithms, eliminating linear/identity map differencesfinding0.792
  Corroborating result on additional task confirming main paper findings
• Non-Linear Representations in LLMsconcept0.783
  Recent work identifying cases where LLM features are not one-dimensionally linear, a caveat to the linearity hypothesis.
• LLMs linearly represent truth-relevant information beyond the plausibility of text, as evidenced by probes trained on likely performing poorly on anti-correlated datasetsclaim0.780
  Establishes that the observed linear structure is not merely a representation of text probability
• Linear representationconcept0.780
  The idea that features are encoded as directions in activation space.
• Non-Linear Representation Hypothesisconcept0.779
  Hypothesis that information may be encoded in arbitrary non-linear subspaces of a neural network
• Accuracy does not vary linearly with latent reflection directions; instead it follows a more non-linear mapping that requires deeper theoretical treatment.claim0.776
  Theoretical limitation identified by the authors distinguishing reflection from stylistic tasks.