The effect of alignment map ϕ complexity on IIA in causal abstraction is an analogue of the probing complexity–accuracy trade-off

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

• Near-perfect IIA can be achieved on randomly initialised models that cannot solve the task, suggesting causal alignment does not require task capabilityclaim0.812
  Empirical support for vacuousness of unrestricted causal abstraction
• Over 80% IIA achieved using complex non-linear alignment maps on randomly initialised MLPs in hierarchical equality taskfinding0.797
  Demonstrates that high IIA can be obtained even when model cannot solve the task
• Causal abstraction is not enough for mechanistic interpretability because it becomes vacuous without assumptions about how models encode informationclaim0.797
  Central thesis of the paper
• Non-linear alignment map ϕ_nonlin achieves near-optimal IIA across all layers on hierarchical equality task, eliminating layer-dependent degradation seen with linear mapsfinding0.791
  Key empirical result: non-linear maps overcome linear maps' failure in deeper layers
• Linear alignment map ϕ_lin shows substantial IIA decrease in third layer for both equality relations and left equality relation algorithms in hierarchical equality taskfinding0.787
  Replicates Geiger et al. 2024b pattern of layer-dependent IIA degradation with linear maps
• An interplay between causal abstraction and feature geometry deepens mechanistic understanding of language modelsclaim0.785
  Methodological claim about the scientific value of combining causal abstraction with representational geometry analysis
• DAS achieves substantial causal effect even on arbitrary input-output mappings where no causal mechanism should existfinding0.782
  Replication of Wu et al. 2023 finding; DAS expressivity concern validated in CausalGym setup
• The And-Or algorithm may not be a true abstraction of the trained MLP's behaviour since it never achieves high IIA in later layers regardless of alignment map complexityhypothesis0.777
  Hypothesis raised in distributive law task analysis