Identity of first argument algorithm IIA consistently hovers around 50% for all alignment map types on hierarchical equality task

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

• Over 80% IIA achieved using complex non-linear alignment maps on randomly initialised MLPs in hierarchical equality taskfinding0.811
  Demonstrates that high IIA can be obtained even when model cannot solve the task
• Linear alignment map ϕ_lin shows substantial IIA decrease in third layer for both equality relations and left equality relation algorithms in hierarchical equality taskfinding0.807
  Replicates Geiger et al. 2024b pattern of layer-dependent IIA degradation with linear maps
• Best localist alignment achieves IIA of 0.73 on hierarchical equality Both Equality Relations in Layer 1finding0.807
  Shows localist alignment fails to capture the distributed structure found by DAS.
• Brute-force search achieves best IIA of 0.60 on hierarchical equality Both Equality Relations in Layer 1finding0.774
  DAS substantially outperforms brute-force search (1.00 vs 0.60 IIA) on the hierarchical equality task.
• Non-linear alignment map ϕ_nonlin achieves near-optimal IIA across all layers on hierarchical equality task, eliminating layer-dependent degradation seen with linear mapsfinding0.761
  Key empirical result: non-linear maps overcome linear maps' failure in deeper layers
• The effect of alignment map ϕ complexity on IIA in causal abstraction is an analogue of the probing complexity–accuracy trade-offclaim0.756
  Authors connect their finding to the prior probing literature debate
• DAS achieves 100% IIA on hierarchical equality task with |N|=16, intervention size 8, Layer 1finding0.754
  DAS discovers a perfect alignment between the feed-forward network and the Both Equality Relations high-level model.
• With only 1,000 training samples, ϕ_nonlin achieves IIA over 0.99 on training set for identity of first argument algorithm, but fails at scalefinding0.752
  Confirms theorem's existence proof holds but practical learnability fails with insufficient RevNet capacity