Brute-force search achieves best IIA of 0.60 on hierarchical equality Both Equality Relations in Layer 1

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

• Brute-force search achieves maximum IIA of 0.60 on MoNLI tasksfinding0.835
  DAS substantially outperforms brute-force search on MoNLI across all models.
• DAS achieves 100% IIA on hierarchical equality task with |N|=16, intervention size 8, Layer 1finding0.803
  DAS discovers a perfect alignment between the feed-forward network and the Both Equality Relations high-level model.
• Best localist alignment achieves IIA of 0.73 on hierarchical equality Both Equality Relations in Layer 1finding0.795
  Shows localist alignment fails to capture the distributed structure found by DAS.
• Identity of first argument algorithm IIA consistently hovers around 50% for all alignment map types on hierarchical equality taskfinding0.774
  Exception to the general trend; attributed to insufficient RevNet capacity rather than algorithm not being implemented
• DAS runs in 502 seconds for hierarchical equality vs. estimated 6e8 seconds for exhaustive brute-force searchfinding0.769
  DAS runtime is invariant with number of testing hypotheses, unlike brute-force search.
• Over 80% IIA achieved using complex non-linear alignment maps on randomly initialised MLPs in hierarchical equality taskfinding0.767
  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 taskfinding0.766
  Replicates Geiger et al. 2024b pattern of layer-dependent IIA degradation with linear maps
• No single layer is universally optimal for probing truth directions; different tasks peak at different layers.claim0.752
  Argues against the single-layer analysis approach of prior work.