Does the hierarchical equality network implement a program that computes w=x and y=z as intermediate values?

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

• The feed-forward network truly implements a symbolic, tree-structured algorithm for hierarchical equality, with abstract equality relations not decomposable into input identitiesclaim0.799
  DAS reveals that the neural network encodes abstract relational structure rather than raw input identities.
• Linear alignment map ϕ_lin shows substantial IIA decrease in third layer for both equality relations and left equality relation algorithms in hierarchical equality taskfinding0.735
  Replicates Geiger et al. 2024b pattern of layer-dependent IIA degradation with linear maps
• Hierarchical Equality Taskconcept0.735
  Task where the input is a sequence w,x,y,z and the label is (w=x)=(y=z); used to test relational reasoning in developmental/cognitive psychology.
• Brute-force search achieves best IIA of 0.60 on hierarchical equality Both Equality Relations in Layer 1finding0.730
  DAS substantially outperforms brute-force search (1.00 vs 0.60 IIA) on the hierarchical equality task.
• Hierarchical structure in interaction topology enables complex multiscale patterns that cannot exist in flat networks.claim0.729
  Explains why biological systems achieve organization across scales while language models struggle; grounds in free energy scaling
• Both Equality Relations Algorithmconcept0.724
  Algorithm computing both equality relations separately before comparing them in hierarchical equality task
• Identity of first argument algorithm IIA consistently hovers around 50% for all alignment map types on hierarchical equality taskfinding0.721
  Exception to the general trend; attributed to insufficient RevNet capacity rather than algorithm not being implemented
• Can Shallow Or Reciprocal Interaction Structures Compute Nonlinearlyquestion0.711