Both Equality Relations Algorithm

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

• Paired Comparison Methodmethod0.733
  Experimental protocol asking observers to compare two systems A and B for degree of life; used to establish objectivity through inter-observer convergence
• Political Equalityconcept0.729
  Democratic principle entitling prolific digital minds constituting a supermajority to political control
• Evolutionary Algorithmsmethod0.728
  Machine learning approach using evolutionary processes to generate and select designs, used to blur the designed vs. evolved distinction
• Linear alignment map ϕ_lin shows substantial IIA decrease in third layer for both equality relations and left equality relation algorithms in hierarchical equality taskfinding0.726
  Replicates Geiger et al. 2024b pattern of layer-dependent IIA degradation with linear maps
• Does the hierarchical equality network implement a program that computes w=x and y=z as intermediate values?question0.724
  Specific research question for the first experiment.
• The feed-forward network truly implements a symbolic, tree-structured algorithm for hierarchical equality, with abstract equality relations not decomposable into input identitiesclaim0.723
  DAS reveals that the neural network encodes abstract relational structure rather than raw input identities.
• Brute-force search achieves best IIA of 0.60 on hierarchical equality Both Equality Relations in Layer 1finding0.721
  DAS substantially outperforms brute-force search (1.00 vs 0.60 IIA) on the hierarchical equality task.
• Next extent algorithmmethod0.718
  Application of Next Closure to enumerate all concept extents of a formal context.