Arithmetic task hierarchy (A1–A3)

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

• Factual task hierarchy (F0–F5)framework0.785
  A controlled six-level hierarchy of factual tasks increasing in complexity from simple city-location recall to double-counting constraints.
• Hierarchical Equality Taskconcept0.763
  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.
• Math/code tasks S ≈ -1.65 at layers 8–12finding0.747
  Task-specific peak anchoring score for structured reasoning domains.
• Under ask-correct, probes trained on arithmetic tasks A1-A3 generalize almost perfectly to factual tasks F0-F2 (AUROC ~1.0), whereas under no-prompt this generalization is largely absent.finding0.747
  Key improvement in cross-task generalization enabled by explicit instruction framing.
• hierarchyconcept0.744
  An ordering of texts via spatial cues like indentation, size, and placement, implying importance.
• Factual tasks F0-F3 reach near-perfect AUROC in early-to-mid layers of Llama-3.1-8B; arithmetic tasks A1-A3 emerge much later; counting tasks F4-F5 emerge late similar to arithmetic.finding0.733
  Core empirical finding about layer-dependent truth direction emergence across task types.
• Hierarchy (Spatial)concept0.725
• The ask-arith prompt shows weaker generalization to factual tasks compared to other explicit prompts, suggesting a specialized arithmetic prompt does not create a unified truth direction across task families.claim0.724
  From the cross-task generalization heatmaps in Appendix B.3.3.