Under ask-correct, arithmetic tasks A1-A2 show gradual AUROC increase peaking only in final layers, unlike the sharp transition under no-prompt.

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

• 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.finding0.848
  Core empirical finding about layer-dependent truth direction emergence across task types.
• 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.finding0.822
  Key improvement in cross-task generalization enabled by explicit instruction framing.
• No-prompt probes show significant AUROC performance drop when evaluated on ask-correct activations, especially at layers where arithmetic truth directions emerge under no-prompt.finding0.815
  Generalization evidence that truth probes are not invariant to model instructions.
• 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.claim0.776
  From the cross-task generalization heatmaps in Appendix B.3.3.
• Probes trained on A1 degrade significantly when evaluated on A2 and more on A3; training on A2 achieves only AUROC ~0.65 on A3.finding0.775
  Shows rapid generalization decay for arithmetic truth directions with each additional operation.
• F0-trained probes in layers 4-10 show inverted separation on F1 (AUROC ≈ 0), systematically misclassifying true statements as false.finding0.767
  Demonstrates that early-layer probes capture sentence polarity rather than truth.
• At layer 0 α=5, detection-adjusted logit difference is +3.19 and control increase is +3.22, a difference of only 0.03 logitsfinding0.756
  Concrete numerical example showing detection and control are nearly identical at peak apparent accuracy
• Pure factual-recall tasks F0-F2 show robust AUROC performance across all instruction template variations.claim0.755
  Contrasts with harder tasks that are sensitive to prompt variations.