Second-order virtual attention head terms contribute negligible marginal loss reduction in the analyzed two-layer attention-only model

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

• In the analyzed two-layer model, second-layer attention head terms dominate the loss reduction compared to first-layer terms and the direct pathfinding0.893
  Result from term importance analysis breaking down loss contribution by layer
• In the analyzed two-layer attention-only model, only K-composition is significant; V- and Q-composition are negligible by Frobenius norm measurefinding0.815
  Result from applying the Frobenius norm composition measurement to all attention head pairs in the two-layer model
• Most attention heads in one-layer models dedicate an enormous fraction of their capacity to copying behaviorclaim0.787
  Empirical observation from examining expanded OV/QK matrices; approximately 10 out of 12 heads show significant copying
• Naive interpretation of attention patterns can be both informative and fundamentally misleading when Q-, K-, or V-composition is presentclaim0.762
  Response to the 'attention as explanation' critique; the paper provides a typology of when attention is and isn't directly interpretable
• Each attention head has two largely independent computations: a QK circuit computing the attention pattern and an OV circuit computing the effect if attended toclaim0.761
  Key decomposition enabling separate analysis of where attention goes and what it does
• Attention heads can be understood as independent operations each adding their output to the residual stream, equivalent to the concatenate-and-multiply formulationclaim0.761
  Mathematical equivalence enabling independent analysis of each attention head
• Two-layer attention-only transformers implement much more complex algorithms via composition of attention heads, detectable directly from weightsclaim0.760
  Core claim for two-layer models; composition creates qualitatively more powerful in-context learning
• We hypothesize that hallucinated rationales in 1B-models result from lack of necessary vision context; incorporating vision features should reduce hallucination and improve rationale quality.hypothesis0.758
  Predictive hypothesis driving the investigation in Section 3.3; supported by experimental evidence.