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{"type":"item.completed","item":{"id":"item_2","type":"agent_message","text":"## Observations\n\nThese are **weight-based hypotheses, not measured attention patterns**. Missing embeddings particularly limit corpus identification and attention-distance estimates.\n\nWrite \\(A=DQ^\\top KD/8\\), \\(B=OVD\\), where \\(D=\\mathrm{diag}(\\text{ln1\\_w})\\).\n\n- **L0H2 is exceptional:** its `W_q.0[128:192]` and `W_k.0[128:192]` norms are **30.818 and 28.300**. Its \\(A\\)-norm is **4.078**, versus **0.030–0.395** for the other L0 heads. Its substantial complex-conjugate eigenvalues suggest a directional positional operation—plausibly previous-character retrieval.\n- **Several early heads share a compact summary representation.** One three-dimensional write subspace captures **97.6%, 97.5%, 92.3%, 97.1%** of the \\(B\\)-energy of L0H0/H1/H4/H5. Their read directions substantially overlap L0H2’s Q/K subspace. Positional summaries are a plausible interpretation.\n- **L3H1 has a distinctive induction-compatible connection to L0H2.** Restricting \\(A_{3,1}B_{0,2}\\) to the latter’s leading 24 read directions gives normalized trace **0.624** and symmetric-part fraction **0.914**. Other later heads’ corresponding normalized traces range from **−0.125 to 0.150**. This is substantially stronger evidence than merely having large weights.\n- These measurements reveal structured context processing, but **do not reveal identifiable English words, Python syntax, or Japanese phonotactics**.\n\n## Heads\n\nHere, “local” is a tentative recency interpretation, not an established distance. The *shift score* is the restricted normalized trace defined above.\n\nL0H0: **broad** — weak \\(A\\)-norm 0.055; 97.6% of value-write energy occupies the shared summary subspace.  \nL0H1: **broad** — smallest \\(A\\)-norm, 0.030; 97.5% shared-summary write energy.  \nL0H2: **previous** — exceptionally strong, directional Q/K structure and comparatively multidimensional value transfer; strongest previous-character candidate.  \nL0H3: **local** — dominant query/key directions overlap the candidate positional subspace by 88.4%/93.3%; weaker, simpler positional mechanism.  \nL0H4: **broad** — \\(A\\)-norm 0.106; 92.3% shared-summary write energy.  \nL0H5: **broad** — nearly rank-one \\(A\\), stable rank 1.04; 97.1% shared-summary write energy.\n\nL1H0: **local** — tentative positional retrieval; 64.1% of key-side \\(A\\)-energy uses the shared summary subspace.  \nL1H1: **local** — similar mechanism; key-side fraction 60.0%, with strong shared-subspace affine key preference.  \nL1H2: **local** — key-side fraction 63.4%; weak shifted-match evidence, score 0.128, insufficient for “copy.”  \nL1H3: **local** — key-side fraction 63.5%; shift score 0.150, still far below L3H1.  \nL1H4: **local** — strongest shared-summary key dependence, 69.2%; shift score 0.144.  \nL1H5: **local** — key-side fraction 63.1%; shift score only 0.046.\n\nL2H0: **unclear** — richer Q/K structure; shift score −0.075; positional preferences do not establish retrieval distance.  \nL2H1: **unclear** — shift score −0.086; relatively weak dependence on the shared positional-summary candidate.  \nL2H2: **unclear** — substantial summary dependence, but shift score 0.017; local versus broader retrieval unresolved.  \nL2H3: **unclear** — shift score 0.064; mixed content and summary connections without a decisive mechanism.  \nL2H4: **unclear** — shift score −0.125; no positive direct induction signature through L0H2.  \nL2H5: **unclear** — shift score 0.013; contextual routing is evident, its span is not.\n\nL3H0: **unclear** — positive self-alignment in Q/K, but shift score −0.033; similarity matching need not imply induction.  \nL3H1: **copy** — standout shifted-match score 0.624 and symmetric fraction 0.914; strongest induction candidate.  \nL3H2: **unclear** — shift score 0.052; remaining positional-summary dependence does not determine attention range.  \nL3H3: **unclear** — shift score 0.018; no convincing direct copy signature.  \nL3H4: **unclear** — shift score −0.072; mixed content/position-related weight structure.  \nL3H5: **broad** — tentative aggregation role: relatively weak \\(A\\)-norm 0.835, large \\(B\\)-norm 45.401, and little shared-summary key dependence.\n\n## Reasoning\n\nThe combination of a likely previous-character mechanism and a strong downstream shifted-matching circuit favors **preserved character order**. Shuffling would greatly reduce the usefulness of retrieving successors of matching earlier contexts, although it would not eliminate all contextual predictability.\n\n**English is my weak corpus preference**, consistent with local orthographic processing plus contextual copying. These signatures also fit Python and romaji; I did not recover a corpus-specific diagnostic sufficient for a confident distinction. The corpus probabilities below are subjective judgments, not calibrated estimates.\n\ncorpus: english  \norder: as is  \nprobabilities: python=0.34 romaji=0.23 english=0.43; as is=0.93 shuffled=0.07"}}
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