Circuit v_virtual_heads (GPT-2)

V-composition (composed-OV ‘virtual heads’, GPT-2) — scope: gpt2

Composed-OV virtual heads: an induction head’s OV output is re-read as the value of a later head (the third Elhage edge type — changes what is moved, not where attention points).

• top V-edges: 5.9->6.7 (ΔV-out 1.32), 5.9->6.0 (ΔV-out 0.60), 5.5->6.7 (ΔV-out 0.87), 5.5->6.6 (ΔV-out 0.72), 5.9->7.3 (ΔV-out 0.54)
• median ΔV-out 0.21387540992208515; static-V↔ΔV-out ρ 0.36; V/K 0.7954648723134081

Cross-model (the value pathway is not GPT-2-only — via the ResidualVM)

Static V-composition ‖W_V^B · OV_A‖ / (‖OV_A‖‖W_V^B‖) — how much of induction head A’s OV output lands in downstream head B’s value-read subspace (a composed-OV virtual head; the same weight basis the catalog scores K/Q composition in, arch-generic incl. GQA). The control is whether induction-A’s V-composition into downstream values exceeds a random non-induction writer’s (specificity).

model	composed-OV writer (induction)	→ reader values	specificity vs random
gpt2	5.5	6.9, 6.6, 7.1, 7.6	+0.008
gpt2-medium	11.1	12.1, 15.14, 13.12, 17.12	+0.031
gpt2-large	19.4	20.14, 26.0, 27.11, 24.8	+0.032
gemma-2-2b	22.3	23.4, 23.5, 23.6, 23.7	+0.013
Llama-3.2-1B	12.15	13.20, 13.21, 13.22, 13.23	+0.035
Qwen2.5-1.5B	19.3	23.0, 23.1, 23.2, 23.3	+0.038

• V-composition is architecture-invariant — in every model an induction head’s OV output feeds downstream heads’ values with positive specificity over a random writer, locally (the induction head feeds the next layers’ value heads). Induction content re-read as a value (a 2-hop OV copy) is a universal motif, completing the cross-model K/Q/V composition-edge triad.
• Scope / honesty. The static signal is weak (specificity ≤0.04) — consistent with the GPT-2 finding that these virtual heads are output-redundant (vcomposition.py; they add ~nothing to the recompile keep-set). In the GQA models the reader values come out as a contiguous block of heads (e.g. Llama 13.20–13.23) because query heads in one KV group share W_V, so their V-composition is identical — a grouping artifact, not four distinct readers. Dynamic ΔV-out confirmation stays GPT-2-validated (ρ(static, ΔV-out) = +0.36).

Data: runs/disassembly/circuits/vcomposition_xmodel_summary.json (vcomposition_xmodel.py, built on the ResidualVM).

Data: runs/disassembly/circuits/atlas_summary.json + the discovery artifacts. Regenerate: circuit_catalog_doc.py.