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Lab notes: what's inside the operator vector?

Follow-up experiments, July 2026 — same rules as the paper: every number recomputable from persisted artifacts, every claim next to the control that could kill it.

The paper showed that a factual thought splits into parts — the thing, and the question being asked of it — and that the question part (the operator vector) can be extracted by averaging, moved around, and written back in. The obvious next question: what IS that vector? Does it mean anything — does it map to words, king − man + woman style? We pointed a logit lens at it (reading any internal vector as "which words does it push up?"), split it, and injected the parts separately.

1 · It reads — and it changes content with depth

Early in the model (≈40% depth), the capital-of vector pushes up topic words: "located at", "seat of". At the layer where it has causal leverage (≈89%), it pushes up example answers: ' Tokyo', ' Paris' — and also ' London' and ' Riyadh', cities that are not answers in our dataset. The vector encodes the category, not a lookup table. The same monotone rise appears in all three models (readability score +1.8 → +8.5 in Qwen3-1.7B, +3.0 → +10.1 in Qwen3-8B, +5.1 → +12.0 in Gemma-2-9B). A control lens built from random projections reads nothing at any depth, and vectors built with permuted labels read as noise.

2 · The question is not its word — and not its answers either

Two dissociations we didn't expect to be this clean:

  • The capital-of vector never aligns with the word " capital" (z ≈ 0 at every layer) while aligning strongly with the city tokens late (z ≈ 14–18). Currency-of starts aligned with the word " currency" and hands over to the answer tokens with depth.
  • The paper's syncretic pair returns: language-of and demonym-of share their answer words ("Italian"), yet the demonym vector never aligns with those shared answers while the language vector does. Two questions, same words, different geometry.

3 · The readable part is not the lever

The headline experiment. We split each operator vector into the exact component a logit lens can see — its projection onto the answer tokens' readout directions, holding 3–7% of the vector's energy — and the rest. Then we injected each part alone, at the paper's calibrated dose, in all three models:

  • the readable part alone does almost nothing (margin shift +0.9 in Qwen3-1.7B, +0.8 in Qwen3-8B, +1.1 in Gemma-2-9B; confidence intervals hugging zero; 0% of pairs flipped);
  • the non-readable rest carries the effect in 20/20 relation pairs in all three models (median 87% of the full effect in Qwen3-8B, 93% in Gemma-2-9B; minimum 79%).

So yes — the vector decodes to meaningful words (contra a recent claim that such projections are universally incoherent), but the decodable part is causally inert: the operation's identity travels in the ~93% of the vector that no logit lens can read. Decodable, but not the lever.

4 · A new face of the dose artifact

At the paper's 4× overdose, injecting just the readable part inflates the answer margin enormously (+66 in Qwen3-8B, +65 in Gemma-2-9B — twice the full vector's effect). Trap: pushing a norm-matched vector built from the wrong relations' answers inflates it too (+24 in both), as do random vectors inside the answer-token span. At high dose, margins in vocabulary-aligned directions are mechanically inflatable — the third appearance of the dose artifact from the paper, and one more reason calibrated doses are the honest readout.

5 · The purest test: a marker with no answers in it

Build the difference language-vector − demonym-vector using only the eight countries where both questions share the same answer — so the resulting marker provably carries almost no answer-token information (1–4% of its energy). Inject it on the four countries where the answers differ (Brazil, Egypt, India, Mexico): it moves the language-vs-demonym preference in the predicted direction in 24 of 24 cells in Qwen3-1.7B — and again 24/24 in Qwen3-8B, and again 24/24 in Gemma-2-9B. 72 of 72 cells, three models, two companies. You can steer which question is being asked without touching which word comes out.

Honest print

  • Generation is relation-heterogeneous: for currency, the non-readable rest alone makes the model speak the answer (94%); for capital, both halves are needed (85% together, ~0% each alone).
  • The readable part's contribution to generation is model-specific, not a scale law: patching it alone reaches 29.5% exact match in Qwen3-8B but only 8.9% in Qwen3-1.7B and 4.9% in Gemma-2-9B — the 8B is the odd one out, and we have no account of why.
  • The marker test has n=4 countries. All 72 cells across three models point the same way, but it is a small n and we say so.

Reproduce it: scripts/op_vocab_portrait.py and scripts/op_vocab_causal.py in jspace-qwen, with committed summary JSONs; scripts/verify_numbers.py recomputes every number above. Context: this speaks to Todd et al. (function vectors decode to answer exemplars) and Nadaf (steerable but not decodable) — both correlational projections; the split above is the causal version, and the syncretic marker is the piece neither could build.

Want the background first? The paper, explained simply · the interactive scene · what's next.