Result: "User:/Assistant:" is the chat map in different coordinates; narrative framing is what collapses it

Superseded (2026-07-23): this framing-half writeup is folded into the combined doc 2026-07-23_one_operator_framing_vs_identity.md, which adds the identity half (#1310, #1639, #1335) and the assistant direct test. Read that one.

Motivation

• The last update left a tension: the assistant context→answer map holds up in plain "User:/Assistant:" transcripts with no chat template, but collapses for generic stories (#825) — even though plain transcripts look superficially story-like.
• This raises the question: why does the mapping hold in "User:/Assistant:" format but not in stories?
• The original story comparison had confounds that could each explain the split:
  • equal predictive R² across formats does not mean the same operator
  • the stories were a different corpus with arbitrary characters, not the assistant persona
  • story activations were read at one position, chosen by convention
  • the story answers were captured teacher-forced
• I ran ablations removing each confound (#1345, #1310): the same conversations rendered in three framings (chat template / plain "User:/Assistant:" / narrative story whose character is named "Assistant"), operator-identity tests, a read-position sweep, and an on-policy story arm.

TLDR

• "User:/Assistant:" is not story-like to the model — it is the same operator as chat, expressed in different linear coordinates:
  • naive cross-format transfer falls short of each format's ceiling (mean deficit −0.10 instruct / −0.43 base), but a fitted general-linear change of coordinates recovers each ceiling to within 0.005–0.008 (nulls ≈ −0.03), in both models
  • instruction tuning pulls the two coordinate systems together: raw operator cosine 0.651 (instruct) vs 0.293 (base); rotation-aligned 0.855 vs 0.732
• Narrative framing collapses the map on identical conversations — a framing effect, not a corpus effect:
  • same conversations, original answers embedded verbatim in a story: R² −0.31 vs +0.24 chat on the same 2,163 rows
  • same conversations, the story character answering freely (on-policy, 2,018 rows): −0.55 vs +0.53 chat — so teacher-forcing is not the cause (it inflates the story read by +0.075)
• The collapse is partly positional, but no read position rescues it:
  • sweeping four other context read positions, the best slot (last token before the answer) rises from −0.31 to −0.02 (adjusted CI −0.04 to +0.01, straddling zero); the max-over-slots deficit vs chat stays wholly negative (−0.26, CI −0.28 to −0.24)
• The failure sits in the story context representation, not the answers — and the operator is still the same one:
  • the story operator reparameterized into chat recovers 0.61 (teacher-forced) / 0.56 (on-policy) against matched-row chat ceilings of 0.24 / 0.53, and chat contexts predict the story answers at 0.56 — the information and the map survive; the story context slot just is not linearly readable
• Fiction characters do support a much weaker per-character map:
  • a fixed-label story character's context→dialogue map clears its shuffle null in both models once each scene is aggregated to one point (base 0.13–0.22, instruct 0.23–0.40) and is character-specific (correct pairing beats the character swap by pooled R² +0.30 base / +0.38 instruct) — so stories do carry a weak per-character map, far below the assistant one
• (The pending Result-3 number from the last update also landed:) instruct single-turn no-template R² = 0.625 (vs 0.654 chat); base 0.578 (vs 0.542 chat) — off-template the base reaches ~93% of instruct strength (vs ~83% with the template), which strengthens the pretraining-inheritance picture

So the answer to the question: the discriminating variable is whether the context ends in a turn-structured speaker-label + response slot, not how story-like the surface text looks. Plain "User:/Assistant:" keeps that structure, so it is the same map up to a linear change of coordinates. Narrative prose genuinely moves the context into coordinates no linear map reads, even though the same operator and the same answer information are still present.

Methodology

• Models: Qwen2.5-7B (pretrained base) vs Qwen2.5-7B-Instruct
• Same rig as the last update: $v_C$ = activation at the end of the context, $v_A$ = mean activation over the answer span, closed-form ridge (GCV-selected penalty), 5-fold conversation-grouped CV, held-out R², layer 19 headline, conversation-level shuffle nulls + bootstrap CIs
• Three framings of the same assistant persona: chat template / plain User: … Assistant: … / narrative prose in which a character named "Assistant" answers a human character's spoken question
• Data per arm: chat and no-template use the parent's 4,724 LMSYS single-turn conversations, answers generated on-policy by the measured model; paired stories re-render 2,163 of those same conversations as instruct-written narrative with the original answer embedded verbatim (capture teacher-forced at the fixed answer span); on-policy stories re-render 2,018 of them with the story character answering freely in its own words (one sample per conversation, temperature 1.0)
• Operator-identity tests: naive cross-framing transfer; Procrustes-aligned operator cosine against a random-rotation null; general-linear reparameterization $A \cdot M \cdot B$ (the Result-2 method from the last update) against matched-capacity nulls

Results:

Result 1: "User:/Assistant:" is the same operator as chat, in different linear coordinates

Equal R² across formats does not establish the same map, so I first tested operator identity directly on the chat / no-template pair.

Methodology (this result):

• Fit the map separately per format on the shared 4,724 conversations (identical folds)
• Apply each format's frozen map in the other format (naive transfer), then retry with fitted linear input/output alignments around the frozen map (reparameterization), against matched-capacity nulls
• Compare the operators directly: raw cosine and Procrustes-aligned cosine vs a rotation null

Takeaways:

• Naive transfer misses each ceiling (mean per-direction deficit −0.103 instruct / −0.430 base, bootstrap CIs excluding zero) — the two formats are not literally the same coordinates
• But a general-linear change of coordinates recovers each format's full ceiling: recovered R² lands between 0.005 below and 0.008 above the target ceiling in all four cells (matched-capacity nulls −0.02 to −0.03) — one operator, two coordinate systems
• Instruction tuning canonicalizes the coordinates: raw operator cosine 0.651 (instruct) vs 0.293 (base), aligned 0.855 vs 0.732 (rotation null ≈ 0.001)
• The single-turn no-template numbers pending in the last update also landed (#825): instruct 0.625 no-template vs 0.654 chat; base 0.578 vs 0.542 — the template helps instruct slightly and hurts the base slightly

Result 2: Narrative framing collapses the map on identical conversations — teacher-forced and on-policy

The parent's story result used a different corpus, so I re-rendered the same conversations as narrative stories, first with the original answers embedded verbatim, then with the story character answering freely.

Methodology (this result):

• 2,700 of the 4,724 shared conversations rendered by the instruct model as short narratives in which a person asks the original question aloud and a character named "Assistant" replies with exactly the original words (Assistant replied: "…"); 2,163 survive the verbatim-embedding + judge gates; capture teacher-forced at the answer span
• An on-policy companion at powered n: 2,018 conversations where the story character answers freely in its own words (no reference answer anywhere in the generation prompt)
• Matched-row chat and plain-text refits on the same conversations as comparators; verdict = the story cell's conversation-bootstrap CI (wholly below zero = framing effect, wholly above = corpus effect)

Takeaways:

• Framing effect, both arms: verbatim-embedded stories read R² −0.31 (CI −0.33 to −0.28) vs chat +0.24 on the same rows; on-policy stories read −0.55 (CI −0.57 to −0.52) vs chat +0.53 — per conversation the story map is worse for 88% / 98.6% of rows
• The matched-row chat ceilings sit below the full-corpus 0.65 because the story gates keep a selected subset (plain text reads 0.02 on the teacher-forced round's rows) — all comparisons here are within the same row set
• Teacher-forcing does not create the collapse: it inflates the story read by +0.075 on matched rows, and the on-policy run is more collapsed (−0.55 vs −0.31)
• The story maps still beat their shuffle nulls (≈ −2.0) — a residual weak signal exists, but the map predicts worse than the answer mean at every layer

Result 3: The collapse is partly positional, but no read position recovers the chat ceiling

The story cells were read at one conventional position (the colon in Assistant replied:), so I swept the read position to check whether the collapse is just a bad slot.

Methodology (this result):

• Four additional context read positions per story — end of the question utterance, last token before the attribution sentence, last token fully before the answer span, and a mean-pool over the attribution phrase — all captured in one teacher-forced forward over the same 2,163 stories (answer-span overlap 0.0 by construction)
• Verdict statistic D = the per-draw max over slots of the paired deficit vs the same-rows chat comparator (1,000 conversation-grouped bootstrap draws; per-slot CIs Bonferroni-adjusted)

Takeaways:

• The anchor's extreme read was partly the slot: the last token before the answer rises from the anchor's −0.31 to −0.02 (adjusted CI −0.04 to +0.01, straddling zero); the other slots read −0.26 to −0.40
• But no position recovers chat: the max-over-slots deficit D = −0.259 (CI −0.276 to −0.243), wholly below zero — at best the story context carries no linear map to the answer at any probed position

Result 4: The failure sits in the story context coordinates; the operator itself reparameterizes into chat

If the operator is shared and only the coordinates differ, the story-side operator should recover the chat ceiling once linearly re-expressed — so I ran the Result-1 reparameterization on the story/chat pair.

Methodology (this result):

• Same data-paired reparameterization as Result 1, both directions, on the paired (teacher-forced) and on-policy story rounds; shuffled-fit and rotation nulls

Takeaways:

• The reparameterization is one-way: the story operator moved into chat recovers 0.61 against the matched-row chat ceiling of 0.24 (teacher-forced) and 0.56 against 0.53 (on-policy), while the chat operator moved into story coordinates fails (−0.17 teacher-forced; +0.16 on-policy, weakly positive at best). Landing above the matched ceiling is partly a two-stage-ridge composite effect (the fitted alignments add capacity), so I read it as the story operator carrying the chat map's content, not as super-recovery
• The answer side is intact: chat contexts predict the story answers at 0.56 — the story answer representation is a normally predictable target; the failure is specifically that nothing linearly reads the story context slot
• I read this as one shared operator whose story-side context coordinates carry framing-specific variability the ridge cannot see through (the alignment asymmetry — context alignments +0.25 story→chat vs −0.26 chat→story, answer alignments ~0.78 both ways — is the errors-in-variables signature)

Result 5: A fixed-label fiction character supports a real but much weaker per-character map

The parent pooled across arbitrary story characters, so I also tested the cleanest story-side analog: one fixed character with a stable name, many stories, one map per character (#1310).

Methodology (this result):

• 4-persona panel, on-policy stories generated per model with the character always under the same label; context→that-character's-dialogue ridge maps, per persona, base and instruct
• Character-swap control (fit on character A, test on character B's dialogue) and scene-level aggregation (one point per scene)

Takeaways:

• Scene-aggregated, all four personas clear their shuffle nulls in both models: base 0.13–0.22, instruct 0.23–0.40
• The map is character-specific: the correct pairing beats the character swap by pooled R² +0.30 (base) / +0.38 (instruct)
• Grain caveat: aggregated R² is not comparable to the per-turn assistant ceiling (0.588 base / 0.673 instruct) — averaging ~5–6 completions per scene mechanically raises attainable R²; at the per-turn grain the fiction maps stay far below the assistant map

Next Steps

• Localize what breaks in the story context coordinates: the collapse is context-side and not positional — a token-position / component ablation of $v_C$ (still the open Q4 from the last update) should say which content the story coordinates scatter.
• Nonlinear probe on the story cells: all story fits are ridge-only; the two-turn result showed the MLP is format-invariant where ridge fails, so an MLP on the story context slot would say whether the collapse is linear-only.
• Base-model paired-story arm: untested (base story generation yields were too low to run); the framing-effect verdict is instruct-only so far.
• Why the assistant map is so much stronger than fiction-character maps (#1335): the per-character maps exist but sit an order below — what the assistant persona has that fixed fiction characters lack is the open question.