KernelNarrative.md

Kernel PE Narrative (Finalized Posture)

Version: May 4, 2026
Scope: Narrative guidance synced to finalized controls and E28/E29/E30/E31 hardening bundle (E28A/B/C/D, E29A/B/C, E30A/B, E31A/B/C/D).

Reproducibility note: The submission package includes an anonymized GitHub repository with the code, scripts, environment specification, and artifact-mapped commands used to reproduce claim-bearing results.

1) One-sentence thesis

RoPE exposes an understudied shift-invariant channel, trained models use that channel in load-bearing but heterogeneous ways, and the resulting evidence supports a bounded case-study narrative: strong head-level specificity (Result I), non-SI-unique collective context (Result II), bounded functional probe sensitivity (Result III), broader heterogeneity beyond the primary trio (E31A), and a CS-inspired framework lens for future prediction (still mixed in expanded refresh, E31B).

2) Claim hierarchy (what is strongest)

1. Primary claim (Result I): permutation-specific SI-kernel subtraction disruption is real and load-bearing; E28A/B/D plus E29A and E30B strengthen head-level specificity and anti-tautology evidence.
2. Supporting organizational observation (Result II): ranked cumulative ablation robustly rejects linear depletion, but matched non-SI controls show this collective nonlinearity is mostly generic.
3. Supporting scoped functional finding (Result III): controlled offset-repetition probe sensitivity is directionally positive in all primary models; strict confound control is model-conditional, broader probe-diversity transfer is non-passing, natural-text long-context transfer is 2/3 model-conditional, and boundary-grid transfer is also 2/3 with non-universal factor directionality.
4. Supporting breadth/coupling extension (E31A/C): expanded model breadth preserves large SI heterogeneity; model-level SI amplitude directionally tracks preferential functional disruption on tested probe suites.
5. Supporting theoretical lens (Appendix H + E31B): corrected Exp7A is mixed at model level (proxy geometry, small effective n), corrected Exp7B remains strongly directional under canonical single-condition calibration, and E31B expanded refresh is mixed; treat the CS stack as framework-level, not mechanism-proof.

3) Post-E28 interpretation anchors

E28A

• 20-bin exact one-tailed permutation testing removes the old small-n fragility.
• Use exact values directly (Llama/Mistral p=5.0e-06, OLMo p=7.05e-04).

E28B

• SI-ranked intervention exceeding importance-matched non-SI control in all 3 models is the cleanest anti-"generic important heads" evidence.

E28D

• R^2_excess tracking supports non-trivial SI beyond local-decay null in Llama/Mistral, but not OLMo.
• Frame as model-conditional strength, not universal.

E29A

• Kernel-transplant specificity supports SI structure-level relevance beyond low-head self-kernel subtraction.
• Use as direct anti-tautology hardening: transplanted high-SI kernels on low heads are more disruptive than low-head self subtraction in all three primary models.

E29B

• Semi-naturalistic long-context passkey families (wiki/code, 256--512 contexts) support preferential SI disruption in Llama and Mistral, not OLMo (2/3 pass).
• Use as bounded functional extension, not universal downstream proof.

E29C

• Qwen2.5-7B quick anchor is non-primary and non-corroborating in this run.
• Keep as directional-only context with no claim promotion.

E30A

• Boundary-grid extension (short/long × high/low regularity) reproduces the same model split as E29B: Llama/Mistral pass, OLMo non-pass (2/3).
• Do not claim a universal factor law: regularity and length contrasts are not directionally consistent across models.

E30B

• Local-bias null-family decomposition (exponential/power-law/window) retains non-trivial excess tracking support in 2/3 models.
• Use as a stronger metric-validity control that complements E28D.

E31A

• Breadth consolidation over 11 models / 7 families shows large SI-amplitude heterogeneity (max/min mean R² ratio 140x).
• Use as descriptive breadth extension, not causal attribution.

E31B

• Expanded proxy coherence-gap refresh is mixed (r=+0.577, rho=+0.500, non-significant at conventional thresholds).
• Keep CS lens as potential framework; do not promote as confirmatory explanatory law.

Exp7A / Exp7B (corrected CS audit posture)

• Exp7A is explicitly proxy-based (analytic PE metadata descriptors, not learned PE-matrix extraction) and should be read at model-level effective n:
  • model-level (n=6): Pearson r=+0.731 (p=0.099), Spearman rho=+0.516 (p=0.295), two-sided permutation p=0.141
  • 36-row table remains exploratory/pseudo-replicated context only
• Exp7B now matches manuscript-calibration wording in canonical outputs:
  • single-condition calibration C=7.057 on Llama-3.1-8B (seq-len 256)
  • six-condition fit: Pearson r=-0.959, Spearman rho=-0.878
  • out-of-sample (n=5, excluding calibrated condition): Pearson remains strong (r=-0.986), Spearman directional/marginal (rho=-0.866)
• Global-fit reference (C=7.834) is retained as sensitivity context, not the canonical calibration mode.

E31C

• Reanalysis across existing probe suites (E12/E29B/E30A) shows strong directional coupling between model mean R² and preferential functional gap.
• Use as bounded “so-what” linkage, explicitly within tested probes/models.

E31D

• Llama naturalistic add-on: SI-targeted ablation > importance-matched non-SI and > permuted controls across 60 prompts.
• Use as bounded practical extension for Result III (single-model add-on, not universal transfer).

E28C

• Broader 7-family transfer non-passing (0/3) is a scope bound, not a failure of all SI functionality.
• Keep Result III explicitly “controlled probe” rather than naturalistic ICL generalization.

4) Tokenizer story (how to state it)

Use tokenizer mediation as a model-conditional implementation story, not as the causal explanation of cross-model SI amplitude heterogeneity.

• Supported: Llama boundary-linked SI behavior is tokenizer-mediated in strict diagnostics.
• Not supported: tokenizer overlap alone explains the 6.5x SI amplitude spread.
• Practical phrasing: tokenizer structure is a routing substrate for SI usage in some models; it does not by itself explain why different models amplify SI to different levels.

5) Representational commitment (status)

Treat representational commitment as a falsifiable synthesis hypothesis, not an established mechanism.

Operational statement:

• Current evidence is consistent with SI channels being stably allocated toward sparse positional/surface routing under current training trajectories.
• Short-horizon adaptation has limited retargeting signal.
• Broader semantic SI use likely requires pretraining-era shaping pressure.
• Any resulting downstream performance improvement is a future-work hypothesis, not a finding of this paper.

Do not claim this hypothesis is causally proven for 7–8B production models.

6) What to avoid

• Avoid “SI-specific collective organization is established.”
  • E24/E24b prevent this.
• Avoid broad “SI drives ICL generally.”
  • E28C bounds transfer; keep “controlled offset-repetition probe sensitivity.”
• Avoid “RoPE vs NoPE solved at 7–8B.”
  • E21 is matched 1.1B proxy evidence.
• Avoid claiming full intervention propagation mechanism is established.
  • Current evidence is load-bearing sensitivity under position-dependent subtraction; full softmax-redistribution diagnostics are still pending.
• Avoid implying Llama and Mistral are independent architecture replications.
  • They are close neighbors; OLMo is a weak-SI divergent anchor.

7) Recommended narrative arc in paper text

1. Question: RoPE provides SI capacity; what do trained models do with it?
2. Empirical surprise: 6.5x amplitude spread, not seed noise (E20).
3. Mechanistic intervention evidence: SI-kernel disruption is real and hardens under E28A/B/D.
4. Specificity hardening: kernel-transplant specificity (E29A) shows SI-structured perturbation relevance beyond generic low-head self perturbation.
5. Metric-validity hardening: richer local-bias-family nulls keep 2/3 support for non-trivial excess tracking (E30B), with OLMo as bounded non-pass.
6. Organization caveat: ranked-ablation nonlinearity is robust but not SI-unique (E24/E24b).
7. Functional scope: controlled probe sensitivity is positive; strict control and transfer results bound scope (E18/E28C/E29B/E30A), with a single-model naturalistic add-on strengthening bounded relevance (E31D).
8. Breadth extension: heterogeneity extends across a wider multi-family panel (E31A); functional coupling is directionally positive in tested suites (E31C).
9. Synthesis: representational commitment as forward hypothesis and prediction target, with CS lens kept framework-level due mixed expanded coherence refresh (E31B).

8) Canonical phrasing snippets

• Result I: “Permutation-specific disruption cost is load-bearing under intervention, with strengthened head-level specificity from E28A/B/D plus kernel-transplant and richer local-bias controls (E29A/E30B).”
• Result II: “Ranked-ablation linear rejection is robust, but matched non-SI controls indicate this collective nonlinearity is not uniquely SI.”
• Result III: “SI intervention preferentially disrupts controlled offset-repetition retrieval probes; strict confound survival is model-conditional and broader probe-family transfer is non-passing.”
• Result III extension: “Natural-text long-context and boundary-grid transfer are partially supported (2/3), reinforcing bounded functional relevance rather than universal downstream claims.”
• Capacity caveat: “Matched proxy-scale TinyLlama evidence supports RoPE>NoPE SI separation; matched 7–8B causal training contrasts remain open.”

9) Non-promoted context (keep brief)

• E22/E23 remain context/future-work; do not use as claim-bearing evidence for main Results I–III in this cycle.
• If mentioned, explicitly mark as exploratory and scale-limited.