Paper Findings
Paper Findings
This note is the current planning surface for the paper's findings and their supporting figures. It supersedes Claims, which remains only as a historical reference for older claim wording.
Claim Versus Finding
Use finding for a paper-facing empirical takeaway that is directly supported by a figure, table, or diagnostic. Use claim internally for broader assertions the paper must support, including conceptual and methodological claims. Use result, theorem, or proposition for theory-facing statements.
Boxed Finding N environments are reasonable if used sparingly. A good target is four or five boxed findings in the main paper, each attached to a main figure or a compact result paragraph. Avoid boxing setup facts, terminology choices, or weakly supported interpretations.
Candidate Main Findings
F1 — Implicit Strategy Structure In The Base Model
Strategy information is decodable in the base model, motivating a factorization that exposes it as a controllable latent variable.
Role: Core.
Primary evidence: Entanglement heatmap and path:paper/figure-production/entanglement_heatmap.
Current figure status: production draft exists.
Decision: use this safer wording because the heatmap directly supports hidden-state decodability, while controllability is the motivation for the router-generator factorization.
F2 — ELBO Under-Specification And Collapse
Standard conditional ELBO is under-specified for strategy-structure recovery: it can preserve marginal behavior while leaving inert or unaligned.
Role: Core.
Primary evidence: ELBO failure wrapfigure, path:paper/figure-production/elbo_failure_dynamics, and ELBO under-specification and the z-ignoring solution.
Current figure status: production variants exist; selected variant pending.
Decision: treat this as a boxed methodology finding if the paper keeps the ELBO-failure wrapfigure. The formal calculation explains why the failure is possible; the figure shows the empirical training dynamics: distributional fidelity rises while posterior-router KL collapses and strategy alignment remains low.
F3 — Strategy-Aligned Router-Generator Factorization
Base-directed reconstruction learns strategy-aligned router-generator factorizations.
Role: Core.
Primary evidence: Latent dynamics, path:paper/figure-production/latent_dynamics, and method metric summaries.
Current figure status: production draft exists.
Decision: support this finding with both latent dynamics and method metric bars. Latent dynamics provides the visual evidence that becomes strategy-structured; metric bars provide quantitative evidence across methods/tasks.
F4 — Base-Directed Mechanisms
The global scale and token weighting mechanisms each affect recovery; their combined variant is the main base-directed objective.
Role: Supporting mechanism/ablation evidence.
Primary evidence: path:paper/figure-production/method_metric_bars and Base-directed reconstruction variants.
Current figure status: production family exists.
Decision: do not treat this as a boxed finding. The global scale and token weighting comparison supports F3 and F5 by explaining which parts of the objective matter.
F5 — Alignment-Reconstruction Frontier
Runs trace an alignment-reconstruction frontier: models that explain more residual surprise with also show stronger strategy alignment.
Role: Core.
Primary evidence: phase-space dynamics figure, method metric bars, and Metrics and frontier language.
Current figure status: production rename is complete; the current figure family lives at path:paper/figure-production/phase_space_dynamics.
Key decision: decide final axis labels and how this figure should coordinate with the main method metric bars.
F6 — Cross-Input Semantic Consistency
Recovered latents show evidence of cross-input semantic consistency, not merely within-input strategy separation.
Role: Core.
Primary evidence: path:paper/figure-production/method_metric_bars, which includes Analogical Consistency as a metric, plus Analogical consistency intervention for the evaluation schematic.
Current figure status: Analogical Consistency is currently present in the method metric bars. No separate production figure is required unless an additional diagnostic shows information not already visible in the bars.
Decision: keep this as a boxed finding, but use conservative wording tied to Analogical Consistency. Do not add a standalone Analogical Consistency bar figure because it would duplicate the method metric bars. Consider a Router Strategy Decodability versus Analogical Consistency scatter as an appendix diagnostic only if it reveals a nontrivial relationship beyond the bar figure.
F7 — Adapted-From-Base Initialization Pathology
Initializing at the base model creates a collapse-prone adaptation regime that requires objective tuning.
Role: Discussion point or supporting analysis.
Primary evidence: Initialization pathology and path:paper/conference-paper/figures/init-pathology.tex.
Current figure status: editorial note exists, but there is not currently a figure directed specifically at this claim and no finalized production artifact has been identified in paper/figure-production.
Key decision: likely treat this as discussion/practical limitation language unless a dedicated figure is developed.
Supporting Findings And Messages
S1 — Lightweight Adaptation
Lightweight adaptation can be sufficient: LoRA-backed router-generator factorizations can recover strategy structure.
Evidence: pretrained variants in path:paper/figure-production/method_metric_bars, possibly with an appendix LoRA-vs-full ablation.
Disposition: likely text paragraph plus appendix figure, unless central to contribution framing.
S2 — Qualitative Controllability
Strategy-conditioned generation is qualitatively controllable: fixing or selecting changes the solution strategy.
Evidence: no active conference-paper figure currently supports this as a standalone qualitative panel.
Disposition: strong reader-facing support; decide whether to integrate into F3 figure/caption or place in appendix.
S3 — Benchmark Setup
The controlled multi-strategy algorithmic benchmark enables precise measurement of strategy alignment and cross-input semantic consistency.
Evidence: Task data and evaluation setup.
Disposition: important setup language, but probably not a boxed finding.
T1 — Theory Result
A positive profiled ELBO margin is sufficient for strategy recovery in the theory model.
Evidence: path:paper/theory_section and Strategy recovery theory language.
Disposition: should be a theory result, not an empirical finding.
Candidate Boxed Findings
The main paper probably should not box every item above. The current candidate boxed set is:
- Implicit strategy structure: strategy information is decodable in the base model, motivating a factorization that exposes it as a controllable latent variable.
- ELBO collapse: standard conditional ELBO preserves observable behavior while leaving the latent unaligned. This finding can live in the methodology section because it motivates the proposed objective.
- Strategy-aligned factorization: base-directed reconstruction learns strategy-aligned router-generator factorizations.
- Alignment-reconstruction frontier: residual surprise explained by tracks strategy alignment across objective variants.
- Cross-input semantic consistency: recovered latents show evidence of reusable strategy semantics across related inputs, as measured by Analogical Consistency.
F4, the comparison of global scale and token weighting, is supporting ablation evidence rather than a boxed finding.
Do not box the adapted-from-base initialization pathology unless a dedicated figure is developed. In the current paper structure, it is better treated as discussion or supporting analysis about the practical difficulty of the adaptation regime.
Current Figure Audit
Motivation Cartoon / Concept Figure
Keep as introduction/motivation figure, not a boxed finding.
Current note: Motivation conceptual plots.
Production status: path:paper/figure-production/concept-figure draft.
Supports: setup and problem framing.
Edits needed: update caption and language to match router-generator factorization and latent strategy variable terminology.
ELBO Failure Dynamics
Keep as methodology wrapfigure or compact diagnostic.
Current note: ELBO failure wrapfigure.
Production status: path:paper/figure-production/elbo_failure_dynamics draft variants.
Supports: F2.
Edits needed: select variant; update caption to standard conditional ELBO, z-ignoring factorization, and collapsed corner language.
Entanglement Heatmap
Keep as main figure.
Current note: Entanglement heatmap.
Production status: path:paper/figure-production/entanglement_heatmap draft.
Supports: F1.
Edits needed: consider retitling around implicit strategy information rather than entanglement.
Latent Dynamics
Keep as main figure or combine with metric summary.
Current note: Latent dynamics.
Production status: path:paper/figure-production/latent_dynamics draft.
Supports: F3.
Edits needed: retitle around strategy-aligned latent dynamics or strategy-structure recovery; verify representative task/run choice.
Method Metric Bars
Main figure.
Current note: Method metric bars.
Production status: path:paper/figure-production/method_metric_bars draft family.
Supports: F3, F4, F6, and S1.
Edits needed: update labels to ELBO, -ELBO, global scale, token weighting, global + token, token inverse. Use Strategy Alignment as the compact figure label for cross-input latent strategy alignment, with the caption defining it as measured by Analogical Consistency.
Alignment Diagnostics
Current analysis figure pair.
Current notes: KL alignment phase space and Token reconstruction strategy alignment scatter.
Production status: path:paper/conference-paper/figures/alignment-diagnostics.tex is input by the experiments section and points to phase-space and metric-association production artifacts.
Supports: F5.
Edits needed: coordinate this current KL/token-reconstruction diagnostic framing with the older alignment-reconstruction frontier language.
Initialization Pathology
Discussion or supporting analysis unless a dedicated figure is developed.
Current note: Initialization pathology.
Production status: TeX include exists at path:paper/conference-paper/figures/init-pathology.tex; no finalized figure-production directory identified.
Supports: F7.
Edits needed: decide role; create or refresh production artifact if retained.
Cross-Input Semantic Consistency / Analogical Consistency
Appendix diagnostic only if it adds information beyond the method metric bars.
Current note: Analogical consistency intervention.
Production status: path:paper/conference-paper/figures/wrap-analogical-consistency.tex is currently input by the experiments section.
Supports: F6.
Edits needed: the current wrapfigure defines the intervention; the quantitative metric remains in the method metric bars. A standalone Analogical Consistency bar plot is not recommended because the same information is already in method metric bars.
Qualitative Strategy-Conditioned Generations
Likely appendix or inset/table near F3.
Current note: none in the active conference-paper figure roster.
Production status: no production artifact identified.
Supports: S2 and F3.
Edits needed: decide whether the paper needs qualitative evidence in main text.
Architecture Schematic
Appendix or methodology figure if needed.
Current note: Architecture parameterization.
Production status: path:paper/shared/figures/architecture-figure/architecture-autoregressive-compact.tex is currently input by the methodology section.
Supports: method explanation.
Edits needed: update terminology to router/generator/shared adapted model.
Token Weighting / Objective Schematic
Consider a dedicated methodology figure note if this becomes important.
Current note: Token-level surprisal-share weighting.
Production status: path:paper/conference-paper/sections/03-methodology.tex includes a token-weighting figure.
Supports: method explanation and F4.
Edits needed: align with global surprisal scale and token-level surprisal weighting language.
Additional Figure Ideas To Consider
Benchmark Overview Table Or Schematic
Show the six task families, examples of problem instances, and strategy annotations. This would support setup clarity rather than a boxed finding.
Base-Directed Reconstruction Mechanism Schematic
A compact method figure explaining global surprisal scale and token-level surprisal weighting. This may be more useful than a dense equation-only methodology passage.
Router Strategy Decodability Versus Analogical Consistency Scatter
Appendix candidate. Plot Router Strategy Decodability against Analogical Consistency across runs or method settings. This is worth including only if it shows a nontrivial relationship not already visible in method metric bars, such as methods with locally decodable strategy information but weaker cross-input consistency.
Analogical Transfer Example Panel
Not recommended for the current paper plan. It would likely be too qualitative and space-expensive relative to the existing metric evidence.
Latent-Region Strategy Consistency Map
Appendix candidate only if it is behavioral or interventional. A representation-only map would likely duplicate router linear-probe and latent-dynamics evidence. It would add value only if it reveals local semantic drift, input-dependent relabeling, or generator behavior not captured by the linear probe.
Final Strategy-Conditioned Generation Table
Show one problem instance with multiple choices producing different solution traces. This would make controllability legible to readers who do not fully trust latent scatter plots.
Theory Preview Diagram
Optional. Could illustrate the profiled score as “latent information minus router-generator cost,” but likely unnecessary unless the theory section feels too abstract.
Immediate Decisions
- Decide the main-body figure roster and space budget.
- Decide whether to create an appendix Router Strategy Decodability versus Analogical Consistency scatter.
- Decide how much main-text space to give the phase-space dynamics figure relative to method metric bars.
- Eventually decide whether to delete Claims or keep it as a historical reference.
