Agent-drafted interpretation, pending human review

Working Interpretation

The Apr27 grid strengthens the paper-facing C5 baseline story: beta-1 raw CVAE rows keep final-answer accuracy near 0.998 and strategy-match rate near 0.997, but their router probe stays near 0.46, giving matched-strategy router scores near 0.461. This is the cleanest current evidence that marginal behavior can look solved while the sampled router fails to expose strategy structure.

The top rows after the Apr30, May01, and May02 extensions are still not a single objective family. tokinv_a0p25_b0p01_lin100 remains the best mean matched score at 0.9176, while the May01 dist0p25_tokcc0p75_a0p25_b0p01_lin100 row enters the next tier at 0.8870 and the May02 dist0p75_tokcc0p25_a0p25_b0p01_lin100 row follows at 0.8825, close to the original tokcc_a0p25_b0p01_lin100, example_inv_surp_b0p01_lin100, and dist_plus_tokcc_a0p25_b0p01_lin100 rows. For paper framing, this argues for naming a normalized/token-reweighted reconstruction family rather than overcommitting to one exact cell until the cross-regime coverage matrix is settled.

The low-beta caveat remains important, but its shape changed relative to the Apr26 design note. In this Apr27 simple-grid run, raw b0p01 rows are better than raw beta-1 rows but do not match the strongest normalized or token-corrected rows. This makes raw low-beta a useful control panel, not the headline method.

The C3 reconstruction-vs-decodability story needs careful wording. Some low reconstruction-ratio rows such as dist_norm_b0p01_lin100 and example_inv_surp_b0p01_lin100 also have high matched scores, which supports the frontier framing. But tokcc_a0p25 has high matched scores while its baseline-normalized reconstruction values are on a different scale, so the paper figure should avoid claiming a universal monotone relation across all reconstruction-component definitions. A defensible C3 figure should either use family-specific reconstruction measures or explicitly show the objective-scale caveat.

The selected paper bars should probably show both the standard raw beta-1 controls and the low-beta raw controls. This preserves the central contrast: raw beta-1 is the standard ELBO-style baseline and is weak on router decodability, while lowering beta alone improves some controls but does not erase the advantage of the strongest normalized/token-corrected settings in this grid.

The refreshed aggregate now has all 504 expected cells complete, with analogical summaries for all complete artifacts. The current narrative should say the main result tables are a 432-run single-task snapshot, while the refreshed within-task figures summarize the full 72-cell multi_task grid in multitask.

May01 Follow-Up Interpretation

The completed May01 follow-up weakens the case for alpha-1 inverse-surprisal token weighting as a main method. Both alpha-1 token-inverse-surprisal rows keep final-answer accuracy high, but their best fixed matched scores are materially below the alpha-0.25 tokinv row: tokinv_a1_eps1em4_b0p01_lin100 is 0.7765 and tokinv_a1_eps1em8_b0p01_lin100 is 0.6511 versus 0.9176 for tokinv_a0p25_b0p01_lin100.

The distribution-normalized/TOK-CC mixtures are more promising as robustness checks. dist0p25_tokcc0p75_a0p25_b0p01_lin100 reaches 0.8870 mean matched score across all six single-task datasets, and dist0p75_tokcc0p25_a0p25_b0p01_lin100 reaches 0.8825, both near the original tokcc_a0p25_b0p01_lin100 row at 0.8811 while keeping the reconstruction component on the small normalized-loss scale. This looks useful for the C3/C5 story because it reduces the objective-scale awkwardness of pure TOK-CC without giving up much router decodability.

C7 Analogical Consistency Interpretation

The analogical-steering results support the C7 framing that the recovered latent has cross-input semantic stability when the router-side latent is already strategy-decodable. Across the 432 complete single-task runs with analogical summaries, analogical set-overlap correlates strongly with the matched-strategy router score (r = 0.9275) and router probe (r = 0.9246), while it is weakly related to sampled strategy-match rate and final-answer accuracy. This is useful because it separates reusable latent semantics from merely producing valid or accurate outputs.

The strongest analogical rows are not exactly identical to the highest matched-router rows. tokinv_a0p25_b0p01_const has the highest mean analogical set-overlap at 0.9535, while tokinv_a0p25_b0p01_lin100 has the highest matched-router score at 0.9176 and analogical set-overlap 0.9502. The May02 dist0p75_tokcc0p25_a0p25_b0p01_lin100 row has analogical set-overlap 0.9316. The paper should therefore avoid implying that analogical transfer is just a restatement of the main matched score. A safer claim is that analogical consistency tracks router factorization quality overall, with some beta/schedule details affecting the cross-input stability diagnostic.

For C7, the most direct paper-supporting figure is the analogical-overlap versus matched-router scatter, with the beta-robustness and agreement-decomposition figures as appendix diagnostics. The three-bar loss-setting summary is useful as a bridge: it shows that the same selected objectives improve router decodability and cross-input semantic consistency, while raw ELBO-style rows remain low on both despite high final-answer and strategy-match rates.

Within-Task Strategy Decodability Interpretation

The complete 72-cell multi_task slice adds an important qualification to the global multi-task probe. Global router probes are low because the metric asks for a single global linear separator over task-prefixed strategies, but within-task probes show that several loss settings still encode strategies clearly when each task is decoded separately. The strongest row, tokcc_a0p25_b0p01_lin100, has global router probe 0.3940 but within-task router probe 0.8936, with posterior within-task probe 0.9985.

This supports a weaker but useful form of latent strategy structure: a latent region may not carry the same strategy meaning across tasks, yet still organize strategies coherently within each task. For the paper, this distinction should be explicit. The global multi-task probe is evidence about shared cross-task strategy coordinates; the within-task probe is evidence about per-task strategy separability under possible coordinate reuse.

The within-task result also makes the multi_task failure mode more diagnostic rather than simply negative. Strong single-task objectives such as token concentration correction still recover per-task strategy geometry in the joint task, but they do not necessarily force a globally aligned strategy atlas. A natural next test is an alignment constraint or task-conditioned affine probe that separates "same linear coordinates across tasks" from "same latent space but task-dependent coordinate meanings."

Paper-Figure Implications

Use figures/apr27_paper_metric_bars_selected_lora.png for the main C5-style decomposition panel: final marginal behavior is high across many settings, but router probe separates standard raw beta-1 baselines from the stronger normalized/token-corrected objectives.

Use figures/apr27_heatmap_matched_score_family_beta_schedule.png as the compact sweep view for appendix or methods-adjacent discussion. It shows the beta and schedule dependence without requiring readers to parse all 30 loss-setting labels.

Use figures/apr27_scatter_reconstruction_vs_matched_score_logx.png only with an objective-scale caveat. It is useful as a frontier plot, but it should not be the only evidence for C3 unless paired with the objective component scale audit from the repo-side report or split by reconstruction family.

Follow-Up Checks

Use the multi-task side report to decide whether the next experiment should target global cross-task alignment, for example with an alignment regularizer or a task-conditioned affine probe diagnostic.

Compare Apr27 dist_plus_tokcc_a0p25_b0p01_lin100 and tokcc_a0p25_b0p01_lin100 against the older Apr24/Apr26 dist_plus_tokcc_a0p5_b0p01_d50_lin50 recommendation before changing the paper's named main method.

For the final paper figure, decide whether the main method is a single row, a selected family, or a two-panel story with dist_norm/example_inv_surp as reconstruction-ratio frontier rows and tokcc as router-factorization evidence.