Current article figures are original SVG diagrams with no measured performance data.

Regenerate the MCMC/amortization cost comparison: python3 assets/blog/learned-sampler/source/render_amortization.py

Regenerate offline and online process diagrams: python3 assets/blog/learned-sampler/source/render_clear_figures.py

Regenerate the shared-backbone LoRA diagram: python3 assets/blog/learned-sampler/source/render_lora.py

Displayed assets: amortized-comparison, offline-stages, lora-sampler, online-cycle, each with a separate mobile composition. The two schedules remain distinct: only online has student-to-sampler feedback after SFT. The comparison separates repeated per-response MCMC search from sampler training and parameter reuse at data-generation time, without claiming a measured speedup.

Earlier categorical/smooth distribution illustrations and source files are kept as unused exploratory assets. The current article no longer depends on A/B ratios. Published baseline scores come from Finetuning with Sampling, arXiv:2610.02140v1, Table 1 math panel. Our displayed numbers are draft estimates, not measurements: Approximately +2 percentage points offline and +3–5 online, with task-level variation. Prior-task values illustrate small gains and losses near the base, not measured retention. Each estimate is derived from an illustrative integer count divided by a specified evaluation size, then rounded only for display. results-data.json records the counts, protocol, sources, and GPQA Diamond assumption. Published baseline rounding is untouched. The prior-task average uses unrounded task percentages; displayed deltas use displayed rounded scores. Counts are planning inputs, not observed outcomes or synthetic run logs. The MCMC + SFT + RL baseline is included as the stronger online comparator.

Regenerate all four result tables and their source-data record: python3 assets/blog/learned-sampler/source/render_tables.py

Verify mathematical identities and sampled gradient relations (requires numpy): python3 assets/blog/learned-sampler/source/verify_math.py

The amortization figure distinguishes response-state updates in MCMC from shared-parameter updates in sampler training. The learned parameters pass into a separate data-generation stage that appends tokens to construct responses; MCMC revises response states. Both routes explicitly terminate in verified SFT data and student SFT. No MCMC trajectories are used as sampler training targets. There are no performance numbers in the diagram. Conceptual references: Finetuning with Sampling (https://aakaran.github.io/finetuning_with_sampling/) and Bengio & Hu on amortized inference (https://yoshuabengio.org/en/blog/scaling-service-reasoning-model-based-ml). Also consulted Bengio’s GFN explanation (https://yoshuabengio.org/en/blog/generative-flow-networks). Offline and online pseudocode are separate.

Opening revision (2026-10-04): SFT efficiency → off-policy mismatch → distribution shift and forgetting → GRPO / OPD → transform the SFT distribution. New references:

• RL’s Razor, arXiv:2509.04259v1: §4 reports the empirical KL–forgetting association; §5 / Appendix A analyze projections under restricted policy-family assumptions. Our Eq. (2–4) corresponds to its rejection-sampling lemma; we do not claim its idealized convergence theorem holds for arbitrary neural-network / GRPO updates.
• Retaining by Doing, ICML 2026 (arXiv:2510.18874v3): §3 gives a Gaussian-mixture explanation, §4.2 tests approximately on-policy SFT, and Appendix A.5 shows that training-task KL does not universally predict forgetting.
• DeepSeekMath, arXiv:2402.03300: §4.1 describes group rollouts and relative-reward advantages. GRPO has no learned critic; the opening does not imply otherwise. The added p_fit = q_data identity is an ideal population-fit explanation, not a forgetting theorem. The KL inequality after Eq. (4) assumes the original data satisfy the same validity constraint. Neither proves retention on unseen tasks.