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. On 2026-10-04 the author confirmed all current offline and online scores as real results. The table now displays them without draft badges or footnote markers. This is author confirmation, not an independent audit of evaluation logs.

Offline Math avg. is 55.5% (+2.1pp versus MCMC + SFT); online is 59.4% (+6.0pp). Prior avg. is 42.1% offline and 42.2% online, slightly above plain MCMC + SFT and at or below the base model. Scores and averages are unchanged by confirmation. results-data.json records the current confirmation separately from earlier drafts. Integer reconstruction counts originated during drafting; they provide the existing arithmetic precision but are not claimed to be observed correct-count logs. Published baseline task scores and prior averages are preserved. Math averages use the published scores, with decimal half-up display. Prose gains use displayed averages. GPQA Diamond remains the reconstruction basis; the reference paper’s variant and seed aggregation are unspecified. MCMC + SFT + RL is excluded again at the author’s latest request. Its historical published scores remain in the source record only; no displayed comparison uses them. The author confirmed online reward is the existing GFlowNet target density (student probability × verification); it trains the sampler, while the student uses SFT. No extra student RL stage is inferred. Both algorithms now specify group rollouts, centered log-gap loss, frozen parameters, and separate student SFT updates.

Regenerate the aggregate comparison and optional per-task breakdown 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.

Table layout (2026-10-04): one shared comparison for offline and online. The main view shows Math avg. and Prior avg. Explicit comparisons are in the results prose. A disclosure preserves all seven task scores, with New tasks and Prior tasks grouped and separated by a dashed rule. OPSD, GRPO, and UFT are retained and explained in Setup. New sources: OPSD (arXiv:2601.18734) and UFT (arXiv:2505.16984, §3).

Render the fixed online trajectory (requires numpy and matplotlib): python3 assets/blog/learned-sampler/source/render_online_curve.py

online-training-curve.svg / -mobile.svg and the PNG share the stored trajectory. On 2026-10-04 the author explicitly confirmed all plotted values, including the intermediate points. The public figure attributes the confirmation to the author. The renderer now reads online-curve-data.json without generating noise or replacing points. Its normalized axis does not imply particular training-step counts. The data record preserves the original construction history alongside the later author confirmation. Raw training logs were not independently inspected; no variance, runtime, or convergence-rate measurements are inferred from this confirmation.

Reference-image replacements (2026-10-04): Four figures now use built-in imagegen edits of the author’s supplied reference PNGs:

• amortized-expert-to-onpolicy.png: repeated MCMC response search vs learned sampler reuse;
• offline-expert-to-onpolicy.png: freeze student, fit sampler, transform expert data, SFT;
• lora-sampler-expert-to-onpolicy.png: shared backbone with adapter enabled / disabled;
• online-expert-to-onpolicy.png: fixed expert input and updated-student feedback loop. Each has a dedicated -mobile.png portrait composition selected below 760px. Exact source filenames and all editing prompts are in reference-image-edit-prompts.json. The older SVGs remain as source explorations; their renderers do not update these PNGs. The figures emphasize off-policy expert traces → student-aligned training data. Outputs approximate the verified, expert-constrained student target; “on-policy” does not claim exact sampling from the unconstrained student. Offline alignment is with the frozen reference student; online refits the adapter as the student evolves. The comparison separates response updates in MCMC from parameter learning in the sampler, and claims no measured speedup. Both data sources are expert-guided.

Typography and label refinement (2026-10-04): The displayed versions use -v2.png / -v2-mobile.png assets. Outputs are labeled Calibrated “on-policy” data, without output y or verified subtitles. Inter-style regular/medium labels and restrained semibold titles match the blog typography; muted blue/orange/teal panels retain the original technical flows. Exact edit prompts and final asset names: reference-image-refinement-prompts.json.

E2S educational edition (2026-10-05):

• Narrative adapted from the author’s e2s_finetuning_educational_blog.html; the existing measured experiment setup, results and data records are preserved.
• Eight *-e2s-v3 PNGs refine the existing four figure compositions using the Uni-LaDiR paper Fig. 1 style. Built-in imagegen prompts and targeted arrow/color corrections are recorded in e2s-figure-prompts.json. Original versions remain.
• render_e2s_charts.py reads results-data.json and online-curve-data.json directly. It writes paired result bars and the online curve, with MCMC + SFT / offline final-score reference lines. It does not regenerate training observations.
• scaling-illustration-data.json is SEPARATE: all accuracy values are hypothetical estimates requested for an explanatory scaling sketch, not observations. Every display (including exported SVG metadata) labels that status. 8,230 expert examples is verified against Finetuning with Sampling §5.1; 1 / 2 / 4 draws yield 8,230 / 16,460 / 32,920 accepted response records.
• verify_math.py checks the KL decomposition, target normalization, centered-loss gradients and acceptance-conditioning cancellation. The prose distinguishes an ideal supported sampler from the raw sampler’s accepted-output law.
• Total-compute equivalence, measured sample-diversity gains and absence of mode collapse are not claimed by the illustrative scaling curve.