The marginal-likelihood estimator is reported to give good estimates only when the sampled latent space is very low-dimensional and enough samples are used; the experiment therefore used 3 latent variables, while estimates at higher dimensionality became unreliable.

openai/gpt-5.6-sol

aaa53caa87

This is an independent reconstruction because the fixed source provides no author implementation or released checkpoints; source-omitted split, initialization, Frey likelihood-variance, annealing, and HMC evaluator details were declared rather than inferred from target values. · Figure 2 does not define the randomness or aggregation behind its reported variance/error bars, so both measured variance fields remain interpretation-unresolved even though their operands and operational definition are fully retained. · The source gives no numerical sufficiency threshold for L=1 or accuracy threshold/ground truth for the marginal estimator's <5-dimensional statement; those control and dimensionality results are descriptive rather than post-hoc pass/fail claims. · Unresolved metric interpretation: exp-fig2-frey-lower-bound::measurement-003: Figure 2 defines the plotted quantity as estimated average variational lower bound per datapoint and equations (7)-(8) define its stochastic estimator, but the caption does not state whether its variance is across latent draws, minibatches, smoothing windows, or runs. The reconstruction therefore reports the maximum unbiased variance across 16 repeated full-split mean L=1 ELBO evaluations without asserting exact equivalence to the omitted source error bars.; exp-fig2-mnist-lower-bound::measurement-003: Figure 2 defines the plotted quantity as estimated average variational lower bound per datapoint and equations (7)-(8) define its stochastic estimator, but the caption does not state whether its variance is across latent draws, minibatches, smoothing windows, or runs. The reconstruction therefore reports the maximum unbiased variance across 16 repeated full-split mean L=1 ELBO evaluations without asserting exact equivalence to the omitted source error bars. · Claim coverage is partial: the supplied measurements do not test the higher-dimensional unreliability component. · The same 3-variable configuration could have been selected even if the estimator remained reliable at higher dimensionality; configuration matching is therefore not a discriminating test. · The paper supplies no numerical definition of “good” or “unreliable” and no ground-truth marginal likelihood against which estimator accuracy can be measured. · This is an independent reconstruction rather than execution of author code or released checkpoints; several evaluator and training details were reconstructed. · The plan was revised after source and environment audit. The revisions correctly bind these two fields to direct architecture counts, but they cannot repair the missing estimator-accuracy evidence. · Only 2 claim measurement(s) were executed; 1 remain unassessed. · This execution covers only part of the compound claim; unassessed measurements: measurement-013. · Only 2 claim measurement(s) were executed; 1 remain unassessed. Current execution reproduces the Figure 3 configuration of 3 latent variables and 100 hidden units. The 3-variable result supports the reported experimental choice, but a chosen configuration cannot establish that the estimator is accurate only in very low dimensions or unreliable at higher dimensions. The supplied claim coverage is partial, and no supplied measurement provides a ground-truth accuracy comparison or defined reliability criterion. Thus the central dimensionality limitation remains unverified even though the configuration counts match exactly.

openai/gpt-5.6-sol

67964ad4cb

This is an independent reconstruction because the fixed source provides no author implementation or released checkpoints; source-omitted split, initialization, Frey likelihood-variance, annealing, and HMC evaluator details were declared rather than inferred from target values. · Figure 2 does not define the randomness or aggregation behind its reported variance/error bars, so both measured variance fields remain interpretation-unresolved even though their operands and operational definition are fully retained. · The source gives no numerical sufficiency threshold for L=1 or accuracy threshold/ground truth for the marginal estimator's <5-dimensional statement; those control and dimensionality results are descriptive rather than post-hoc pass/fail claims. · Unresolved metric interpretation: exp-fig2-frey-lower-bound::measurement-003: Figure 2 defines the plotted quantity as estimated average variational lower bound per datapoint and equations (7)-(8) define its stochastic estimator, but the caption does not state whether its variance is across latent draws, minibatches, smoothing windows, or runs. The reconstruction therefore reports the maximum unbiased variance across 16 repeated full-split mean L=1 ELBO evaluations without asserting exact equivalence to the omitted source error bars.; exp-fig2-mnist-lower-bound::measurement-003: Figure 2 defines the plotted quantity as estimated average variational lower bound per datapoint and equations (7)-(8) define its stochastic estimator, but the caption does not state whether its variance is across latent draws, minibatches, smoothing windows, or runs. The reconstruction therefore reports the maximum unbiased variance across 16 repeated full-split mean L=1 ELBO evaluations without asserting exact equivalence to the omitted source error bars. · Claim coverage is partial: the decisive higher-dimensional estimator-reliability measurement was not among the supplied measurements. · The paper does not define numerical meanings for “good estimates,” “enough samples,” or “unreliable,” and the reconstruction has no ground-truth marginal likelihood against which to measure accuracy. · Finite estimates, acceptance rates, dispersion, ESS, or draw-count drift alone cannot establish estimator accuracy; the same architecture observations could occur even if the central reliability claim were false. · This is an independent reconstruction with disclosed source-omitted choices for initialization, splitting, annealing, and HMC evaluator tuning; these do not affect the two architecture counts but prevent treating the broader workflow as exactly equivalent. · The revised plan’s definitions for these two fields are accepted because they agree with both the paper and captured executions; that agreement does not validate the broader revised evaluator protocol. · Only 2 claim measurement(s) were executed; 1 remain unassessed. · This execution covers only part of the compound claim; unassessed measurements: measurement-013. · Only 2 claim measurement(s) were executed; 1 remain unassessed. Current execution reproduces the two covered Figure 3 architecture settings: the paper specifies 3 latent variables and 100 hidden units, and the executed AEVB, wake-sleep, and MCEM configurations used those values. However, these configuration matches do not establish the central reliability claim: no ground-truth marginal likelihood or source-defined reliability criterion demonstrates that the estimator is accurate below 5 dimensions, requires enough samples, or becomes unreliable at higher dimensions. Because claim coverage is partial and the decisive reliability comparison is uncovered, the overall claim remains inconclusive.

openai/gpt-5.6-sol

7a569c14ce

This is an independent reconstruction because the fixed source provides no author implementation or released checkpoints; source-omitted split, initialization, Frey likelihood-variance, annealing, and HMC evaluator details were declared rather than inferred from target values. · Figure 2 does not define the randomness or aggregation behind its reported variance/error bars, so both measured variance fields remain interpretation-unresolved even though their operands and operational definition are fully retained. · The source gives no numerical sufficiency threshold for L=1 or accuracy threshold/ground truth for the marginal estimator's <5-dimensional statement; those control and dimensionality results are descriptive rather than post-hoc pass/fail claims. · Unresolved metric interpretation: exp-fig2-frey-lower-bound::measurement-003: Figure 2 defines the plotted quantity as estimated average variational lower bound per datapoint and equations (7)-(8) define its stochastic estimator, but the caption does not state whether its variance is across latent draws, minibatches, smoothing windows, or runs. The reconstruction therefore reports the maximum unbiased variance across 16 repeated full-split mean L=1 ELBO evaluations without asserting exact equivalence to the omitted source error bars.; exp-fig2-mnist-lower-bound::measurement-003: Figure 2 defines the plotted quantity as estimated average variational lower bound per datapoint and equations (7)-(8) define its stochastic estimator, but the caption does not state whether its variance is across latent draws, minibatches, smoothing windows, or runs. The reconstruction therefore reports the maximum unbiased variance across 16 repeated full-split mean L=1 ELBO evaluations without asserting exact equivalence to the omitted source error bars. · Only one of three claim-side measurements was covered, so the whole claim cannot be promoted beyond inconclusive. · The paper supplies neither ground-truth marginal likelihood nor quantitative definitions of “good,” “sufficient samples,” or “unreliable.” · This was an independent reconstruction with unreported evaluator initialization, warmup, step-size tuning, annealing, and density-estimator details filled in by the reconstruction. · The post-source-audit plan revision correctly clarified that 5 is an excluded boundary, but its parser still carries that value from the source rather than deriving it from execution. · Only 1 claim measurement(s) were executed; 2 remain unassessed. · This execution covers only part of the compound claim; unassessed measurements: measurement-014, measurement-015. · Only 1 claim measurement(s) were executed; 2 remain unassessed. The paper does state that good estimates require a sampled space of less than 5 dimensions and sufficient samples, and that Figure 3 used 3 latent variables because higher-dimensional estimates were unreliable. The rerun completed matched z=3, 5, and 10 training and multi-chain evaluations at 50 and 200 draws, but the measured value 5 was copied as source-side context rather than empirically recovered. The rerun found finite estimates at every dimension and reported dispersion, approximate ESS, and draw-budget drift, but without ground-truth marginal likelihood or a source-defined criterion for “good” or “unreliable,” these diagnostics cannot establish estimator accuracy or the claimed boundary. The same observations could occur even if estimates above the boundary were accurate. Because claim coverage is partial and two claim components were not supplied as measurements, the overall claim also remains inconclusive.