PaperlayerView exact revision on arXiv

Source-linked AI summary

Scalable Diffusion SBI for Compositional Inference under Simulator Misspecification

Vincent D. Zaballa, Elliot E. Hui

arXiv:2609.36950v1cs.LGq-bio.QMstat.ML

TL;DR

SBI must handle heterogeneous observations, hierarchical latents, and simulator discrepancy, but these needs are often treated separately. This paper combines compositional and hierarchical diffusion sampling with path-regularized likelihood adaptation. In the BMP application, adaptation improves predictions in some design regions while worsening them in others, and shifts posterior marginals toward a least-squares reference while retaining spread.

  • Problem

    SBI methods must address heterogeneous observations, shared and group-specific latent structure, and systematic simulator discrepancies, challenges typically treated as distinct problems.

    Source: §1 · p. 1

  • Method

    The framework reuses a pretrained joint diffusion model for observation composition and sampling-time hierarchy, and fine-tunes its likelihood with path-space regularization while transferring updates to posterior inference.

    Source: §1 · p. 2, §3.2 · p. 5

  • Results

    Fine-tuning improves predictions throughout the BMPR2-knockdown competition series and at lower BMP4 doses, but often increases error in the NMuMG competition series; BMP posterior marginals generally shift toward the reference while retaining substantial spread.

    Source: §4.4 · p. 9

  • Takeaways & Limitations

    The methods support diffusion SBI across changing observation sets, hierarchical latent structure, and simulator misspecification without requiring the pretrained model to anticipate all downstream structure.

    Source: §5 · p. 9

    Fine-tuning at a fixed reference parameter can improve misspecified regions while degrading regions that were already well modeled.

    Source: §5 · p. 9

Abstract

from arXiv · show

Simulation-based inference is challenging when many heterogeneous observations must be composed, hierarchical latent structure must be preserved, and the simulator is misspecified relative to observed data. We develop sampling and fine-tuning methods for diffusion-based inference in design-conditional settings, where the same simulator is queried across different experimental conditions $\xi$. We extend compositional score-based inference with a continuous-time diffusion coefficient that accounts for the number of observations, avoiding Jacobian and auxiliary-covariance corrections. We introduce Hierarchical Blockwise Diffusion Sampling (HBDS), which infers shared parameters and group-specific latent states using a single pretrained model, with the hierarchy specified only at sampling time. Together, these methods support variable observation sets and groupings without retraining. To address misspecification, we introduce path-regularized fine-tuning that adapts the learned likelihood to observations and transfers corrections to posterior inference. Using Girsanov's theorem, we quantify path divergence between pretrained and fine-tuned models across experimental designs and interpret it alongside predictive errors to distinguish candidate misspecification correction from unnecessary adaptation. We evaluate compositional sampling on exact-score Gaussian and Simple Likelihood, Complex Posterior benchmarks, HBDS with analytic and learned scores on a controlled hierarchical model, and fine-tuning and localization on a separate analytic model with known design-dependent discrepancy. Finally, we apply the framework to 940 measurements across four cell lines in a mechanistic Bone Morphogenetic Protein signaling model, where fine-tuning improves posterior-predictive accuracy relative to the pretrained model and shifts posterior marginals toward the least-squares reference while retaining spread.

1 INTRODUCTION

The paper targets SBI settings with heterogeneous observations, shared and group-specific latents, and simulator discrepancy. It combines compositional sampling, hierarchy at sampling time, and likelihood adaptation in a reusable diffusion-based inference framework.

1 INTRODUCTION

  • The framework addresses the joint challenge of many heterogeneous observations, shared and group-specific latent variables, and systematic simulator discrepancies.Mechanistic simulators encode scientific knowledge in latent parameters, while SBI can amortize inference when likelihoods are intractable.Source: §1 · p. 1
  • A single pretrained conditional model serves as a reusable inference engine for composing observations, adding hierarchy at sampling time, and adapting to observed data.The paper aims to retain posterior inference in the original mechanistic parameterization.Source: §1 · p. 2
  • Its contributions include an observation-count-dependent diffusion coefficient, HBDS for shared and group-specific latents, and path-space adaptation and localization.The proposed composition method avoids Jacobian and auxiliary-covariance costs; HBDS reuses one joint model and introduces hierarchy only during sampling.Source: §1 · p. 2
  • The framework is applied to a BMP signaling simulator with 60 shared parameters, five receptor quantities per cell line, and 940 observations.The paper presents this as a large-scale systems-biology application of composition, hierarchy, and misspecification-aware adaptation.Source: §1 · p. 2

2 BACKGROUND

The background establishes design-conditional SBI notation, mask-conditioned joint diffusion models, and score-based reverse-time sampling. These components provide the basis for conditional inference across designs and latent variables.

2.1 DESIGN-DEPENDENT SIMULATION-BASED INFERENCE

  • In design-dependent SBI, experimental condition ξ changes the joint model and resulting posterior, and simulated prior-predictive data train amortized estimators.The targets include the posterior p(θ | y, ξ) and surrogate likelihood p(y | θ, ξ).Source: §2.1 · pp. 2–3

2.2 MASK-CONDITIONED JOINT DIFFUSION MODELS

  • Mask-conditioned joint diffusion models represent variables as tokens and use condition masks to distinguish fixed variables from latent variables.An attention mask can encode the expert model’s graphical structure; masked denoising score matching trains the conditional score.Source: §2.2 · p. 3

2.3 SCORE-BASED DIFFUSION SAMPLING

  • A learned conditional score defines reverse diffusion sampling, which integrates a reverse SDE from a tractable Gaussian terminal distribution while holding conditioned variables fixed.The background uses a variance-preserving SDE as the continuous-time limit of forward Gaussian noising.Source: §2.3 · p. 3

3 METHODS

The methods adapt a joint diffusion surrogate to observations, quantify adaptation through path-space divergence, and compose scores for variable-sized observation sets. HBDS extends this compositional approach to shared parameters and group-specific latent states.

3.1 FINE-TUNING TO ADDRESS MODEL MISSPECIFICATION

  • Likelihood fine-tuning at a fixed reference parameter optimizes sampled responses against observations while regularizing departure from the pretrained output law.Shared token-aware embeddings and FiLM representations allow likelihood updates to transfer to posterior queries; in the BMP example, posterior marginals shift toward the reference while retaining substantial spread.Source: §3.1 · p. 4

3.2 LOCALIZING SIMULATOR MISSPECIFICATION WITH PATH-SPACE DIVERGENCE

  • Path-space KL measures changes to the complete reverse-SDE trajectory law, and Girsanov’s theorem provides a way to quantify that divergence.Because generated responses are projections of trajectories, path-space KL upper-bounds endpoint divergence; evaluating it at θref yields a non-negative field over designs.Source: §3.2 · p. 5

3.3 COMPOSITIONAL SAMPLING

  • F-NPSE-SDE composes per-observation posterior scores using an observation-count-dependent diffusion coefficient, allowing observation sets to vary without retraining.The schedule requires score evaluations but avoids score Jacobians and auxiliary covariance estimation; optional Langevin corrections explore the compositional marginal.Source: §3.3 · p. 6

3.4 HIERARCHICAL BLOCKWISE DIFFUSION SAMPLING

  • HBDS alternates group-specific latent updates conditioned on each group’s data with shared-parameter updates using all groups.It yields one globally consistent parameter vector and distinct local states without training a separate hierarchical estimator or tokenizing the complete dataset.Source: §3.4 · p. 7

4 EXPERIMENTS

Experiments evaluate compositional sampling, hierarchical inference, fine-tuning under misspecification, and a 940-observation BMP application. Results span Gaussian and SLCP benchmarks, controlled hierarchical and analytic models, and the BMP model.

4 EXPERIMENTS

  • The experiments test compositional sampling on exact-score Gaussian and learned-score SLCP benchmarks, HBDS on a controlled hierarchy, and fine-tuning on analytic and BMP settings.The BMP application combines fine-tuning with HBDS across 940 observations.Source: §4 · p. 7, §4.4 · p. 9

4.1 EVALUATING F-NPSE-SDE

  • In the Gaussian benchmark at n = 100 and T = 400, F-NPSE-SDE is competitive with GAUSS and JAC, matches F-NPSE, and improves over Langevin in maximum sliced Wasserstein distance.The comparison uses exact compositional scores and posteriors.Source: §4.1 · p. 7, Table 1 · p. 7
  • On SLCP at n = 30, GAUSS and JAC remain most accurate, while F-NPSE-SDE improves over Langevin and F-NPSE in sliced Wasserstein distance and MMD.The samplers share the same frozen network within each comparison; F-NPSE-SDE avoids JAC’s score Jacobians and GAUSS’s auxiliary DDIM rollouts.Source: §4.1 · p. 7, Table 1 · p. 7

4.2 EVALUATING POOLED COMPOSITIONAL SAMPLING AND HBDS

  • With groups requiring different latent modes, pooled sampling cannot represent both, whereas HBDS retains separate group states alongside shared θ.The learned-score illustration uses 20 observations, ten per group, generated with θ = 1.Source: §4.2 · p. 8, Figure 4 · p. 8

4.3 FINE-TUNING UNDER SIMULATOR MISSPECIFICATION

  • In the analytic misspecification toy, fine-tuning reduces error near the omitted discrepancy bump but adds errors elsewhere; PT/FT autoguidance lowers MAE to 0.12.Without autoguidance, mean path divergence inside the misspecified region is 4.73 times that outside and correlates with the discrepancy (Pearson r = 0.75).Source: §4.3 · p. 8, Figure 5 · p. 8
  • Across the BMP observation- and LSR-budget sweep, FT achieves the lowest mean median predictive distance, while FMCPE-LSR has lower best-draw RMSE.Both metrics assess predictions through the original simulator, so the comparison remains subject to its misspecification.Source: §4.3 · p. 8

4.4 BMP APPLICATION

  • HBDS with FT (λ = 5 × 10^-4) yields RMSE 0.34 and median distance 14.94, versus pooled sampling’s 0.36 and 66.77.In the BMP application, fine-tuning improves predictions at some designs but increases error at others; these local differences often coincide with path divergence.Source: §4.4 · p. 9

5 DISCUSSION

The methods are presented as reusable tools for changing observation sets, hierarchical structure, and simulator misspecification. The discussion notes approximation limits and motivates design-dependent adaptation guided by prediction error and path divergence.

5 DISCUSSION

  • The framework adapts a pretrained SBI model to downstream observation sets and hierarchical structure rather than requiring the model to anticipate them during training.The discussion links this flexibility to use across simulator misspecification as well.Source: §5 · p. 9
  • Compositional sampling and HBDS rely on approximate intermediate-time posteriors; more accurate targets or learned flow maps could improve them.Fine-tuning at a fixed reference can help misspecified regions while degrading regions already modeled well, motivating design-dependent adaptation guided by predictive error and path divergence.Source: §5 · p. 9

APPENDICES

The appendices derive compositional transition scores under reverse–forward consistency, then prescribe an observation-count-dependent continuous-time diffusion coefficient. The coefficient controls a chosen Gaussian noising process, not an exact reverse process for the full product posterior.

A.1 EXISTENCE OF CUMULATIVE TRANSITION SCORE

  • Under exact reverse–forward consistency, the cumulative transition combines per-observation reverse scores with a common forward-kernel correction.The derivation clarifies the cumulative transition score under these assumptions; it does not establish an exact reverse kernel for the joint posterior.Source: §A.1 · p. 17

A.2 DERIVATION OF THE REVERSE TRANSITION KERNEL

  • The Gaussian transition’s compositional precision factor depends jointly on observation count and noise schedule, rescaling the aggregate score and normalized reverse-transition variance.Its mean and variance define a DDPM-style predictor.Source: §A.2 · p. 19

A.3 DERIVING THE CONTINUOUS-TIME DIFFUSION COEFFICIENT

  • The continuous-time coefficient realizes prescribed reduced noising variance for n > 1, depends only on time and observation count, and avoids score Jacobians and auxiliary covariance estimates.This variance prescription is a modeling choice, not the infinitesimal limit of the discrete transition or an exact reverse process for the product bridge.Source: §A.3 · pp. 20–21

A.4 LANGEVIN REFINEMENT AND NUMERICAL ACCURACY

Langevin corrections can improve exploration between predictor steps, but their step size trades off numerical bias against exploration. Stability alone does not ensure accurate sampling.

A.4 LANGEVIN REFINEMENT AND NUMERICAL ACCURACY

  • For ηg(t)^2 > 4v, identical-noise trajectories amplify their separation, showing that stability depends on step size and diffusion relative to target variance.At ηg(t)^2 = 6v, the deterministic update sends a displacement from the mean to twice as far on the opposite side.Source: §A.4 · p. 22
  • In the Gaussian illustration, stable ULA still has stationary variance v/[1 − ηg(t)^2/(4v)], exceeding the target variance v.Reducing g(t)^2 or η lowers this discretization bias but slows exploration; increasing the correction count alone does not remove it.Source: §A.4 · p. 22
  • The observation-count-dependent coefficient reduces update scale and stationary-variance inflation within the stable range, but step size and correction count still require tuning.Rules for selecting both rely on assumptions including smooth, strongly log-concave intermediate densities and controlled score error.Source: §A.4 · p. 22

A.5 EXPERIMENTAL EVALUATION

The exact-score Gaussian experiments compare compositional diffusion coefficients at matched sampling cost, while the SLCP benchmark uses frozen learned scores. In the Gaussian sweep, the derived coefficient improves finite-budget accuracy, including below the local instability threshold.

A.5 EXPERIMENTAL EVALUATION

  • At n = 100, mean sW falls from 0.0153 to 0.0074, approximately 52%, with the derived coefficient; it lowers sW in all 45 paired comparisons for n > 1.The two coefficients produce identical samples at n = 1, and the absolute improvement peaks near n = 8 rather than increasing monotonically.Source: Figure 7 · p. 24, §A.5 · p. 25
  • In Figure 7(f), ordinary VP crosses the local contraction limit R = 1, indicating numerical amplification, while the derived coefficient stays below 1; accuracy improves even below this threshold.R(n) is a local diagnostic, not a guarantee of global stability or a measure of accumulated sampling error.Source: §A.5 · pp. 24–25
  • The Gaussian comparison tracks empirical covariance against its analytic target and measures endpoint sW at matched cost using five paired seeds.Each method used 800 full compositional-score calls per run; endpoint sW compares against 1,000 exact-posterior draws.Source: §A.5 · p. 25

A.6 EXACT-SCORE GAUSSIAN BENCHMARK

  • The exact-score Gaussian sweep uses common data seeds, 1,000 posterior particles, and 400 reverse steps across observation counts from 1 to 100.F-NPSE-SDE comparisons include one or five Langevin corrections per predictor.Source: §A.6 · p. 25

A.7 SLCP BENCHMARK

  • The SLCP benchmark compares samplers at n = 1, 14, and 30 using frozen score networks and reference posteriors across 25 common test instances per network seed.It reports sliced Wasserstein distance, MMD, and C2ST; the supplied passage gives the setup but no benchmark outcome.Source: §A.7 · pp. 25–26

A.8 COMPUTATIONAL COST OF COMPOSITIONAL SAMPLERS

The appendices compare the computational demands of compositional samplers, clarify the scope of the variance-prescription contribution, and detail HBDS block updates. In the tested BMP implementation, Jacobian and covariance methods imposed prohibitive runtime or memory costs.

A.8 COMPUTATIONAL COST OF COMPOSITIONAL SAMPLERS

  • F-NPSE-SDE costs O(T(L + 1)PnCs) score-evaluation work and O(Pd) working state, while JAC adds Jacobian computation and GAUSS requires covariance-estimation rollouts.HBDS repeats such computations inside conditional block updates for JAC and nests GAUSS rollouts, whereas F-NPSE-SDE stores only the HBDS particle state beyond common activations.Source: §A.8 · p. 26
  • In the tested BMP experiments, JAC increased HBDS sampling from approximately one hour to more than ten hours, while GAUSS exhausted GPU memory estimating covariances across 940 designs.Both methods were omitted from the subsequent BMP evaluation; this is an implementation-specific observation, not an impossibility of adapting them.Source: §A.8 · p. 26

A.9 COMPOSITIONAL SAMPLING RELATED WORKS

  • The compositional contribution is a variance prescription and compatible diffusion coefficient built on F-NPSE, not the factorization or score-composition idea itself.The resulting time- and observation-count-dependent log-SNR shift is neither ordinary VP reparameterization nor score damping, and does not establish an exact reverse process for the full posterior.Source: §A.9 · pp. 26–27

B HIERARCHICAL BLOCKWISE DIFFUSION SAMPLING DETAILS

  • HBDS approximates the noised joint posterior with conditional scores, refining local receptor blocks before updating shared parameters using all groups.Its block updates use predictor–corrector steps; the observation count for each local block is its group size, while the shared-parameter block uses the total count.Source: B HIERARCHICAL BLOCKWISE DIFFUSION… · p. 27

B.1 TOY SIMULATOR MODEL EXAMPLE

The toy model tests whether hierarchical inference can preserve distinct group-specific latent modes while sharing a continuous parameter. HBDS reuses a joint score model and introduces hierarchical blockwise updates at sampling time.

B.1 TOY SIMULATOR MODEL EXAMPLE

  • The toy model uses a discrete group latent and continuous θ, with observations generated as x = 5k + θ + ε and ε ∼ N(0, 1).The single-observation posterior is analytically tractable and serves as ground truth for evaluation.Source: §B.1 · p. 28
  • When groups favor different latent modes, the hierarchical posterior can represent the oracle structure, whereas a pooled posterior forces one shared latent explanation.For observations near +5 and −5, distinct group latents explain both with θ ≈ 0.Source: §B.1 · p. 29

B.2 HIERARCHICAL SBI RELATED WORKS

  • HBDS reuses one joint score model and alternates local and global updates during reverse diffusion, rather than training separate estimators for the hierarchical factorization.The distinction from related hierarchical score models is conditional-model reuse and blockwise sampling, not hierarchical composition itself.Source: §B.2 · pp. 29–30
  • For nested BMP observations, HBDS composes scores within receptor blocks and across groups, allowing observation subsets to change without retraining when the model learned the needed conditionals.Each cell line shares a receptor vector across 235 ligand-dose observations, while biophysical parameters are shared across cell lines.Source: §B.2 · p. 30

C BMP SIGNALING PATHWAY MATHEMATICAL MODEL

The BMP model links ligand-dose responses to shared biochemical parameters and cell-line-specific receptor states. The receptor hierarchy incorporates qPCR-informed biological constraints, while the LSR comparison highlights identifiability concerns.

C BMP SIGNALING PATHWAY MATHEMATICAL MODEL

  • The BMP dataset has 940 measurements across four cell lines and 235 ligand-dose conditions per line, with 60 shared biophysical parameters and a five-dimensional receptor state per line.Each single-observation latent state therefore contains 65 quantities.Source: C BMP SIGNALING PATHWAY MATHEMATICAL… · p. 30

D CELL RECEPTOR HIERARCHICAL MODELING

  • The receptor hierarchy partially pools receptor-specific baseline means and variances, while condition effects and multiplicative knockdown shifts represent variability and targeted reductions.The receptor prior uses qPCR-informed measurements and truncated lognormal support for positive receptor levels bounded by h.Source: D CELL RECEPTOR HIERARCHICAL MODELING · pp. 31–32

E.1 CALIBRATED RECEPTOR DIFFUSION

  • FT has an all-data RMSE of 0.26; the historical LSR all-data error is not a consistently aggregated baseline until its original evaluation protocol is reconciled.LSR receptor estimates can assign some knockdown lines higher basal receptor levels than the parent, so low predictive error alone does not establish physical plausibility.Source: §E.1 · pp. 32–33

E.2 BMP POSTERIOR-SAMPLING ABLATIONS

The BMP experiments compare pooled sampling and HBDS, pretrained and fine-tuned models, and fine-tuning objectives regularized in path space. Fine-tuning and HBDS show the strongest reported predictive-fit pattern, with the experiments’ single-seed settings and objective assumptions defining the scope.

E.2 BMP POSTERIOR-SAMPLING ABLATIONS

  • The pooled-versus-HBDS BMP comparison uses 940 observations; HBDS keeps separate receptor states by cell line, but results are single-seed and its block updates differ from pooled resampling passes.Both samplers use 100 diffusion steps and five Langevin corrections per step.Source: §E.2 · p. 33
  • Fine-tuning improves both predictive-fit metrics over its matched pretrained model under pooled sampling and HBDS; for each fine-tuned architecture, HBDS yields lower errors than pooled sampling, while FiLM fine-tuning has the lowest reported values among completed comparisons.Source: §E.2 · p. 33

F PRETRAINING DETAILS

  • Pretraining uses 1,000 parameter draws across 940 designs, with joint, posterior, likelihood, and random conditioning masks; heavier posterior and likelihood masking tended toward overconfidence.Increasing joint masking improved generalization, while embedding concatenation before projection empirically produced more stable training and better posterior quality.Source: F PRETRAINING DETAILS · pp. 33–34

G.1 FINE-TUNING OBJECTIVE AND OPTIMIZATION

  • The fine-tuning reward penalizes both mean prediction error and predictive variance, and the BMP reference θref is fixed at the LSR best-fit solution, an important hyperparameter.In the single-seed sweep, omitting Langevin corrections yielded lower errors than adding them for every tested regularization strength.Source: §G.1 · pp. 34–35

G.2 PATH-SPACE FORMULATION AND GIRSANOV’S THEOREM

  • Girsanov’s change of measure relates pretrained and fine-tuned path laws when they share an initial law and diffusion coefficient, under stated existence and integrability assumptions.The drift change reweights reference trajectories; the corresponding control energy bounds path divergence.Source: §G.2 · p. 36

G.3 STOCHASTIC OPTIMAL CONTROL CONNECTION

  • Path-regularized stochastic control upper-bounds the endpoint objective rather than rewriting it identically, and optimizes score-network parameters without a separate control network.Design-specific divergence budgets and adaptive multipliers are proposed as future extensions, not implemented methods.Source: §G.3 · p. 37

G.4 FISHER–RAO OPTIMIZATION ANALYSIS

This analysis develops Fisher path-space geometry for proposal refinement and design sensitivity, then reviews simulator-misspecification adaptation, embedding-based transfer, and an FMCPE-LSR comparison. With all 940 BMP observations and 4,816 LSR fits, FMCPE-LSR attains lower best-draw RMSE than PT or FT, but not lower median distance.

G.4 FISHER–RAO OPTIMIZATION ANALYSIS

  • Fisher geometry can refine proposal particles by combining predictive-reward motion with prior drift and stochastic exploration, leaving Fisher-null directions available for unresolved variation.The update uses the parameter Fisher block and its pseudoinverse; the procedure alternates proposal updates with likelihood fine-tuning across proposal particles.Source: §G.4 · p. 38
  • Large design sensitivity may guide simulation acquisition or fine-tuning curricula, but sensitivity alone does not establish misspecification and should be read with predictive error or path divergence.The appendix also proposes using parameter–design coupling to separate parameter effects that local design changes can mimic from residual parameter information.Source: §G.4 · p. 39

G.5 RELATED WORK ON SIMULATOR MISSPECIFICATION IN SBI

  • Existing SBI robustness methods address simulator misspecification, but a gap remains in transferring improved predictive accuracy to posterior inference.The unknown true data-generating process is typically unavailable, and mismatch can contribute to poor SBI performance.Source: §G.5 · p. 40

G.6 RELATED WORK ON DIFFUSION FINE-TUNING

  • The selected fine-tuning approach adapts likelihoods to observed design–response pairs with a PT path-law penalty, then interprets path divergence alongside predictive error to distinguish correction from unnecessary adaptation.The method conditions adaptation on simulator-aligned reference parameters and transfers the correction to posterior queries; the design-specific penalties discussed are a proposed extension.Source: §G.6 · p. 43

G.7 EMBEDDING-BASED TRANSFER LEARNING

  • Token-aware FiLM modulates value–identity embeddings by token identity and latent-or-conditioned state, so likelihood fine-tuning updates representations reused by posterior queries.The condition state also enters the transformer explicitly, while bounded modulation limits separation between latent and conditioned embeddings.Source: §G.7 · p. 43

G.8 FMCPE-LSR BASELINE

  • With all 940 observations and 4,816 LSR fits, FMCPE-LSR RMSE is 0.175 versus 0.252 for PT and 0.245 for FT, while median distance is 31.05 versus 11.11 and 10.38, respectively.No FMCPE-LSR configuration surpasses either simformer on mean median distance; FMCPE-LSR requires subset-specific training, unlike the reused PT/FT models.Source: §G.8 · p. 44

G.9 DESIGN-DEPENDENT MISSPECIFICATION TOY

The design-dependent toy examines how fine-tuning and sampling-time score blending behave when discrepancy varies across experimental conditions. Adaptation can improve predictions near the discrepancy while worsening already accurate regions, and its effects depend on regularization and blending weight.

Posterior and likelihood trade-off

  • More aggressive full-network fine-tuning lowers posterior W2 to 0.03 but raises correct-region likelihood RMSE to 0.32, exposing a trade-off hidden by posterior metrics alone.Adaptation can move the posterior toward the truth while degrading a likelihood that was already accurate away from the discrepancy.Source: §G.9 · p. 45

Design-localized error and adaptation

  • MAE decreases from 0.31 to 0.20 inside the misspecified region, but increases from 0.11 to 0.15 outside it; path divergence correlates 0.75 with discrepancy and averages 4.73 times higher inside.The analysis used one training seed, one dataset of 10 observations, and one generating parameter vector, making it a controlled diagnostic rather than a multi-seed benchmark.Source: §G.9 · p. 45

Regularization trade-off

  • Increasing λ from 1 to 10 reduces RMSE outside the misspecified region by about 3%, but raises it inside from 0.25 to 0.29; no tested FT model improves full-grid RMSE over PT.Stronger regularization reduces response adjustment and path divergence while weakening correction near the omitted bump.Source: §G.9 · p. 45

Sampling-time autoguidance

  • At w = 0.5, score blending gives full-grid MAE 0.12 versus 0.14 for PT and 0.15 for FT, but the best weight was selected retrospectively and improvement varies by design.Weights above 1 increased full-grid error beyond FT.Source: §G.9 · p. 46

G.10 BMP MISSPECIFICATION EVALUATION

Design-level diagnostics show that fine-tuning often improves predictions over the pretrained model, but its comparison with least-squares fits varies by condition. Fine-tuned posterior marginals generally move toward the least-squares reference while retaining spread.

G.10 BMP MISSPECIFICATION EVALUATION

  • The LSR ensemble retains 4,816 fits grouped by global fitting cost, but local best-fit assignments can favor a globally higher-cost group.Local assignments use each group's mean squared error at a design, so global cost labels do not determine condition-specific fit quality.Source: §G.10 · pp. 46–47, Figure 13 · p. 48
  • Intermediate pretrained–fine-tuned score-blending weights reduce average predictive error while limiting path divergence, without retraining.The sweep varies the sampling weight from pretrained to fine-tuned scores and compares error with divergence from the pretrained model.Source: Figure 12 · p. 47
  • At fixed least-squares parameters, fine-tuning improves predictions throughout the displayed BMPR2-knockdown series and at lower BMP4 doses, while least squares fits some other conditions better.The remaining better-fit regions include the NMuMG competition series and higher-dose titration.Source: §G.10 · p. 47
  • Fine-tuning improves over the pretrained model across many conditions, but comparisons with least-squares fits remain mixed; gains occur with both alternative and dominant parameter groups.Path divergence corresponds qualitatively to some departures from the dominant least-squares group.Source: §G.10 · p. 47, Figure 14 · p. 49
  • The authors leave broader evaluation of design-adaptive curricula and divergence-aware regularization for future work.Remaining regions where least squares performs better indicate that the current fine-tuning procedure does not fully exploit the potential for localized correction.Source: §G.10 · pp. 47–48
  • Fine-tuned posterior marginals generally shift toward the fitted least-squares reference while retaining substantial spread rather than collapsing to the anchor.Figure 15 shows the pretrained and fine-tuned marginals alongside the fitted reference across 30 binding affinities and 30 phosphorylation efficiencies.Source: §G.10 · p. 48, Figure 15 · p. 50
Loading 2609.36950v1…