Predicting Unseen Scientific Interactions: Conditional Flow Models Hallucinate Non-Additive Effects

Sam Gijsen; Moritz Seiler; Kerstin Ritter

cs.LGOct 14, 2026

Predicting Unseen Scientific Interactions: Conditional Flow Models Hallucinate Non-Additive Effects

Authors: Sam Gijsen, Moritz Seiler, Kerstin Ritter

Abstract

Conditional generative models are increasingly used for scientific prediction beyond the direct training support. Yet scientific questions often concern whether one intervention changes the effect of another. Such interactions can be of primary interest while explaining little of the total variation, allowing models to appear accurate overall without recovering the relevant scientific effect. It remains unclear how these models learn interactions and when these successfully extrapolate to unseen conditions. We therefore study interaction recovery in flow-matching models using a physiological time-series simulator, drug dose-response data, combinatorial cell perturbations, and molecular conformer generations, where we separate recovery from hallucinated interaction structure. In the controlled setting, individual effects are learned much earlier than interactions and models hallucinate interactions where none exist. Across settings, we find qualitatively different generalization problems, with successful prediction depending on whether condition structure continues from observed to held-out targets. When it does, interactions are recoverable. If not, models can generate plausible responses while missing the interaction. We furthermore find that hallucinations increase as targets become less identifiable, and that successful interaction recovery in output space can fail under nonlinear readouts. Finally, we show that aggregate fidelity metrics can conceal whether models learn and extrapolate interactions.

Figures & tables

Panel of Figure 1 — Figure 1: Aggregate generation quality does not guarantee accurate predicted interactions. Two conditions are sampled with equal distance off the training support but in different directions (1). Both samples score well on normalized endpoint error ( $\mathcal{E}_{\text{end}}$ ), far below a trivial baseline (2). But decomposing the prediction into the component along the true interaction ( $\alpha$ ) and the orthogonal, unrelated component ( $\beta$ ) distinguishes the samples into interaction recovery ( $\checkmark$ ) and attenuated interaction with hallucinated structure ( $\approx$ ) (3). Finally, applying a readout function $g$ can considerably change the results ( $\checkmark\xrightarrow{g}\times$ ), with less recovery and yet more hallucinated structure in the readout space compared to output space.

Metric	Definition	$1$ corresponds to
$\mathcal{E}_{\text{end}}$	$\mathrm{RMS}(\hat{Y}-Y)\,/\,\mathrm{RMS}(Y-Y_{0})$	predicting the baseline
$\mathcal{E}_{\text{add}}$	$\mathrm{RMS}(\hat{\tilde{Y}}-\tilde{Y})\,/\,\mathrm{RMS}(Y-Y_{0})$	an error the size of the total response
$\mathcal{E}_{I}$	$\\|\hat{I}-I\\|\,/\,\\|I\\|$	predicting zero interaction
$\alpha,\beta$	Section 2.1	-

Table 1: Metrics overview.

Panel of Figure 2 — Figure 2: Held-out designs across the four systems. Please see Section 2.5 for details.

Figure 3: Learning dynamics for PPG targets in the training set (ID) and unseen targets (OOD) for separate regions of condition space. We show mean dynamics of the joint model across three random seeds, with faint lines indicating single-seed runs.

Figure 4: Interaction errors for unseen PPG targets. The left panel shows errors in the output (waveform) representation and readout (AC/DC) representation, while the right panel shows a magnified view of the (same) waveform results. The interaction strength

\gamma

was modulated

1\rightarrow 0

and is indicated by a

\text{dark}\rightarrow\text{bright}

marker color gradient. Mean over training and inference seeds.

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 6: Maps showing the non-additive interaction projected onto the primary truth interaction mode. Colors indicate the signed interaction amplitude, normalized by the $\gamma=1$ low-low truth RMS. The dotted square indicates the held-out region of condition space (corresponding to PPG LL 25%). To aid visualisation, we clip the colormap to [0.5%, 99.5%] of the maximum amplitude.

Figure 7: Held-out evaluation across the training trajectory for the Cokol et al. [2011] dose-response setting and for the Norman et al. [2019] perturbation data. While the former shows synchronous dynamics for aggregate and non-additive metrics due to a smoothness-constrained held-out region of condition space, the latter shows decoupling. Specifically, whereas

\mathcal{E}_{I}

begins to increase after 30K steps,

\mathcal{E}_{end}

continues to decrease up to 50K steps. The shading indicates checkpoint selection based on validation endpoint error, highlighting that using endpoint error for model selection can be suboptimal for interaction prediction.

Component	Configuration
Tissue geometry	Epidermis/dermis/subcutaneous thicknesses: $0.20/1.50/18.30$ mm; $0.05$ -mm isotropic voxels; $18\times 18\times 20$ -mm domain.
Source and detectors	Normally incident uniform disk source, radius $1.6$ mm; four spherical detectors of radius $0.25$ mm at 3, 4, 5, and 6 mm.
Optical constants	Refractive index $n=1.4$ ; anisotropy $g=0.9$ ; shared reduced-scattering law $\mu_{s}^{\prime}(\lambda)=6.25(\lambda/1000\,\mathrm{nm})^{-1.4}$ cm -1 .
Absorbers	Eumelanin in epidermis; water and lipid in all layers; collagen in dermis; oxygenated/deoxygenated hemoglobin in dermis and subcutaneous tissue.
Photon-path bank	35 scattering settings; $10^{8}$ photons per setting; 5-ns MCX time window; fixed paths reused for absorption replay.

Appendix

Table 3: PPG simulator configuration.

	$\alpha$	$\beta$	$\mathcal{E}_{I}$	$\mathcal{E}_{\text{end}}$
Neighborhood	$0.688\pm 0.014$	$0.631\pm 0.010$	$0.704\pm 0.005$	$0.436\pm 0.003$
Parents only	$0.696\pm 0.018$	$0.689\pm 0.018$	$0.754\pm 0.024$	$0.467\pm 0.015$
Distant	$0.758\pm 0.023$	$0.791\pm 0.003$	$0.828\pm 0.005$	$0.513\pm 0.003$
Neighb. $-$ parents	$-0.007\pm 0.018$	$-0.059\pm 0.027$	$-0.050\pm 0.029$	$-0.031\pm 0.018$
	$[-0.062,0.031]$	$[-0.122,-0.008]$	$[-0.107,-0.013]$	$[-0.066,-0.008]$
Parents $-$ distant	$-0.062\pm 0.025$	$-0.102\pm 0.021$	$-0.074\pm 0.025$	$-0.046\pm 0.015$

Appendix

Table 4: Anchored GEOM results. Arm values are mean

\pm

SD over three training seeds. Paired differences are mean

\pm

seed SD of per-seed differences with 95% scaffold-family bootstrap intervals in brackets.

Detail	PPG	Dose-response	Perturbation	Conformers
Output	$16\times 64$ waveform	96-point trajectory	PCA-500 expression	3D coordinates, all atoms
Architecture	Conv-patch DiT	Symmetric MLP	Residual MLP	ET-Flow equivariant transformer (O(3), post-hoc parity)
Width / depth	128 / 4	256 / 3	512 / 4	160 / 20
Attention heads	4	N/A	N/A	8
Parameters	0.86M (both)	0.51M each	3.03M	8.34M
Conditioning	2 factors; + presence bits (shared)	Drug-token set	Gene-token set	Molecular graph (atom/bond features)

Appendix

Table 5: Implementation details for the four experimental settings. For molecular conformers, we follow [ Hassan et al., 2024 ] .

Conditional Generative Modeling

Conditional generative modeling learns to produce data distributions steered by labels, inputs, text, or physical and structural constraints.

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