MapPFN: Learning Causal Perturbation Maps in Context

Marvin Sextro; Weronika Kłos; Gabriel Dernbach

cs.LGJan 28, 2026

MapPFN: Learning Causal Perturbation Maps in Context

Authors: Marvin Sextro, Weronika Kłos, Gabriel Dernbach

Organizations: Machine Learning Group, Technische Universität Berlin, Berlin, Germany · Berlin Institute for the Foundations of Learning and Data (BIFOLD) · Aignostics, Berlin, Germany · Institute of Pathology, Charité - Universitätsmedizin Berlin, Berlin, Germany

Abstract

Planning effective interventions in biological systems requires treatment-effect models that adapt to unseen biological contexts by identifying their specific underlying mechanisms. Yet single-cell perturbation datasets span only a handful of biological contexts, and existing methods cannot leverage new interventional evidence at inference time to adapt beyond their training data. To meta-learn a perturbation effect estimator, we present MapPFN, a prior-data fitted network (PFN) pre-trained on a synthetic biological prior with causal interventions, decoupling pre-training from limited wet-lab data. Unlike existing methods, MapPFN uses in-context learning to map a sequence of experiments to a post-perturbation distribution, enabling a single pre-trained model to adapt to new datasets and gene sets. Our results show that combining synthetic pre-training with fine-tuning on real single-cell data improves perturbation predictions across biological contexts. The code, model and data are available at https://marvinsxtr.github.io/MapPFN.

Figures & tables

Figure 1: MapPFN overview. MapPFN uses in-context learning (ICL) to predict perturbation effects in unseen biological contexts. During pre-training, we draw structural causal models (SCMs) or synthetic gene regulatory networks (GRNs)

\psi

to generate samples from the observational distribution

\mathbf{Y}^{\text{obs}}

and a context set of interventional distributions

\mathcal{C}=\{(t_{k},\mathbf{Y}^{\text{int}}_{k})\}_{k=1}^{K}

, where

t_{k}

denotes a perturbation (do-intervention). Given

\smash{\mathbf{Y}^{\text{obs}}}

and the context set

\mathcal{C}

, MapPFN predicts post-perturbation distributions

\mathbf{Y}^{\text{int}}_{q}

arising from unseen interventions

t_{q}

. During pre-training, MapPFN meta-learns how to map between pre- and post-perturbation distributions across many causal structures

\psi

by minimizing

\mathcal{L}(\hat{\mathbf{Y}}_{q}^{\text{int}},\mathbf{Y}^{\text{int}}_{q})

. At inference time, MapPFN predicts cell-level post-perturbation distributions

\mathbf{Y}^{\text{int}}_{q}\in\mathbb{R}^{\text{cells}\times\text{genes}}

in one step through amortized inference, without requiring knowledge of the underlying causal structure

\psi

Methods	Covariates	Observational	Interventional
CPA, CondOT, CellFlow	✓	✗	✗
MFM, STATE	✓	✓	✗
MapPFN (ours)	✓	✓	✓

Table 1: Overview of perturbation models by conditioning capability. Columns indicate whether a method conditions on covariates, observational populations, or interventional populations. While all baselines require interventional data as a supervision target, MapPFN uniquely conditions on interventional data via in-context learning.

Method	$\text{W}_{2}$ $\downarrow$	MMD ( $\times 10^{-3}$ ) $\downarrow$	RMSE $\downarrow$	PDS $\downarrow$	MR $\rightarrow 1$
CondOT [ 47 ]	$13.85\pm 0.12$	$5.14\pm 0.01$	$0.15\pm 0.00$	$0.11\pm 0.02$	$0.09\pm 0.01$
MFM [ 13 ]	$\resizebox{1492769}{422343}{{13.73}}\pm 0.16$	$4.81\pm 0.19$	$0.15\pm 0.01$	$0.09\pm 0.03$	$0.12\pm 0.00$
MapPFN (ours)	$\resizebox{1492769}{422343}{{13.69}}\pm 0.05$	$\resizebox{1165088}{422343}{{4.28}}\pm 0.06$	$\resizebox{1165088}{422343}{{0.14}}\pm 0.00$	$\resizebox{1165088}{422343}{{0.01}}\pm 0.01$	$\resizebox{1165088}{422343}{{0.99}}\pm 0.02$
Identity	$17.61\pm 0.14$	$12.98\pm 0.35$	$0.28\pm 0.01$	$0.49\pm 0.01$	$0.00\pm 0.00$
Observed	$9.82\pm 0.08$	$3.66\pm 0.06$	$0.07\pm 0.00$	$0.00\pm 0.00$	$1.00\pm 0.00$

Table 2: Evaluation of MapPFN within a prior of linear SCMs. Mean

\pm

std over three training seeds. Bold indicates results within one standard deviation of the best. In this controlled setting, MapPFN successfully meta-learns perturbation prediction.

Dataset	Method	$\text{W}_{2}$ $\downarrow$	MMD ( $\times 10^{-3}$ ) $\downarrow$	RMSE $\downarrow$	PDS $\downarrow$	MR $\rightarrow 1$	AUPRC $\uparrow$
Melanoma	CPA [ 11 ]	$\resizebox{1492769}{422343}{{15.97}}\pm 0.82$	$152.13\pm 46.92$	$0.13\pm 0.01$	$0.49\pm 0.01$	$0.71\pm 0.07$	$0.03\pm 0.01$
	CondOT [ 47 ]	$22.19\pm 0.91$	$\resizebox{1165088}{422343}{{6.78}}\pm 0.33$	$\resizebox{1165088}{422343}{{0.10}}\pm 0.00$	$0.06\pm 0.02$	$0.04\pm 0.00$	$0.41\pm 0.05$
	MFM [ 13 ]	$20.75\pm 1.05$	$\resizebox{1165088}{422343}{{6.50}}\pm 0.46$	$\resizebox{1165088}{422343}{{0.09}}\pm 0.01$	$0.11\pm 0.05$	$0.11\pm 0.01$	$0.46\pm 0.07$
	CellFlow [ 12 ]	$22.28\pm 0.59$	$\resizebox{1165088}{422343}{{6.80}}\pm 0.49$	$\resizebox{1165088}{422343}{{0.10}}\pm 0.01$	$0.40\pm 0.02$	$0.02\pm 0.00$	$0.20\pm 0.06$
	STATE [ 14 ]	$20.79\pm 0.83$	$7.39\pm 1.19$	$\resizebox{1165088}{422343}{{0.09}}\pm 0.01$	$0.17\pm 0.18$	$\resizebox{1165088}{422343}{{0.95}}\pm 0.05$	$0.42\pm 0.23$
	MapPFN (pre-trained)	$22.25\pm 1.33$	$63.34\pm 17.79$	$0.32\pm 0.04$	$0.22\pm 0.04$	$\resizebox{1165088}{422343}{{1.01}}\pm 0.05$	$0.34\pm 0.07$

Table 3: Comparison of MapPFN against baselines across two single-cell perturbation datasets. Benchmark on a melanoma [ 4 ] and a leukemia [ 5 ] cell line. We report MapPFN (1) pre-trained on synthetic data and (2) fine-tuned on real data. MapPFN improves perturbation predictions across biological contexts by combining synthetic pre-training with fine-tuning on real single-cell data. The Mean and Linear baselines predict a single bulk profile per perturbation, so distributional metrics do not apply (

-

). Mean

\pm

std over five data splits (see Appendix D.1 ), each averaged over ten resampling seeds. Bold indicates results within one standard deviation of the best.

Configuration	$\text{W}_{2}$ $\downarrow$	MMD ( $\times 10^{-3}$ ) $\downarrow$	RMSE $\downarrow$	PDS $\downarrow$	MR $\rightarrow 1$	AUPRC $\uparrow$
MapPFN (pre-trained)	$22.25\pm 1.33$	$63.34\pm 17.79$	$0.32\pm 0.04$	$0.22\pm 0.04$	$1.01\pm 0.05$	$0.34\pm 0.07$
$-$ counterfactual prior	$69.15\pm 7.82$	$143.51\pm 7.78$	$0.94\pm 0.06$	$0.18\pm 0.02$	$3.16\pm 0.37$	$0.08\pm 0.03$
$-$ interventional context	$40.99\pm 4.93$	$101.05\pm 9.67$	$0.65\pm 0.06$	$0.29\pm 0.04$	$1.85\pm 0.18$	$0.25\pm 0.05$
MapPFN (fine-tuned)	$21.05\pm 0.62$	$6.57\pm 0.56$	$0.09\pm 0.01$	$0.02\pm 0.01$	$0.98\pm 0.01$	$0.62\pm 0.02$
MapPFN (random init)	$24.34\pm 0.90$	$52.33\pm 3.49$	$0.31\pm 0.02$	$0.19\pm 0.06$	$1.13\pm 0.02$	$0.09\pm 0.03$

Table 4: Ablation of the counterfactual paired prior, interventional context and synthetic pre-training on the melanoma dataset. Removing the counterfactual prior replaces paired data with unpaired interventional distributions. Removing the interventional context implies conditioning only on observational data. Random init trains the same architecture from scratch on real data, without synthetic pre-training. Mean

\pm

std over five data splits, each averaged over ten resampling seeds.

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Symbol	Description	Range
$k$	Number of gene groups/modules	$\{1,2,3\}$
$p$	Sparsity term (avg. regulators per gene)	$[1.5,3.0]$
$\delta_{\text{in}}$	In-degree uniformity term	$[10,300]$
$\delta_{\text{out}}$	Out-degree uniformity term	$[1,30]$
$w$	Modularity term (within-group connectivity)	$[1,900]$

Appendix

Table 5: GRN structure parameters for the graph generator.

Symbol	Description	Range
Simulation parameters
$k$	Interaction strengths	$[1.0,5.0]$
$b$	Master regulator production rates	$[0.5,2.0]\cup[3.0,5.0]$
$\gamma$	Hill function coefficients (nonlinearity)	$[1.5,2.5]$
$\lambda$	Decay rates per gene	$[0.5,1.0]$
$\zeta$	Stochastic process noise scale	$[0.5,1.5]$

Appendix

Table 6: SERGIO simulation and technical noise parameters.

Figure 4: Data split. Each box represents a dataset

\mathbf{Y}^{\text{int}}_{ij}\in\mathbb{R}^{N\times d}

sampled from the SCM

\psi_{i}

under treatment

t_{j}

. Green boxes are part of the training data and purple boxes are withheld for evaluation.

Method	Hyperparameter	Search Range
MapPFN	Classifier-free guidance weight	$\{1.0,1.5,2.0,2.5,3.0\}$
CPA	Following the tuning protocol of PerturBench [ 51 ] .
CondOT	Hidden dimensions	$\{64,128,256\}$
	Hidden layers	$\{2,3,4\}$
	Learning rate	$\{10^{-3},10^{-4},10^{-5}\}$
MFM	k-nearest neighbors	$\{0,10,50,100\}$

Appendix

Table 7: Hyperparameter search ranges for each method.

Panel of Figure 5 — Figure 5: MapPFN scales with more data at inference time. Both the number of perturbation experiments in context and the number of cells per perturbation improve prediction quality, demonstrating that MapPFN adapts to the available data via in-context learning.

Figure 6: Coverage of the synthetic biological prior over real single-cell data distributions. Distributions of non-zero expression values (left) and log fold changes (right) for the synthetic biological prior, the melanoma [ 4 ] and leukemia [ 5 ] datasets. Log fold change values are clipped to the

[1,99]

percentile range for visualization.

Architecture	Parameters	$\text{W}_{2}$ $\downarrow$	MMD ( $\times 10^{-3}$ ) $\downarrow$	RMSE $\downarrow$	PDS $\downarrow$	MR $\rightarrow 1$	AUPRC $\uparrow$
MMDiT [ 22 ]	25.97M	$\resizebox{1492769}{422343}{{22.25}}\pm 1.33$	$\resizebox{1492769}{422343}{{63.34}}\pm 17.79$	$\resizebox{1165088}{422343}{{0.32}}\pm 0.04$	$\resizebox{1165088}{422343}{{0.22}}\pm 0.04$	$\resizebox{1165088}{422343}{{1.01}}\pm 0.05$	$\resizebox{1165088}{422343}{{0.34}}\pm 0.07$
DiT [ 43 ]	27.66M	$23.87\pm 1.58$	$\resizebox{1492769}{422343}{{51.47}}\pm 18.50$	$\resizebox{1165088}{422343}{{0.35}}\pm 0.06$	$\resizebox{1165088}{422343}{{0.19}}\pm 0.04$	$1.12\pm 0.04$	$0.22\pm 0.08$

Appendix

Table 8: Architecture ablation comparing MMDiT against DiT. Performance on the melanoma dataset [ 4 ] . Mean

\pm

std over five data splits, each averaged over ten resampling seeds. Bold indicates results within one standard deviation of the best.

Holdout	Method	$\text{W}_{2}$ $\downarrow$	MMD ( $\times 10^{-3}$ ) $\downarrow$	RMSE $\downarrow$	PDS $\downarrow$	MR $\rightarrow 1$	AUPRC $\uparrow$
IFN- $\gamma$	CondOT [ 47 ]	$22.19\pm 0.91$	$\resizebox{1165088}{422343}{{6.78}}\pm 0.33$	$\resizebox{1165088}{422343}{{0.10}}\pm 0.00$	$0.06\pm 0.02$	$0.04\pm 0.00$	$0.41\pm 0.05$
	STATE [ 14 ]	$\resizebox{1492769}{422343}{{20.79}}\pm 0.83$	$7.39\pm 1.19$	$\resizebox{1165088}{422343}{{0.09}}\pm 0.01$	$0.17\pm 0.18$	$\resizebox{1165088}{422343}{{0.95}}\pm 0.05$	$0.42\pm 0.23$
	MapPFN (pre-trained)	$22.25\pm 1.33$	$63.34\pm 17.79$	$0.32\pm 0.04$	$0.22\pm 0.04$	$\resizebox{1165088}{422343}{{1.01}}\pm 0.05$	$0.34\pm 0.07$
	MapPFN (fine-tuned)	$\resizebox{1492769}{422343}{{21.05}}\pm 0.62$	$\resizebox{1165088}{422343}{{6.57}}\pm 0.56$	$\resizebox{1165088}{422343}{{0.09}}\pm 0.01$	$\resizebox{1165088}{422343}{{0.02}}\pm 0.01$	$\resizebox{1165088}{422343}{{0.98}}\pm 0.01$	$\resizebox{1165088}{422343}{{0.62}}\pm 0.02$
TIL co-culture	CondOT [ 47 ]	$17.59\pm 0.41$	$8.86\pm 0.66$	$0.11\pm 0.01$	$\resizebox{1165088}{422343}{{0.06}}\pm 0.01$	$0.06\pm 0.01$	$0.49\pm 0.12$
	STATE [ 14 ]	$\resizebox{1492769}{422343}{{16.47}}\pm 0.36$	$\resizebox{1165088}{422343}{{8.28}}\pm 0.55$	$\resizebox{1165088}{422343}{{0.09}}\pm 0.01$	$0.15\pm 0.03$	$0.91\pm 0.01$	$0.50\pm 0.07$

Appendix

Table 9: Performance across three holdout cell states of the melanoma dataset. Mean

\pm

std over five data splits, each averaged over ten resampling seeds. Bold indicates results within one standard deviation of the best for each holdout.

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Abstract

Single-Cell Perturbation Modeling

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