P2P: Cross-View Population Denoising for Unpaired Single-Cell Perturbation Response Prediction

• Population responses are the practical target because biological conclusions usually rely on many cells.Source: §1 · p. 2
• Destructive sequencing leaves control and perturbed cells unpaired, while condition-level heterogeneity makes arbitrary cell pairing mix effects with sampling variation.Source: §1 · p. 2
• Two stochastic views from one condition share a reproducible population response, enabling cross-view supervision without cell correspondences.Source: §1 · p. 2
• P2P combines empirical effect memory with a neural residual and predicts population means and gene-wise variance, separating effect recovery from response heterogeneity.Source: §1 · p. 2

• Statistical perturbation models link pooled CRISPR assignments to transcriptional changes, while scGen and CPA model latent responses and covariates and GEARS uses gene relationships for multigene prediction.Source: §2 · p. 2
• scVI and scvi-tools model latent variables, totalVI and MultiVI extend to multimodal data, and scGPT learns gene representations through generative pretraining.Source: §2 · p. 2
• Seurat, scArches, Cell BLAST, Scanpy, and UMAP support integration, reference mapping, search, analysis, and visualization, whereas perturbation prediction must preserve signed responses relative to matched controls.Source: §2 · p. 2
• Network and dynamical methods represent regulatory programs, variant signals, state transitions, and relational structure; P2P instead uses symmetric aggregation to encode cell populations and evaluates recovered effects at population, gene, and graph-derived levels.Source: §2 · pp. 2–3

3.1 PROBLEM FORMULATION AND CROSS-VIEW SUPERVISION

• P2P defines the condition effect as the difference between perturbed and control population means, then trains predictions from one control view against another perturbed view without cell-level correspondences.Source: §3.1 · p. 3

3.2 P2P ARCHITECTURE

• The architecture maps a control cell set and structured perturbation information to a population-effect readout, with target views providing training supervision.Source: §3.2 · p. 3, Figure 2 · p. 4

3.2.1 PERMUTATION-INVARIANT POPULATION ENCODING

• The permutation-invariant set encoder combines an attention-weighted summary with unweighted dispersion, preserving heterogeneity while making the representation insensitive to cell order.Source: §3.2.1 · p. 3

3.2.2 STRUCTURED PERTURBATION AND CONTEXT ENCODING

• Perturbation tokens are pooled with padding masked; combination conditions add pair interactions, while context and dose are encoded separately for the residual branch.Source: §3.2.2 · p. 4

3.2.3 MEMORY-GATED EFFECT PREDICTION

• A learned gate interpolates between empirical condition-effect memory and a neural residual, with the gate initialized to give memory approximately 0.75 weight.Source: §3.2.3 · p. 4

3.2.4 HETEROSCEDASTIC OUTPUT

• A second head predicts gene-wise log variance, enabling optional population samples to represent response variation while uncertainty quality is evaluated separately from point prediction.Source: §3.2.4 · p. 5

3.2.5 EFFECT-CENTRIC CROSS-VIEW OBJECTIVE

• The effect-centric objective combines a weighted effect-distance term, effect correlation, variance matching, and consistency between predictions for the same condition.Source: §3.2.5 · p. 5

3.3 POPULATION INTERPRETATION

• Cross-view supervision targets population first moments when view errors have conditional mean zero and sampling distributions match; the implementation fixes data roles and records possible overlap for small conditions.Source: §3.3 · p. 5

4.1 DATASETS AND PROTOCOL

• The benchmark uses processed AnnData files for an unfolded-protein-response CRISPRi screen, a single- and paired-CRISPRa screen, and two essential-gene CRISPRi screens.All Norman analyses use the processed file’s A549 cell-type label; Figure 3 shows differences in dataset scale and condition coverage, with an 80-cell support reference.Source: §4.1 · pp. 5–6, Figure 3 · p. 6

4.2 BASELINES AND METRICS

• The comparison evaluates GenePert, LinearPert, SLIM, Scouter, and scPILOT using expression error and correlation, effect correlation, and DEG ranking and direction metrics.DEGs meet the stated Welch-test and Benjamini-Hochberg threshold and an absolute effect of at least 0.1; expression Pearson is similar across methods on Adamson and Norman, where GenePert scores highest.Source: §4.2 · p. 6, §4.3 · p. 6

4.3 MAIN RESULTS

• P2P obtains the best RMSE, Effect Pearson, DEG F1, and DEG AP on all four datasets; on K562, Effect Pearson rises to 0.7018 from 0.6432 and DEG F1 to 0.1784 from 0.0671.Table 1 reports means and sample standard deviations across five seeds; Figure 4 shows representative observed and predicted effects.Source: §4.3 · p. 6, Table 1 · p. 7, Figure 4 · p. 7

4.4 ABLATION OF CROSS-VIEW SUPERVISION AND EFFECT COMPONENTS

• Removing dual-view supervision raises RPE1 RMSE from 0.0910 to 0.0987 and lowers Effect Pearson from 0.6609 to 0.6412; removing memory yields RMSE 0.1049 and DEG AP 0.2088.The no-pair-interaction variant has RMSE 0.1123 and DEG F1 0.1742; removing cross-view consistency and effect correlation raises RMSE to 0.1016 and reduces principal effect metrics.Source: §4.4 · pp. 7–8, Table 2 · p. 8

4.5 POPULATION AND BIOLOGICAL STRUCTURE

• P2P samples move from the control cloud toward the observed perturbed mean across all four datasets, as visualized in a shared PCA coordinate system.Figure 5 shows one representative task per dataset.Source: §4.5 · p. 8, Figure 5 · p. 8
• For Adamson EIF2S1, observed and predicted graphs preserve the sign pattern of dominant local effects, while residuals concentrate on fewer nodes.The module panel reports local effect structure from the supplied gene graph.Source: §4.5 · p. 8, Figure 6 · p. 9

4.6 EFFECT FIDELITY AND TRANSFER READOUT

• Gene-level comparisons retain response ordering, while signed error segments show the direction and magnitude of residuals for the largest-response genes.Figure 7 presents representative genes from Adamson, Norman, Replogle K562, and Replogle RPE1.Source: §4.6 · p. 8, Figure 7 · p. 9
• The memory-assisted transfer readout tests adaptation to a different observed support population while retaining target training memory and the supplied perturbation vocabulary.Source support cells fill the control-set slot, and target test cells are used only for scoring.Source: §4.6 · p. 8

5 CONCLUSION

• Across four datasets, P2P shows its clearest gains on effect correlation and DEG ranking.The conclusion identifies these as measures relevant to biological prioritization.Source: §5 · p. 9
• P2P uses cross-view supervision to learn from stochastic views of unpaired control and perturbed cell sets.The model combines a memory-gated set approach with a neural residual for context, dose, and combination structure.Source: §5 · p. 9
• The transfer readout demonstrates adaptation across observed support populations under the stated memory-assisted protocol.Source: §5 · p. 9

AI USE STATEMENT

• Generative AI tools were used to improve manuscript readability and organization.Source: AI USE STATEMENT · p. 10
• The authors reviewed the edited text and checked every scientific claim against implementation and evaluation files.Source: AI USE STATEMENT · p. 10
• The authors state that AI tools did not generate experimental data, alter measurements, select favorable seeds, or replace author verification.Source: AI USE STATEMENT · p. 10

ETHICS STATEMENT

• Improved population-level perturbation prediction could be misused to infer sensitive biological responses or make misleading claims about identifiable samples.Source: ETHICS STATEMENT · p. 10
• The authors encourage using single-cell expression data only when relevant rights and permissions are available.Source: ETHICS STATEMENT · p. 10
• The work uses de-identified public or project-provided datasets and reports no human-participant recruitment or processing of personally identifying information.Source: ETHICS STATEMENT · p. 10

REPRODUCIBILITY STATEMENT

• The paper specifies the stochastic views, encoders, memory-gated residual, heteroscedastic head, and cross-view objective, alongside datasets, baselines, metrics, and a five-seed evaluation.Code, configurations, scripts, protocol files, and reproduction instructions will be released.Source: REPRODUCIBILITY STATEMENT · p. 10

A IMPLEMENTATION DETAILS

• The model uses set-normalized attention, masks the perturbation vocabulary before pooling, and enables pair interactions only for multiple active tokens.The fused state feeds linear delta and log-variance heads; log variance is clipped from -8 to 4.Source: A IMPLEMENTATION DETAILS · p. 12
• Training uses AdamW, a plateau-based learning-rate schedule, mixed precision, gradient clipping, validation-loss early stopping, and atomic checkpoint writes.The paper reports approximately three hours of training on an NVIDIA RTX 4090 with 24 GB of memory.Source: REPRODUCIBILITY STATEMENT · p. 10, A IMPLEMENTATION DETAILS · p. 12

B EVALUATION AUDIT

• Target test cells are never model inputs, but the vocabulary comes from the processed file, making the supplied benchmark transductive with respect to token identity.Direct readout uses target control test cells; transfer readout instead supplies source support cells to the control slot, with target train-role memory in both.Source: B EVALUATION AUDIT · p. 12

View sampling

• For larger conditions, views are disjoint samples without replacement; smaller conditions use independent sampling with replacement, so they are not independent experimental replicates.Under either sampling mode, the conditional expectation remains the target population mean.Source: C CROSS-VIEW OBJECTIVE AND… · p. 12

Gene-weighted effect loss

• The effect loss upweights genes with measurable responses, while ε prevents division by zero and reduces domination by unchanged genes.Equation 16 applies these weights inside Smooth L1 before averaging across genes.Source: C CROSS-VIEW OBJECTIVE AND… · p. 13

Variance objective

• The variance head combines a moment target with a Gaussian term, and its log-space comparison keeps genes with different expression scales comparable.The variance objective is separated from the point-prediction metrics reported in the main text.Source: C CROSS-VIEW OBJECTIVE AND… · p. 13

Consistency term

• The consistency term couples predicted means and log variances across update directions before population sampling, constraining deterministic predictions independently of a particular ε draw.The prose identifies bℓ as predicted log variance.Source: C CROSS-VIEW OBJECTIVE AND… · p. 13

Memory readout

• The condition memory is computed from role means, while the neural branch receives the encoded control set and condition state.The direct-readout memory is introduced in the implementation passage.Source: C CROSS-VIEW OBJECTIVE AND… · p. 13

Transfer readout

• The supplied transfer evaluation defines two readouts and reports the setting as memory-assisted because source-support sampling noise enters the transfer memory.The passage points to Equations 19 and 20 for the readout definitions.Source: C CROSS-VIEW OBJECTIVE AND… · p. 13

Data inventory

• The processed files contain 485,292 cells and 1,747 active conditions after filtering, while the fixed evaluation retains 1,259 condition tasks across four datasets.The totals distinguish eligible conditions from tasks assigned to fixed train, validation, support, and test roles.Source: D PROTOCOL, DATA INVENTORY, AND METRICS · p. 13

Objective and readout settings

• NLL and effect losses each include direct and crossed terms with multiplier 0.25, and Table 3 lists the outer weights and readout settings.The loss weights and readout choices are fixed before evaluation.Source: D PROTOCOL, DATA INVENTORY, AND METRICS · p. 13, Table 3 · p. 14

Metrics

• DEG metrics use a Welch test with Benjamini-Hochberg correction and an absolute-effect threshold; expression metrics use population means, while Effect Pearson uses control-subtracted effects.Equation 21 defines the DEG set used for DEG F1, DEG average precision, and DEG Direction.Source: D PROTOCOL, DATA INVENTORY, AND METRICS · p. 13

Robustness and implementation

• Figure 8 reports stability across supplied seeds, reduced effect and ranking quality after component removals, and predicted dispersion that tracks absolute error across tasks.Training used an NVIDIA RTX 4090 GPU with 24 GB of memory and took approximately three hours.Source: D PROTOCOL, DATA INVENTORY, AND METRICS · p. 13, Figure 8 · p. 14

Agreement diagnostics

• Figures 10 and 11 provide parity-residual and Bland-Altman views; the latter plots P2P-minus-observed effect against the observed and predicted effect mean with mean-difference and 95 percent agreement limits.These views matter because high correlation can coexist with scale-dependent bias.Source: E ADDITIONAL VISUAL EVIDENCE · p. 14, Figure 10 · p. 16, Figure 11 · p. 17

Population, combination, and gene-effect cases

• Figure 12 shows control, observed-perturbation, and P2P sample clouds with means, while Figure 13 covers Norman combinations and Figure 14 ranks gene effects for representative cases.The combination cases exercise masked token pooling and the pair-interaction block.Source: E ADDITIONAL VISUAL EVIDENCE · p. 14, Figure 12 · p. 17, Figure 13 · p. 18

Ranking and robustness diagnostics

• Figure 9 summarizes top-k overlap, direction agreement by effect magnitude, residual distributions, and the task-level Effect Pearson versus DEG AP frontier.Figure 8 places component ablations alongside seed variation and predictive-dispersion diagnostics.Source: E ADDITIONAL VISUAL EVIDENCE · p. 14, Figure 9 · p. 15

Predictive intervals

• Figure 15 compares observed effects with P2P means and 90 percent predictive intervals for representative genes across four datasets.Interval coverage is reported as a distributional property alongside point metrics.Source: E ADDITIONAL VISUAL EVIDENCE · p. 15, Figure 15 · p. 19

Appendix scope

• The appendix figures are diagnostic views of the fixed evaluation, exposing population displacement, signed gene effects, combination behavior, agreement structure, and predictive dispersion.Figure 12 complements the main population projection with sample clouds and population means.Source: E ADDITIONAL VISUAL EVIDENCE · p. 15