Interpretable Causal Representation Learning for Biological Data in the Pathway Space

Carlos Ruiz-Arenas; David Gomez-Cabrero; Idoia Ochoa; Irene Marin-Go\~ni; Jan Voges; Jesper Tegner; Jesus de la Fuente; Mikel Hernaez; Robert Lehmann; Vincenzo Lagani

REVIEW 4 major objections 7 minor 22 references

Interpretable Causal Representation Learning for Biological Data in the Pathway Space

T0 review · 4 major / 7 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read SENA-discrepancy-VAE learns causal latent factors that are readable as combinations of biological pathway activities while matching the predictive accuracy of its non-interpretable baseline on unseen double perturbations.

desk verdict SENA-δ is a useful interpretable encoder for discrepancy-VAE with solid predictive benchmarks, but the causal identifiability claim doesn't hold because interventions shift Z and U = Z^T (I-A)^{-1} couples factors. read the letter →

arxiv 2506.12439 v1 pith:ZB5IL4RL submitted 2025-06-14 cs.LG q-bio.QMstat.ML

Jesus de la Fuente , Robert Lehmann , Carlos Ruiz-Arenas , Jan Voges , Irene Marin-Goñi , Xabier Martinez-de-Morentin , David Gomez-Cabrero , Idoia Ochoa

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Jesper Tegner Vincenzo Lagani Mikel Hernaez

This is my paper · ORCID

classification cs.LGq-bio.QMstat.ML

keywords interpretablecausalrepresentationlearningdiscrepancy-VAESENA-δencoderPerturb-seqpathwayactivitysingle-celltranscriptomicsinterventionpredictionGeneOntology

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper's claim is that a causal representation learner for single-cell perturbation data can be made interpretable in terms of known biological processes without giving up predictive power. Its model, SENA-discrepancy-VAE, replaces the black-box encoder of discrepancy-VAE with a two-layer masked network that first computes activity levels for a curated set of Gene Ontology pathways, then maps those activities linearly onto the latent causal factors. On the task of predicting gene expression under unseen double-gene perturbations in the Norman2019 K562 dataset, the model achieves a maximum mean discrepancy of 1.5849 for predicted double-perturbation distributions and a control-sample reconstruction error of 0.02134 at 105 latent factors with $\lambda=0.1$, essentially matching or slightly beating the original non-interpretable model (1.5981 and 0.02152). The paper also reports that the inferred causal graph among latent factors recapitulates known biological relationships, such as hydrogen peroxide production influencing endothelial cell morphogenesis, and that pathway activities containing the knocked-out gene show the strongest differential activation. If this holds, biologically grounded causal representations can be extracted from Perturb-seq data and used to predict and explain the effects of unseen genetic and drug perturbations.

What carries the argument

The load-bearing object is the SENA-$\delta$ encoder, a two-layer masked MLP. Its first layer maps gene expression $x$ to pathway activities $\alpha$ using a sparsity mask $M$ defined by $M_{i,k}=1$ if gene $i$ belongs to pathway $k$ and $\lambda$ otherwise, so each pathway activity is a weighted sum of the expression of its genes with a small allowance for unannotated genes; its second layer maps $\alpha$ linearly to the mean and variance of the Gaussian exogenous variables $Z_j$, making every latent causal factor a linear combination of pathway activities. This construction reconciles the biological fact that a gene knockout shifts many processes with the CRL requirement, inherited from discrepancy-VAE theory, that each intervention target exactly one latent factor: the single target becomes a composite of pathway activities. The decoder stays polynomial, so the identifiability theorem (latent factors recoverable up to permutation and scaling) continues to apply, and the path matrix $(I-A)^{-1}$ of the learned causal DAG converts meta-pathway activities into the causal pathway archetypes $U$.

What would settle it

Train SENA-discrepancy-VAE on a synthetic linear-Gaussian causal model with known single-target interventions and compare the inferred intervention-to-factor assignments and adjacency matrix with the ground truth; if the recovered assignments are not equivalent up to permutation and scaling, the claimed causal interpretation fails. On real data, a direct biological test is to knock out a gene that sits in two pathways assigned to two different latent factors and measure whether the expression shift activates both factors, which the model predicts it should not.

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Extended reading notes

Core claim

The central discovery is that pathway knowledge can be injected directly into the encoder of a causal representation learner while preserving the identifiability guarantees that make the latent factors causal. The SENA-$\delta$ encoder computes pathway activities $\alpha = \sigma((W \odot M)^\top x)$, where the mask $M$ encodes gene--pathway membership, and then parameterizes each latent exogenous variable $Z_j$ as a linear combination of those activities: $\mu_j = \alpha^\top \delta_j^{(\mu)}$ and $\sigma_j^2 = \alpha^\top \delta_j^{(\sigma)}$. Because each causal factor is $U = Z^\top(I-A)^{-1}$, every latent factor has an expected value that is a linear readout of pathway activities through the learned causal DAG, so the factors can be read as combinations of biological processes rather than anonymous axes. Empirically, the paper shows this design matches or slightly improves on the non-interpretable discrepancy-VAE when predicting unseen double perturbations, and that the learned factors and causal edges are biologically meaningful, stable across hyperparameters, and validated by differential-activation tests on two Perturb-seq datasets.

Load-bearing premise

The load-bearing premise is that every perturbation changes exactly one hidden causal factor: the single-target intervention assumption inherited from discrepancy-VAE theory, which the paper itself concedes in the Discussion keeps the method from fully disentangling how biological processes, perturbations, and latent factors relate.

Editorial extensions

If this is right

At 105 latent factors and $\lambda=0.1$, SENA-discrepancy-VAE predicts unseen double-gene perturbations with MMD 1.5849 on the predicted distributions and a control-sample reconstruction MSE of 0.02134, compared with 1.5981 and 0.02152 for the original MLP-encoder discrepancy-VAE; interpretability is therefore not bought at the cost of predictive accuracy on this benchmark.
The inferred causal graph can be read as relationships between biological processes: the model recovers a path from catechol-containing compound biosynthesis through hydrogen peroxide biosynthesis to endothelial cell morphogenesis, matching known regulatory biology in an unsupervised way.
The pathway activity layer is itself informative: for knockout perturbations, pathways containing the targeted gene show significantly higher differential activation than other pathways (DAR > 1 for nearly all of the 37 evaluated knockouts), so the same encoder can be used to flag which biological processes a perturbation engages.
The meta-pathway activities are significantly associated with high-level Gene Ontology categories in permutation tests, indicating that the data-driven second layer groups specific pathways into broader, biologically coherent programs.
On the Wessels2023 dataset, where perturbations have similar transcriptomic effects, both models collapse all single-gene perturbations onto a single latent factor; this shows the limit of the approach when biological signal is weak, a finding the paper itself reports.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Because $\lambda>0$ lets genes outside a pathway contribute to its activity, the learned weights on masked edges are a candidate resource for discovering missing gene--pathway memberships; a gene whose masked weight remains large across perturbations would be a testable, unannotated member of that pathway, an extension the paper does not perform.
The single-target intervention assumption forces overlapping pathway sets to share a latent factor, so the framework would become more general if the identifiability theory were relaxed to interventions that shift a sparse set of factors; the paper itself marks this as the next step.
If pathway activity levels are largely conserved across cell types, the fixed gene--pathway mask could allow causal factors to be aligned across tissues by retraining only the second layer of the encoder, enabling transfer of perturbation-response predictions between cell lines; this is a reader inference, not a paper claim.
The generative structure of the model (sample $Z$, compute $U = Z^\top(I-A)^{-1}$, pass through the polynomial decoder) can produce counterfactual expression profiles for interventions never observed, pointing toward in silico drug-combination screening; the paper demonstrates double-perturbation prediction but does not frame the model as a screening platform.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: this is a real engineering contribution with a formal hole in the causal claim. If you read it, read the architecture and the ablation carefully; don't cite the identifiability.

What's new: SENA-δ, a masked linear encoder that injects GO pathway membership into the discrepancy-VAE encoder, so each latent factor is a linear combination of pathway activities. That's a sensible way to get a biological vocabulary into CRL, and the authors are honest that they trade representational flexibility for interpretability. On Norman2019, λ=0.1 matches or slightly beats the MLP-encoder discrepancy-VAE on MMD and MSE at 105 latent factors, and the Wessels2023 results are there, though they need higher λ to stay comparable. The ablation study with λ sweep is careful. They ship code and data. That's all real.

The problems. First, the Appendix I 'validation' with r=1.00 is an identity. E(U_j)=α^T Δ L_j follows from the definitions of μ, Δ, L; running cells through the model and checking the arithmetic confirms the code, not the biology. Presenting it as experimental validation is misleading.

Second, and more important: the identifiability guarantee doesn't transfer. The theorem requires each intervention to target exactly one causal factor U_i. The architecture's interventional encoder applies a learnable shift to Z, and U = Z^T (I-A)^{-1}. Unless (I-A)^{-1} is monomial, a shift in one Z component changes several U components, so the intervention targets a multi-dimensional set in U-space. The Section 3 argument that linear combinations 'seamlessly' reconcile multi-BP effects with single-target interventions conflates the encoder's gene-to-pathway mixing with the intervention target in U-space. The Discussion concedes the single-target limitation, but the model's own mechanism violates it. That means 'inferring causal latent factors' is not backed by the cited theorems. This is not a minor point: it's the difference between 'causal' and 'interpretable linear encoder'.

The empirical interpretability evidence (DA/DAR, UMAP, known H2O2-endothelial relationship) is softer but not circular—it uses external GO annotations and shows real signal. The 'first effort' framing is overbroad; earlier biologically informed VAEs and post-hoc enrichment analyses exist, even if they lack CRL guarantees.

Bottom line: useful paper, honest about some limits, but the load-bearing causal claim is unsupported. Who's it for: people working on interpretable CRL or perturbation prediction who want a concrete architectural variant and a benchmark. I'd send it to a serious referee—the engineering is solid enough. I'd cite the architecture, not the identifiability.

Referee Report

4 major / 7 minor

Summary. The paper proposes SENA-discrepancy-VAE, an extension of discrepancy-VAE in which the MLP encoder is replaced by a two-layer masked encoder (SENA-delta) that maps gene expression to the activity levels of Gene Ontology biological processes and then linearly maps those activities to the mean and variance of latent meta-pathway variables Z, with causal factors defined as U = Z^T (I-A)^{-1}. The model is trained on unperturbed and single-gene Perturb-seq data from Norman2019 and Wessels2023 and evaluated on prediction of double-gene perturbation distributions (MMD) and reconstruction (MSE). The authors report that SENA-discrepancy-VAE with lambda=0.1 matches or slightly improves on the original discrepancy-VAE at latent dimension 105, while providing pathway-based interpretations of latent factors and a causal graph with apparently plausible edges. The paper also presents DA/DAR analyses suggesting that BPs containing the targeted gene are more differentially activated, and an appendix 'validation' of the linear mapping between pathway activities and latent factors.

Significance. The intended contribution, an interpretable causal representation learning method for Perturb-seq that preserves predictive performance, is valuable and the architectural idea is simple and reusable. The paper provides code, uses two real datasets, and includes extensive ablations; the finding that a constrained, pathway-masked encoder can match a free MLP encoder at high latent dimension is informative. However, the formal causal claim is not fully supported: the transfer of identifiability guarantees is not established, and the empirical interpretability evidence is partly definitional. If the authors can clarify or relax the theoretical claims and add controls for the interpretability metrics, the paper would be a solid contribution to interpretable single-cell modeling.

major comments (4)

[Section 3, Figure 1, Appendix I] The manuscript does not establish that the trained SENA-discrepancy-VAE satisfies the single-target intervention assumption under which discrepancy-VAE is identifiable. The interventional branch applies a learnable shift to the meta-pathway activities Z, and with U = Z^T (I-A)^{-1}, a shift in one Z_j changes multiple U_i through the generally non-monomial matrix L. If the intended target is the single U_j whose noise is shifted, this should be stated and the sparsity of the learned shift in U-space should be verified; otherwise the guarantees of Ahuja et al. (2023) and Zhang et al. (2024) do not transfer. The Discussion in Section 7 concedes that the single-target assumption prevents full disentanglement of BPs, perturbations and latent factors, which further weakens the 'principled identifiability' claim in the Introduction.
[Appendix I, Eq. (10) and Fig. 5] The 'experimental validation' reporting r=1.00 is circular. E(U_j)=E(Z^T)L_j=mu^T L_j=alpha^T Delta^(mu) L_j is an algebraic identity that follows immediately from the definitions of mu, Delta and L, so the perfect correlation only verifies that the code implements the stated linear algebra; it provides no evidence about biological interpretability. This exercise should be reframed as a software sanity check, and the interpretability claims should rest on the DA/DAR analyses instead.
[Section 4.3 and Section 6.3] The Hits@100 and DAR metrics are partly self-referential. A BP is classified as 'affected' by perturbation p exactly when it contains the targeted gene in the mask M, and the SENA layer computes that BP's activity as a weighted sum that includes the targeted gene's expression. Because a KO changes the targeted gene's expression, a positive differential activation for 'affected' BPs is substantially built into the construction, independent of what the model learns. The paper should include a control, e.g., permuted gene-BP masks or a fixed random-weight SENA layer, to demonstrate that the learned weights add biological signal beyond the mask.
[Section 6.2] The biological validity of the inferred causal graph is supported only by a small number of manually selected edges (e.g., factor 15 to 69), and Appendix II shows stability across hyperparameters but not correctness. Without a quantitative comparison to known regulatory interactions or a blinded evaluation, the claim that the model 'recapitulat[es] known biological causal relationships' is anecdotal. This is load-bearing for the causal-interpretation claim and should be addressed with a systematic evaluation.

minor comments (7)

[Introduction] In the Introduction, 'yielding talent factors' should read 'yielding latent factors'.
[Section 2.1] The heading 'CASUAL REPRESENTATION LEARNING' contains a typo and should be 'CAUSAL REPRESENTATION LEARNING'.
[Eq. (4)] Equation (4) uses the indicator function I[.] without defining it; please define the notation or use standard indicator notation.
[Table 1] The caption of Table 1 states 'mean ± variance', but the reported quantities appear to be standard deviations; the caption should be corrected.
[Figure 8 caption] The caption of Figure 8 refers to 'Eq.??'; the equation number is missing and should be filled in.
[Section 6.2 and Section 6.3] There are typos in gene names: 'JUNE' in Section 6.2 should be 'JUN', and 'TXB3' in Section 6.3 should be 'TBX3'.
[Appendix V] The dataset is called 'Wessels2023' in the text but the cited paper is Wessels et al. (2022); please unify the dataset label with the reference.

Circularity Check

2 steps flagged · score 6.0 of 10

SENA's interpretability 'validations' are algebraic identities of the encoder definition; the double-perturbation predictive benchmark is independent.

self definitional [Appendix I, Eqs. (6)-(10) and Fig. 5]
"Finally, we experimentally validated, using the Norman2019 dataset, that Eq. (9) holds for both the original discrepancy-VAE (MLP), and the proposed SENA-δ model for both λ={0,0.1}... There is a perfect correlation among these two terms, and this patterns is maintained across models and perturbations."

Eq. (10) is not an empirical relation: U is defined as Z^T (I-A)^{-1} in Eq. (8), E(Z_j)=mu_j=alpha^T delta_j^{(mu)} in Eqs. (6)-(7), so E(U_j)=mu·L_j=alpha^T Delta^{(mu)} L_j holds by pure algebra. The Figure 5 scatter compares two computations of the same definitional quantity, so the reported r=1.00 is guaranteed. The 'experimental validation' therefore checks arithmetic, not whether the latent factors are biologically meaningful.
self definitional [Section 4.3, Eqs. (1), (4)-(5); used in Section 6.3]
"we define Wp as the set of BPs that contain the targeted gene i: Wp ={BP k|Mi,k = 1}. ... Intuitively, we would expect BPs containing the targeted gene to be the most affected by the intervention, while the other processes should only suffer indirect effects."

The same mask M both constructs the pathway activities in Eq. (1) (alpha = sigma((W⊙M)^T x)) and labels BPs as 'affected' in Wp. For a perturbation of gene i, every BP in Wp receives x_i directly through M_{i,k}=1, so a knockout-induced change in x_i mechanically feeds into alpha_k. Hits@N and DAR therefore partly measure the encoder's own input wiring rather than an independent biological signal; the affected/not-affected split is not external to the model definition even though the mask values come from GO.

full rationale

The strongest circularity is in Appendix I: Eq. (10) is an algebraic identity following from U=Z^T(I-A)^{-1}, E(Z)=mu, and mu=alpha^T Delta, so the r=1.00 'experimental validation' is a tautology, not an empirical result. A second definitional loop affects the interpretability metrics: Section 4.3 labels BPs as 'affected' using the same mask M that builds the SENA layer's alpha in Eq. (1), so elevated differential activation for those BPs is partly enforced by construction. These are genuine circular validations of the interpretability claim. However, the paper's other central claim—comparable predictive performance on unseen double perturbations—is benchmarked against discrepancy-VAE and GEARS on held-out double KOs in Table 1 and on the Wessels dataset in Table 5; this part is external and non-circular. The gap between the single-target identifiability assumption and the coupled mapping U=Z^T(I-A)^{-1} is a correctness or assumption-violation concern, not a circularity, and the Discussion's concession that the assumption 'does not allow CRL methods to thoroughly disentangle' supports that concern without changing the circularity score. Overall, partial circularity in the interpretability evidence, with independent predictive content, warrants a score of 6.

Assumptions & free parameters 4 free parameters · 4 assumptions · 2 invented entities

The central claim rests on the CRL identifiability theory of Ahuja/Zhang (single-target interventions, polynomial decoder, DAG), on the linear pathway-activity parameterization, and on the completeness of the curated GO gene sets. The only fitted quantities are the network weights and the hyperparameters listed above; the paper does not introduce a new physical entity, but it does define new latent constructs (meta-pathway activities and causal pathway archetypes) whose existence is supported only by the model's own predictive performance and by qualitative biological matches.

free parameters (4)

Mask relaxation lambda = 0, 0.1, 1e-2, 1e-3 (ablation); lambda=0.1 and lambda=0 for main model
Eqs. (1)-(2) set weight lambda for genes outside an annotated pathway. The trade-off between prediction (better at 0.1) and strict interpretability (better at 0) is controlled by this hand-tuned hyperparameter.
Latent dimension d = 5, 10, 35, 70, 105 (Norman2019); 14, 28, 50 (Wessels2023)
Number of causal factors/meta-pathways is chosen by search; Table 1 shows MMD and MSE vary strongly with d, so the central comparison is conditional on this choice.
BP selection thresholds = GO terms with <30 genes, >=5 genes in data, overlap removal, ancestor removal, resulting in 454 BPs
Section 4.2; the set of prior-knowledge gene sets defines the SENA mask and therefore the interpretation. Thresholds are taken from a companion method rather than derived.
Hits@100 N = 100
Eq. (4); the interpretability headline depends on ranking affected pathways in the top 100 of differential activation; no sensitivity analysis for N is reported.

assumptions (4)

domain assumption Each intervention targets exactly one latent causal factor and the latent causal graph is a DAG.
Inherited from discrepancy-VAE identifiability theory (Ahuja et al. 2023; Zhang et al. 2024); invoked in Section 3 and the Discussion. The paper acknowledges that gene knockouts affect multiple biological processes, so this assumption is in tension with biology.
domain assumption The decoder h is a full-rank polynomial and the encoder f is non-collapsing.
Needed for identifiability up to permutation and scaling; taken from Zhang et al. Theorem 2 and used without reproof in Sections 2 and 3.
domain assumption Pathway activity is a linear function of gene expression, and meta-pathway expectations are linear in pathway activity.
Eqs. (1) and (3)/(6). The interpretability of latent factors rests on these linear maps; non-linear BP activity would break the direct reading of factors as combinations of processes.
domain assumption The curated GO gene sets are a faithful and sufficiently complete prior for active biological processes in the studied cell lines.
Section 4.2. If the selected GO terms are not the active processes in K562/THP1, the SENA layer imposes the wrong structure and 'biological meaningfulness' is circular.

invented entities (2)

Meta-pathway activities Z_j
purpose: Latent exogenous variables defined as linear combinations of biological process activity scores, connecting pathway space to causal factors.
The model predicts unseen double perturbations, but the Z_j themselves have no falsifiable handle outside the model; their biological relevance is assessed using the model's own activity definitions and GO annotations.
Causal pathway archetypes U_i
purpose: Latent causal factors in the identified causal graph, defined as U = Z^T (I-A)^{-1}, used for perturbation prediction and causal edges.
These are the reparameterized causal factors from discrepancy-VAE theory. The paper validates their biological meaning qualitatively against known H2O2/endothelial findings, not via an external prospective test.

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Cite this review

Pith. "Pith review of Interpretable Causal Representation Learning for Biological Data in the Pathway Space." pith.science (2026). https://pith.science/paper/ZB5IL4RL

@misc{pith2026250612439,
  author       = {Pith},
  title        = {Pith review of: Interpretable Causal Representation Learning for Biological Data in the Pathway Space},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZB5IL4RL}},
  note         = {Machine review of arXiv:2506.12439}
}

read the original abstract

Predicting the impact of genomic and drug perturbations in cellular function is crucial for understanding gene functions and drug effects, ultimately leading to improved therapies. To this end, Causal Representation Learning (CRL) constitutes one of the most promising approaches, as it aims to identify the latent factors that causally govern biological systems, thus facilitating the prediction of the effect of unseen perturbations. Yet, current CRL methods fail in reconciling their principled latent representations with known biological processes, leading to models that are not interpretable. To address this major issue, we present SENA-discrepancy-VAE, a model based on the recently proposed CRL method discrepancy-VAE, that produces representations where each latent factor can be interpreted as the (linear) combination of the activity of a (learned) set of biological processes. To this extent, we present an encoder, SENA-{\delta}, that efficiently compute and map biological processes' activity levels to the latent causal factors. We show that SENA-discrepancy-VAE achieves predictive performances on unseen combinations of interventions that are comparable with its original, non-interpretable counterpart, while inferring causal latent factors that are biologically meaningful.

Figures

Figures reproduced from arXiv: 2506.12439 by the authors.

**Figure 1.** Model overview. SENA-discrepancy-VAE modifies the encoder of discrepancy-VAE to enforce a biologically-driven training through a pathway-based mask M. 4 EXPERIMENTAL SETTINGS To first assess the learning capabilities of our proposed architecture, we performed several ablation studies using the proposed encoder within simple autoencoder (AE) and variational-AE (VAE) architectures. Our aim is to first assess whether t… view at source ↗

**Figure 2.** SENA-discrepancy-VAE causal graph on the Norman2019 data. Latent factors are represented by word clouds of associated BPs. Arrows indicate causal influences. Interpretation of the SENA-discrepancyVAE latent factors. The proposed model offers the possibility of inspecting its encoder for deriving the BPs composing the latent factors. By construction, each perturbation will target a single latent factor Ui , which … view at source ↗

**Figure 3.** SENA, µ and σ 2 layers interpretability analysis. A. DA score for the three perturbations presenting the highest number of affected BPs among Wa and Wa¯. B. DAR of the 37 analyzed perturbations when varying the latent space dimensions. For every dimension, genes with the highest DAR are highlighted. C. DA score across the evaluated perturbations at the output of the µ and σ 2 layers among affected and not affected B… view at source ↗

Figures from the paper (11 more)

**Figure 4.** Figure 4: DA score of 6 most significant (KO, BP) pairs. A. UMAP of all intervened cells across the KO genes presenting the 6 largest DA scores. B-F. UMAP from A colored by the differential activation score on each cell across genes within each evaluated BP [PITH_FULL_IMAGE:fi…

**Figure 5.** Figure 5: Experimental validation of derived Eq. 9. A-C. Experimental analysis of derived Eqs. 9 and 10 for the original discrepancy-VAE (MLP) architecture (A), SENA-δλ=0.1 (B) and SENA-δλ=0 (C), respectively. Here x-axis represent the expected latent factors U extracted by forw…

**Figure 6.** Figure 6: Edge robustness analysis for the inferred causal graph. A. Edge values (mean of the inferred graph upper triangular. Results are averaged across λ = {0, 0.1, 10−2 , 10−3}. B. Edge consistency across the aforementioned λ’s. C-G. Coefficient of Variation (mean over stand…

**Figure 7.** Figure 7: Study on genesets aggregation at the latent factor level. A-B. Permutation test on the latent factor contribution for level 2 genesets versus random aggregations of genesets, for λ = 0 (A) and λ = 0.1 (B). Results are shown for the first latent factor C. Heatmap depict…

**Figure 8.** Figure 8: Ablation studies on interpretability and sparsity. A. Percentage of affected gene sets in the top 100 DA BPs for several SENA-based architectures and λ values. B. Sparsity evaluation according to Eq.??. ATest MSE (x10 ) -2 B 1 2 3 4 6 0 50 100 150 200 250 Epoch SENA (λ…

**Figure 9.** Figure 9: Ablation studies for AE-type architecture. Test MSE evaluation for AE-based architectures for SENA (A) and SENA-δ (B) encoders. 19 [PITH_FULL_IMAGE:figures/full_fig_p019_9.png]

**Figure 10.** Figure 10: Ablation studies of the number of BPs used in SENA-δλ=0. On each experiment, a minimum number of genes per BP is imposed, which reduces the total number of BPs used after the SENA layer. A. Test KLD as a function of the minimum number of genes within eachBP. B. Summar…

**Figure 11.** Figure 11: Comparison of Norman and Wessels datasets. A. UMAP representation of single-gene and combinatorial perturbations captured in the Norman2019 dataset. Each point represents the pseudo-bulk expression profile of a genetic perturbation. B. UMAP representation of the Wesse…

**Figure 12.** Figure 12: SENA layer analysis. Masked and non-masked gradients for SENA-discrepancy-VAE at the output of the SENA layer, for λ values of 0 (A), 10−3 (B), 0.01 (C) and 0.1 (D). Barplot showing matrix M values is depicted next to each histogram. 24 [PITH_FULL_IMAGE:figures/full_…

**Figure 13.** Figure 13: Differential Activation Scores analysis. DA score analysis for targeted and non-affected BPs along the 37 single-gene perturbations present in the input gene expression matrix. 25 [PITH_FULL_IMAGE:figures/full_fig_p025_13.png]

**Figure 14.** Figure 14: Mapping between latent factors and perturbations genes. Mapping distribution of knocked out genes and latent factors, from SENA-discrepancy-VAE (λ = 0) and discrepancy-VAE (MLP encoder) for several values of latent dimensions {105, 70, 35, 10, 5}. We generated this m…

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

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and in this section’s Table 6 to compare against MSE. When analyzing these results, we found that the MSE on double perturbations exhibited scores 10 times larger than the one reported during training for validation folds (0.00368 ± 0.000363 across different latent dimension sizes for one seed), which suggest a potential lack of generalization. Moreover, ...

work page arXiv 2025

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Moreover, the number of genes that are differentially expressed following a perturbation is generally lower in the Wessels2023 study than in Norman2019 (Fig

While in the Norman2019 datasets cells affected by different perturbations tend to cluster separately (panel A), most of the interventions in Wessels2023 are grouped together (panel B), indicating similar profiles. Moreover, the number of genes that are differentially expressed following a perturbation is generally lower in the Wessels2023 study than in N...

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per perturbation in the Norman2019 and Wessels2023 dataset. Table 5: Performance comparison between SENA-discrepancy-V AE and discrepancy-V AE on the Wessel2023 dataset across different lambda values and latent factors for double perturbation samples. Note that KLD and L1 losses are not dependent on the samples, but computed after the training process is ...

work page arXiv