Biologically Informed Deep Neural Networks for Multi-Omic Integration, Pathway Activity Inference and Risk Stratification in Cancer

Le Ou-Yang; Min Wu; Pedro Henrique da Costa Avelar; Sophia Tsoka

REVIEW 4 major objections 10 minor 299 references

Biologically Informed Deep Neural Networks for Multi-Omic Integration, Pathway Activity Inference and Risk Stratification in Cancer

T0 review · 4 major / 10 minor · reviewed 2026-07-07 · glm-5.2

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Pith's one-line read Pathway-Constrained Autoencoders Integrate Six Omics Layers for Cancer Subtyping and Survival Prediction

desk verdict Solid multi-omics extension of prior PAAE work with useful repeatability findings, but the 'superior representations' claim overreaches given no external multi-omics validation and no modern multi-omics baselines. read the letter →

arxiv 2607.05306 v1 pith:UYW3BJS2 submitted 2026-07-06 cs.LG

Pedro Henrique da Costa Avelar , Le Ou-Yang , Min Wu , Sophia Tsoka This is my paper

classification cs.LG

keywords pathwayactivityautoencodermulti-omicsintegrationinterpretabledeeplearningbreastcancerbiologicallyinformedneuralnetworkinferenceShapleyvaluesurvivalprediction

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 introduces the Pathway Activity Autoencoder (PAAE), a deep learning architecture that constrains its internal structure to match known biological pathways, so that each internal unit corresponds to a specific, named pathway and produces a directly interpretable activity score. The authors extend this framework from single-omics to multi-omics integration across six molecular layers (gene expression, methylation, mutation, RPPA protein, copy number, and microRNA) in breast cancer, and evaluate early versus late integration strategies. They find that late integration—training separate pathway-constrained models per omics layer and combining their outputs—consistently outperforms early integration, which feeds all layers into a single model simultaneously. Through an adapted Shapley value analysis across all 63 possible omics layer combinations, they show that gene expression, RPPA protein, and microRNA layers contribute the most to downstream classification and survival prediction, while mutation data often harms early integration. A large-scale repeatability study (2,560 models) demonstrates that increasing dropout on the pathway activity layer improves cross-run consistency but degrades predictive performance beyond a phase transition at 70–80% dropout. The authors also construct a fully interpretable decision tree using only five pathway activity scores that separates breast cancer subtypes with reasonable accuracy and validates on an external cohort, and they identify the Valine, Leucine, and Isoleucine Degradation pathway as a potentially underexplored biomarker with cross-cohort survival stratification.

What carries the argument

Pathway Activity Autoencoder (PAAE): an autoencoder whose encoder is partitioned into pathway-specific sub-encoders, each receiving only the molecular features mapped to genes in one biological pathway and outputting a single activity score; these scores are concatenated into a pathway activity vector that is further compressed into a latent space and then decoded to reconstruct the full input. Late integration trains separate PAAE models per omics layer and combines their pathway activity vectors by concatenation or averaging. Early integration concatenates all omics layers before feeding them into a single PAAE.

What would settle it

If pathway activity scores fail to correlate with direct experimental measurements of pathway activity (e.g., from phosphoproteomics or perturbation assays), the interpretability claims would be undermined regardless of downstream classification performance.

Watch

Extended reading notes

Core claim

The central object is the pathway activity score: a single scalar per pathway, produced by a sub-encoder that sees only the genes belonging to that pathway, trained jointly to reconstruct the full molecular input. The paper claims these scores are biologically meaningful because they separate cancer subtypes in unsupervised clustering, rank consistently across independent cohorts, stratify patient survival, and map onto pathways with known cancer relevance. The second central finding is that late multi-omics integration—combining independently learned pathway activity scores from separate omics layers—outperforms early integration, and that gene expression, RPPA, and microRNA are the highest

Load-bearing premise

The paper assumes that pathway activity scores learned by the autoencoder are biologically meaningful representations of actual pathway activity, rather than artifacts of the reconstruction objective. The model optimizes mean squared error of the full molecular input, not biological fidelity of pathway scores, and the paper validates only downstream predictive utility and cross-cohort consistency—not comparison to gold-standard pathway activity measurements or perturbation实验.

Editorial extensions

If this is right

If pathway activity scores are biologically faithful, they could serve as a standard intermediate representation for clinical decision support, allowing clinicians to see which named pathways drive a patient's subtype classification and survival risk.
The finding that late integration outperforms early integration suggests that cross-omics interactions within individual pathways are less informative than layer-specific pathway signals combined downstream, which has practical implications for how multi-omics models should be architected.
The Shapley value analysis of omics layer contributions could guide data collection priorities: if gene expression, RPPA, and microRNA carry most of the signal, clinical multi-omics panels might be streamlined.
The dropout phase transition at 70–80%—where repeatability sharply increases but performance collapses—identifies a regime boundary that other biologically informed neural networks should test for.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Here's my read on the PAAE multi-omics paper (arXiv:2607.05306). The bottom line: it's a legitimate extension of the authors' prior pathway-activity autoencoder framework, with a genuinely useful dropout study and a reasonable Shapley-value decomposition of omics layer contributions. But the abstract's claim of 'superior latent representations' is not supported by the evidence as stated — the multi-omics experiments have no external validation and no modern multi-omics baselines. What's actually new and good: the repeatability study is the strongest part. They train 2560 models across dropout rates and find a phase transition between 70-80% dropout where repeatability spikes but predictive power collapses. That's a concrete, useful finding for anyone working with BINNs. The Shapley-value adaptation for quantifying per-omics-layer marginal contributions is a clean idea and the results (gene expression, RPPA, and microRNA contributing most; mutation hurting early integration) are plausible and well-presented. The decision tree case study is a nice illustration of interpretability, and the cross-cohort consistency of MI rankings from TCGA to Metabric for the single-omics model is real evidence. The soft spots, in order of importance: First, the multi-omics claims rest entirely on within-TCGA cross-validation. The authors acknowledge Metabric is incompatible, but this means every multi-omics result — the integration comparisons, the Shapley analysis, the survival predictions — is unvalidated externally. Second, the baselines (AE, VAE, PACL, PASL, PathME) are carried over from the single-omics predecessor. None are multi-omics integration methods. So 'superior' is only established against non-multi-omics models on a single dataset. The stress-test note is right that this is the more concrete deficiency. Third, the SMOTE-before-cross-validation in the decision tree case study risks leakage, though this is a minor issue since the case study is illustrative, not load-bearing. Fourth, code is stated as future, not shipped. The reader's concern about pathway scores being optimized for reconstruction MSE rather than biological fidelity is philosophically valid but proportionally less pressing — the cross-cohort consistency and survival stratification provide indirect evidence, and this is a shared limitation across the BINN literature. I'd disagree slightly with the reader's soundness score of 5.0 — the experimental work is extensive and carefully executed; the problem is overclaiming, not unsoundness. This paper is for readers working on biologically-informed neural networks or multi-omics integration who want practical guidance on integration strategies and regularization. It deserves a serious referee. The main revision ask should be: tone down 'superior' to what's actually shown, add at least one modern multi-omics baseline, and ideally find a compatible external dataset or at least a held-out TCGA split reported separately.

Referee Report

4 major / 10 minor

Summary. This manuscript extends the authors' prior Pathway Activity Autoencoder (PAAE) framework to the multi-omics setting, applying it to TCGA-BRCA data for subtype classification and survival prediction. The paper introduces early and late integration strategies for combining six omics layers, presents a large-scale repeatability study (2560 models) on the effect of dropout on pathway activity representations, provides an interpretable decision-tree case study using top-ranked pathways, and adapts Shapley value analysis to quantify per-omics-layer marginal contributions. The authors find that late integration generally outperforms early integration, that gene expression, RPPA, and microRNA are the strongest contributors, and that excessive dropout improves repeatability but harms predictive performance. External validation is performed for single-omics experiments (TCGA to Metabric) but is not possible for multi-omics due to Metabric's missing modalities.

Significance. The manuscript addresses a practically important problem — how to integrate multi-omics data in a biologically informed, interpretable manner — and the PAAE framework's architectural constraint to pathway gene sets is a reasonable design choice. The repeatability study is commendable in scale (2560 models) and yields a useful, actionable finding: dropout improves cross-run consistency but degrades signal beyond a phase transition at 70–80%. The Shapley-value decomposition of omics-layer contributions is a thoughtful addition. The interpretable decision-tree case study with cross-cohort validation (TCGA to Metabric) for single-omics is a concrete demonstration of clinical translatability. Code is promised upon acceptance, which would support reproducibility.

major comments (4)

§3.3 and §4.5: The central claim that multi-omics integration yields 'superior latent representations' (Abstract, §5) rests entirely on within-TCGA cross-validation against baselines (AE, VAE, PACL, PASL, PathME) that are all single-omics methods carried over from the predecessor paper (Supp. B). No modern multi-omics integration method (e.g., MOFA+, VEGA, DeepMOCCA, or similar) is included as a comparator. The claim of 'superior' is thus not established relative to the state of the art in multi-omics integration; it is established only relative to the authors' own single-omics baselines applied to concatenated inputs. This is load-bearing for the paper's central contribution. The authors should either (a) soften the 'superior' claim to 'beneficial relative to single-omics PAAE' or (b) add at least one dedicated multi-omics integration baseline.
§3.3: The authors state that external validation is not performed for multi-omics because 'the Metabric dataset lacks several omics layers.' This means all multi-omics claims — integration benefit, late vs. early comparison, per-layer Shapley contributions — are supported by a single-cohort internal cross-validation on TCGA-BRCA only. Given that the single-omics results show notable train-to-test performance drops (e.g., decision-tree AUC drops from 0.85 on TCGA to 0.74 on Metabric in Fig. 21), the absence of any external check on the multi-omics claims is a significant gap. The authors should explicitly acknowledge this as a primary limitation in §5 and qualify the multi-omics conclusions accordingly, or discuss whether a subset of layers available in both cohorts could support a partial external validation.
§2.2 and Supp. F: The survival analysis uses a 5-year time window (1825 days) and tertile stratification, both of which appear to be chosen without prior justification. The 5-year cutoff is applied uniformly across all pathways and genes. For the Cox-PH models used in §4.5 (Fig. 9), it is unclear whether the same window and stratification apply, and whether the variance threshold (0.01) and L2 penalty (0.001) described in §3.3 were selected post-hoc. These choices affect which features pass significance filtering (Fig. 4) and which models are ranked highest (Fig. 9). The authors should state whether these parameters were pre-specified or selected on the training data, and ideally provide a sensitivity analysis for at least the time-window choice.
§4.1 and Supp. C: The claim that pathway activity scores are 'biologically meaningful' is supported by cross-cohort MI consistency (Fig. 2), literature support for selected pathways, and survival stratification (Fig. 4). However, the reconstruction objective (Eq. 2) optimizes MSE on the full molecular input, not biological fidelity of pathway scores. No comparison against gold-standard pathway activity metrics (e.g., PROGENy, perturbation-derived activity scores) is performed. While the authors provide necessary conditions (predictive utility, consistency), they do not provide sufficient evidence for biological validity of the scores themselves. This concern is load-bearing for the interpretability claims (decision tree, pathway rankings, survival stratification). The authors should either add a comparison against at least one established pathway activity scoring method or explicitly re-

minor comments (10)

Abstract: 'use linear models that may overlook complex interactions' — the phrase 'use' should be 'using' for grammatical consistency.
§2.1, Eq. (2): The optimization objective is written as min_{Ω,Γ} (x̂−x)² without the expectation or summation over samples. This should be clarified (e.g., mean over the batch) for precision.
§2.5, Eq. (10): The Shapley value adaptation uses f as the median of marginal contributions, but the equation as written does not clearly show how the median enters. A brief clarifying sentence would help readers.
§4.3: The 'phase transition' between 70% and 80% dropout is mentioned but not mechanistically explained. A brief hypothesis (e.g., effective number of active pathways dropping below a threshold) would strengthen the discussion.
Figure 8: The x-axis labels for omics combinations are very dense and difficult to read. Consider faceting by number of omics layers or using a more compact encoding.
§4.5: The statement that mutation and CNV layers 'performed worse than random chance' for survival (Fig. 9) is surprising and deserves brief discussion of possible causes (e.g., sparse binary features, small sample size effects).
Supp. B: The description of baseline adaptations (PACL, PASL, PathME) notes several compatibility and stability issues (CPU-only training, NaN/Inf values). These are important caveats that should be briefly mentioned in the main text where baseline comparisons are discussed, so readers can assess fairness.
References: Several citations are to preprints (e.g., Selby et al. 2024, Uyar et al. 2021, Wissel et al. 2022). Where peer-reviewed versions exist, they should be updated.
§3.2: SMOTE is applied prior to training the decision tree, but it is unclear whether it was applied only to the training fold or before cross-validation. This should be clarified to rule out data leakage.
Figure 4 caption: The genes shown (DEGS2, MCCC1, OXCT1) represent 4 of 7 significant genes in TCGA. It would help to list all 7 genes in a supplementary table for completeness.

Simulated Author's Rebuttal

4 responses · 0 unresolved

We thank the referee for a thorough and constructive report. The comments identify legitimate gaps in our comparator set, external validation, parameter justification, and pathway activity score validation. We address each point below and commit to revisions for all four major comments, ranging from softening claims and adding limitations to conducting new sensitivity analyses and comparisons with established pathway scoring methods.

read point-by-point responses

Referee: §3.3 and §4.5: The central claim that multi-omics integration yields 'superior latent representations' rests entirely on within-TCGA cross-validation against single-omics baselines. No modern multi-omics integration method (MOFA+, VEGA, DeepMOCCA) is included. The claim of 'superior' is not established relative to the state of the art.

Authors: The referee is correct that our baselines are carried over from the single-omics predecessor paper and that no dedicated multi-omics integration method is included as a comparator. We agree that the word 'superior' in the Abstract and §5 overstates what our experiments establish. Our results demonstrate that multi-omics integration within the PAAE framework is beneficial relative to single-omics PAAE, and that late integration generally outperforms early integration within our framework — but we have not shown superiority over other multi-omics integration methods. We will revise the manuscript in two ways: (1) we will soften 'superior latent representations' to 'beneficial relative to single-omics PAAE' or equivalent language throughout the Abstract and Discussion; (2) we will add at least one dedicated multi-omics integration baseline. We plan to include MOFA+ as a comparator, since it is widely used, operates on multi-omics factor decomposition, and can be applied to our TCGA-BRCA data with the same downstream evaluation pipeline. We note that VEGA, which is architecturally related to our pathway-constrained approach, is also a strong candidate and we will consider including it as well. We cannot honestly claim that our current experiments establish superiority over the state of the art in multi-omics integration, and the revised manuscript will reflect this. revision: yes
Referee: §3.3: External validation is not performed for multi-omics because Metabric lacks several omics layers. All multi-omics claims are supported by single-cohort internal cross-validation on TCGA-BRCA only. The absence of any external check on multi-omics claims is a significant gap given the train-to-test performance drops seen in single-omics.

Authors: This is a fair and important point. We acknowledge that all multi-omics claims rest on within-TCGA-BRCA cross-validation, and the referee is correct that the single-omics train-to-test drops (e.g., decision-tree AUC from 0.85 to 0.74) illustrate the risk of overfitting to a single cohort. We will make the following revisions: (1) We will explicitly acknowledge the absence of multi-omics external validation as a primary limitation in §5 and qualify the multi-omics conclusions accordingly. (2) We will investigate whether a partial external validation is feasible using the subset of omics layers available in both cohorts. TCGA and Metabric share gene expression, copy number, and mutation data; a partial multi-omics external validation on these three layers, while not covering the full six-layer setting, would provide at least some cross-cohort evidence. We will report the results of this analysis if the data compatibility is sufficient, and if not, we will state this explicitly. We note that methylation platform differences (Illumina 27K vs 450K) and the absence of RPPA and microRNA in Metabric prevent a full multi-omics external validation, and this will be stated clearly. revision: yes
Referee: §2.2 and Supp. F: The survival analysis uses a 5-year time window (1825 days) and tertile stratification without prior justification. It is unclear whether the variance threshold (0.01) and L2 penalty (0.001) in §3.3 were selected post-hoc. The authors should state whether these parameters were pre-specified or selected on the training data, and provide a sensitivity analysis for the time-window choice.

Authors: We appreciate the referee raising this issue. To be transparent: the 5-year time window, tertile stratification, variance threshold (0.01), and L2 penalty (0.001) were not pre-specified based on prior clinical or biological rationale. They were selected during the development of the analysis pipeline, primarily on the TCGA training data, to ensure numerical stability (e.g., the variance threshold was introduced to exclude features that perfectly determined survival status in cross-validation folds, which impeded Cox-PH convergence). We agree that this should be stated explicitly and that the sensitivity of the results to these choices should be assessed. In the revision, we will: (1) clearly state in §2.2 and Supp. F that these parameters were selected on the training data and were not pre-specified; (2) provide a sensitivity analysis for the time-window choice, e.g., comparing 3-year, 5-year, and 7-year cutoffs on the survival stratification results (Fig. 4); (3) provide a sensitivity analysis for the variance threshold and L2 penalty on the multi-omics survival results (Fig. 9). If the results are robust to these variations, this will strengthen the claims; if not, we will report the dependence honestly. revision: yes
Referee: §4.1 and Supp. C: The claim that pathway activity scores are 'biologically meaningful' is supported by cross-cohort MI consistency, literature support, and survival stratification, but the reconstruction objective optimizes MSE, not biological fidelity. No comparison against gold-standard pathway activity metrics (PROGENy, perturbation-derived scores) is performed. The authors should add a comparison or explicitly reframe the claim.

Authors: The referee correctly identifies a gap between what we claim ('biologically meaningful') and what we demonstrate. Our evidence — cross-cohort MI consistency, survival stratification, and literature support for identified pathways — provides necessary conditions for biological relevance, but does not constitute sufficient evidence for biological validity of the scores themselves, particularly given that the reconstruction objective optimizes MSE on molecular inputs rather than biological fidelity of pathway activities. We will address this in two ways: (1) We will add a comparison against at least one established pathway activity scoring method. PROGENy is a natural choice because it provides perturbation-derived pathway activity scores for a focused set of well-characterized signaling pathways, and we can directly compare our PAAE-derived scores against PROGENy scores in terms of downstream task performance (subtype classification, survival prediction) and cross-cohort consistency. We will also consider including a simpler method such as GSVA or ssGSEA as an additional reference point. (2) We will reframe the 'biologically meaningful' language to be more precise, distinguishing between 'predictively useful and consistent across cohorts' (which we demonstrate) and 'biologically validated pathway activity' (which would require comparison to gold-standard metrics). The revised language will accurately reflect the evidence provided. revision: yes

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity; self-citation establishes base architecture but does not force new results

full rationale

The paper builds on the authors' own PAAE framework (da Costa Avelar et al. 2023, 2024), but this self-citation establishes the base autoencoder architecture (Eqs. 1-2), not the central claims of the present paper. The new contributions—multi-omics integration strategies (Eqs. 5-8), Shapley value omics-layer contribution analysis (Eq. 9-10), dropout robustness studies (2560 models), and the interpretable decision-tree case study—are each evaluated against external benchmarks: TCGA-BRCA and Metabric datasets, PAM50 clinical labels, KEGG/Hallmark/miRTarBase pathway databases, and standard metrics (ROC AUC, C-index, MI, logrank tests). Pathway selection via OvR MI is performed on the training set (TCGA) and validated on an external cohort (Metabric) with cross-cohort consistency explicitly reported (Sec. 4.1). Survival stratification selects genes by ANPW ranking and logrank significance on TCGA, then confirms significance and directionality matching on Metabric (Sec. 4.2, Supplementary F). No step reduces to its inputs by construction: the reconstruction objective (Eq. 2) defines what the pathway scores optimize for, but the paper's biological-meaningfulness claims are supported by external evidence (cross-cohort MI consistency, survival stratification, literature support), not by definition. The gap between reconstruction-optimized scores and biological fidelity is a correctness risk, not a circularity. The self-citation chain is present but not load-bearing for the new results. Score 1 reflects the minor self-citation for the base framework, which is standard and does not raise circularity concerns.

Assumptions & free parameters 9 free parameters · 5 assumptions · 0 invented entities

The paper does not invent new biological entities, particles, or forces. It introduces no new mathematical objects beyond standard autoencoder components. The pathway activity scores are reformulations of standard neural network hidden unit outputs constrained by pathway structure. All free parameters are standard hyperparameters selected via cross-validation or fixed from prior work. The variance threshold (0.01) and survival time window (1825 days) are post-hoc choices that affect survival analysis results.

free parameters (9)

Pathway encoder hidden layer sizes = [32] or [32,16]
Selected via internal 8-fold CV grid search on TCGA RNAseq; controls pathway activity encoder capacity.
Latent space dimensionality = 64
Fixed across all models; chosen during internal validation.
Dropout rate on pathway activity layer = 0.0 to 0.9 in repeatability study; 0.5 for main models
Swept in repeatability study; 0.5 used as default from prior single-omics validation.
Learning rate = 1e-4
Fixed for Adam optimizer across all experiments.
Number of training epochs = 1024
Fixed across all experiments.
L2 regularization for survival models = 0.001
Applied in multi-omics survival analysis (Sec. 3.3).
Variance threshold for survival features = 0.01
Features with variance below this over survival statuses are excluded (Sec. 3.3); post-hoc filtering.
Survival time window = 1825 days (5 years)
Set as time window limit for survival analyses (Supp. F).
Number of top pathways selected per subtype = 5
Used for interpretable decision tree case study; chosen to match number of PAM50 subtypes.

assumptions (5)

domain assumption Biological pathway gene sets (KEGG, Hallmark) accurately represent underlying biological processes
The entire framework depends on pathway definitions being biologically meaningful; invoked throughout Sec. 2.1 and used for all architectural constraints.
domain assumption Reconstruction of the full molecular input is a suitable objective for learning meaningful pathway activity scores
Eq. 2 uses MSE reconstruction as the sole training objective; the interpretability of pathway scores depends on this assumption, stated in Sec. 2.1.
domain assumption CpG-to-gene mapping from Illumina 450K annotation correctly associates methylation sites with their regulating genes
Used for methylation layer pathway mapping (Sec. 3.3); manufacturer-provided mapping may not capture regulatory relationships accurately.
domain assumption miRTarBase experimentally validated miRNA-target interactions are comprehensive enough for pathway mapping
Used for microRNA layer pathway mapping (Sec. 3.3); validated targets may miss true interactions.
domain assumption PAM50 subtypes derived from gene expression are the correct classification target for multi-omics integration
All classification tasks use PAM50 labels; since PAM50 is gene-expression-based, gene expression layer's dominance may be partially tautological (acknowledged in Sec. 4.6).

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Cite this review

Pith. "Pith review of Biologically Informed Deep Neural Networks for Multi-Omic Integration, Pathway Activity Inference and Risk Stratification in Cancer." pith.science (2026). https://pith.science/paper/UYW3BJS2

@misc{pith2026260705306,
  author       = {Pith},
  title        = {Pith review of: Biologically Informed Deep Neural Networks for Multi-Omic Integration, Pathway Activity Inference and Risk Stratification in Cancer},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UYW3BJS2}},
  note         = {Machine review of arXiv:2607.05306}
}

read the original abstract

Integrating complex, multi-omics data presents significant challenges. Existing approaches often face a trade-off between model interpretability and representational capacity, with most either relying on post-hoc interpretation or use linear models that may overlook complex interactions. We report Pathway Activity Autoencoders for the multi-omics setting, which embed prior knowledge via pathway-informed architectural constraints, fostering interpretability, while preserving representational power. Our multi-omic framework is applied in the context of breast cancer and is evaluated in survival prediction and subtype classification with results indicating a positive effect of integration. We conduct analysis of individual omics layer impact on end-task performance, revealing that gene, protein, and microRNA expression layers provide the strongest contribution. Repeatability studies indicate that, while dropout improves model robustness and consistency, excessive regularisation can reduce predictive performance. Finally, visualizations of the learned feature space illustrate the framework's intrinsic transparency and clinical relevance. The results underscore the value of multi-omic integration and delineate the impact of individual omics layers, establishing practical guidelines for integration within our framework. Overall, our pathway activity autoencoder frameworks yield superior latent representations that are biologically meaningful and are directly translatable into clinically relevant insights.

Figures

Figures reproduced from arXiv: 2607.05306 by the authors.

**Figure 1.** Diagram of the PAAE model. The representation learning module (left) receives a subset of the input gene expression [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 2.** Clustermap based on cosine distances between sample-level inferred pathway activity vectors in [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** Subtype distribution overlaid on 2D UMAP projection of the inferred pathway activity vectors [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

Figures from the paper (20 more)

**Figure 4.** Figure 4: Kaplan-Meier Curves for the pathways (4a,4b) and genes (4c-4e) that showed statistically signif [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]

**Figure 5.** Figure 5: Plot illustrating the average Centered Kernel Alignment (CKA) similarity and the average [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]

**Figure 6.** Figure 6: Decision tree generated after training it on pathway activity vectors of the PAAE KEGG model [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]

**Figure 7.** Figure 7: 2D UMAP featuremaps for TCGA (top six) and Metabric (bottom six) datasets for pathway [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]

**Figure 8.** Figure 8: ROC AUC of one-vs-rest logistic regression for all combinations of omics layer in early, late [PITH_FULL_IMAGE:figures/full_fig_p015_8.png]

**Figure 10.** Figure 10: Marginal contribution of each omics layer to the classification performance, measured by ROC [PITH_FULL_IMAGE:figures/full_fig_p017_10.png]

**Figure 11.** Figure 11: The clustermap using the cosine distance between samples’ inferred pathway activity vectors [PITH_FULL_IMAGE:figures/full_fig_p033_11.png]

**Figure 12.** Figure 12: The clustermap using the cosine distance between samples’ inferred pathway activity vectors for [PITH_FULL_IMAGE:figures/full_fig_p034_12.png]

**Figure 13.** Figure 13: Average ROC AUC (left) from a one-vs-rest Logistic Regression and Concordance Index (right) [PITH_FULL_IMAGE:figures/full_fig_p034_13.png]

**Figure 14.** Figure 14: The learned pathway space when applying, from left to right, 0%, 10%, 50%, 80%, and 90% [PITH_FULL_IMAGE:figures/full_fig_p035_14.png]

**Figure 15.** Figure 15: The average Kendall τ -b coefficient between pathway rankings obtained from models trained with different random seeds on the MO-TCGA-BRCA dataset, based on mutual information. We compare nonconsensus (reg) models between themselves (top 3), non-consensus against ali…

**Figure 16.** Figure 16: The average Kendall τ -b coefficient between pathway rankings obtained from models trained with different random seeds on the MO-TCGA-BRCA dataset, based on concordance index. We compare nonconsensus (reg) models between themselves (top 3), non-consensus against alig…

**Figure 17.** Figure 17: Boxplots of the concordance index of a pathway obtained from models trained with different [PITH_FULL_IMAGE:figures/full_fig_p037_17.png]

**Figure 18.** Figure 18: Boxplots of the mutual information between a pathway and PAM50 labels, obtained from models [PITH_FULL_IMAGE:figures/full_fig_p038_18.png]

**Figure 19.** Figure 19: Average top-k agreement of Concordance-Index rankings between models models trained with different random seeds. Models are labelled as either Aligned Consensus Model (right) or not (left). Shaded regions indicate model variance. 38 [PITH_FULL_IMAGE:figures/full_fig_…

**Figure 20.** Figure 20: Average top-k agreement the mutual information rankings between models models trained with different random seeds. Models are labelled as either Aligned Consensus Model (right) or not (left). Shaded regions indicate model variance. 39 [PITH_FULL_IMAGE:figures/full_fi…

**Figure 21.** Figure 21: Confusion matrices (left) and receiver operating characteristic curves (right) for a constrained [PITH_FULL_IMAGE:figures/full_fig_p040_21.png]

**Figure 22.** Figure 22: 2-dimensional UMAP reprentations of the TCGA (top) and Metabric (bottom) datasets, for the [PITH_FULL_IMAGE:figures/full_fig_p041_22.png]

**Figure 23.** Figure 23: Accuracy of one-vs-rest logistic regression for all combinations of omics layer in early, late [PITH_FULL_IMAGE:figures/full_fig_p042_23.png]

**Figure 26.** Figure 26: Marginal contribution of each omics layer to survival prediction, measured by concordance index [PITH_FULL_IMAGE:figures/full_fig_p044_26.png]

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