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. 2026 Aug 6;27(4):bbag425. doi: 10.1093/bib/bbag425

Sparsity is all you need: rethinking biologically informed neural networks

Isabella Caranzano 1, Corrado Pancotti 2, Cesare Rollo 3,4, Flavio Sartori 5, Pietro Liò 6, Piero Fariselli 7,✉, Tiziana Sanavia 8,✉
PMCID: PMC13446513  PMID: 42561153

Abstract

Biologically informed neural networks are increasingly adopted in bioinformatics under the premise that embedding biological knowledge into model architectures yields more accurate and interpretable predictions. This approach has driven a growing literature of pathway-informed models aiming to move beyond black-box learning by explicitly encoding biological structure. However, it remains unclear whether these models exploit biological knowledge or instead benefit from a different inductive bias. Here, we systematically investigate this question across 29 state-of-the-art pathway-informed neural networks by explicitly decoupling biological annotations from network architecture. For each evaluable model, we implement a structure-matched randomization protocol, in which pathway annotations are replaced with random associations while preserving sparsity and architectural constraints, allowing for a direct comparison under controlled conditions. Across multiple prediction tasks, datasets, and evaluation metrics, the randomized models consistently match or outperform their biologically informed counterparts. Moreover, pathway-informed models show no systematic advantage in interpretability: randomized models recover disease-associated biomarkers with comparable accuracy and yield highly correlated feature rankings. Our results reveal that the performance gains commonly attributed to biological pathway integration arise predominantly from sparsity-induced regularization rather than from biological knowledge itself. We provide a general evaluation workflow to test whether biological priors contribute predictive information beyond sparsity, offering practical guidance for the development of biology-aware neural networks. The code implementing the proposed methodology is available on GitHub at https://github.com/compbiomed-unito/Pathway_Randomization.

Keywords: biologically informed neural networks, pathway-based deep learning, model randomization analysis, multi-omics integration, cancer genomics

Introduction

Genes and molecular entities organize into pathways, biological processes, and regulatory mechanisms. This structured knowledge can guide neural network design in bioinformatics and biomedical applications. Encoding this structure directly into neural network architectures appears to offer a way to move beyond black-box prediction, combining strong predictive performance with built-in biological interpretability [1]. This premise has driven the rapid adoption of biologically informed neural networks (BINNs), in which curated annotations from databases such as Kyoto Encyclopedia of Genes and Genomes (KEGG) [2] and Reactome [3] constrain model architectures or input representations. Across multi-omics applications, BINNs are increasingly used for classification, regression, and survival analysis, often with the explicit claim that embedding biological knowledge improves both generalization and interpretability [4].

Early approaches introduced a single pathway layer into multilayer perceptrons [5–8], combined with sparse coding mechanisms such as dropout and gene–pathway pruning based on curated annotations [9–14]. Subsequent works extended this paradigm by incorporating biological information across multiple layers, modeling pathway interactions, or representing pathways as independent subnetworks [15–19]. More recent models incorporate attention mechanisms, transformers or variational autoencoders to further increase representational capacity while retaining pathway structure [20–22]. Across these designs, pathway annotations shape network topology, ensuring that functionally related entities share connections while pruning interactions based on curated knowledge. Alternative strategies exploit pathway information through data transformation, enabling architectures designed for non-tabular data. Graph neural networks (GNNs) represent genes or pathways as nodes connected according to pathway-specific relationships [23, 24], or model pathway–pathway interactions via graph convolutional or attention-based layers [25–29]. Hybrid approaches combine GNNs with pathway aggregation modules [30], or integrate interaction networks through shared GNN layers and meta-graph representations for downstream prediction [31] (a schematic representation is shown in Fig. 1).

Figure 1.

Workflow showing two strategies for integrating pathway and omics data into neural networks, alongside randomized alternatives that preserve structure while removing biological pathway meaning.

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Schematic representation of pathway integration approaches in neural networks for omics data and their relative randomization. Pathway information can be incorporated in two ways (panels a and c): (a) A neural network utilizing pathway information by enforcing structured connections, introducing sparsity in the model. (b) A structure-matched randomized counterpart in which connections are assigned independently of pathway annotations while preserving network sparsity. (c) A data transformation strategy that incorporates pathway information to convert tabular omics data into graphs or images. (d) A randomized data transformation approach that generates graphs or images through a randomization procedure rather than predefined pathway structures.

Despite their diversity, these methods share a key feature: pathway annotations act primarily as a sparsity prior, reducing the number of trainable parameters and constraining the space of representable functions. From a learning-theoretic perspective, this design reflects compositional sparsity, where complex functions are decomposed into interactions over limited input subsets. This principle underlies the success of convolutional, graph, and transformer neural networks, which leverage structured sparsity to mitigate the curse of dimensionality [32–36].

BINNs can therefore be viewed as a specific representation of this principle. By grouping genes into pathways or organizing pathways into hierarchical modules, structured sparsity is imposed on feature interactions, using biological knowledge as a mechanism for implementing a compositional structure [37–40]. However, architectural constraints shape the hypothesis space without uniquely determining internal representations. As a result, these internal representations may deviate from their intended biological meaning, even when predictions remain accurate. This raises a fundamental and largely unexplored question: do BINNs exploit biological knowledge beyond the sparsity they impose, or do they succeed primarily because biological annotations impose structured sparsity, regardless of their biological meaning? Answering this requires more than comparing BINNs to their fully connected baselines. It requires isolating biological annotations from architectural effects by introducing appropriate null models that preserve sparsity and structure while removing biological meaning.

In this work, we systematically evaluate 29 state-of-the-art pathway-informed neural networks by explicitly decoupling biological annotations from architectural structure. For each model for which an experimental evaluation was feasible, we built a randomized counterpart in which pathway annotations were replaced with random associations that preserved sparsity and structural constraints. This framework allows us to test a fundamental hypothesis: if biological pathway knowledge contributes predictive information beyond sparsity, then disrupting that knowledge while preserving structure should degrade performance and interpretability. Conversely, if the randomized models perform comparably, the contribution of biological annotations must be reconsidered. Finally, we propose a structured evaluation protocol, in the form of a workflow, to assess when and whether the integration of pathway information is beneficial. This methodology is applicable across different BINN architectures, prediction tasks, and data modalities, providing a robust benchmark for systematically comparing biologically informed models against their structure-matched randomized counterparts.

Results

State-of-the-art pathway-informed approaches in deep learning

We reviewed state-of-the-art pathway-informed neural network studies and examined their methods, assumptions, and reported results. We then applied the proposed evaluation protocol to systematically compare each model with its structure-matched randomized counterpart. We selected models with publicly available code to ensure reproducible comparison. Table 1 summarizes recent BINNs that integrate pathway annotations either into the model architecture or into the organization of the input data. The models included at each analysis level are described in detail in Supplementary Table S1. As shown in Fig. 2, models address tasks ranging from classification to survival analysis and regression. Tables S2–S5 in Supplementary Data summarize feature space and sample statistics. Most models rely on Reactome [3] and KEGG [2], with additional resources including PID [41], BioCarta [42], MSigDB [43], GO BP [44], ConsensusPathDB [45], WikiPathways [46], and Enrichr-KG [47]. Some models exploit gene–pathway associations as priors, while others include gene–gene and pathway–pathway interactions.

Table 1.

Overview of deep learning models integrating pathway information for various prediction tasks. Models are categorized by publication year, journal, prediction task, pathway source, code availability, data availability, and input data type.

Model Year Journal Prediction task Pathway Source Code Data Data Type
PASNet [9] 2018 BMC Bioinformatics Binary classification long-term VS Short-term survival Reactozme ✓ ✓ Gene expression
CoxPASNet [10] 2018 IEEE International Conference on Bioinformatics and Biomedicine (BIBM) 2018 Survival analysis Reactome ✓ ✓ Gene expression
MiNet [11] 2019 ISBRA 2019 Survival analysis Reactome ✓ ✓ Gene expression, CNV, DNA methylation
pathDNN [12] 2020 Journal of Chemical Information and Modeling Drug sensitivity prediction KEGG ✓ ✓ Gene expression, drug targets
Multi-scale NN [5] 2020 Plos one Prediction of disease, pathway, and gene associations Reactome ✓ ✓ Gene expression
GCN-MAE [23] 2020 Bioinformatics Cancer subtype classification KEGG Code not available X Gene expression
P-NET [15] 2021 Nature Cancer state prediction Reactome ✓ ✓ Mutations, CNA
PathCNN [48] 2021 Bioinformatics Binary classification long-term versus Short-term survival KEGG ✓ NB: Only processed data Gene expression, DNA methylation, CNV
PathDeep [6] 2021 International Journal of Molecular Sciences Classification cancer versus normal tissue MSigDB ✓ NB: Only toy dataset available Gene expression
PathGNN [24] 2022 BMC Bioinformatics Binary classification long-term versus Short-term survival Reactome ✓ ✓ Gene expression, clinical data
MPVNN [7] 2022 Bioinformatics Survival analysis Unknown ✓ ✓ Gene expression
GCS-Net [16] 2022 Journal of Oncology Binary classification long-term versus Short-term survival Reactome Code not available X CNV, Somatic mutations, clinical data
REDDA [29] 2022 Computers in Biology and Medicine Drug-disease association prediction KEGG ✓ ✓ Drugs Informations, Proteomics, Gene Expression
ReGeNNe [49] 2023 Bioinformatics Classification (kidney stage, kidney vs liver, binary survival for ovarian) PID, BioCarta, Reactome ✓ X Gene expression
BINN [17] 2023 Nature Communications Phenotypes classification Reactome ✓ ✓ Proteomic Data
PINNet [18] 2023 Frontiers in Aging Neuroscience Alzheimer disease classification KEGG, GO BP ✓ ✓ Gene expression
PGLCN [25] 2023 Computational and Structural Biotechnology Journal Tumor mutation burden prediction Reactome X Github with empty files, not usable Gene expression, CNV, Methylation
PathExpSurv [13] 2023 BMC Bioinformatics Survival analysis KEGG ✓ ✓ Gene Expression
EMGNN [31] 2023 Bioinformatics Cancer gene prediction Consensus PathDB ✓ X Mutations, CNA, Methylation, Gene expression
DeepKEGG [20] 2024 Briefings in Bioinformatics Cancer recurrence prediction - Binary classification KEGG ✓ ✓ mRNA expression, SNV, miRNA
GraphPath [28] 2024 Bioinformatics Cancer status classification KEGG ✓ ✓ CNA, Mutation
Pathformer [21] 2024 Bioinformatics Disease diagnosis and prognosis KEGG, PID, Reactome, BioCarta ✓ ✓ Gene expression (or multimodal)
Autosurv [22] 2024 Precision Oncology Survival analysis Reactome ✓ ✓ Gene expression, miRNA
CRESCENT [26] 2024 IEEE Journal of Biomedical and Health Informatics Cancer survival analysis Consensus-PathDB Code not available X Gene expression
DeepBINN [19] 2024 2024 11th IEEE Swiss Conference on Data Science (SDS) Septic acute kidney injury phenotype classification MSigDB X X Proteomics
Multilevel-GNN [30] 2024 Briefings in Bioinformatics Tumor risk prediction KEGG ✓ ✓ Gene expression, CNV, Methylation, Clinical data
APNet [14] 2025 Bioinformatics Prediction of COVID-19 severity Enrichr-KG, KEGG,ref3, GO BP, WikiPathways 2021 ✓ ✓ Bulk plasma proteomics, Single-cell RNA sequencing
HallmarkGraph [27] 2025 Bioinformatics Hierarchical tumor subtypes classification Reactome ✓ ✓ Gene expression
KNET [8] 2025 Computational Biology and Chemistry Drug response prediction KEGG Code not available X Gene expression, Mutations, CNV
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Figure 2.

Circular bar charts summarizing pathway-informed neural network studies by data type, publication year, pathway database, prediction task, and model architecture.

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Circular bar plots summarizing characteristics of deep learning models that integrate pathway information. The plots show distributions for (a) input data types used, (b) publication year, (c) pathway database sources, (d) prediction tasks, and (e) model architectures (FFNN-MLP: feed-forward neural network - multi-layer perceptron, GNN: graph neural network, CNN: convolutional neural network, AE: autoencoders). Each segment’s length corresponds to the count of models within each category.

Benchmarking biological priors against structure-matched null models

For each method reported in Table 1, we compared the original pathway-informed model with a structure-matched randomized counterpart in which biological priors were replaced by random associations while preserving network sparsity and architectural constraints. Twenty independent train/test splits were evaluated for each model.

Across all prediction tasks, randomized models achieved performance statistically indistinguishable from biologically informed counterparts (Fig. 3; Table 2). In addition, for models such as MPVNN, BINN, pathDNN, and APNet, randomized versions significantly outperformed the original pathway-informed models (paired Wilcoxon signed-rank test P-values <.01).

Figure 3.

Violin plots comparing pathway-informed and randomized model performance across metrics, showing that randomized models generally match or outperform biologically informed counterparts.

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Model performance comparison across accuracy, AUC, C-index, F1 macro, and R-square metrics using violin plots. Models are grouped as pathway-informed (pink) and Randomized (green). The width reflects the distribution of scores, with central lines for median values and box plots indicating interquartile ranges. Models for which randomized versions significantly outperform pathway-informed versions are bolded in the x-axis labels. The results for the MPVNN, PathExpSurv, and DeepKEGG models represent average outcomes across different tumor types considered (detailed findings for each specific tumor type are provided in the Supplementary Data).

Table 2.

Table summarizing the performance comparison between pathway-informed and randomized versions of various deep learning models across different evaluation metrics. Each model’s performance is reported in terms of its specific metric (e.g. AUC, C-index, accuracy, R-squared), alongside the corresponding mean Inline graphic SD values. The table also includes the execution time for each model, with a legend denoting the time required for 20 runs, categorized as follows: + represents seconds, ++ represents minutes, +++ represents hours, and ++++ represents days. For certain models, the performance is further divided into Omic-Pathway Network (OP), Pathway-Pathway Network (PP), or a combination of both (OP + PP), to reflect the different configurations evaluated. Bolded values indicate cases where the randomized version outperformed the pathway-informed version. Results for MPVNN, PathExpSurv, and DeepKEGG correspond to averages across the different tumor types evaluated (detailed results are provided in Supplementary Tables S12–S14).

Model Metric Pathway-informed model Randomized model Execution time
PASNet AUC 0.600 Inline graphic 0.067 0.608 Inline graphic 0.065 ++
CoxPASNet C-Index 0.672 Inline graphic 0.002 0.672 Inline graphic 0.002 ++
MiNet C-Index 0.650 Inline graphic 0.020 0.652 Inline graphic 0.025 +++
pathDNN Inline graphic 0.801 Inline graphic 0.007 0.806 Inline graphic 0.007 +++
Multi-scale NN Accuracy 0.660 Inline graphic 0.013 0.659 Inline graphic 0.014 +++
P-NET AUC 0.899 Inline graphic 0.021 OP 0.896 Inline graphic 0.024 PP 0.887 Inline graphic 0.025 OP + PP 0.892 Inline graphic 0.027 ++
PathCNN AUC 0.745 Inline graphic 0.011 0.746 Inline graphic 0.007 ++
PathGNN AUC 0.693 Inline graphic 0.067 0.687 Inline graphic 0.060 ++++
MPVNN C-Index 0.632 Inline graphic 0.081 0.645 Inline graphic 0.086 +++
REDDA AUC 0.899 Inline graphic 0.221 0.964 Inline graphic 0.050 +++
BINN Accuracy 0.944 Inline graphic 0.023 OP 0.958 Inline graphic 0.016 OP + PP 0.937 Inline graphic 0.017 ++
PINNet AUC 0.974 Inline graphic 0.062 0.974 Inline graphic 0.064 +
PathExpSurv C-Index 0.934 Inline graphic 0.029 0.936 Inline graphic 0.027 +++
DeepKEGG AUC 0.892 Inline graphic 0.088 0.897 Inline graphic 0.090 ++
Autosurv C-Index 0.734 Inline graphic 0.048 0.732 Inline graphic 0.048 +++
Multilevel-GNN C-Index 0.665 Inline graphic 0.029 0.657 Inline graphic 0.020 +++
GraphPath Accuracy 0.867 Inline graphic 0.026 PP 0.878 Inline graphic 0.032 ++++
Pathformer F1 Macro 0.609 Inline graphic 0.077 OP 0.614 Inline graphic 0.071 OP + PP 0.587 Inline graphic 0.067 ++++
APNet AUC 0.999 Inline graphic 0.000 1.000 Inline graphic 0.000 ++
HallmarkGraph Accuracy 0.948 Inline graphic 0.021 0.947 Inline graphic 0.022 ++
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These findings were consistent across evaluation metrics (AUC, accuracy, C-index, and F1 score), datasets, and repeated randomization trials (Supplementary Fig. S1). Moreover, no significant differences were observed between the performance distribution obtained from a single randomization and those obtained across 30 independent randomizations (Kolmogorov–Smirnov test, all P >.05), indicating that the results are not driven by favorable random seeds.

Pathway-informed neural networks differ substantially in computational cost. Across the evaluated models, training times ranged from seconds to multiple days per run, with the most complex architectures, such as graph-based and transformer-based models, requiring orders of magnitude more computation (Table 2).

The role of sparsity as a structural prior in BINNs

The previous analysis showed that biologically inspired neural networks perform equivalently or worse than randomized counterparts. By construction, these randomized networks preserved exactly the same level of sparsity found in their biologically informed counterparts.

We then investigated whether the level of sparsity introduced by the pathway annotations might be optimal for model performance. To this end, we compared randomized neural networks at different sparsity levels around those induced by the biological pathway annotations.

Tables S6–S9 in Supplementary Data illustrate pathway-induced sparsity levels exploited by the original implementation of each biologically informed model. Overall, the pathway-induced sparsity ranged between 59.2% observed with the miRNA-Pathway information used by DeepKEGG (Supplementary Table S8) and 99.99% in the pathway–pathway network exploited by P-NET (Supplementary Table S9).

In Fig. 4, we report the results for the five neural networks that can be feasibly trained and tested under different conditions: BINN, DeepKEGG, PASNet, PathCNN, and PINNet. Considering the biological information exploited by these tools, most models operated at high sparsity levels. Excluding the application of DeepKEGG to miRNA-based pathway annotations (achieving a sparsity between 59.2% and 66.9% across different tumors, as shown in Supplementary Table S8), the other methods employed networks constrained by sparsity levels ranging between 96.8% (BINN) and 99.5% (PINNet). Comparing the original models with randomized counterparts across different sparsity levels, we found that the sparsity levels induced by pathway annotations yielded performance comparable to, or significantly worse than, the best-performing sparsity levels identified using randomized networks across the 60%–99% sparsity range. Statistically significant improvements favoring sparsity induced by randomization were observed only for BINN and DeepKEGG (maximum P-value Inline graphic). These findings suggest that the sparsity induced by biological annotations was suboptimal compared to alternative sparsity levels achieved through randomization, indicating that pathway annotations primarily act as a hard-coded sparsity prior and that its biological origin does not necessarily provide an optimal inductive bias. To complement the sparsity-level analysis, we further investigated whether the number of pathways included in the model affected predictive performance (see Supplementary Fig. S2). Specifically, we evaluated the same five representative models while progressively varying the fraction of retained pathways from 0.10 to 1.00. For each pathway fraction, pathway-informed models were compared with structure-matched randomized counterparts that preserved the same number of pathways and structural constraints. Overall, increasing the number of pathways did not lead to a consistent improvement in predictive performance. In most cases, performance reached a plateau before the full set of pathways was included, and randomized models remained comparable to their pathway-informed counterparts.

Figure 4.

Performance distributions across sparsity levels for selected models, showing that pathway-induced sparsity is often comparable to or worse than alternative random sparsity levels.

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Effect of sparsity level on predictive performance. Green boxplots represent the performance (measured as accuracy or AUC) of each model—BINN, DeepKEGG, PASNet, PathCNN, and PINNet—across varying sparsity levels (60%–99%). Pink boxplots indicate performance at the sparsity level induced by pathway information. For DeepKEGG, the pink boxplots are repeated, as the pathway-induced sparsity level varies across omics, ranging from 63.7% for miRNAs to 98.9% for mRNAs. In general, boxplots illustrate the distribution of performance across runs, while violin plots provide density estimates. The dashed pink line indicates the performance achieved at the pathway-induced sparsity level. Pathway-Induced sparsity levels for all models are reported in Tables S6, S8, and S9 in the Supplementary Data.

Comparison of biological information extracted by pathway-informed models and their randomized counterparts

A key motivation for BINNs is biological interpretability. To assess whether biological priors improve the identification of disease-relevant features or whether the interpretability can instead arise independently of biological annotations, we examined whether structure-matched randomized models are still able to identify disease-relevant biomarkers. We focused on four representative pathway-informed architectures (PINNet, DeepKEGG, BINN, and PASNet) for which feature-level interpretability analyses are feasible and comparable. In the original studies, interpretability was evaluated using heterogeneous and sometimes non-reproducible criteria, often without providing a consistent ranking of features. To enable a fair comparison with the randomized counterparts, which cannot support pathway-level interpretation by construction, we adopted feature importance as a common interpretability proxy. This approach allows us to test whether biological pathway information is necessary to prioritize disease-associated features over unrelated ones. Disease-feature associations were obtained from widely used curated resources, including DisGeNet [50] and GeDiPNet [51] (see Fig. 5 caption for the model-specific disease contexts and resources: Sepsis/BINN, Liver Hepatocellular Carcinoma (LIHC)/DeepKEGG, Glioblastoma Multiforme (GBM)/PASNet, and Alzheimer's Disease (AD)/PINNet).

Figure 5.

Feature-importance boxplots comparing disease-associated and unrelated features in pathway-informed and randomized models, with randomized models showing comparable biomarker prioritization.

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Comparative feature importance of disease-associated features across pathway-informed and randomized models. Boxplots display the distribution of feature importance scores for disease-associated features (colored green) and unrelated ones (colored pink), across four models and disease contexts: (a) BINN - Sepsis, (b) DeepKEGG - LIHC, (c) PASNet - GBM, and (d) PINNet - AD. For each disease context, we compared pathway-informed models to their randomized counterparts, evaluating the ability of each model to assign higher importance to condition-specific features. Significant differences (red asterisks) between related and unrelated features scores were observed for the randomized BINN model (P =.027, panel a), the randomized PASNet model (P =.040, panel c), and both pathway-informed and randomized versions of the PINNet model for AD (P <.001, panel d). For clarity, we report only the results based on mRNA features for the DeepKEGG model, which integrates multiple data modalities. Analyses performed on SNV and miRNA features yielded consistent findings, with no statistically significant differences between pathway-informed and randomized models in their ability to prioritize biologically relevant features. Features of interest related to the analyzed diseases were obtained from curated databases such as DisGeNet [50], GeDiPNet [51], GeneCards [52], and AlzGene [53].

In BINN, PASNet, and PINNet, disease-associated features received significantly higher importance scores in the randomized version, whereas this distinction was not significant in the corresponding pathway-informed versions of BINN and PASNet (Fig. 5). For PINNet, significant separation between AD-related and unrelated genes was observed in both the pathway-informed and randomized settings, consistent with the original study and disease–gene annotations from the AlzGene database [53]. Finally, for DeepKEGG, using the same attribution procedure as in the original work, neither the pathway-informed nor the randomized model showed a significant difference in importance scores between LIHC-related and unrelated features. Restricting the analysis to the top 100 ranked features, both models identified a comparable number of LIHC-associated genes (11 and 13, respectively). Moreover, feature rankings between the pathway-informed and randomized models were moderately to strongly correlated (Spearman’s Inline graphic for DeepKEGG and Inline graphic for BINN; Fig. S3 in Supplementary Data), indicating substantial alignment in attribution patterns despite the absence of biological pathway annotations.

Overall, these results suggest that the ability to identify disease-relevant biomarkers does not systematically depend on biological pathway annotations, but can emerge from sparsity-induced architectural constraints alone. The strong agreement between feature importance rankings obtained from pathway-informed and randomized models challenges the assumption that pathway annotations are essential for guiding feature selection. Instead, feature-level interpretability appears to reflect the structured inductive bias imposed by the model architecture rather than the biological information encoded by pathway annotations.

Discussion

In this study, we show that the empirical success of BINNs is largely explained by structural sparsity imposed by biological priors rather than by the biological semantics of pathway annotations, and we provide a practical evaluation protocol to test their contribution. Across multiple learning scenarios, datasets and metrics, models in which pathway information was randomized while preserving architectural constraints consistently matched or, in several cases, outperformed their biologically informed counterparts (Fig. 3). These findings indicate that the predictive gains commonly attributed to biological pathways do not require biologically meaningful connectivity.

Our results further demonstrate that randomized sparsification alone reproduces the performance benefits associated with pathway integration. Repeated randomization experiments on BINN, DeepKEGG, PASNet, PathCNN, and PINNet confirmed that model behavior is not sensitive to specific random seeds (Supplementary Fig. S1). Moreover, the sparsity levels induced by pathway annotations often do not coincide with those yielding optimal performance (Fig. 4). In models such as BINN and DeepKEGG, the best predictive accuracy was achieved at sparsity levels differing from those imposed by biological pathways, highlighting that pathway-derived sparsity does not necessarily constitute an optimal inductive bias. Collectively, these results suggest that sparsity should be treated as a tunable modeling choice rather than as a fixed property dictated by biological priors.

Several factors may explain why pathway integration provides no consistent benefits beyond sparsity (Fig. 6). First, curated pathway annotations cover only a subset of gene products, potentially excluding predictive features. Second, pathway-based sparsity can lead to ‘superposed internal representations,’ in which units combine unrelated signals, rather than encoding biologically coherent modules [54]. Such representations may support accurate prediction while deviating substantially from the intended biological interpretation. Third, relevant genes may be overlooked because they are absent from pathway databases.

Figure 6.

Conceptual diagram summarizing possible reasons for similar performance between pathway-informed and randomized models, including pathway incompleteness, redundancy, static annotations, and representational mismatch.

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Hypothetical causes for the alignment in performance between pathway-informed and randomized models. Despite integrating biological knowledge, randomized models often perform comparably or better with respect to models incorporating pathway information. This figure summarizes several hypothetical factors that may contribute to explain this phenomenon.

In addition, pathway resources provide static representations of inherently dynamic processes. Pathway activity varies across cell types, disease states and environments, yet current models typically rely on fixed annotations. Extensive pathway overlap further complicates interpretation, as redundancy among pathways can blur distinctions between modules. These limitations suggest that the lack of benefit observed here reflects not a failure of biology per se, but a mismatch between its representation and how learning objectives exploit it.

A central motivation for pathway-informed models is interpretability. However, our analysis reveals that interpretability outcomes fail to meaningfully distinguish biologically informed models from their randomized counterparts. Across models, both pathway-informed and randomized networks identified disease-associated features with comparable importance (Fig. 5), and feature importance rankings were often strongly correlated (Supplementary Fig. S3). Feature ablation experiments further demonstrated that removing highly predictive features did not uncover latent advantages of pathway information (Supplementary Fig. S4), indicating that biological priors are not merely masked by dominant biomarkers. These results suggest that feature-level interpretability metrics primarily reflect architectural inductive bias, rather than the biological correctness of pathway annotations.

Despite the promise of intrinsic explainability in BINNs, often contrasted with potentially unstable post hoc attribution methods [1], evaluation of explanation quality remains largely ad hoc. Most existing studies report only a small subset of top-ranked pathways or features, without assessing reproducibility across data splits or external cohorts. Moreover, interpretability analyses that perturb individual pathway nodes in isolation do not reflect the distributed and nonlinear nature of neural network representations. As emphasized in a recent work, explainability should be treated as a first-class design objective rather than as an afterthought [55].

Taken together, our findings do not imply that biological knowledge or pathways are intrinsically irrelevant or dispensable in predictive modeling. Rather, they suggest that, when pathway annotations are used mainly as fixed architectural masks or static sparse connectivity patterns, their contribution cannot be readily disentangled from the regularization induced by sparsity. Future work may therefore explore biologically informed constraints that more directly influence the learning objective, such as context-dependent pathway activity, mechanistic consistency penalties, or experimentally grounded interaction priors, rather than relying solely on architectural masking.

More broadly, our results highlight the need for rigorous, structure-matched null models when evaluating biologically informed architectures. To this end, we introduce a general benchmarking workflow (Fig. 7) that enables systematic comparison between pathway-informed models and randomized counterparts across different pathway-informed architectures and prediction tasks. Such comparison is essential to determine whether improvements arise from biological insight or from generic inductive biases. Future biologically informed models should therefore demonstrate benefits beyond sparsity through appropriate controls and falsifiable benchmarks. Only then can claims of biological interpretability be grounded in biological contribution rather than architectural illusion.

Figure 7.

Flowchart illustrating a benchmarking workflow for pathway-informed neural networks, including data integration, graph construction, randomization, model evaluation, sparsity optimization, and feature interpretation.

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Guidelines for integrating pathway information into predictive models with rigorous benchmarking. This figure outlines a principled workflow for incorporating biological pathway knowledge into omics-based predictive models while ensuring robust validation against randomized baselines. (a) Datasets from pathway (e.g. Reactome, KEGG) and omics sources (e.g. TCGA, PCAWG) are combined to build a bipartite graph linking omic features to pathways or a simple graph linking pathways to each another. (b) The graph is encoded as a binary matrix either representing feature-to-pathway or pathway-to-pathway associations. (c) The graph structure is embedded into the model via a sparse omic-pathway module that enriches standard omics data with biologically informed connectivity or by modifying the structure of the input data (e.g. in GNN- and CNN-based models). (d) To assess the added value of true biological structure, a randomization step permutes pathway connections while preserving degree distributions, ensuring a fair comparison. (e) Optional optimization step: Optimize the sparsity of the omic-pathway graph to achieve better predictive performance. This is done using a cross-validation framework. In this step, the original degree distribution constraint is relaxed, allowing for a more flexible exploration of graph structures that may enhance model accuracy. (f) Statistical analyses and feature attribution methods (e.g. SHAP) are employed to compare model performance and feature relevance between biologically informed and randomized counterparts. This workflow enables rigorous validation of pathway integration, ensuring that observed improvements are due to meaningful biological priors.

Materials and methods

We outline practical guidelines for integrating pathway information into omics-based predictive models, following the schema displayed in Fig. 7. We formalize these guidelines as a step-by-step evaluation protocol. This workflow shows how to (i) combine pathway and omics data, (ii) encode these associations into graph representations, (iii) embed the resulting structures into neural network architectures, and (iv) benchmark performance against randomized baselines. These guidelines offer a clear framework that summarizes the following Methods section, helping researchers identify whether performance gains come from biological priors or from sparsity-induced regularization. This protocol is general and can be applied to any pathway-informed architecture or omics-based predictive task.

Randomization procedure

Prior biological knowledge was encoded as either a bipartite graph, connecting features (e.g. genes) to pathways or a simple graph, connecting pathways to one another. Details on graph structures and metrics are reported in Supplementary Data. Considering feature–pathway associations (the same procedure can also be applied to pathway–pathway associations), let Inline graphic be a binary matrix of dimensions Inline graphic:

graphic file with name DmEquation1.gif (1)

where Inline graphic and Inline graphic represent the number of features (e.g. genes, SNVs, miRNAs etc.) and the number of pathways, respectively. The matrix entries Inline graphic take values 1 (association) or 0 (no association).

The total number of connections in the matrix is defined as:

graphic file with name DmEquation2.gif (2)

The number of features associated with each pathway Inline graphic is given by:

graphic file with name DmEquation3.gif (3)

The pathway randomization procedure generates a null model by permuting the associations Inline graphic according to the pathway annotations. The permutation preserves the following constraints:

  1. Preservation of the total number of associations:  
    graphic file with name DmEquation4.gif (4)
    where Inline graphic is the matrix resulting after randomization.
  2. Preservation of the number of features per pathway:  
    graphic file with name DmEquation5.gif (5)

  3. Uniform sampling of connections: The reassignment of the connections is performed uniformly among all possible configurations satisfying the above constraints, ensuring that no additional structural bias is introduced.

The randomization operation can be performed through a uniform permutation of the connections while maintaining the above constraints. The algorithm for this process is:

  1. Extract a list of all existing Inline graphic’s in matrix Inline graphic along with their respective indices Inline graphic.

  2. Shuffle this list uniformly.

  3. Redistribute the Inline graphic’s in the matrix Inline graphic while ensuring that each column Inline graphic maintains the same number of connections Inline graphic as in the original matrix.

This procedure preserves the sparsity structure of the original matrix.

In the approach illustrated in Fig. 1, panel (a), neuron connections within neural networks were replaced with random ones, while maintaining the same number of connections per neuron. This preserves the architectural sparsity induced by pathway annotations. Similarly, in the modality shown in Fig. 1, panel (c), randomization involved transforming tabular data into structured data by substituting the original pathway priors. Specifically, in GNNs, this was achieved by introducing random connections among the nodes in the input graphs. For CNNs, the randomization step consisted of constructing a ”pathway image” by assigning random omics-related entities (e.g. genes, SNVs, miRNAs, etc.) to each pathway. In both cases, the number of connections in the network or the number of omics-related entities per pathway was preserved to maintain the same level of sparsity that was achieved through biological priors. This ensures that the randomization process mirrors the structural characteristics of the original models, preserving the sparsity effects while eliminating the biological information encoded by the pathway annotations.

Hyperparameter selection

After randomizing the model structures, both pathway-informed models and their randomized counterparts were trained and evaluated to compare predictive performance. For each model, 20 independent 80/20 train/test splits were generated, with stratification according to task-specific labels when required. To ensure reproducibility, the exact seeds used to generate the 20 train/test splits and the 30 randomization-stability trials are reported in Supplementary Table S11. When hyperparameter values were explicitly provided by the original authors, these values were used for both model versions. When original hyperparameters were unavailable or incomplete, hyperparameters were selected using five-fold cross-validation on the training set only. The best-performing hyperparameter configuration across validation folds was then retrained on the full training set and evaluated on the held-out test set. The same optimization protocol and search space were applied to pathway-informed and randomized versions, and the validation metric matched the primary evaluation metric of the corresponding task. When early stopping was implemented in the original model code, we retained the original criterion; otherwise, no additional early stopping procedure was introduced. Further details are reported in Supplementary Table S10.

Extended analysis of pathway-informed models

In addition to comparing predictive performance between randomized and pathway-informed models, further analyses were performed on PINNet, the fastest model to run, along with four other models: BINN, DeepKEGG, PASNet, and PathCNN.

Randomization trials

The randomization procedure described above was repeated 30 times, modifying the seed for the randomization functions, ensuring that each trial sampled a different set of connections among the Inline graphic possible ones. For each randomization, the model was run 20 times. This was done to ensure that the results obtained with a single randomization were not due to a particularly favorable random seed.

Optimal sparsity level

We tested whether the biological contribution of pathway annotations lies not in the particular connections they encode, but in the overall level of sparsity they impose on the neural network. To this end, we first constructed a sparse neural network in which sparsity was defined by the number of pathway-derived connections, Inline graphic, and compared its performance with that of a fully connected model. We then varied the number of retained connections between 60% and 99% of all possible connections, i.e.

graphic file with name DmEquation6.gif (6)

Randomization was performed by uniformly sampling from all possible connections while ensuring that the total number of connections is equal to the desired sparsity level Inline graphic. In contrast to the previous randomization procedure, the number of connections assigned to each pathway was not constrained, allowing connections to be distributed freely across pathways.

The sparsity thresholds were chosen by varying around the biological sparsity induced by the pathways. As shown in Supplementary Tables S6 and S8, the most common level of pathway-induced sparsity was approximately 97%–99%, while for miRNA in the DeepKEGG model, it was around 59%–66%. Statistical comparisons were applied to determine whether pathway-informed sparsity provided an advantage over arbitrary levels of sparsity.

In addition, to evaluate whether the number of pathways affected predictive performance, we performed a pathway-fraction analysis on BINN, DeepKEGG, PASNet, PathCNN, and PINNet by retaining 10%, 25%, 50%, 75%, and 100% of the available pathways. For each fraction, pathway-informed models were compared with randomized counterparts preserving the same number of retained pathways and structural constraints, using the same 20 train/test splits adopted in the main analysis.

Model interpretability and feature importance

Finally, we investigated the interpretability of the models to assess whether, even in the absence of pathway information, the randomized model could still identify relevant biomarkers for the disease under study. Feature importance was estimated using the interpretability methods described in the original studies. For BINN, interpretability analyses were performed using SHAP (SHapley Additive exPlanations). In order to take into account the node connectivity and to avoid possible biases due to highly connected nodes, the resulting SHAP values were adjusted using the logarithm of the number of nodes in each node’s reachable subgraph. Feature importance in PINNet was calculated through Deep SHAP, using the DeepExplainer SHAP package in Python. The obtained SHAP values were then aggregated across different cross-validation folds to obtain the final attribution scores, normalized as z-scores. For DeepKEGG, a simplified version of the DeepLIFT method was used. In this approach, the contribution of each feature to the model predictions is computed by multiplying the gradient of the output with respect to the input by the difference between the actual outputs and a reference activation (which was set to zero in this study). The feature importance was then obtained by aggregating across all samples to assess the overall relevance. In PASNet, since no interpretability module was provided in the corresponding GitHub repository of the model, a basic permutation importance approach was employed. Specifically, each feature was separately permuted, while keeping all the others fixed. Drops in performance were measured to estimate the features’ relevance to the model output. Features were then ranked in descending order of performance impact. To assess the biological relevance of the model-derived feature rankings, we then compared the importance scores of disease-related features, derived from curated databases, with those of unrelated ones, for both pathway-informed models and their randomized counterparts. For each method, we considered the list of features associated with the specific disease investigated in the original study. Specifically, for BINN, Sepsis-related features (n = 249) were obtained from GeneCards and DisGeNet. For DeepKEGG, LIHC-related genes (n = 428) were retrieved from GeDiPNet. PASNet used 183 genes linked to Glioblastoma multiforme from GeDiPNet [51] and DisGeNet [50]. Finally, for PINNet (AD), 681 Alzheimer’s-related genes were retrieved from the AlzGene database [53].

Feature ablation study

A feature ablation study was conducted on the models, assessing whether removing highly informative features for the prediction task would highlight the role of the pathways. This analysis tested whether the influence of the pathways was somehow being overshadowed by the contribution of highly predictive features. To identify and discard highly discriminative features from each dataset, we employed a Mann-Whitney U test-based approach. After each set of features was removed, the performance of the pathway-informed and randomized model versions was compared again.

Statistical analysis

Comparisons of predictive performance between biologically informed models and their randomized counterparts were performed using the Wilcoxon signed-rank test. When analyses encompassed multiple cancer types, P-values were combined using Fisher’s combined probability test. Differences in feature importance between disease-associated and non-disease-associated features were assessed using the Mann–Whitney U test. Spearman’s rank correlation coefficient was used to assess the concordance of feature rankings between biologically informed models and their randomized counterparts. P-values <.05 were considered statistically significant.

Computational resources and limitations of evaluated methods

All prediction analyses were executed on an NVIDIA GeForce RTX 4070 Max-Q GPU with 8 GB of memory. For models with higher memory demands (e.g. Autosurv, GraphPath, and Pathformer), a Tesla V100 SXM2 GPU with 32 GB of memory was utilized.

Unfortunately, several models could not be evaluated due to specific limitations. It was not possible to perform the performance comparison for models GCN-MAE and GCS-Net due to the unavailability of the code in their respective GitHub repositories. Additionally, models PathDeep, ReGeNNe, and PGLCN could not be included in the analysis because the necessary data for making predictions were not available.

Finally, we excluded the PathCNN model from the interpretability analyses since they were carried out using Gradient-weighted Class Activation Mapping (Grad-CAM) methods and focused on the pathway images provided as input to the model, thereby identifying entire pathways as important features. In such a setting, randomization fundamentally changes the semantic meaning of the pathway images, making any comparison of the most important features meaningless since, in the randomized model, those features no longer correspond to actual biological pathways.

Key points

  • We propose a structure-matched randomization protocol to isolate the contribution of biological pathway annotations from the effects of sparsity in neural networks.

  • Across the experimentally evaluable pathway-informed models, randomized counterparts achieve comparable or superior predictive performance.

  • Biological pathway annotations do not confer a systematic advantage in interpretability, as randomized models recover disease-associated biomarkers with comparable effectiveness and correlated feature rankings.

  • We provide a general benchmarking workflow demonstrating that predictive performance and interpretability can arise from structural constraints alone.

Supplementary Material

Paper_Pathway_BIB_Supp_bbag425
paper_pathway_bib_supp_bbag425.pdf (9.4MB, pdf)
Supplementary_Data_Reviewed_FL_bbag425
supplementary_data_reviewed_fl_bbag425.zip (9KB, zip)

Acknowledgements

We thank the Fondazione Compagnia di San Paolo for supporting the ON-AIR project, of which this work is a part. I.C. acknowledges support from the University of Torino under the PhD programme in Complex Systems for Quantitative Biomedicine. T.S. acknowledges support from the PRIN project ”Investigating the role of NF-YA isoform/lncRNA axis in mesoderm specification” (Grant ID: 20224TWKNJ). We also thank the Internationalization” program and PNRR M4C2 HPC—1.4 ”CENTRI NAZIONALI”—Spoke 8.

Contributor Information

Isabella Caranzano, AI and Computational Biomedicine Unit, Department of Medical Sciences, University of Torino, Via Santena 19, 10126 Torino, Italy.

Corrado Pancotti, Helmholtz Zentrum München, Helmholtz AI Central Unit, Ingolstädter Landstraße 1, 85764 Oberschleißheim-Neuherberg, Germany.

Cesare Rollo, Department of Computer Science, University of Copenhagen, Universitetsparken 1, 2100 Copenhagen, Denmark; Center for Health Data Science, Department of Public Health, University of Copenhagen, Øster Søgade 16B, 10.1, 1355 Copenhagen, Denmark.

Flavio Sartori, AI and Computational Biomedicine Unit, Department of Medical Sciences, University of Torino, Via Santena 19, 10126 Torino, Italy.

Pietro Liò, Department of Computer Science and Technology, University of Cambridge, William Gates Building, 15 JJ Thomson Ave, CB3 0FD Cambridge, United Kingdom.

Piero Fariselli, AI and Computational Biomedicine Unit, Department of Medical Sciences, University of Torino, Via Santena 19, 10126 Torino, Italy.

Tiziana Sanavia, AI and Computational Biomedicine Unit, Department of Medical Sciences, University of Torino, Via Santena 19, 10126 Torino, Italy.

Author contributions

Conceptualization: I.C., P.F. and T.S.; Formal Analysis, Methodology, Validation and Visualization: I.C.; Supervision: P.F. and T.S.; Writing—original draft: I.C.; Writing—review & editing: I.C., T.S., P.F., P.L., C.P., C.R. and F.S. All authors read and approved the final manuscript.

Conflicts of interest

The authors declare that they have no competing interests.

Funding

This work was supported by the Italian Ministry of University and Research through the ”Grant for Internationalization” program.

Data availability

The code used for the pathway connections randomization procedure can be found at the link: https://github.com/compbiomed-unito/Pathway_Randomization. This repository provides tools for pathway randomization in neural networks for omics data analysis, including functions to shuffle pathway connections while preserving specific constraints (e.g. desired sparsity levels). Code and datasets used to train the specific models were obtained from their respective repositories. A list of the models along with the links to their repositories can be found in the Supplementary data.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Paper_Pathway_BIB_Supp_bbag425
paper_pathway_bib_supp_bbag425.pdf (9.4MB, pdf)
Supplementary_Data_Reviewed_FL_bbag425
supplementary_data_reviewed_fl_bbag425.zip (9KB, zip)

Data Availability Statement

The code used for the pathway connections randomization procedure can be found at the link: https://github.com/compbiomed-unito/Pathway_Randomization. This repository provides tools for pathway randomization in neural networks for omics data analysis, including functions to shuffle pathway connections while preserving specific constraints (e.g. desired sparsity levels). Code and datasets used to train the specific models were obtained from their respective repositories. A list of the models along with the links to their repositories can be found in the Supplementary data.

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