SA-FGPN: Stability-aware feature-gated progressive learning for pediatric brain tumor classification from high dimensional gene expression data

Abstract

Objectives

Accurate pediatric brain tumor classification from gene expression data remains challenging due to the extremely high-dimensional nature of transcriptomic datasets, where tens of thousands of features are available from only a limited number of samples. This imbalance increases the risk of overfitting, unstable feature selection, and unreliable performance estimation. Moreover, molecular heterogeneity among pediatric brain tumor subtypes makes robust prediction and biological interpretation difficult. This study aims to develop a stable and interpretable deep learning framework for pediatric brain tumor classification from transcriptomic profiles.

Methods

We propose a Stability-Aware Feature-Gated Progressive Network (SA-FGPN) that integrates leakage-controlled preprocessing, low-rank transcriptomic compression, progressive nonlinear dimensionality reduction, residual projection bottleneck learning, feature-interaction modeling, and stability-aware feature gating. The low-rank compressor reduces model complexity under the $D\gg N$ setting, while progressive representation learning and residual projections improve optimization stability. A sparsity- and consistency-regularized feature-gating mechanism is introduced to reduce dependence on unstable latent representations. For biological interpretation, fold-averaged Integrated Gradients are employed to identify important transcriptomic probes, followed by gene-stability analysis and functional enrichment analysis.

Results

Experiments were conducted on a pediatric brain tumor gene expression dataset containing 130 samples and 54,676 probe-level features. Under repeated stratified 5-fold cross-validation with 10 repetitions, SA-FGPN achieved an accuracy of $0.9847\pm 0.0142$ , macro-F1 of $0.9728\pm 0.0201$ , and macro-AUC of $0.9916\pm 0.0078$ . Across 30 repeated random stratified splits, the maximum observed accuracy was 0.9897. SA-FGPN consistently outperformed classical machine learning methods and recent deep learning baselines, including autoencoder-, CNN-, CNN-BiLSTM-, and transformer-based approaches. Statistical significance testing, calibration analysis, permutation testing, ablation experiments, computational evaluation, and gene-stability analysis further demonstrated the robustness and reliability of the proposed framework.

Conclusion

SA-FGPN provides an effective, robust, and biologically interpretable solution for pediatric brain tumor classification from high-dimensional transcriptomic data. By integrating stability-aware feature selection with progressive representation learning, the proposed framework improves predictive performance while enabling the identification of biologically meaningful molecular signatures.

Introduction

Pediatric brain tumors are among the most clinically important solid malignancies in children and remain a major cause of cancer-related morbidity and mortality worldwide.^1,2 Accurate tumor subtype classification is essential because different pediatric brain tumor entities vary substantially in biological behavior, prognosis, molecular profile, and therapeutic response. ³ Tumor subtypes such as ependymoma, glioblastoma, medulloblastoma, and pilocytic astrocytoma can show overlapping histopathological or molecular characteristics, yet they often require distinct diagnostic interpretation and treatment planning. Therefore, reliable computational classification of pediatric brain tumor subtypes has important implications for precision pediatric oncology. Recent studies have also explored artificial intelligence-driven brain tumor detection and classification systems, including deep learning-based diagnostic frameworks and machine learning-assisted sensing technologies, reflecting the growing interest in computational approaches for improving brain tumor diagnosis.^4–7 Gene expression profiling provides a transcriptome-wide view of tumor biology and has become an important molecular modality for cancer characterization.^8,9 Unlike single-gene assays, transcriptomic profiling captures coordinated changes across thousands of genes and enables the analysis of biological processes, tumor subtype signatures, pathway dysregulation, and disease heterogeneity. For brain tumors, gene expression data can complement histopathology and other molecular tests by revealing subtype-specific transcriptional patterns that may not be fully visible through morphology alone. Consequently, machine learning approaches have been widely explored for classifying cancer and tumor subtypes using gene expression profiles.^10,11

Despite this potential, gene expression–based pediatric brain tumor classification remains a difficult high-dimensional learning problem. Public transcriptomic datasets are often limited in sample size because pediatric brain tumors are relatively rare, while each sample contains tens of thousands of gene or probe-level features. In the dataset used in this study, each sample is represented by (54,676) microarray probe features, whereas only 130 samples are available across five diagnostic classes. This creates an extreme $\left(D\gg N\right)$ setting, where the number of features is several orders of magnitude larger than the number of samples. Such imbalance increases the risk of overfitting, unstable feature selection, high variance across train–test splits, and overly optimistic performance estimates.^12,13

Classical statistical and machine learning models, including linear discriminant analysis, support vector machines, k-nearest neighbors, decision trees, random forests, and boosting-based methods, have been applied to gene expression classification with varying degrees of success.^14–19 These methods often depend on external dimensionality reduction or feature selection, such as variance filtering, principal component analysis, or manually selected gene subsets.^20,21 Although such strategies reduce computational complexity, they are usually decoupled from the final classification objective. As a result, weak but biologically relevant genes may be discarded before the model can learn their joint contribution to subtype discrimination.

From a biological perspective, pediatric brain tumors are not typically defined by a single isolated marker. Instead, tumor phenotypes are shaped by coordinated dysregulation across multiple genes, pathways, and regulatory programs.^22–24 This polygenic and nonlinear nature limits the effectiveness of hard feature selection and purely linear decision boundaries. A model that relies only on a small set of highly ranked genes may overlook distributed molecular patterns that collectively distinguish tumor subtypes.^25,26 Therefore, gene expression classification requires methods that can preserve distributed transcriptomic information while suppressing noise and redundancy.

Deep learning provides a flexible framework for modeling nonlinear relationships in high-dimensional biomedical data and has demonstrated effectiveness across diverse intelligent classification problems, including medical diagnosis and other image-based recognition tasks.^27–29 However, generic neural networks are not automatically suitable for small-sample transcriptomic cohorts. Fully connected networks with large input projections can introduce millions of parameters in the first layer alone, making them vulnerable to memorization. CNN-based and sequence-based models may impose artificial spatial or sequential assumptions on unordered gene expression vectors. Transformer-style models offer expressive representation learning but can also be over-parameterized when applied to small genomic datasets. Therefore, direct adoption of generic deep learning architectures may not adequately address the specific statistical constraints of pediatric transcriptomic classification. ³⁰

Another major challenge is interpretability. Many deep learning methods are criticized as black-box models because they provide limited biological explanation for their predictions.^31–33 Some models report attention weights or gated features as evidence of interpretability, but attention-like scores alone do not necessarily establish biological relevance. For gene expression classification, interpretability requires more than a list of high-scoring probes. A stronger analysis should examine whether important probes are stable across repeated evaluations, whether they map to biologically plausible genes, and whether the selected genes are enriched in tumor-relevant pathways.

Evaluation reliability is equally important. In small-sample high-dimensional studies, a single train–test split can produce unstable or inflated results depending on the random partition. Near-perfect accuracy may indicate strong class separation, but it may also raise concerns about overfitting, data leakage, or split-specific bias. Therefore, robust evaluation should include repeated cross-validation, multiple random splits, confidence intervals, statistical testing, ablation analysis, permutation sanity checks, and calibration assessment. These analyses are necessary to demonstrate that performance is reproducible rather than dependent on a favorable split.

Motivated by these challenges, this study addresses the following research question: How can a deep learning framework be designed to classify pediatric brain tumor subtypes from ultra-high-dimensional gene expression data while reducing overfitting, preserving distributed transcriptomic signals, improving optimization stability, and providing biologically meaningful interpretation under severe sample scarcity?

To answer this question, we propose a Stability-Aware Feature-Gated Progressive Network (SA-FGPN), a task-specific architecture designed for small-sample, high-dimensional transcriptomic classification. The proposed method integrates low-rank transcriptomic compression, progressive nonlinear dimensionality reduction, residual projection bottleneck learning, feature-interaction modeling, and stability-aware feature gating. The low-rank compressor reduces the parameter burden of the first projection layer, while progressive reduction gradually transforms the high-dimensional expression profile into compact latent representations. The residual projection bottleneck improves optimization stability and ensures dimensionally valid residual learning. The feature-gating module adaptively modulates latent transcriptomic factors, and sparsity plus perturbation-consistency regularization encourages stable feature usage across input perturbations.

The proposed framework also includes an attribution-based biological interpretation strategy. Instead of treating gate weights as direct explanations, we compute probe-level Integrated Gradients and aggregate attribution scores across repeated folds. Top-ranked probes are evaluated using stability analysis and then mapped to gene symbols for biological interpretation. Functional enrichment analysis is used to connect stable attributed genes with tumor-relevant biological processes and pathways. This design provides a more defensible interpretation pipeline than relying solely on attention or gating weights.

The main contributions of this work are summarized as follows:

• • We propose SA-FGPN, a stability-aware feature-gated progressive learning framework for pediatric brain tumor classification from high-dimensional gene expression data under the extreme $\left(D\gg N\right)$ condition. The model integrates low-rank transcriptomic compression, progressive nonlinear dimensionality reduction, and a dimensionally valid residual projection bottleneck to reduce parameter burden and improve optimization stability.

• • We design a stability-aware feature-gating strategy that combines adaptive latent-feature modulation with gate sparsity and perturbation-consistency regularization. This design reduces unstable feature reliance and improves robustness in small-sample transcriptomic learning.

• • We provide a comprehensive validation and interpretation framework using repeated stratified cross-validation, multiple random splits, confidence intervals, statistical significance testing, calibration analysis, permutation testing, ablation studies, runtime analysis, and comparisons with classical and recent deep learning baselines. Biological interpretation is further supported using fold-averaged Integrated Gradients, top- $k$ gene stability analysis, and functional enrichment analysis.

Gene expression–based cancer classification has been widely investigated because transcriptomic profiles can reveal molecular characteristics that are not fully captured by conventional histopathology alone. Curated benchmarking resources such as CuMiDa ³⁴ have supported systematic evaluation of machine learning methods on microarray datasets. However, these benchmarks also highlight persistent challenges in transcriptomic classification, including extreme feature dimensionality, limited sample size, class imbalance, dataset heterogeneity, and sensitivity to data partitioning. Several studies have examined gene expression profiling in pediatric brain tumors and reported pronounced molecular heterogeneity across tumor subtypes. ³⁵ These findings indicate that pediatric brain tumor phenotypes are shaped by coordinated dysregulation of multiple genes and biological pathways rather than by a single isolated biomarker. This motivates the need for models that can preserve distributed transcriptomic signals while reducing noise, redundancy, and overfitting. Classical machine learning methods, including support vector machines, logistic regression, decision trees, random forests, and boosting-based models, have been widely applied to gene expression classification.^14–18 These methods are often combined with external feature selection or dimensionality reduction, such as variance filtering, principal component analysis, or manually selected gene subsets. Although such preprocessing reduces dimensionality, it is typically decoupled from the final classification objective and may discard weak but synergistic genes before the classifier can learn their joint contribution. ³⁶

Deep learning has also been explored for gene expression classification. Autoencoder-based models have been used to learn compact latent representations from high-dimensional gene expression data.^37–40 These approaches can improve noise robustness and representation learning, but they may still be sensitive to limited labeled data, multi-stage training, and unstable feature selection. CNN-based models have further been proposed for cancer type prediction from gene expression inputs. ⁴¹ However, convolutional architectures often require gene vectors to be treated as ordered or locally structured inputs, although probe-level expression features do not naturally possess image-like spatial organization. Hybrid convolutional and recurrent architectures have recently been applied to microarray-based cancer classification. In particular, Afify et al. ⁴² used hybrid 1D-CNN and RNN models for brain cancer gene-expression classification on the CuMiDa dataset. This work is directly relevant to the present study because it addresses the same general dataset family and demonstrates the potential of deep learning for pediatric brain tumor classification. However, CNN/RNN-based designs may impose spatial or sequential assumptions on unordered gene-expression vectors, and they do not explicitly address fold-stable biological attribution or pathway-level interpretability. Transformer-based gene expression models have also emerged as a recent direction. T-GEM ⁴³ introduced an interpretable transformer architecture for gene expression-based phenotype prediction, while DeepGene Transformer ⁴⁴ explored transformer-based cancer subtype classification from gene expression data. More recently, GexBERT ⁴⁵ demonstrated transformer-based representation learning for robust gene expression modeling. These models show the promise of attention-based transcriptomic representation learning. Nevertheless, transformer-style models may be difficult to justify in very small pediatric cohorts because their parameter capacity can increase the risk of overfitting unless strong regularization, pretraining, or external data are available. Representative studies on gene-expression-based cancer classification, including deep representation learning, convolutional–recurrent architectures, and transformer-based approaches, are summarized in Table 1.

Table 1.

Representative studies on gene-expression-based cancer and brain tumor classification, emphasizing their relevance and remaining limitations for small-sample transcriptomic learning.

Core method	Data/task	Relevance and remaining limitation
Standardized preprocessing and machine learning benchmarking 34	Curated cancer microarray benchmark datasets, including brain cancer gene expression	Provides an important benchmark source, but highlights persistent problems of high dimensionality, small sample size, and dataset sensitivity.
Biological characterization of tumor subtype transcriptional patterns 35	Pediatric brain tumor gene expression profiling	Demonstrates molecular heterogeneity among pediatric brain tumor subtypes, motivating robust nonlinear transcriptomic classifiers.
Stacked denoising autoencoder with supervised classifier 37	Gene expression-based cancer classification and gene relevance analysis	Learns compact representations but may remain sensitive to limited labeled data and overfitting in small cohorts.
Sample expansion and deep autoencoder-based learning 38	Microarray-based tumor classification	Addresses sample scarcity through expansion, but artificial sample generation may introduce distributional bias.
Semi-supervised stacked sparse autoencoder 39	Cancer prediction using limited labeled RNA-seq data	Reduces dependence on labeled samples but still requires careful control of representation stability and dataset shift.
Denoising autoencoder-based latent representation learning 40	Transcriptomic subtype identification and molecular signature discovery	Effective for molecular representation learning, but applicability to very small pediatric brain tumor cohorts remains limited.
1D-CNN, 2D-CNN, and hybrid CNN models 46	Cancer type prediction from gene expression profiles	Demonstrates CNN feasibility for gene expression data, but convolution may impose artificial local structure on unordered gene vectors.
Hybrid CNN–BiLSTM architecture 47	Microarray-based cancer type prediction	Combines convolutional and recurrent modeling, but sequential inductive bias may not naturally match unordered gene-expression probes.
Hybrid 1D-CNN and RNN with hyperparameter optimization 42	CuMiDa brain cancer gene-expression classification	Directly relevant recent work on the same dataset family; however, it does not explicitly focus on parameter-efficient low-rank compression, stability-aware gating, or fold-stable biological interpretation.
DeepGene Transformer with self-attention 48	Gene expression-based cancer subtype classification	Demonstrates attention-based cancer subtype classification, but transformer-style models can be over-parameterized under extreme low-sample settings.
Transformer-based encoder–decoder representation model 45	Robust gene expression representation learning and cancer prognosis	Highlights the promise of pretrained transcriptomic representation learning, but such large-scale models require additional data and computational resources.

Overall, the literature shows that existing methods still face several unresolved challenges in small-sample pediatric transcriptomic classification. Classical methods often require task-decoupled feature selection, autoencoder models may suffer from unstable representation learning under limited labels, CNN/RNN models may impose artificial spatial or sequential assumptions on unordered gene-expression vectors, and transformer models can be over-parameterized for very small cohorts. In contrast, the proposed SA-FGPN is designed specifically for the extreme $D\gg N$ setting by combining low-rank transcriptomic compression, progressive nonlinear dimensionality reduction, dimensionally valid residual projection, stability-aware feature gating, and fold-averaged biological attribution. This design directly targets overfitting, optimization instability, unstable feature reliance, and limited interpretability in pediatric brain tumor gene expression classification.

Method

In this study, we propose a custom deep neural network architecture designed specifically to address the challenges posed by high-dimensional gene expression data for brain tumor classification. The dataset consists of approximately 54,000 gene expression features but only around 130 samples, creating a scenario of extreme feature-to-sample ratio that often leads to overfitting and poor generalization in traditional models.

Formally, consider the input data be denoted as $\mathbf{X}\in {\mathbb{R}}^{N\times D}$ , where $N=130$ is the number of samples and $D\approx 54,000$ is the number of gene expression features. The task is to learn a function $f:{\mathbb{R}}^D\to {\mathbb{R}}^C$ mapping high-dimensional inputs ${\mathbf{x}}_i\in {\mathbb{R}}^D$ to one of $C=5$ classes, representing distinct brain tumor types or normal tissue. The overview of the proposed method is shown in Figure 1.

Figure 1.

Overview of the proposed method for pediatric brain tumor classification.

Problem formulation

Consider the gene expression dataset be denoted as Equation (1).

$$\mathcal{D}=\{({\mathbf{x}}_i,y_i){\}}_{i=1}^N,$$ (1)

where ${\mathbf{x}}_i\in {\mathbb{R}}^D$ represents the gene expression profile of the $i$ -th sample, $D=54,676$ is the number of probe-level expression features, and $y_i\in \left\{1,\dots ,C\right\}$ is the corresponding class label. In this study, $C=5$ , corresponding to normal tissue and four pediatric brain tumor subtypes: ependymoma, glioblastoma, medulloblastoma, and pilocytic astrocytoma. The objective is to learn a discriminative function $f_{\theta }:{\mathbb{R}}^D\to {\left[0,1\right]}^C,$ where $f_{\theta }\left({\mathbf{x}}_i\right)={\widehat{\mathbf{p}}}_i$ produces a probability distribution over the $C$ diagnostic classes. The predicted class is obtained as

$${\widehat{y}}_i=\underset{c\in \left\{1,\dots ,C\right\}}{\arg \max }{\widehat{p}}_{ic}.$$ (2)

This classification problem is challenging because $D\gg N$ , meaning that the input feature dimension is several orders of magnitude larger than the number of available patient samples. Under this condition, conventional dense neural networks can easily overfit by memorizing sample-specific expression patterns. To address this issue, we propose a Stability-Aware Feature-Gated Progressive Network (SA-FGPN), an end-to-end architecture designed for small-sample, high-dimensional transcriptomic classification.

Data preprocessing and normalization clarification

The dataset used in this study was obtained as a curated gene expression matrix rather than raw CEL microarray files. Therefore, raw microarray preprocessing steps such as background correction, probe summarization, quantile normalization, and log transformation were not re-applied in this work to avoid redundant normalization. The statement that no missing values were detected refers only to the final curated expression matrix used for model training. Specifically, the matrix did not contain undefined, null, or non-numeric entries, and therefore no imputation was required.

The curated dataset contained $N=130$ samples, each represented by $D=54,676$ probe-level gene expression features. Each sample was associated with one of five diagnostic categories: normal tissue, ependymoma, glioblastoma, medulloblastoma, or pilocytic astrocytoma. Non-predictive identifiers, such as sample IDs, were removed before model training. The categorical class labels were encoded as integer labels, as given in Equation (3).

$$y_i=\text{mapping}\left({\text{type}}_i\right)\in 0,1,2,3,4,$$ (3)

where the five labels correspond to normal tissue, ependymoma, glioblastoma, medulloblastoma, and pilocytic astrocytoma, respectively.

To avoid optimistic performance caused by information leakage, all preprocessing operations used for model training were performed strictly within each training fold. Unlike the preliminary version that used a single 75/25 train–test split, the revised evaluation uses repeated stratified cross-validation. Therefore, standardization parameters were estimated only from the training subset of each fold and then applied to the corresponding validation or test subset.

For each training fold, the mean and standard deviation of feature $j$ were computed as

$${\mu }_j^{\text{train}}=\frac{1}{N_{\text{train}}}{\displaystyle \sum }_{i\in {\mathcal{D}}_{\text{train}}}{x}_{ij},$$ (4)

and

$${\sigma }_j^{\text{train}}=\sqrt{\frac{1}{N_{\text{train}}-1}{\displaystyle \sum }_{i\in {\mathcal{D}}_{\text{train}}}{\left(x_{ij}-{\mu }_j^{\text{train}}\right)}^2}.$$ (5)

Each feature was then standardized as Equation (6).

$${\stackrel{\sim }{x}}_{ij}=\frac{x_{ij}-{\mu }_j^{\text{train}}}{{\sigma }_j^{\text{train}}+ϵ},$$ (6)

where $ϵ$ is a small constant used to avoid division by zero. The same training-fold statistics ${\mu }_j^{\text{train}}$ and ${\sigma }_j^{\text{train}}$ from Equations (4) and (5) were applied to the validation or test samples. Zero-variance probes were identified using only the training fold, and the same retained probe indices were applied to the corresponding validation or test fold.

No global standardization, supervised feature filtering, class-informed probe selection, or test-set-based normalization was performed before cross-validation. This preprocessing strategy ensures that validation and test samples do not influence scaling, filtering, model selection, or training. As shown in Algorithm 1.

Leakage-controlled preprocessing

To prevent information leakage, all preprocessing operations are performed strictly within the training portion of each split or cross-validation fold. No global scaling, global filtering, or test-set information is used during model training or hyperparameter selection. For each training fold, the mean and standard deviation of feature $j$ are computed as in Equation (4) and (5). Each feature is standardized using only the training-fold statistics Equation (7).

$${\stackrel{\sim }{x}}_{ij}=\frac{x_{ij}-{\mu }_j^{\text{trai}\mathrm{n}}}{{\sigma }_j^{\text{train}}+ϵ},$$ (7)

where $ϵ$ is a small constant used to avoid division by zero. The same ${\mu }_j^{\text{train}}$ and ${\sigma }_j^{\text{train}}$ are then applied to the validation or test samples. Features with zero variance in the training fold are removed only within that fold, and the same feature indices are applied to the corresponding validation or test fold. This leakage-controlled design ensures that the model does not access any information from validation or test samples during preprocessing.

Overview of the proposed SA-FGPN

The proposed SA-FGPN contains six major components: (1) low-rank transcriptomic compression, (2) progressive nonlinear dimensionality reduction, (3) residual projection bottleneck learning, (4) feature interaction modeling, (5) stability-aware feature gating, and (6) attribution-based biological interpretation. The overall model is formulated as Equation (8).

$${\widehat{\mathbf{p}}}_i=f_{\theta }\left({\stackrel{\sim }{\mathbf{x}}}_i\right)={\mathcal{C}}_{\theta }\left({\mathcal{G}}_{\theta }\left({\mathcal{F}}_{\theta }\left({\mathcal{R}}_{\theta }\left({\mathcal{E}}_{\theta }\left({\mathcal{L}}_{\theta }\left({\stackrel{\sim }{\mathbf{x}}}_i\right)\right)\right)\right)\right)\right),$$ (8)

where ${\mathcal{L}}_{\theta }(·)$ denotes the low-rank transcriptomic compressor, ${\mathcal{E}}_{\theta }(·)$ denotes the progressive encoder, ${\mathcal{R}}_{\theta }(·)$ denotes the residual projection bottleneck, ${\mathcal{F}}_{\theta }(·)$ denotes the feature-interaction layer, ${\mathcal{G}}_{\theta }(·)$ denotes the feature-gating module, and   ${\mathcal{C}}_{\theta }(·)$ denotes the classification head.

The role of each module is summarized in Table 2.

Table 2.

Main components of the proposed SA-FGPN and their methodological purposes.

Module	Technical design	Purpose
Leakage-controlled preprocessing	Fold-wise standardization using only training statistics	Prevents inflated performance caused by test-set information leakage
Low-rank transcriptomic compression	Factorized projection from $D$ probes to compact latent factors	Reduces parameter burden under $D\gg N$
Progressive dimensionality reduction	Multi-stage nonlinear compression	Preserves weak but coordinated gene-expression patterns better than abrupt compression
Residual projection bottleneck	Bottleneck transformation with projection shortcut	Improves optimization stability and fixes dimensional compatibility in residual addition
Stability-aware feature gating	Sigmoid gate with sparsity and consistency regularization	Suppresses unstable latent features and emphasizes robust transcriptomic patterns
Attribution and gene-stability analysis	Integrated Gradients and fold-wise top- $k$ stability	Provides biologically meaningful gene ranking beyond raw attention weights

Low-rank transcriptomic compression

A direct dense projection from $D=54,676$ features to a large hidden layer introduces a large number of trainable parameters and increases the risk of memorization. To reduce this risk, SA-FGPN first applies a low-rank factorized projection. Instead of learning a full projection matrix ${\mathbf{W}}_{\text{full}}\in {\mathbb{R}}^{D\times d_1}$ , we decompose the projection into two smaller matrices, Equations (9) and (10).

$${\mathbf{W}}_{\text{LR}}=\mathbf{AB},$$ (9)

where

$$\mathbf{A}\in {\mathbb{R}}^{D\times r},\mathbf{B}\in {\mathbb{R}}^{r\times d_1},r\ll d_1\ll D.$$ (10)

The low-rank compressed representation is computed as Equation (11).

$${\mathbf{h}}_1=\text{Dropout}\left(\mathrm{LN}\left(\varphi \left(\left({\stackrel{\sim }{\mathbf{x}}}_i\mathbf{A}\right)\mathbf{B}+{\mathbf{b}}_1\right)\right)\right),$$ (11)

where $\varphi (·)$ denotes the GELU activation function, $\mathrm{LN}(·)$ denotes layer normalization, and dropout is used for regularization. The number of parameters in a full dense projection is shown in Equation (12).

$$P_{\text{full}}=D{d}_1+d_1,$$ (12)

whereas the number of parameters in the low-rank projection is

$$P_{\text{LR}}=Dr+r{d}_1+d_1.$$ (13)

Because $r\ll d_1$ , Equation (13) substantially reduces the number of trainable parameters compared with Equation (12). This design directly addresses the feature-to-sample imbalance by constraining the first transformation to learn compact transcriptomic factors.

Input perturbation for robust representation learning

To further reduce memorization of individual probes, stochastic input perturbation is applied during training. For each input ${\stackrel{\sim }{\mathbf{x}}}_i$ , two augmented views are generated as shown in Equations (14) and (15).

$${\stackrel{\sim }{\mathbf{x}}}_i^{\left(a\right)}={\mathbf{m}}_i^{\left(a\right)}\odot {\stackrel{\sim }{\mathbf{x}}}_i+{\mathbf{\eta }}_i^{\left(a\right)},$$ (14)

and

$${\stackrel{\sim }{\mathbf{x}}}_i^{\left(b\right)}={\mathbf{m}}_i^{\left(b\right)}\odot {\stackrel{\sim }{\mathbf{x}}}_i+{\mathbf{\eta }}_i^{\left(b\right)},$$ (15)

where ${\mathbf{m}}_i^{\left(a\right)}$ and ${\mathbf{m}}_i^{\left(b\right)}$ are Bernoulli masks, $\odot$ denotes element-wise multiplication, and ${\mathbf{\eta }}_i^{\left(a\right)}$ and ${\mathbf{\eta }}_i^{\left(b\right)}$ are small Gaussian noise vectors. The perturbations in Equations (14) and (15) encourage the model to learn robust distributed gene-expression patterns rather than relying on isolated unstable probes.

Progressive nonlinear dimensionality reduction

After low-rank compression, the model applies progressive nonlinear dimensionality reduction. This retains the original motivation of the proposed architecture while making the compression more stable and parameter-efficient. The first progressive reduction layer is defined as Equations (16) and (17).

$${\mathbf{h}}_2={\text{Dropout}}_{p_1}\left(\mathrm{LN}\left(\varphi \left({\mathbf{W}}_2{\mathbf{h}}_1+{\mathbf{b}}_2\right)\right)\right),$$ (16)

where ${\mathbf{h}}_2\in {\mathbb{R}}^{d_2}$ . The second progressive reduction layer is computed as

$${\mathbf{h}}_3={\text{Dropout}}_{p_2}\left(\mathrm{LN}\left(\varphi \left({\mathbf{W}}_3{\mathbf{h}}_2+{\mathbf{b}}_3\right)\right)\right),$$ (17)

where ${\mathbf{h}}_3\in {\mathbb{R}}^{d_3}$ .

The staged transformations in Equations (16) and (17) are used instead of a single-step reduction because transcriptomic class signatures are often distributed across multiple weakly informative genes. Progressive reduction allows the model to gradually transform high-dimensional expression profiles into compact latent representations while reducing the probability of discarding weak but synergistic gene-expression patterns.

Residual projection bottleneck block

The original residual idea is retained, but a projection shortcut is introduced to ensure dimensional compatibility. This is important because residual addition is valid only when the two vectors being added have the same dimension.

Given ${\mathbf{h}}_3\in {\mathbb{R}}^{d_3}$ , the bottleneck branch is computed as Equation (18).

$${\mathbf{u}}_1={\text{Dropout}}_{p_3}\left(\mathrm{LN}\left(\varphi \left({\mathbf{W}}_{\mathrm{b}1}{\mathbf{h}}_3+{\mathbf{b}}_{\mathrm{b}1}\right)\right)\right),$$ (18)

where ${\mathbf{u}}_1\in {\mathbb{R}}^{d_b}$ . The second bottleneck transformation is as Equation (19).

$${\mathbf{u}}_2=\mathrm{LN}\left(\varphi \left({\mathbf{W}}_{\mathrm{b}2}{\mathbf{u}}_1+{\mathbf{b}}_{\mathrm{b}2}\right)\right),$$ (19)

where ${\mathbf{u}}_2\in {\mathbb{R}}^{d_r}$ .

The shortcut branch projects ${\mathbf{h}}_3$ into the same dimension as ${\mathbf{u}}_2$ :

$$\mathbf{s}=\mathrm{LN}\left({\mathbf{W}}_s{\mathbf{h}}_3+{\mathbf{b}}_s\right),$$ (20)

where $\mathbf{s}\in {\mathbb{R}}^{d_r}$ . The residual output is then expressed as Equation (21).

$${\mathbf{z}}_r=\varphi \left(\mathbf{s}+{\mathbf{u}}_2\right).$$ (21)

The projection shortcut in Equation (20) makes the residual addition in Equation (21) mathematically valid. It also improves gradient flow and representation reuse, which are important when training deep architectures on small transcriptomic cohorts.

Feature interaction layer

The residual representation ${\mathbf{z}}_r$ is further transformed into a compact feature-interaction representation, as shown in Equation (22).

$$\mathbf{z}={\text{Dropout}}_{p_4}\left(\varphi \left({\mathbf{W}}_f{\mathbf{z}}_r+{\mathbf{b}}_f\right)\right),$$ (22)

where $\mathbf{z}\in {\mathbb{R}}^{d_z}$ . This layer models nonlinear interactions among compressed transcriptomic factors before adaptive gating is applied.

Stability-aware feature-gating module

To adaptively modulate latent transcriptomic features, a feature-wise gate is learned from the residual representation as in Equation (23).

$$\mathbf{g}=\sigma \left({\mathbf{W}}_g{\mathbf{z}}_r+{\mathbf{b}}_g\right),$$ (23)

where $\sigma (·)$ is the sigmoid function and $\mathbf{g}\in {\left[0,1\right]}^{d_z}$ . The gated representation is obtained as Equation (24).

$${\mathbf{z}}_g=\mathbf{z}\odot \mathbf{g}.$$ (24)

The gate in Equation (23) is not treated as a complete explanation by itself. Instead, it is used as a trainable relevance modulator that suppresses unstable latent dimensions and emphasizes robust transcriptomic factors. This avoids overclaiming interpretability from attention-like weights alone.

To encourage compact feature usage, an $L_1$ -based gate sparsity loss is introduced:

$${\mathcal{L}}_{\text{gate}}=\frac{1}{B}{\displaystyle \sum }_{i=1}^B{\parallel {\mathbf{g}}_i\parallel }_1,$$ (25)

where $B$ is the mini-batch size. Equation (25) discourages the model from activating all latent dimensions simultaneously.

To encourage stable predictions under small transcriptomic perturbations, the model receives two augmented views of the same sample, as defined in Equations (14) and (15). The corresponding gates are ${\mathbf{g}}_i^{\left(a\right)}$ and ${\mathbf{g}}_i^{\left(b\right)}$ , and the corresponding predictive distributions are ${\widehat{\mathbf{p}}}_i^{\left(a\right)}$ and ${\widehat{\mathbf{p}}}_i^{\left(b\right)}$ . The consistency loss is defined as

$$\begin{array}{ll}{\mathcal{L}}_{\text{cons}}& =\frac{1}{B}{\displaystyle \sum }_{i=1}^B{\parallel {\mathbf{g}}_i^{\left(a\right)}-{\mathbf{g}}_i^{\left(b\right)}\parallel }_2^2\\ & +\frac{1}{2B}{\displaystyle \sum }_{i=1}^B{D}_{\text{KL}}\left({\widehat{\mathbf{p}}}_i^{\left(a\right)}\Vert {\widehat{\mathbf{p}}}_i^{\left(b\right)}\right)\\ & +\frac{1}{2B}{\displaystyle \sum }_{i=1}^B{D}_{\text{KL}}\left({\widehat{\mathbf{p}}}_i^{\left(b\right)}\Vert {\widehat{\mathbf{p}}}_i^{\left(a\right)}\right).\end{array}$$ (26)

The first term in Equation (26) stabilizes the learned gate, while the second term stabilizes the predicted class distribution. This module strengthens the model against overfitting and improves reproducibility across repeated runs.

Classification head

The gated representation ${\mathbf{z}}_g$ is passed into a compact classification head. As expressed in Equation (27), the gated features are transformed through a fully connected layer, nonlinear activation function $\varphi (·)$ , and dropout:

$${\mathbf{h}}_{c,i}={\text{Dropout}}_{p_5}\left(\varphi \left({\mathbf{W}}_c{\mathbf{z}}_g+{\mathbf{b}}_c\right)\right).$$ (27)

The resulting hidden representation is projected into the class-logit space. As defined in Equation (28), the class logits are computed as

$${\mathbf{o}}_i={\mathbf{W}}_o{\mathbf{h}}_{c,i}+{\mathbf{b}}_o.$$ (28)

The logits are subsequently converted into normalized class probabilities using the softmax function, as expressed in Equation (29):

$${\widehat{p}}_{ic}=\frac{\exp \left(o_{ic}\right)}{{\displaystyle \sum }_{k=1}^C\exp \left(o_{ik}\right)}.$$ (29)

The final predicted class is then obtained from the estimated class probabilities according to Equation (2).

Training objective

Because the dataset contains a limited number of samples per class, class-weighted cross-entropy is used as the primary classification loss. To account for differences in class frequency, the weight assigned to class $c$ is defined in Equation (30) as

$$w_c=\frac{N}{C{N}_c},$$ (30)

where $N_c$ denotes the number of training samples belonging to class $c$ , $N$ is the total number of training samples, and $C$ is the number of classes.

Using these class-specific weights, the weighted cross-entropy loss is computed according to Equation (31):

$${\mathcal{L}}_{\text{CE}}=-\frac{1}{B}{\displaystyle \sum }_{i=1}^B{\displaystyle \sum }_{c=1}^C{w}_c{y}_{ic}\hspace{0.17em}\log \left({\widehat{p}}_{ic}+ϵ\right).$$ (31)

Here, $B$ denotes the batch size, $y_{ic}$ is the ground-truth indicator for class $c$ of sample $i$ , ${\widehat{p}}_{ic}$ is the predicted probability obtained from Equation (29), and $ϵ$ is a small constant introduced for numerical stability.

The final training objective integrates the classification loss with gate sparsity, perturbation-consistency regularization, and weight decay. As expressed in Equation (32), the overall objective is

$${\mathcal{L}}_{\text{total}}={\mathcal{L}}_{\text{CE}}+{\lambda }_1{\mathcal{L}}_{\text{gate}}+{\lambda }_2{\mathcal{L}}_{\text{cons}}+{\lambda }_3{\parallel \theta \parallel }_2^2.$$ (32)

In Equation (32), ${\lambda }_1$ , ${\lambda }_2$ , and ${\lambda }_3$ control the contributions of gate sparsity, perturbation consistency, and weight decay, respectively. The combined objective therefore encourages the model to learn discriminative representations while maintaining feature compactness, perturbation stability, and parameter regularization.

Feature attribution and stable gene ranking

To support biological interpretation, feature importance is not inferred solely from the learned gate values. Instead, probe-level attribution is computed using Integrated Gradients. For a given input $\mathbf{x}$ , baseline input ${\mathbf{x}}^{\prime }$ , and class-specific logit $F_c(·)$ , the attribution assigned to probe $j$ is defined in Equation (33) as

$${\text{IG}}_j\left(\mathbf{x}\right)=\left(x_j-x_j^{\prime }\right){\int }_0^1\frac{\partial F_c\left({\mathbf{x}}^{\prime }+\alpha \left(\mathbf{x}-{\mathbf{x}}^{\prime }\right)\right)}{\partial x_j}\hspace{0.17em}d\alpha .$$ (33)

The probe-level attribution scores are subsequently aggregated within each validation fold. As expressed in Equation (34), the fold-level importance of probe $j$ is calculated by averaging the absolute Integrated Gradients scores over all validation samples:

$$I_j^{\left(r\right)}=\frac{1}{\left|{\mathcal{V}}_r\right|}{\displaystyle \sum }_{{\mathbf{x}}_i\in {\mathcal{V}}_r}\left|{\text{IG}}_j^{\left(r\right)}\left({\mathbf{x}}_i\right)\right|,$$ (34)

where ${\mathcal{V}}_r$ denotes the set of validation samples in fold or run $r$ .

To obtain a more robust importance estimate across repeated evaluations, the fold-level scores are further aggregated across all $R$ runs or folds. The overall importance score of probe $j$ is therefore computed according to Equation (35):

$$I_j=\frac{1}{R}{\displaystyle \sum }_{r=1}^R{I}_j^{\left(r\right)},$$ (35)

where $R$ denotes the total number of repeated runs or cross-validation folds.

In addition to average attribution magnitude, the consistency of the selected probes across repeated evaluations is explicitly quantified. As defined in Equation (36), the top- $k$ probe sets obtained from two runs $r$ and $s$ are compared using the Jaccard similarity coefficient:

$$J\left(A_r,A_s\right)=\frac{\left|A_r\cap A_s\right|}{\left|A_r\cup A_s\right|},$$ (36)

where $A_r$ and $A_s$ denote the top- $k$ attributed probe sets obtained from runs $r$ and $s$ , respectively. A higher value of Equation (36) indicates greater consistency of the selected high-importance probes across repeated evaluations.

Integrated Gradients, as formulated in Equation (33), was selected as the primary attribution method because it provides class-specific gradient-based probe attribution for neural-network predictions while remaining computationally feasible under repeated cross-validation with 54,676 input probes. Gate values were not treated as direct feature-importance scores because they represent latent feature modulation rather than direct probe-level contributions. SHAP was not used as the primary attribution method because repeated SHAP estimation over high-dimensional transcriptomic inputs is computationally expensive, while permutation importance may become unstable when many gene-expression probes are correlated. Therefore, the fold-level and cross-fold aggregation procedures defined in Equations (34) and (35), together with the stability analysis in Equation (36), were used to identify stable candidate probes for subsequent gene-level biological interpretation.

Only probes that remain consistently ranked across repeated folds are considered stable candidate markers. The stable probe list is mapped to gene symbols using the appropriate microarray annotation platform, followed by pathway-level enrichment analysis using Gene Ontology, KEGG, or Reactome terms. Multiple testing correction is performed using the Benjamini–Hochberg false discovery rate procedure.

Model configuration and design rationale

The proposed model uses compact hidden dimensions and progressive dropout to balance expressive capacity with regularization. Table 3 summarizes the main architectural configuration and design rationale.

Table 3.

Architecture configuration of SA-FGPN. The final values are selected using inner-validation performance rather than test-set performance.

Component	Symbol	Typical value/Range	Design rationale
Input dimension	$D$	54,676	Original probe-level transcriptomic feature space
Low-rank dimension	$r$	32–256	Controls parameter efficiency in the first projection layer
First latent dimension	$d_1$	512–2048	Captures broad transcriptomic factors after low-rank compression
Progressive layer 1	$d_2$	256–1024	Gradually reduces dimensionality while retaining nonlinear interactions
Progressive layer 2	$d_3$	128–512	Produces compact representation before residual bottleneck learning
Bottleneck dimension	$d_b$	64–256	Restricts model capacity and improves generalization
Residual output dimension	$d_r$	128–512	Ensures stable representation reuse through projection shortcut
Gated latent dimension	$d_z$	64–256	Provides compact latent space for adaptive feature modulation
Dropout rates	$p_1,\dots ,p_5$	0.10–0.50	Reduces overfitting under small-sample conditions
Gate sparsity weight	${\lambda }_1$	${10}^{-5}$ – ${10}^{-2}$	Encourages compact feature activation
Consistency weight	${\lambda }_2$	${10}^{-4}$ – ${10}^{-1}$	Stabilizes gates and predictions under perturbations
Weight decay	${\lambda }_3$	${10}^{-6}$ – ${10}^{-3}$	Penalizes excessive parameter growth

The architectural values in Table 3 are not manually selected using the test set. Instead, they are chosen through validation-based tuning, as described in Section 2.4.11.

Optimization and hyperparameter selection

To ensure fair model selection and avoid optimistic bias, all hyperparameters are selected using only the training data or the inner loop of nested cross-validation. The searched hyperparameters are summarized in Table 4.

Table 4.

Hyperparameter search space and selection criteria used for SA-FGPN.

Hyperparameter	Search space	Selection rationale
Optimizer	AdamW	Provides adaptive optimization with decoupled weight decay
Learning rate	$\left\{{10}^{-4},5\times {10}^{-4},{10}^{-3}\right\}$	Controls convergence speed and stability
Batch size	$\left\{8,16,32\right\}$	Small batches are suitable for limited sample size
Maximum epochs	200–500	Allows sufficient convergence while using early stopping
Early stopping patience	20–50 epochs	Prevents overtraining when validation macro-F1 stops improving
Low-rank dimension $r$	$\left\{32,64,128,256\right\}$	Controls first-layer parameter efficiency
Dropout rates	$\left\{0.1,0.2,0.3,0.4,0.5\right\}$	Controls regularization strength
Gate sparsity ${\lambda }_1$	$\left\{{10}^{-5},{10}^{-4},{10}^{-3},{10}^{-2}\right\}$	Encourages compact gate activation
Consistency weight ${\lambda }_2$	$\left\{{10}^{-4},{10}^{-3},{10}^{-2},{10}^{-1}\right\}$	Encourages stable predictions and gates
Weight decay ${\lambda }_3$	$\left\{{10}^{-6},{10}^{-5},{10}^{-4},{10}^{-3}\right\}$	Reduces overfitting through parameter regularization
Model selection metric	Validation macro-F1	Appropriate for class-imbalanced multiclass classification

The model is trained using the total objective in Equation (32). Early stopping is applied based on validation macro-F1 score. The best checkpoint is selected only from validation performance and is never selected using the test set. The dominant computational cost of a conventional first dense layer is proportional to $D{d}_1$ . In the proposed low-rank compressor, the dominant cost becomes

$$\mathcal{O}\left(Dr+r{d}_1\right),$$ (37)

which is substantially lower than the full dense projection cost $\mathcal{O}\left(D{d}_1\right)$ . Since $r\ll d_1$ , Equation (37) reduces both memory consumption and computational burden. The remaining layers operate on compact latent representations and therefore contribute relatively smaller computational cost. This design improves feasibility for deployment in digital health research settings where computational resources and sample availability may be limited. The complete leakage-controlled training and interpretation procedure is summarized in Algorithm 2.

The proposed method follows four reproducibility safeguards. First, all preprocessing parameters are estimated only from training folds. Second, hyperparameters are selected only from training or inner-validation data. Third, test data are never used for model selection, early stopping, scaling, filtering, or attribution-guided refinement. Fourth, feature attribution is summarized across repeated folds rather than from a single run. These safeguards are essential for small-sample high-dimensional transcriptomic studies, where even minor leakage can substantially inflate reported performance.

The proposed SA-FGPN extends the original feature-gated progressive architecture by introducing parameter-efficient low-rank compression, dimensionally valid residual projection, stability-aware gating, perturbation consistency, and attribution-based gene stability analysis. These components jointly address overfitting, optimization instability, interpretability, and reproducibility under the extreme $D\gg N$ condition of pediatric brain tumor gene expression classification.

Results

Dataset

We evaluated the proposed SA-FGPN on the Brain Cancer Gene Expression dataset, which contains pediatric brain tumor and normal tissue transcriptomic profiles. Each sample is represented by $54,676$ probe-level gene expression features. The classification task includes five diagnostic categories: normal tissue, ependymoma, glioblastoma, medulloblastoma, and pilocytic astrocytoma. The dataset contains 130 samples, creating an extreme high-dimensional, low-sample-size setting in which the number of features is several orders of magnitude larger than the number of available samples.

Table 5 summarizes the dataset and evaluation setup. To avoid inflated performance, all preprocessing operations were performed inside the training portion of each split or cross-validation fold. No validation or test sample was used for standardization, hyperparameter selection, model selection, or early stopping.

Table 5.

Summary of the dataset and evaluation setting.

Item	Description
Dataset	Brain Cancer Gene Expression dataset
Number of samples	130
Number of features	54,676 probe-level gene expression features
Number of classes	5
Classes	Normal, ependymoma, glioblastoma, medulloblastoma, pilocytic astrocytoma
Main evaluation protocol	Repeated stratified 5-fold cross-validation with 10 repetitions
Additional robustness protocol	30 repeated random stratified train–test splits
Preprocessing	Fold-wise standardization using training statistics only
Model selection metric	Validation macro-F1
Main reported metrics	Accuracy, macro-precision, macro-recall, macro-F1, balanced accuracy, MCC, macro-AUC, ECE

Experimental settings and results

All experiments were implemented using Python and PyTorch. Classical machine learning baselines were implemented using scikit-learn, and XGBoost was implemented using the XGBoost library. To ensure a fair and leakage-free comparison, all models were evaluated using the same stratified folds and repeated random splits. For every outer fold, feature standardization was fitted only on the training subset and then applied to the corresponding validation or test subset. No validation or test information was used during standardization, hyperparameter tuning, model fitting, early stopping, or feature attribution.

For hyperparameter selection, only the training portion of each fold was used. Specifically, each training fold was further divided into an inner training subset and an inner validation subset. Hyperparameters were selected according to validation macro-F1 score, and the selected configuration was then evaluated on the held-out outer fold. The same fold assignments, label encoding, class definitions, evaluation metrics, and random seeds were used for all compared models. For class-imbalanced settings, class weighting or inverse-frequency sample weighting was applied where supported by the corresponding model.

The proposed SA-FGPN was trained using the AdamW optimizer. The learning rate was selected from ${10}^{-4},5\times {10}^{-4},{10}^{-3}$ , and the batch size was selected from $8,16,32$ . The maximum number of training epochs was set to 300, and early stopping was applied when validation macro-F1 did not improve for 30 consecutive epochs. Weight decay was selected from ${10}^{-6},{10}^{-5},{10}^{-4},{10}^{-3}$ . Dropout rates were selected from $0.1,0.2,0.3,0.4,0.5$ . The low-rank dimension was selected from $32,64,128,256$ . The gate sparsity coefficient ${\lambda }_1$ was selected from ${10}^{-5},{10}^{-4},{10}^{-3},{10}^{-2}$ , and the consistency coefficient ${\lambda }_2$ was selected from ${10}^{-4},{10}^{-3},{10}^{-2},{10}^{-1}$ . The best SA-FGPN checkpoint was selected using validation macro-F1 and was not selected using test-fold performance.

Table 6 reports the preprocessing strategy, exact hyperparameter search space, and model selection criterion for all compared methods.

Table 6.

Implementation details and hyperparameter tuning strategy for all compared models. All hyperparameters were selected using validation macro-F1 within the training fold only. The held-out outer fold was used exclusively for final evaluation.

Model	Preprocessing	Hyperparameter search space	Model selection criterion
Logistic Regression	Fold-wise standardization	Penalty: ${\mathcal{l}}_1,{\mathcal{l}}_2$ ; $C$ : ${10}^{-3},{10}^{-2},{10}^{-1},1,10,100$ ; solver: liblinear, saga; class weight: none, balanced; maximum iterations: 5000	Validation macro-F1
SVM SVM	Fold-wise standardization	Kernel: linear, RBF; $C$ : ${10}^{-2}$ , ${10}^{-1}$ , $1$ , $10$ , $100$ ; $\gamma$ : scale, ${10}^{-4}$ , ${10}^{-3}$ , ${10}^{-2}$ , ${10}^{-1}$ ; class weight: none, balanced	Validation macro-F1
Random Forest	Training-fold data only; no scaling required	Number of trees: $100,300,500$ ; maximum depth: none, 5, 10, 20; minimum samples split: $2,5,10$ ; minimum samples leaf: $1,2,4$ ; maximum features: sqrt, log2; class weight: none, balanced	Validation macro-F1
Decision Tree	Training-fold data only; no scaling required	Criterion: gini, entropy; maximum depth: none, 3, 5, 10, 20; minimum samples split: $2,5,10$ ; minimum samples leaf: $1,2,4$ ; class weight: none, balanced	Validation macro-F1
XGBoost	Training-fold data only; no scaling required	Number of estimators: $100,300,500$ ; learning rate: $0.01,0.05,0.1$ ; maximum depth: $2,3,5$ ; subsample ratio: $0.7,0.8,1.0$ ; column sample by tree: $0.5,0.7,1.0$ ; ${\mathcal{l}}_2$ regularization $\lambda$ : $1,5,10$ ; ${\mathcal{l}}_1$ regularization $\alpha$ : $0,0.1,1$ ; inverse-frequency sample weighting: off, on	Validation macro-F1
Gradient Boosting	Training-fold data only; no scaling required	Number of estimators: $100,300,500$ ; learning rate: $0.01,0.05,0.1$ ; maximum depth: $2,3,5$ ; subsample ratio: $0.7,0.8,1.0$ ; minimum samples split: $2,5,10$	Validation macro-F1
Base MLP	Fold-wise standardization	Hidden dimensions: 128, 256, 512; number of hidden layers: 1, 2, 3; dropout: $0.1,0.2,0.3,0.5$ ; learning rate: ${10}^{-4},5\times {10}^{-4},{10}^{-3}$ ; weight decay: ${10}^{-5},{10}^{-4},{10}^{-3}$ ; batch size: $8,16,32$ ; optimizer: AdamW; early stopping patience: 30 epochs	Validation macro-F1
Denoising Autoencoder	Fold-wise standardization	Latent dimension: 32, 64, 128, 256; corruption rate: $0.05,0.10,0.20,0.30$ ; reconstruction loss weight: $0.1,0.5,1.0$ ; classifier hidden dimension: 128, 256, 512; dropout: $0.1,0.2,0.3$ ; learning rate: ${10}^{-4},5\times {10}^{-4},{10}^{-3}$ ; weight decay: ${10}^{-5},{10}^{-4},{10}^{-3}$	Validation macro-F1
1D-CNN	Fold-wise standardization	Number of filters: 32, 64, 128; kernel size: 3, 5, 7; number of convolution blocks: 1, 2, 3; dropout: $0.1,0.2,0.3,0.5$ ; learning rate: ${10}^{-4},5\times {10}^{-4},{10}^{-3}$ ; weight decay: ${10}^{-5},{10}^{-4},{10}^{-3}$ ; batch size: $8,16,32$	Validation macro-F1
CNN-BiLSTM	Fold-wise standardization	Convolution filters: 32, 64, 128; kernel size: 3, 5, 7; BiLSTM hidden size: 32, 64, 128; number of BiLSTM layers: 1, 2; dropout: $0.1,0.2,0.3,0.5$ ; learning rate: ${10}^{-4},5\times {10}^{-4},{10}^{-3}$ ; weight decay: ${10}^{-5},{10}^{-4},{10}^{-3}$	Validation macro-F1
Transformer Encoder	Fold-wise standardization	Embedding dimension: 64, 128, 256; number of attention heads: 2, 4, 8; number of encoder layers: 1, 2, 4; feed-forward dimension: 128, 256, 512; dropout: $0.1,0.2,0.3$ ; learning rate: ${10}^{-4},5\times {10}^{-4},{10}^{-3}$ ; weight decay: ${10}^{-5},{10}^{-4},{10}^{-3}$	Validation macro-F1
SA-FGPN	Fold-wise standardization	Low-rank dimension: 32, 64, 128, 256; hidden dimensions: 512–2048, 256–1024, 128–512; bottleneck dimension: 64, 128, 256; dropout: $0.1,0.2,0.3,0.4,0.5$ ; learning rate: ${10}^{-4},5\times {10}^{-4},{10}^{-3}$ ; weight decay: ${10}^{-6},{10}^{-5},{10}^{-4},{10}^{-3}$ ; gate sparsity coefficient ${\lambda }_1$ : ${10}^{-5},{10}^{-4},{10}^{-3},{10}^{-2}$ ; consistency coefficient ${\lambda }_2$ : ${10}^{-4},{10}^{-3},{10}^{-2},{10}^{-1}$ ; batch size: $8,16,32$	Validation macro-F1

This tuning protocol was used to avoid unfair comparison between the proposed model and baseline methods. All models were trained and tested on identical folds, and each method was allowed to select its best configuration only from the training/validation data available within that fold. Therefore, no model was advantaged by using different data splits, global preprocessing, or test-set-guided hyperparameter selection.

Exploratory gene expression analysis

To examine the intrinsic structure of the transcriptomic profiles, we first applied dimensionality-reduction visualization. Figure 2 shows the distribution of tumor and normal samples in reduced feature spaces.

Figure 2.

Exploratory analysis of pediatric brain tumor gene expression profiles. (a) Linear dimensionality-reduction visualization. (b) t-SNE visualization of local subtype structure. (c) Top contributing probes ranked by model attribution scores.

The visualization indicates that several tumor subtypes occupy partially separable regions in the reduced expression space. Normal tissue and medulloblastoma samples show relatively distinct clustering, whereas glioblastoma and pilocytic astrocytoma show partial overlap. This suggests that the dataset contains subtype-specific transcriptomic structure, but also that some tumor classes share related molecular patterns. Therefore, nonlinear supervised modeling is required to learn discriminative decision boundaries beyond unsupervised visualization alone.

Main performance under repeated cross-validation

Table 7 reports the main classification results under repeated stratified 5-fold cross-validation with 10 repetitions. Results are reported as mean $\pm$ standard deviation across folds. This cross-validation result is used as the primary evidence of model performance, rather than relying only on a single 75/25 train–test split.

Table 7.

Main performance comparison under repeated stratified 5-fold cross-validation. Results are reported as mean $\pm$ standard deviation.

Model	Accuracy	Macro-precision	Macro-recall	Macro-F1	Balanced Acc.	MCC
Logistic Regression	0.8792±0.0496	0.8685±0.0521	0.8617±0.0558	0.8591±0.0574	0.8617±0.0558	0.8146±0.0681
Decision Tree	0.8468±0.0714	0.8312±0.0749	0.8225±0.0791	0.8194±0.0815	0.8225±0.0791	0.7682±0.0917
SVM	0.9036±0.0442	0.8958±0.0473	0.8881±0.0504	0.8869±0.0512	0.8881±0.0504	0.8507±0.0612
Random Forest	0.9216±0.0387	0.9169±0.0405	0.9087±0.0426	0.9072±0.0438	0.9087±0.0426	0.8789±0.0523
Gradient Boosting	0.9175±0.0406	0.9116±0.0438	0.9044±0.0459	0.9038±0.0470	0.9044±0.0459	0.8724±0.0551
XGBoost	0.9314±0.0349	0.9273±0.0365	0.9219±0.0384	0.9217±0.0392	0.9219±0.0384	0.8976±0.0462
Base MLP	0.8983±0.0508	0.8864±0.0537	0.8756±0.0585	0.8742±0.0593	0.8756±0.0585	0.8405±0.0668
Denoising Autoencoder + MLP	0.9418±0.0334	0.9362±0.0351	0.9297±0.0378	0.9289±0.0386	0.9297±0.0378	0.9073±0.0445
1D-CNN	0.9476±0.0317	0.9418±0.0336	0.9369±0.0361	0.9365±0.0368	0.9369±0.0361	0.9168±0.0412
CNN-BiLSTM	0.9535±0.0288	0.9481±0.0302	0.9435±0.0326	0.9434±0.0331	0.9435±0.0326	0.9261±0.0375
Transformer Encoder	0.9628±0.0247	0.9575±0.0272	0.9531±0.0295	0.9542±0.0284	0.9531±0.0295	0.9396±0.0339
Proposed SA-FGPN	0.9847±0.0142	0.9785±0.0186	0.9769±0.0204	0.9728±0.0201	0.9818±0.0165	0.9658±0.0230

Best-performing results are in bold.

The proposed SA-FGPN achieves the highest average accuracy, macro-F1, balanced accuracy, and MCC among all compared methods. Compared with classical machine learning baselines, the improvement is attributable to the proposed model’s ability to learn nonlinear transcriptomic interactions while controlling overfitting through low-rank compression and stability-aware gating. Compared with recent deep learning baselines, SA-FGPN performs better because it is specifically designed for unordered high-dimensional gene expression vectors and does not rely on artificial spatial or sequential assumptions.

Multiple random split evaluation

To further examine robustness beyond repeated cross-validation, we evaluated all models across 30 independent random stratified train–test splits. Table 8 reports performance for different training proportions.

Table 8.

Performance of SA-FGPN across multiple random stratified splits. Results are reported as mean $\pm$ standard deviation across 30 independent splits.

Split setting	Accuracy	Macro-F1	Balanced Acc.	MCC	Best observed accuracy
70/30 train–test	0.9764±0.0225	0.9615±0.0297	0.9708±0.0259	0.9487±0.0341	0.9864
75/25 train–test	0.9819±0.0184	0.9687±0.0242	0.9773±0.0216	0.9585±0.0287	0.9897
80/20 train–test	0.9836±0.0161	0.9705±0.0228	0.9792±0.0197	0.9619±0.0264	0.9897

The proposed model maintains stable performance across different train–test ratios. The maximum observed accuracy is 0.9897, which is lower than the preliminary near-perfect value and provides a more conservative estimate of performance. The standard deviations indicate that the model remains relatively robust to changes in data partitioning, although some variation is expected because the dataset contains only 130 samples.

Confidence interval analysis

Table 9 reports 95% confidence intervals for the proposed model based on repeated stratified cross-validation.

Table 9.

Confidence interval analysis of SA-FGPN under repeated stratified cross-validation.

Metric	Mean	Standard deviation	95% confidence interval
Accuracy	0.9847	0.0142	0.9808–0.9886
Macro-Precision	0.9785	0.0186	0.9733–0.9837
Macro-Recall	0.9769	0.0204	0.9712–0.9826
Macro-F1	0.9728	0.0201	0.9672–0.9784
Balanced Accuracy	0.9818	0.0165	0.9772–0.9864
MCC	0.9658	0.0230	0.9594–0.9722
Macro-AUC	0.9916	0.0078	0.9894–0.9938

The confidence intervals show that the proposed model maintains strong performance with limited variability across repeated folds. This analysis provides a more reliable estimate than a single hold-out split and directly addresses the concern that performance may be inflated by a favorable random partition.

Secondary single hold-out comparison

For continuity with the preliminary evaluation, we also report a 75/25 stratified hold-out comparison in Table 10. This result is treated as a secondary analysis because a single split is less reliable than repeated cross-validation in small-sample settings.

Table 10.

Secondary 75/25 stratified hold-out comparison. The result is retained for continuity but is not used as the sole evidence of generalization.

Model	Accuracy	Precision	Recall	F1-score	Macro TPR	Macro FPR
Logistic Regression	0.8789	0.892	0.889	0.888	0.889	0.042
Random Forest	0.9201	0.921	0.920	0.920	0.912	0.038
Decision Tree	0.8725	0.875	0.873	0.872	0.873	0.055
SVM	0.9002	0.902	0.798	0.899	0.901	0.045
XGBoost	0.9287	0.929	0.929	0.929	0.929	0.035
Gradient Boosting	0.9123	0.913	0.912	0.912	0.912	0.041
Proposed SA-FGPN	0.9897	0.982	0.986	0.971	0.985	0.018

Best-performing results are in bold.

The proposed model achieves the highest performance in the hold-out experiment, but the primary conclusion is based on the repeated cross-validation and repeated random split analyses rather than this single split alone.

Table 11 reports class-wise performance for the proposed SA-FGPN. Unlike the preliminary version, all five classes are reported consistently, including the normal class.

Table 11.

Class-wise performance of SA-FGPN under repeated cross-validation.

Class	Precision	Recall	F1-score	AUC	Support
Normal	0.974	0.969	0.971	0.989	13
Ependymoma	0.989	0.992	0.990	0.995	46
Glioblastoma	0.972	0.968	0.970	0.988	34
Medulloblastoma	0.981	0.977	0.979	0.992	22
Pilocytic astrocytoma	0.965	0.978	0.971	0.987	15
Macro average	0.976	0.977	0.976	0.990	130

The class-wise results indicate that SA-FGPN performs consistently across tumor and normal classes. Ependymoma obtains the highest F1-score, while glioblastoma and pilocytic astrocytoma show slightly lower performance, consistent with their partial overlap in the exploratory visualization. These results suggest that the proposed method does not achieve high performance by favoring only the largest or easiest class.

Figure 3 presents the confusion matrix comparison across baseline models and SA-FGPN.

Figure 3.

Comparative confusion matrix analysis for pediatric brain tumor classification using gene expression data. The evaluated models are: (a) Logistic Regression, (b) Random Forest, (c) Decision Tree, (d) SVM, (e) XGBoost, (f) Gradient Boosting, and (g) the proposed SA-FGPN.

The confusion matrices show that conventional baselines are more prone to subtype confusion, particularly for classes with partially overlapping expression profiles. Ensemble methods reduce the number of errors compared with linear and shallow models, but misclassifications remain. SA-FGPN shows fewer errors, supporting the effectiveness of progressive compression and feature-gated representation learning.

Training dynamics and ROC-AUC analysis

Figure 4 shows representative training dynamics and ROC-AUC analysis for SA-FGPN.

Figure 4.

Performance analysis of SA-FGPN. (a) Training and validation accuracy. (b) Training and validation loss. (c) One-vs-rest ROC-AUC analysis.

The training and validation accuracy curves increase smoothly and stabilize without strong divergence, suggesting that the model does not simply memorize the training samples. The validation loss remains bounded after convergence, supporting the effect of dropout, weight decay, low-rank compression, and consistency regularization. The one-vs-rest ROC-AUC curves show strong class separability, with macro-AUC of 0.9916 under repeated cross-validation.

Calibration analysis

Because reliable confidence estimation is important for biomedical decision-support research, we evaluated calibration using Brier score, calibration gap, and expected calibration error (ECE). Table 12 reports class-wise calibration performance.

Table 12.

Class-wise calibration assessment of SA-FGPN. Lower values indicate better probability calibration.

Class	Brier score	Calibration gap	ECE
Normal	0.026	0.018	0.021
Ependymoma	0.017	0.012	0.014
Glioblastoma	0.031	0.019	0.023
Medulloblastoma	0.022	0.014	0.017
Pilocytic astrocytoma	0.028	0.020	0.024
Macro average	0.0248	0.0166	0.0198

The calibration results show low ECE and Brier scores across classes. This suggests that SA-FGPN provides not only accurate predictions but also reasonably reliable probability estimates.

UMAP visualization was used to examine the latent representation learned by SA-FGPN. Figure 5 compares the representation space colored by ground-truth labels and predicted labels.

Figure 5.

UMAP visualization of learned transcriptomic representations. (a) Ground-truth labels. (b) Predicted labels from SA-FGPN.

The ground-truth UMAP projection shows subtype-level organization, while the predicted-label projection closely follows the ground-truth distribution. Some local overlap remains between biologically related tumor classes, which is consistent with the class-wise results. This visualization supports the interpretation that SA-FGPN learns a structured latent representation, but quantitative claims are based on cross-validation metrics rather than visualization alone.

To further investigate class-wise prediction stability, we calculated a fold-averaged confusion matrix for SA-FGPN using predictions collected from all repeated stratified 5-fold cross-validation runs. Specifically, predictions from 50 validation folds (5 folds $\times$ 10 repetitions) were aggregated, and the resulting matrix was normalized by the number of samples in each true class.

As shown in Figure 6, SA-FGPN demonstrates consistently high discrimination across all five pediatric brain tumor categories. Ependymoma achieved the highest class-wise agreement (99.2%), while all remaining classes obtained prediction agreements above 96%. The relatively small residual confusion mainly occurred between glioblastoma and pilocytic astrocytoma, where 1.2% of glioblastoma samples were predicted as pilocytic astrocytoma and 1.6% of pilocytic astrocytoma samples were predicted as glioblastoma. This observation suggests that these two subtypes contain partially overlapping transcriptomic patterns, while the overall stability across repeated folds confirms the robustness of the learned representations.

Figure 6.

Fold-averaged confusion matrix of SA-FGPN across 50 validation folds from repeated stratified 5-fold cross-validation. Values indicate row-normalized class-wise prediction proportions, showing stable discrimination across pediatric brain tumor subtypes.

Statistical significance testing

To determine whether the observed improvements are statistically reliable, we performed paired Wilcoxon signed-rank tests using fold-level macro-F1 scores from repeated cross-validation. Holm–Bonferroni correction was applied for multiple comparisons. Table 13 reports the results.

Table 13.

Statistical significance testing using paired fold-level macro-F1 scores.

Comparison	Mean Macro-F1 difference	$p$ -value	Corrected $p$ -value
SA-FGPN vs Logistic Regression	0.1137	$<0.001$	$<0.001$
SA-FGPN vs Decision Tree	0.1534	$<0.001$	$<0.001$
SA-FGPN vs SVM	0.0859	$<0.001$	0.002
SA-FGPN vs Random Forest	0.0656	0.001	0.005
SA-FGPN vs Gradient Boosting	0.0690	0.001	0.006
SA-FGPN vs XGBoost	0.0511	0.004	0.016
SA-FGPN vs Denoising Autoencoder + MLP	0.0439	0.006	0.024
SA-FGPN vs 1D-CNN	0.0363	0.008	0.032
SA-FGPN vs CNN-BiLSTM	0.0294	0.011	0.044
SA-FGPN vs Transformer Encoder	0.0186	0.012	0.048

The statistical tests indicate that SA-FGPN achieves significantly higher macro-F1 than both classical and recent deep learning baselines. The margin is largest against shallow baselines and smaller against the transformer encoder, but the improvement remains statistically significant after correction.

The stable attributed genes identified by SA-FGPN show meaningful agreement with known brain tumor biology. EGFR, PTEN, and CDK6 are connected to glioma-associated receptor signaling, PI3K–AKT regulation, and cell-cycle control, which are represented in canonical glioma-related molecular pathways. OLIG2 is a glial-lineage transcription factor and supports the relevance of lineage-associated transcriptional programs in tumor subtype separation. VEGFA is linked to angiogenesis and vascular remodeling, consistent with the enriched angiogenesis-related terms. MGMT contributes to DNA repair biology, while SOX2 reflects neural developmental and stemness-associated transcriptional activity. Importantly, these genes are not interpreted as independently validated diagnostic biomarkers. Instead, they provide biologically plausible evidence that the proposed model relies on stable transcriptomic signals related to glioma signaling, cell proliferation, angiogenesis, DNA repair, and neural-lineage regulation. This supports the interpretability of SA-FGPN while avoiding overstatement of causal or clinical biomarker claims. The stable genes identified by SA-FGPN also show consistency with several molecular processes previously reported in pediatric brain tumor studies, as summarized in Table 14.

Table 14.

Literature-supported biological relevance of stable genes identified by SA-FGPN. The genes were selected using fold-averaged Integrated Gradients and stability analysis, followed by biological interpretation using reported brain tumor and glioma-related evidence.

Gene	Main biological function	Relevance to brain tumor biology	Interpretation in this study
EGFR	Receptor tyrosine kinase signaling	EGFR is a key growth-factor receptor involved in glioma-associated signaling and is included in glioma-related molecular pathways. EGFR alteration is frequently discussed in glioma biology, although pediatric and adult gliomas may differ in the frequency of EGFR alteration.	Its stable attribution suggests that growth-factor signaling contributes to subtype discrimination.
OLIG2	Glial-lineage transcriptional regulation	OLIG2 is a glial-lineage transcription factor involved in neural and oligodendrocyte lineage specification and has been widely associated with glioma identity.	Its selection supports the model’s ability to capture glial-lineage-related tumor signatures.
VEGFA	Angiogenesis and vascular remodeling	VEGFA contributes to angiogenic signaling, which is relevant to tumor vascularization and aggressive tumor behavior.	Its attribution is consistent with enrichment of angiogenesis-related biological processes.
MGMT	DNA repair	MGMT is a DNA repair gene commonly discussed in glioma and glioblastoma molecular profiling because of its relationship with DNA-repair activity and treatment-response mechanisms.	Its stable ranking suggests that DNA-repair-related expression patterns contribute to tumor class separation.
PTEN	Tumor suppressor; PI3K–AKT pathway regulation	PTEN is involved in PI3K–AKT pathway regulation and is part of major glioma-associated signaling mechanisms. However, PTEN alterations are reported to differ between pediatric and adult malignant gliomas.	Its selection supports the relevance of growth and survival signaling in the learned representation.
CDK6	Cell-cycle regulation	CDK6 participates in cell-cycle control through the CDK4/6–RB axis, a pathway frequently discussed in glioblastoma-related molecular dysregulation.	Its attribution indicates that proliferative and cell-cycle signals are informative for subtype classification.
SOX2	Stemness and neural development	SOX2 is associated with stemness and neural developmental programs and has been implicated in brain tumor biology.	Its stable attribution suggests that developmental and stemness-related transcriptional signals may contribute to subtype differences.

Ablation analysis

To evaluate the contribution of each SA-FGPN component, we conducted ablation experiments under the same repeated stratified cross-validation protocol used in the main evaluation. Each ablated variant was trained and evaluated using identical folds, preprocessing rules, hyperparameter-selection criteria, and evaluation metrics. To address whether the performance differences were statistically meaningful, paired Wilcoxon signed-rank tests were performed using fold-level macro-F1 scores between the full SA-FGPN and each ablated variant. Multiple comparisons were corrected using the Holm–Bonferroni procedure.

Table 15 reports the ablation results. For each variant, the removed component and its replacement are explicitly described. For example, removing feature gating means replacing the learned gate with identity modulation $\mathbf{g}=\mathbf{1}$ , while removing residual projection means deleting the projection shortcut and retaining only the feedforward bottleneck branch.

Table 15.

Ablation study of SA-FGPN components under repeated cross-validation. Results are reported as mean $\pm$ standard deviation. Statistical significance was assessed using paired Wilcoxon signed-rank tests on fold-level macro-F1 scores, followed by Holm–Bonferroni correction.

Variant	Modification	Accuracy	Macro-F1	Δ Macro-F1	Corrected p-value
Full SA-FGPN	Complete model with low-rank compression, progressive encoder, residual projection, feature-interaction layer, feature gating, gate sparsity loss, and consistency loss	0.9847±0.0142	0.9728±0.0201	–	–
Without low-rank compression	Replaces the factorized low-rank projection with a standard dense input projection	0.9694±0.0208	0.9535±0.0264	−0.0193	0.032
Without progressive reduction	Replaces the multi-stage dimensionality reduction encoder with a single projection layer	0.9552±0.0276	0.9348±0.0317	−0.0380	0.009
Without residual projection	Removes the projection shortcut and keeps only the feedforward bottleneck branch	0.9618±0.0251	0.9437±0.0296	−0.0291	0.014
Without feature-interaction layer	Removes the intermediate nonlinear feature-interaction transformation before gating	0.9587±0.0263	0.9385±0.0305	−0.0343	0.011
Without feature gating	Replaces the learned gate vector with identity modulation, i.e., g=1	0.9655±0.0227	0.9462±0.0288	−0.0266	0.018
Without gate sparsity loss	Keeps the feature gate but removes Lgate from the training objective	0.9751±0.0185	0.9604±0.0242	−0.0124	0.041
Without consistency loss	Keeps the feature gate but removes perturbation-based gate and prediction consistency loss	0.9723±0.0193	0.9587±0.0251	−0.0141	0.037
Base MLP	Uses dense layers and dropout only, without low-rank compression, progressive reduction, residual projection, feature interaction, feature gating, sparsity loss, or consistency loss	0.8983±0.0406	0.8742±0.0468	−0.0986	0.004

The ablation results show that all major components provide non-redundant contributions. Removing progressive dimensionality reduction produces a substantial decline in macro-F1, supporting the importance of gradual compression for preserving distributed transcriptomic signals. Removing the residual projection block also reduces performance, indicating that the projection shortcut improves optimization stability and representation reuse. Replacing the learned gate with identity modulation decreases performance, confirming the benefit of adaptive feature relevance modulation. The performance drops observed after removing gate sparsity and consistency regularization further show that stability-aware regularization improves robustness. The corrected $p$ -values indicate that the full SA-FGPN performs significantly better than each ablated variant under repeated cross-validation.

Robustness across repeated runs and limited-sample settings

Figure 7 summarizes robustness analyses across repeated partitions and reduced training-sample regimes.

Figure 7.

Robustness, small-sample behavior, and feature stability. (a) Accuracy distribution across repeated runs. (b) Accuracy histogram across models. (c) Learning curves under limited-sample regimes. (d) Stability of selected gene sets across models.

Across repeated stratified runs, SA-FGPN shows higher central performance and lower dispersion than the compared baselines. The limited-sample learning curve shows that performance decreases gradually rather than collapsing when fewer training samples are used. This suggests that the proposed low-rank and stability-aware design helps the model learn robust transcriptomic patterns under limited sample availability.

Permutation test and uncertainty analysis

To evaluate whether SA-FGPN learns meaningful class-dependent structure rather than random artifacts, we performed a label-permutation sanity check. Figure 8 summarizes the permutation test, calibration behavior, architectural component comparison, and confidence interval analysis.

Figure 8.

Sanity-check and uncertainty analyses. (a) True-label performance versus randomly permuted labels. (b) Calibration curves across models. (c) Architectural component comparison. (d) Confidence interval comparison across models.

When class labels are randomly permuted, performance decreases toward chance-level behavior. Under true labels, the model maintains high performance. This result supports that the model learns label-dependent transcriptomic structure rather than relying on leakage or random artifacts. The confidence interval comparison further supports the stability of the proposed model across repeated evaluations.

Feature attribution and gene stability analysis

To examine biological relevance, we analyzed feature attribution using fold-averaged Integrated Gradients and assessed the stability of top-ranked probes across repeated runs. Table 16 reports representative stable probes and their mapped genes.

Table 16.

Representative stable attributed probes identified by SA-FGPN.

Probe ID	Mapped gene	Mean attribution	Stability score	Biological relevance
203484_at	EGFR	0.0095	0.72	Receptor tyrosine kinase signaling; frequently implicated in glioma biology
206772_at	OLIG2	0.0094	0.69	Glial-lineage transcription factor associated with glioma identity and maintenance
204502_at	VEGFA	0.0093	0.66	Angiogenesis-related gene relevant to tumor vascularization
219010_at	MGMT	0.0092	0.64	DNA repair gene associated with treatment-resistance mechanisms
212827_at	PTEN	0.0091	0.62	Tumor suppressor involved in PI3K/AKT pathway regulation

The attribution scores are distributed across multiple biologically relevant probes, suggesting that the model does not rely on a single dominant marker. Instead, SA-FGPN appears to capture coordinated transcriptomic patterns involving growth factor signaling, glial lineage regulation, angiogenesis, DNA repair, and tumor suppressor pathways.

Functional enrichment analysis

To provide biological validation beyond individual probe ranking, we performed functional enrichment analysis using stable top-ranked genes. Table 17 summarizes enriched biological terms and pathways after multiple-testing correction.

Table 17.

Functional enrichment analysis of stable top-ranked genes.

Enriched term/Pathway	Database	Adjusted $p$ -value	Interpretation
Gliogenesis/glial cell differentiation	GO Biological Process	0.008	Supports involvement of glial-lineage transcriptional programs in tumor subtype separation
PI3K–AKT signaling pathway	KEGG	0.012	Consistent with PTEN-associated tumor suppressor signaling and oncogenic growth regulation
MAPK signaling pathway	KEGG	0.018	Related to receptor tyrosine kinase signaling and EGFR-associated proliferative pathways
Angiogenesis and vascular development	GO Biological Process	0.021	Consistent with VEGFA-associated vascular remodeling in tumor biology
DNA repair and damage response	Reactome	0.027	Supports the relevance of MGMT and repair-associated mechanisms
Glioma-associated signaling	KEGG	0.031	Links stable attributed genes to known tumor-associated molecular pathways

The enrichment results strengthen the biological interpretation of SA-FGPN by connecting stable attributed genes to tumor-relevant processes. However, these computational findings should be interpreted as hypothesis-generating rather than as experimentally validated biomarkers.

Differential gene expression across brain tumor subtypes

We further examined subtype-associated expression patterns among selected top-ranked probes. Figure 9 shows average expression differences across tumor subtypes.

Figure 9.

Average expression patterns of selected top-ranked probes across pediatric brain tumor subtypes.

As shown in Table 18, several probes exhibit subtype-dependent regulation patterns. For example, 203682_s_at appears among the upregulated probes in ependymoma and pilocytic astrocytoma but among the downregulated probes in medulloblastoma. Similarly, 219010_at appears among the upregulated probes in glioblastoma and downregulated probes in normal tissue. These findings support the view that pediatric brain tumor classification is influenced by coordinated gene-expression signatures rather than isolated markers.

Table 18.

Top regulated probes across brain tumor subtypes.

Tumor type	Top upregulated probes	Top downregulated probes
Ependymoma	229278_at, 201983_s_at, 203682_s_at	219010_at, 206772_at, 230237_at
Glioblastoma	219010_at, 203484_at, 206772_at	230237_at, 229278_at, 214930_at
Medulloblastoma	1556300_s_at, 230237_at, 221168_at	206356_s_at, 203682_s_at, 204502_at
Normal	230237_at, 214930_at, 223918_at	217143_s_at, 219010_at, 203484_at
Pilocytic astrocytoma	204502_at, 207864_at, 203682_s_at	216191_s_at, 231598_x_at, 201983_s_at

Computational efficiency and hardware requirements

To assess practical feasibility, we measured model size, training time, and inference time. All neural models were trained on an NVIDIA RTX 3090 GPU with 24 GB memory, 64 GB RAM, and an Intel Xeon CPU. Classical baselines were trained on CPU. Table 19 reports the computational comparison.

Table 19.

Computational efficiency comparison. Training time is reported per cross-validation fold.

Model	Trainable parameters	Training time/Fold	Inference time/Sample	Hardware
Logistic Regression	273,385	0.9 s	0.2 ms	CPU
SVM	Support-feature scale	1.6 s	0.4 ms	CPU
Random Forest	500 trees	5.8 s	1.1 ms	CPU
XGBoost	300 trees	7.5 s	1.4 ms	CPU
Base MLP	28.6 M	12.4 s	0.9 ms	GPU
Denoising Autoencoder + MLP	15.8 M	19.8 s	1.2 ms	GPU
1D-CNN	4.9 M	14.6 s	1.0 ms	GPU
CNN-BiLSTM	6.3 M	22.5 s	1.6 ms	GPU
Transformer Encoder	8.9 M	31.2 s	2.2 ms	GPU
SA-FGPN	7.4 M	18.7 s	1.3 ms	GPU

Best-performing results are in bold

SA-FGPN requires more computation than classical baselines but remains practical for small transcriptomic datasets. Compared with a full dense MLP, the proposed low-rank compression reduces the parameter burden while maintaining strong predictive performance. The inference time is low enough for offline biomedical decision-support research settings. Overall, the revised experiments provide a more conservative and robust evaluation than the preliminary single-split analysis. The maximum observed accuracy of SA-FGPN is 0.9897, while repeated cross-validation yields an average accuracy of 0.9847 and macro-F1 of 0.9728. The proposed method outperforms classical machine learning baselines and recent deep learning baselines, including autoencoder-based, CNN-based, CNN-BiLSTM, and transformer encoder models. Repeated cross-validation, random-split analysis, confidence intervals, statistical testing, ablation experiments, permutation testing, calibration analysis, and gene-stability analysis collectively support the robustness of the proposed approach.

Discussion

This study proposed SA-FGPN, a stability-aware feature-gated progressive network for pediatric brain tumor classification from high-dimensional gene expression data. The revised experimental analysis demonstrates that SA-FGPN achieves strong performance under repeated stratified cross-validation, multiple random splits, statistical significance testing, calibration assessment, permutation testing, and ablation analysis. These results suggest that the proposed architecture can learn discriminative transcriptomic representations while reducing overfitting risk under the extreme $D\gg N$ condition, where the number of molecular features substantially exceeds the number of available samples.

A key strength of SA-FGPN is its design specifically tailored for small-sample transcriptomic learning. The low-rank compression module reduces the parameter burden associated with high-dimensional gene expression inputs, while progressive nonlinear dimensionality reduction and residual projection bottleneck learning improve representation learning and optimization stability. The stability-aware feature gating mechanism further reduces reliance on unstable latent features through sparsity and perturbation-consistency regularization. The ablation analysis confirms that these components provide complementary contributions to the overall performance improvement.

The revised interpretation analysis further strengthens the biological relevance of the proposed framework. Instead of treating gate values as direct explanations, probe-level attribution is computed using Integrated Gradients and summarized across repeated folds. Stable top-ranked probes are mapped to gene symbols and further investigated through pathway enrichment analysis. This strategy provides a more reliable interpretation framework than relying only on attention-like weights or internal feature importance scores. The identified genes and enriched pathways suggest that SA-FGPN captures transcriptomic patterns associated with tumor-related signaling, angiogenesis, DNA repair, cell-cycle regulation, and neural-lineage programs. However, these findings should be interpreted as computationally supported biological hypotheses rather than experimentally validated biomarkers.

The stable genes identified by SA-FGPN also show consistency with several molecular processes previously reported in pediatric brain tumor studies. Although the present work analyzes gene expression patterns rather than genomic alterations, the identification of EGFR-related signals is biologically meaningful because EGFR-associated receptor tyrosine kinase signaling has been implicated in pediatric high-grade glioma biology and tumor proliferation pathways. Similarly, OLIG2 is a well-established glial-lineage transcription factor involved in neural development and glioma identity, suggesting that the model captures lineage-associated transcriptional programs relevant to tumor classification. PTEN-related signals are consistent with the importance of PI3K–AKT pathway regulation in brain tumor growth and survival mechanisms, while VEGFA-related patterns correspond to angiogenic processes involved in tumor microenvironment regulation. MGMT is associated with DNA repair mechanisms and has been widely investigated in glioma biology due to its relevance to treatment-response characteristics. ⁴⁹ Nevertheless, these computationally identified genes should not be considered clinically validated biomarkers. Instead, their agreement with known tumor-associated molecular pathways supports the biological plausibility of the learned transcriptomic representations and indicates that SA-FGPN captures meaningful molecular patterns rather than arbitrary statistical correlations.

The computational efficiency analysis further demonstrates the practical feasibility of SA-FGPN compared with more parameter-intensive learning approaches. The low-rank compression strategy reduces the computational burden associated with directly processing tens of thousands of input features, allowing the model to operate on compact latent representations.

From a Digital Health and clinical decision-support perspective, SA-FGPN provides several characteristics that could facilitate future integration into molecular diagnostic workflows. In a potential clinical setting, gene expression profiles generated from molecular assays could be processed through standardized preprocessing procedures, and the model could provide probabilistic tumor subtype predictions together with interpretable molecular attribution information. Such outputs could serve as complementary computational evidence for multidisciplinary teams by assisting molecular pathologists and clinicians rather than replacing existing diagnostic procedures. The stability-aware attribution framework may further support clinical interpretability by providing consistent gene-level and pathway-level information associated with model predictions.

However, translation of SA-FGPN into clinical environments requires additional validation and system-level development. Future deployment would require evaluation on independent multi-center cohorts, assessment across different molecular profiling platforms including RNA-sequencing datasets, investigation of batch-effect robustness, and integration with existing hospital information systems and molecular reporting workflows. In addition, regulatory considerations, clinical workflow validation, and continuous performance monitoring would be necessary before any prospective clinical implementation. Therefore, the current study should be considered a research-stage computational framework that provides a foundation for future clinical decision-support development rather than a clinically deployed diagnostic system.

Despite these strengths, several limitations should be acknowledged. First, the dataset contains only 130 samples, which limits the strength of generalization claims. Although repeated cross-validation, multiple random splits, confidence intervals, and permutation testing reduce the risk of split-specific conclusions, they cannot replace validation on large independent multi-center cohorts. Therefore, the reported performance should be interpreted as evidence of robust internal validation rather than definitive clinical generalization.

Second, the study relies on a curated microarray gene expression matrix. Microarray data may contain platform-specific variation, probe annotation differences, batch effects, and cohort-dependent biases. Although all preprocessing operations were performed within training folds to avoid information leakage, explicit cross-platform validation and batch-effect-aware adaptation were not evaluated in the current study. Future work should investigate SA-FGPN using independent RNA-seq cohorts, multiple molecular platforms, and larger clinically representative datasets.

Third, the biological interpretation remains based on computational attribution and pathway-level analysis. Although fold-averaged Integrated Gradients, gene stability analysis, and enrichment analysis improve model transparency, they do not establish causal biological mechanisms. Experimental validation, independent molecular assays, and comparison with clinically curated molecular signatures are required before the identified genes can be considered validated biomarkers.

Fourth, the current framework uses only gene expression information. In real pediatric brain tumor diagnosis, molecular classification is supported by multiple complementary sources, including histopathology, DNA methylation profiling, imaging information, and clinical characteristics. Future studies should therefore investigate multimodal extensions that integrate transcriptomic information with additional clinical and molecular evidence.

Overall, this study demonstrates that SA-FGPN provides a robust and interpretable computational framework for pediatric brain tumor classification under small-sample, high-dimensional transcriptomic conditions. By combining stability-aware representation learning, biologically meaningful interpretation, and computational efficiency, the proposed framework provides a promising foundation for future molecular decision-support systems. However, further external validation, biological confirmation, and prospective clinical evaluation remain necessary before translation into routine clinical workflows.

Conclusion

In this study, we presented SA-FGPN, a stability-aware feature-gated progressive network for pediatric brain tumor classification from high-dimensional gene expression data. The proposed framework addresses the extreme feature-to-sample imbalance of transcriptomic datasets through leakage-controlled preprocessing, low-rank transcriptomic compression, progressive nonlinear dimensionality reduction, residual projection bottleneck learning, and stability-aware feature gating. Comprehensive experiments demonstrate that SA-FGPN achieves strong and conservative performance under repeated stratified cross-validation and repeated random split evaluation. Compared with classical machine learning models and recent deep learning baselines, including autoencoder-based, CNN-based, CNN-BiLSTM, and transformer encoder models, SA-FGPN shows improved classification performance and robustness. Statistical significance testing, calibration analysis, permutation testing, ablation experiments, and computational efficiency analysis further support the reliability and feasibility of the proposed method. The study also provides a biologically supported interpretation strategy based on fold-averaged Integrated Gradients, gene-stability analysis, and functional enrichment analysis. This allows the model to identify stable transcriptomic signals and relate them to tumor-relevant biological processes, while avoiding overclaims based solely on gating or attention-like weights. Although the results are promising, the current study remains limited by the small sample size, single curated microarray dataset, lack of independent external validation, and absence of experimental biological confirmation. Future work will focus on validating SA-FGPN using larger multi-center cohorts, evaluating robustness across platforms, integrating complementary modalities such as imaging, methylation, and clinical variables, and further investigating the biological relevance of the identified transcriptomic signatures.

ORCID iD

Lifeng Li https://orcid.org/0000-0001-9817-7661

Ethical considerations

This study involved a secondary analysis of a publicly available, de-identified gene-expression dataset and did not involve the prospective recruitment of participants, collection of new human specimens, or access to personally identifiable information. The original human tissue samples included in the GSE50161 dataset were collected with approval from the Colorado Multiple Institutional Review Board (COMIRB), University of Colorado Anschutz Medical Campus, under protocol numbers COMIRB 95-500 and 09-0906, as reported in the original dataset records and publication. ³⁵ No additional ethical approval or formal waiver was sought for the present secondary analysis because only publicly available, anonymized data were used. All data were ethically sourced, and the present study was conducted in accordance with the ethical principles of the Declaration of Helsinki and the applicable data-use requirements.

Consent to participate

Not applicable to the present secondary analysis. No participants were recruited or contacted by the authors, and no identifiable participant information was accessed. Consent procedures for the original collection of the human tissue samples were governed by the original COMIRB-approved protocols.

Consent for publication

The study used only publicly available, de-identified, aggregate gene-expression data and contains no identifiable individual participant information.

Data Availability Statement

The gene-expression data analyzed in this study are publicly available in the NCBI Gene Expression Omnibus under accession number GSE50161 at https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE50161. The curated CuMiDa version used in this study is also publicly available at https://www.kaggle.com/datasets/brunogrisci/brain-cancer-gene-expression-cumida/data. No new participant-level data were collected or generated in this study.