Omics data, such as transcriptomics, proteomics, and metabolomics, provide critical insights into disease mechanisms and clinical outcomes. However, their high dimensionality, small sample sizes, and intricate biological networks pose major challenges for reliable prediction and meaningful interpretation. Graph Neural Networks (GNNs) offer a promising way to integrate prior knowledge by encoding feature relationships as graphs. Yet, existing methods typically rely solely on either an externally curated feature graph or a data-driven generated one, which limits their ability to capture complementary information. To address this, we propose the external and generated Graph Neural Network (engGNN), a dual-graph framework that jointly leverages both external known biological networks and data-driven generated graphs. Specifically, engGNN constructs a biologically informed undirected feature graph from established network databases and complements it with a directed feature graph derived from tree-ensemble models. This dual-graph design produces more comprehensive embeddings, thereby improving predictive performance and interpretability. Through extensive simulations and real-world applications to gene expression data, engGNN consistently outperforms state-of-the-art baselines. Beyond classification, engGNN provides interpretable feature importance scores that facilitate biologically meaningful discoveries, such as pathway enrichment analysis. Taken together, these results highlight engGNN as a robust, flexible, and interpretable framework for disease classification and biomarker discovery in high-dimensional omics contexts.

Deep residual networks (ResNets) have demonstrated better generalization performance than deep feedforward networks (FFNets). However, the theory behind such a phenomenon is still largely unknown.

Residual connections remain ubiquitous in modern neural network architectures nearly a decade after their introduction. Their widespread adoption is often credited to their dramatically improved trainability: residual networks train faster, more stably, and achieve higher accuracy than their feedforward counterparts. While numerous techniques, ranging from improved initialization to advanced learning rate schedules, have been proposed to close the performance gap between residual and feedforward networks, this gap has persisted. In this work, we propose an alternative explanation: residual networks do not merely reparameterize feedforward networks, but instead inhabit a different function space. We design a controlled post-training comparison to isolate generalization performance from trainability; we find that variable-depth architectures, similar to ResNets, consistently outperform fixed-depth networks, even when optimization is unlikely to make a difference. These results suggest that residual connections confer performance advantages beyond optimization, pointing instead to a deeper inductive bias aligned with the structure of natural data.

Additional Feedback: ### On my overall decision I am willing to largely upgrade my decision, if the authors can provide strong evidence that's easy to check (i.e. "safety checks") to support the correctness of their propositions/theorems. But since the size m of the hidden layers becomes infinite, the set of weights tends to a fixed limiting distribution: the same for all layers. Therefore, when m goes to infinity, the time-varying component gets smoothed out. So, when L now becomes infinite, we exactly recover an unrolled, 1-layer recurrent neural network. By Representer theorem - By the representer theorem - Fig.2, caption: CIFAR102 - CIFAR2 Reply to author response ----------------------------- Thank you for the additional plots provided in your response, which indeed nicely confirm your main theorems.

After the thorough discussion among the reviewers, there is a consensus that this is a good paper that warrants acceptance. There were some skepticisms in the initial reviews, but the authors have provided a rebuttal which addressed most of the major concerns. The reviewers have updated their reviews/scores accordingly. Hence, the paper is accepted as a poster. Based on my own judgement, the presentation of this paper should be improved in the camera-ready version.

Deep residual networks (ResNets) have demonstrated better generalization performance than deep feedforward networks (FFNets). However, the theory behind such a phenomenon is still largely unknown. Specifically, we first show that under proper conditions, as the width goes to infinity, training deep ResNets can be viewed as learning reproducing kernel functions with some kernel function. We then compare the kernel of deep ResNets with that of deep FFNets and discover that the class of functions induced by the kernel of FFNets is asymptotically not learnable, as the depth goes to infinity. In contrast, the class of functions induced by the kernel of ResNets does not exhibit such degeneracy. Our discovery partially justifies the advantages of deep ResNets over deep FFNets in generalization abilities.

Three-phase PWM rectifiers are adopted extensively in industry because of their excellent properties and potential advantages. However, while the IGBT has an open-circuit fault, the system does not crash suddenly, the performance will be reduced for instance voltages fluctuation and current harmonics. A fault diagnosis method based on deep feedforward network with transient synthetic features is proposed to reduce the dependence on the fault mathematical models in this paper, which mainly uses the transient phase current to train the deep feedforward network classifier. Firstly, the features of fault phase current are analyzed in this paper. Secondly, the historical fault data after feature synthesis is employed to train the deep feedforward network classifier, and the average fault diagnosis accuracy can reach 97.85% for transient synthetic fault data, the classifier trained by the transient synthetic features obtained more than 1% gain in performance compared with original transient features. Finally, the online fault diagnosis experiments show that the method can accurately locate the fault IGBTs, and the final diagnosis result is determined by multiple groups results, which has the ability to increase the accuracy and reliability of the diagnosis results.

A unique challenge in predictive model building for omics data has been the small number of samples (n) versus the large amount of features (p). This "n p" property brings difficulties for disease outcome classification using deep learning techniques. Sparse learning by incorporating external gene network information such as the graph-embedded deep feedforward network (GEDFN) [19] model has been a solution to this issue. However, such methods require an existing feature graph, and potential mis-specification of the feature graph can be harmful on classification and feature selection. To address this limitation and develop a robust classification model without relying on external knowledge, we propose a forest graph-embedded deep feedforward network (forgeNet) model, to integrate the GEDFN architecture with a forest feature graph extractor, so that the feature graph can be learned in a supervised manner and specifically constructed for a given prediction task. To validate the method's capability, we experimented the forgeNet model with both synthetic and real datasets. The resulting high classification accuracy suggests that the method is a valuable addition to sparse deep learning models for omics data.

Gene expression data represents a unique challenge in predictive model building, because of the small number of samples $(n)$ compared to the huge amount of features $(p)$. This "$n<