Aug 2026· Neural Networks· Vol 205 Pt B, pp.
109464
· 0 citations· 12 references
Medicine
TL;DR
The Stable Reaction-Diffusion encoder (SRD) provides a trajectory-stabilizing forward evolution mechanism that explicitly controls propagation drift and finite-depth sensitivity, rather than simply stacking additional message-passing layers.
Abstract
Deep Graph Neural Networks (GNNs) often degrade when many propagation layers are stacked. Although this phenomenon is commonly associated with over-smoothing, node-wise similarity alone does not fully describe deep representation failure. During propagation, node representations form a layer-wise trajectory that may become unstable, lose traceability to input information, or collapse into a low-dimensional subspace. Motivated by this view, we formulate deep GNN degradation as a problem of representation trajectory control. The framework integrates three complementary controls along a shared representation trajectory. The Stable Reaction-Diffusion encoder (SRD) provides a trajectory-stabilizing forward evolution mechanism that explicitly controls propagation drift and finite-depth sensitivity, rather than simply stacking additional message-passing layers. A deterministic depth-normalized traceability constraint (RDC) encourages intermediate input-space targets to remain traceable to the original features through graph-aware residual consistency. A Rank-Rate Constraint (RRC) penalizes excessive inter-layer decay of logarithmic numerical rank to slow premature subspace degeneration. We position the method as an integration and diagnostic framework rather than a new propagation operator. Theoretical analysis and experiments demonstrate the effectiveness, robustness, and stability of the proposed trajectory-control framework.
Deep graph neural networks(GNNs) suffer from oversmoothing- a progressive collapse of node representation towards a low information subspace as network depth increases because the normalized graph propagation operator is repeatedly applied directly to the hidden representations. In this work we study Householder Graph Neural Network (HouseGNN). Rather than updating the hidden state like standard GCN, HouseGNN uses the aggregated neighbourhood message solely to estimate a reflection direction; the node embedding is then updated by a Householder reflector followed by GroupSort, yielding a piecewise orthogonal layer that preserves Euclidean norm at every node and at every depth. We prove three core properties: (i) every internal layer preserves the node-wise Euclidean norm; (ii) the Householder reflector is scale scale and sign-invariant in the message; and (iii) pairwise distance between nodes can change through mismatch between node-wise orthogonal operators.
Oversmoothing is a fundamental limitation of deep graph neural networks (GNNs), where repeated message passing causes node representations to become increasingly similar, eventually collapsing toward a low-dimensional subspace. This phenomenon limits the effective depth of message-passing architectures and motivates the search for mechanisms that preserve representation diversity. In this paper, we study a recurrent graph neural network in which independent Gaussian noise is injected after every propagation step and analyze the resulting architecture as a stochastic dynamical system. Under a standard global contraction assumption on the deterministic update, we prove that the hidden representations form a geometrically ergodic Markov chain admitting a unique invariant probability measure. Our main theoretical result establishes an explicit positive lower bound on the expected stationary Dirichlet energy, proportional to both the noise variance and the spectral gap of the underlying graph. Consequently, the stationary representations cannot collapse onto the constant manifold, providing a rigorous guarantee that asymptotic oversmoothing is prevented in the sense of non-vanishing Dirichlet energy. Our analysis reveals persistent stochastic perturbations as a fundamentally different mechanism for combating oversmoothing, complementing existing deterministic approaches based on residual connections, normalization, and graph rewiring. Finally, numerical experiments on both linear and nonlinear recurrent graph neural networks closely match the theoretical predictions, illustrating the emergence of a stationary distribution and the predicted dependence of the limiting Dirichlet energy on the noise intensity.
DeltaGNN is introduced, to the best of the authors' knowledge, among the first scalable (featuring linear computational and memory complexity overhead) and generalizable (capable of effectively handling graphs with diverse homophily, density, and topology) architectures for long-range and short-range interaction detection.
Kevin Mancini, Islem Rekik· IEEE Transactions on Pattern...· 2 citations
This work proposes a novel Adaptive Dual-level Collaborative GNN associated with an adaptive dual-level collaborative mechanism, and shows that the ADC-GNN can inject the learned high-level information back into the node level, forming a closed-loop, bidirectional optimization process.
Graph Autoencoder Uncovering Descriptive Information (GAUDI), an unsupervised graph deep learning framework designed to capture both local details and global structure, is introduced, providing new insights into emergent phenomena across diverse scientific domains.
