Normalization Stabilizes Shallow Graph Networks but Cannot Stop Deep Oversmoothing

Graph convolutional networks (GCNs) lose accuracy as they get deeper, a phenomenon known as oversmoothing, and researchers have long disagreed about whether normalization techniques can counteract it. A new controlled empirical study published in Neural Processing Letters revisits that question under unusually strict conditions: a vanilla GCN architecture, fully fixed hyperparameters, no architectural augmentations, six normalization schemes, six node-classification benchmarks, and network depths from 1 to 20, totaling 3,600 experimental runs.

The study reports three main observations. First, the effects of normalization concentrate at the transition from one to two layers and show diminishing returns beyond depth 3. At a single layer, normalization is structurally inoperative, and all six schemes behave identically. Second, once depth reaches six or more, the graph’s topology governs the accuracy trajectory. Among the topological properties tested, homophily—the tendency of connected nodes to share labels—was the only statistically significant predictor of depth-sensitivity, with a correlation of -0.87 and a p-value of 0.02. Spectral gap, degree, and clustering were not significant within the dataset family studied.

Third, normalization substantially reduces cross-seed training variance—by up to 90 percent at depth 2 on dense graphs—but it does not prevent eventual collapse. Depth-20 results confirmed continued degradation on all datasets, with Cora accuracy falling from 0.75 to 0.57 and then to 0.31 as depth increased.

Statistical testing sharpened the comparison between schemes. Wilcoxon signed-rank tests at depth 10 showed that BatchNorm and GraphNorm significantly outperformed the no-normalization baseline, while NodeNorm significantly underperformed it, all with p-values below 0.001.

The authors frame these findings as a redefinition of what normalization can and cannot do in deep graph networks. Rather than acting as a remedy for propagation-driven oversmoothing, normalization functions as an optimization stabilizer at shallow-to-moderate depth. The practical implication is that practitioners seeking depth-robust graph models should look beyond normalization alone and consider how the homophily of their graphs will shape performance as layers accumulate.

Beyond the empirical results, the paper contributes a reproducible stress-test protocol for evaluating depth-robust mechanisms in graph neural networks. By holding hyperparameters fixed and sweeping depth systematically across multiple benchmarks and schemes, the design isolates the interaction between depth, normalization, and graph structure that earlier, less controlled comparisons may have confounded. The work is published as open access, with the accepted version citable under a permanent DOI ahead of the final Version of Record.

Subject of Research: How depth, normalization schemes, and graph topology affect oversmoothing in vanilla graph convolutional networks.

Article Title: Depth, Normalization, and Graph Structure in Vanilla GCNs: A Controlled Empirical Study

Article References: Zheng, G., & Liu, X. (2026). Depth, Normalization, and Graph Structure in Vanilla GCNs: A Controlled Empirical Study. Neural Processing Letters. https://doi.org/10.1007/s11063-026-11892-9

Image Credits: AI Generated

DOI: 10.1007/s11063-026-11892-9

Keywords: graph neural networks, oversmoothing, normalization, GCN, node classification, homophily, deep learning, benchmark study, reproducibility, Depth, Graph, Structure