# Theoretical Learning Performance of Graph Neural Networks: The Impact of Jumping Connections and Layer-wise Sparsification

arXiv: https://arxiv.org/abs/2507.05533 · HTML: https://mlsanity.com/paper/2507.05533/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 51 of its 59 references that are in the map.
- First posted on arXiv 7 Jul 2025.

## Builds on (most cited first, 30 of 51)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Gradient Descent Provably Optimizes Over-parameterized Neural Networks](https://mlsanity.com/paper/1810.02054/) (2018)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [Cluster-GCN: An Efficient Algorithm for Training Deep and Large Graph Convolutional Networks](https://mlsanity.com/paper/1905.07953/) (2019)
- [DeepGCNs: Can GCNs Go as Deep as CNNs?](https://mlsanity.com/paper/1904.03751/) (2019)
- [Towards Understanding Ensemble, Knowledge Distillation and Self-Distillation in Deep Learning](https://mlsanity.com/paper/2012.09816/) (2020)
- [Learning Overparameterized Neural Networks via Stochastic Gradient Descent on Structured Data](https://mlsanity.com/paper/1808.01204/) (2018)
- [Adaptive Sampling Towards Fast Graph Representation Learning](https://mlsanity.com/paper/1809.05343/) (2018)
- [Layer-Dependent Importance Sampling for Training Deep and Large Graph Convolutional Networks](https://mlsanity.com/paper/1911.07323/) (2019)
- [On the equivalence between graph isomorphism testing and function approximation with GNNs](https://mlsanity.com/paper/1905.12560/) (2019)
- [How Powerful are Spectral Graph Neural Networks](https://mlsanity.com/paper/2205.11172/) (2022)
- [Graph Neural Tangent Kernel: Fusing Graph Neural Networks with Graph Kernels](https://mlsanity.com/paper/1905.13192/) (2019)
- [Drawing Early-Bird Tickets: Towards More Efficient Training of Deep Networks](https://mlsanity.com/paper/1909.11957/) (2019)
- [Graph Convolution over Pruned Dependency Trees Improves Relation Extraction](https://mlsanity.com/paper/1809.10185/) (2018)
- [Rethinking the Expressive Power of GNNs via Graph Biconnectivity](https://mlsanity.com/paper/2301.09505/) (2023)
- [A Unified Lottery Ticket Hypothesis for Graph Neural Networks](https://mlsanity.com/paper/2102.06790/) (2021)
- [Feature Purification: How Adversarial Training Performs Robust Deep Learning](https://mlsanity.com/paper/2005.10190/) (2020)
- [Recovery Guarantees for One-hidden-layer Neural Networks](https://mlsanity.com/paper/1706.03175/) (2017)
- [What Can ResNet Learn Efficiently, Going Beyond Kernels?](https://mlsanity.com/paper/1905.10337/) (2019)
- [How Powerful are K-hop Message Passing Graph Neural Networks](https://mlsanity.com/paper/2205.13328/) (2022)
- [A PAC-Bayesian Approach to Generalization Bounds for Graph Neural Networks](https://mlsanity.com/paper/2012.07690/) (2020)

## Abstract (arXiv)

Jumping connections enable Graph Convolutional Networks (GCNs) to overcome over-smoothing, while graph sparsification reduces computational demands by selecting a sub-matrix of the graph adjacency matrix during neighborhood aggregation. Learning GCNs with graph sparsification has shown empirical success across various applications, but a theoretical understanding of the generalization guarantees remains limited, with existing analyses ignoring either graph sparsification or jumping connections. This paper presents the first learning dynamics and generalization analysis of GCNs with jumping connections using graph sparsification. Our analysis demonstrates that the generalization accuracy of the learned model closely approximates the highest achievable accuracy within a broad class of target functions dependent on the proposed sparse effective adjacency matrix A^*. Thus, graph sparsification maintains generalization performance when A^* preserves the essential edges that support meaningful message propagation. We reveal that jumping connections lead to different sparsification requirements across layers. In a two-hidden-layer GCN, the generalization is more affected by the sparsified matrix deviations from A^* of the first layer than the second layer. To the best of our knowledge, this marks the first theoretical characterization of jumping connections' role in sparsification requirements. We validate our theoretical results on benchmark datasets in deep GCNs.