# Neural Structured Prediction for Inductive Node Classification

arXiv: https://arxiv.org/abs/2204.07524 · HTML: https://mlsanity.com/paper/2204.07524/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 55 references that are in the map.
- First posted on arXiv 15 Apr 2022.

## Builds on (most cited first, 29 of 29)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [Neural Architectures for Named Entity Recognition](https://mlsanity.com/paper/1603.01360/) (2016)
- [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)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [End-to-end Sequence Labeling via Bi-directional LSTM-CNNs-CRF](https://mlsanity.com/paper/1603.01354/) (2016)
- [Predicting multicellular function through multi-layer tissue networks](https://mlsanity.com/paper/1707.04638/) (2017)
- [Discriminative Embeddings of Latent Variable Models for Structured Data](https://mlsanity.com/paper/1603.05629/) (2016)
- [Continuous Graph Neural Networks](https://mlsanity.com/paper/1912.00967/) (2019)
- [Large-Scale Learnable Graph Convolutional Networks](https://mlsanity.com/paper/1808.03965/) (2018)
- [GMNN: Graph Markov Neural Networks](https://mlsanity.com/paper/1905.06214/) (2019)
- [Loopy Belief Propagation for Approximate Inference: An Empirical Study](https://mlsanity.com/paper/1301.6725/) (2013)
- [Neural Enhanced Belief Propagation on Factor Graphs](https://mlsanity.com/paper/2003.01998/) (2020)
- [Efficient Probabilistic Logic Reasoning with Graph Neural Networks](https://mlsanity.com/paper/2001.11850/) (2020)
- [Combining Generative and Discriminative Models for Hybrid Inference](https://mlsanity.com/paper/1906.02547/) (2019)
- [Empower Sequence Labeling with Task-Aware Neural Language Model](https://mlsanity.com/paper/1709.04109/) (2017)
- [A Flexible Generative Framework for Graph-based Semi-supervised Learning](https://mlsanity.com/paper/1905.10769/) (2019)
- [CopulaGNN: Towards Integrating Representational and Correlational Roles of Graphs in Graph Neural Networks](https://mlsanity.com/paper/2010.02089/) (2020)
- [Semi-Supervised Node Classification on Graphs: Markov Random Fields vs. Graph Neural Networks](https://mlsanity.com/paper/2012.13085/) (2020)

## Built on by (most cited first, 13 of 13)

- [Fully-inductive Node Classification on Arbitrary Graphs](https://mlsanity.com/paper/2405.20445/) (2024)
- [CLNode: Curriculum Learning for Node Classification](https://mlsanity.com/paper/2206.07258/) (2022)
- [Understanding Non-linearity in Graph Neural Networks from the Bayesian-Inference Perspective](https://mlsanity.com/paper/2207.11311/) (2022)
- [Joint Entity and Relation Extraction with Span Pruning and Hypergraph Neural Networks](https://mlsanity.com/paper/2310.17238/) (2023)
- [Graph Neural Networks Intersect Probabilistic Graphical Models: A Survey](https://mlsanity.com/paper/2206.06089/) (2022)
- [Rethinking Independent Cross-Entropy Loss For Graph-Structured Data](https://mlsanity.com/paper/2405.15564/) (2024)
- [View Space: Learning Representation across Arbitrary Graphs](https://mlsanity.com/paper/2512.11561/) (2025)
- [Diffusion Probabilistic Models for Structured Node Classification](https://mlsanity.com/paper/2302.10506/) (2023)
- [MGM: Global Understanding of Audience Overlap Graphs for Predicting the Factuality and the Bias of News Media](https://mlsanity.com/paper/2412.10467/) (2024)
- [Unleashing the potential of GNNs via Bi-directional Knowledge Transfer](https://mlsanity.com/paper/2310.17132/) (2023)
- [I-MPN: Inductive Message Passing Network for Efficient Human-in-the-Loop Annotation of Mobile Eye Tracking Data](https://mlsanity.com/paper/2406.06239/) (2024)
- [ReDiSC: A Reparameterized Masked Diffusion Model for Scalable Node Classification with Structured Predictions](https://mlsanity.com/paper/2507.14484/) (2025)
- [Though Language Models Err While They Strive: Conformal Prediction for Self-Correcting Scientific Generation](https://mlsanity.com/paper/2607.16704/) (2026)

## Abstract (arXiv)

This paper studies node classification in the inductive setting, i.e., aiming to learn a model on labeled training graphs and generalize it to infer node labels on unlabeled test graphs. This problem has been extensively studied with graph neural networks (GNNs) by learning effective node representations, as well as traditional structured prediction methods for modeling the structured output of node labels, e.g., conditional random fields (CRFs). In this paper, we present a new approach called the Structured Proxy Network (SPN), which combines the advantages of both worlds. SPN defines flexible potential functions of CRFs with GNNs. However, learning such a model is nontrivial as it involves optimizing a maximin game with high-cost inference. Inspired by the underlying connection between joint and marginal distributions defined by Markov networks, we propose to solve an approximate version of the optimization problem as a proxy, which yields a near-optimal solution, making learning more efficient. Extensive experiments on two settings show that our approach outperforms many competitive baselines.