# On the Unreasonable Effectiveness of Feature propagation in Learning on Graphs with Missing Node Features

arXiv: https://arxiv.org/abs/2111.12128 · HTML: https://mlsanity.com/paper/2111.12128/

## Key facts

- Cited by 63 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 62 references that are in the map.
- First posted on arXiv 23 Nov 2021.

## Builds on (most cited first, 30 of 35)

- [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)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [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)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [Modeling polypharmacy side effects with graph convolutional networks](https://mlsanity.com/paper/1802.00543/) (2018)
- [The Surprising Power of Graph Neural Networks with Random Node Initialization](https://mlsanity.com/paper/2010.01179/) (2020)
- [Random Features Strengthen Graph Neural Networks](https://mlsanity.com/paper/2002.03155/) (2020)
- [Continuous Graph Neural Networks](https://mlsanity.com/paper/1912.00967/) (2019)
- [Geometric Matrix Completion with Recurrent Multi-Graph Neural Networks](https://mlsanity.com/paper/1704.06803/) (2017)
- [Scalable Graph Neural Networks via Bidirectional Propagation](https://mlsanity.com/paper/2010.15421/) (2020)
- [On Positional and Structural Node Features for Graph Neural Networks on Non-attributed Graphs](https://mlsanity.com/paper/2107.01495/) (2021)

## Built on by (most cited first, 30 of 63)

- [Data Augmentation for Deep Graph Learning: A Survey](https://mlsanity.com/paper/2202.08235/) (2022)
- [Learning to Reconstruct Missing Data from Spatiotemporal Graphs with Sparse Observations](https://mlsanity.com/paper/2205.13479/) (2022)
- [A Survey on Fairness for Machine Learning on Graphs](https://mlsanity.com/paper/2205.05396/) (2022)
- [Learnable Topological Features for Phylogenetic Inference via Graph Neural Networks](https://mlsanity.com/paper/2302.08840/) (2023)
- [Confidence-Based Feature Imputation for Graphs with Partially Known Features](https://mlsanity.com/paper/2305.16618/) (2023)
- [TouchUp-G: Improving Feature Representation through Graph-Centric Finetuning](https://mlsanity.com/paper/2309.13885/) (2023)
- [Recent Advances in Reliable Deep Graph Learning: Inherent Noise, Distribution Shift, and Adversarial Attack](https://mlsanity.com/paper/2202.07114/) (2022)
- [EGG-GAE: scalable graph neural networks for tabular data imputation](https://mlsanity.com/paper/2210.10446/) (2022)
- [Tractable Probabilistic Graph Representation Learning with Graph-Induced Sum-Product Networks](https://mlsanity.com/paper/2305.10544/) (2023)
- [Does Black-box Attribute Inference Attacks on Graph Neural Networks Constitute Privacy Risk?](https://mlsanity.com/paper/2306.00578/) (2023)
- [GRAFENNE: Learning on Graphs with Heterogeneous and Dynamic Feature Sets](https://mlsanity.com/paper/2306.03447/) (2023)
- [Supercharging Graph Transformers with Advective Diffusion](https://mlsanity.com/paper/2310.06417/) (2023)
- [Missing Value Imputation for Multi-attribute Sensor Data Streams via Message Propagation (Extended Version)](https://mlsanity.com/paper/2311.07344/) (2023)
- [Spatiotemporal Implicit Neural Representation as a Generalized Traffic Data Learner](https://mlsanity.com/paper/2405.03185/) (2024)
- [Uncertainty-Aware Robust Learning on Noisy Graphs](https://mlsanity.com/paper/2306.08210/) (2023)
- [Efficient Anatomical Labeling of Pulmonary Tree Structures via Deep Point-Graph Representation-based Implicit Fields](https://mlsanity.com/paper/2309.17329/) (2023)
- [Toward General and Robust LLM-enhanced Text-attributed Graph Learning](https://mlsanity.com/paper/2504.02343/) (2025)
- [Recovering Missing Node Features with Local Structure-based Embeddings](https://mlsanity.com/paper/2309.09068/) (2023)
- [AmGCL: Feature Imputation of Attribute Missing Graph via Self-supervised Contrastive Learning](https://mlsanity.com/paper/2305.03741/) (2023)
- [Network-wide Freeway Traffic Estimation Using Sparse Sensor Data: A Dirichlet Graph Auto-Encoder Approach](https://mlsanity.com/paper/2503.15845/) (2025)
- [Self-supervised Guided Hypergraph Feature Propagation for Semi-supervised Classification with Missing Node Features](https://mlsanity.com/paper/2302.08250/) (2023)
- [Enhanced Graph Neural Networks with Ego-Centric Spectral Subgraph Embeddings Augmentation](https://mlsanity.com/paper/2310.12169/) (2023)
- [Incomplete Graph Learning: A Comprehensive Survey](https://mlsanity.com/paper/2502.12412/) (2025)
- [Spatiotemporal Imputation with Graph-Informed Flow Matching](https://mlsanity.com/paper/2606.06682/) (2026)
- [TwERC: High Performance Ensembled Candidate Generation for Ads Recommendation at Twitter](https://mlsanity.com/paper/2302.13915/) (2023)
- [Gradient Flow of Energy: A General and Efficient Approach for Entity Alignment Decoding](https://mlsanity.com/paper/2401.12798/) (2024)
- [Augmenting Textual Generation via Topology Aware Retrieval](https://mlsanity.com/paper/2405.17602/) (2024)
- [Graph Your Own Prompt](https://mlsanity.com/paper/2509.23373/) (2025)
- [Rethinking GNNs and Missing Features: Challenges, Evaluation and a Robust Solution](https://mlsanity.com/paper/2601.04855/) (2026)
- [Designing weighted and multiplex networks for deep learning user geolocation in Twitter](https://mlsanity.com/paper/2112.06999/) (2021)

## Abstract (arXiv)

While Graph Neural Networks (GNNs) have recently become the de facto standard for modeling relational data, they impose a strong assumption on the availability of the node or edge features of the graph. In many real-world applications, however, features are only partially available; for example, in social networks, age and gender are available only for a small subset of users. We present a general approach for handling missing features in graph machine learning applications that is based on minimization of the Dirichlet energy and leads to a diffusion-type differential equation on the graph. The discretization of this equation produces a simple, fast and scalable algorithm which we call Feature Propagation. We experimentally show that the proposed approach outperforms previous methods on seven common node-classification benchmarks and can withstand surprisingly high rates of missing features: on average we observe only around 4% relative accuracy drop when 99% of the features are missing. Moreover, it takes only 10 seconds to run on a graph with ~2.5M nodes and ~123M edges on a single GPU.