# Tensor-view Topological Graph Neural Network

arXiv: https://arxiv.org/abs/2401.12007 · HTML: https://mlsanity.com/paper/2401.12007/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 76 references that are in the map.
- First posted on arXiv 22 Jan 2024.

## Builds on (most cited first, 30 of 41)

- [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)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [T-GCN: A Temporal Graph ConvolutionalNetwork for Traffic Prediction](https://mlsanity.com/paper/1811.05320/) (2018)
- [Deep Learning on Graphs: A Survey](https://mlsanity.com/paper/1812.04202/) (2018)
- [Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generation](https://mlsanity.com/paper/1806.02473/) (2018)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [Graph Learning: A Survey](https://mlsanity.com/paper/2105.00696/) (2021)
- [PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures](https://mlsanity.com/paper/1904.09378/) (2019)
- [Deep Learning with Topological Signatures](https://mlsanity.com/paper/1707.04041/) (2017)
- [Towards Sparse Hierarchical Graph Classifiers](https://mlsanity.com/paper/1811.01287/) (2018)
- [On the Expressive Power of Deep Learning: A Tensor Analysis](https://mlsanity.com/paper/1509.05009/) (2015)
- [Graph Convolutional Networks with EigenPooling](https://mlsanity.com/paper/1904.13107/) (2019)
- [Topological Graph Neural Networks](https://mlsanity.com/paper/2102.07835/) (2021)
- [A Stable Multi-Scale Kernel for Topological Machine Learning](https://mlsanity.com/paper/1412.6821/) (2014)
- [Does GNN Pretraining Help Molecular Representation?](https://mlsanity.com/paper/2207.06010/) (2022)
- [Tensor SVD: Statistical and Computational Limits](https://mlsanity.com/paper/1703.02724/) (2017)
- [Graph Neural Networks: Taxonomy, Advances and Trends](https://mlsanity.com/paper/2012.08752/) (2020)
- [Tensor Regression Networks](https://mlsanity.com/paper/1707.08308/) (2017)

## Built on by (most cited first, 12 of 12)

- [RTD-Lite: Scalable Topological Analysis for Comparing Weighted Graphs in Learning Tasks](https://mlsanity.com/paper/2503.11910/) (2025)
- [Conditional Prediction ROC Bands for Graph Classification](https://mlsanity.com/paper/2410.15239/) (2024)
- [Conditional Uncertainty Quantification for Tensorized Topological Neural Networks](https://mlsanity.com/paper/2410.15241/) (2024)
- [Tensor-Fused Multi-View Graph Contrastive Learning](https://mlsanity.com/paper/2410.15247/) (2024)
- [PHLP: Sole Persistent Homology for Link Prediction - Interpretable Feature Extraction](https://mlsanity.com/paper/2404.15225/) (2024)
- [Topological Alignment of Shared Vision-Language Embedding Space](https://mlsanity.com/paper/2510.10889/) (2025)
- [Tucker Diffusion Model for High-dimensional Tensor Generation](https://mlsanity.com/paper/2604.00481/) (2026)
- [TEAFormers: TEnsor-Augmented Transformers for Multi-Dimensional Time Series Forecasting](https://mlsanity.com/paper/2410.20439/) (2024)
- [Topological Eigenvalue Theorems for Tensor Analysis in Multi-Modal Data Fusion](https://mlsanity.com/paper/2409.09392/) (2024)
- [Frequent subgraph-based persistent homology for graph classification](https://mlsanity.com/paper/2512.24917/) (2025)
- [Dual-Channel Tensor Neural Networks: Finite-Sample Theory and Conformal Structure Selection](https://mlsanity.com/paper/2605.19122/) (2026)
- [Signed Graph Pre-Training and Prompt Learning](https://mlsanity.com/paper/2609.25722/) (2026)

## Abstract (arXiv)

Graph classification is an important learning task for graph-structured data. Graph neural networks (GNNs) have recently gained growing attention in graph learning and have shown significant improvements in many important graph problems. Despite their state-of-the-art performances, existing GNNs only use local information from a very limited neighborhood around each node, suffering from loss of multi-modal information and overheads of excessive computation. To address these issues, we propose a novel Tensor-view Topological Graph Neural Network (TTG-NN), a class of simple yet effective topological deep learning built upon persistent homology, graph convolution, and tensor operations. This new method incorporates tensor learning to simultaneously capture Tensor-view Topological (TT), as well as Tensor-view Graph (TG) structural information on both local and global levels. Computationally, to fully exploit graph topology and structure, we propose two flexible TT and TG representation learning modules that disentangle feature tensor aggregation and transformation and learn to preserve multi-modal structure with less computation. Theoretically, we derive high probability bounds on both the out-of-sample and in-sample mean squared approximation errors for our proposed Tensor Transformation Layer (TTL). Real data experiments show that the proposed TTG-NN outperforms 20 state-of-the-art methods on various graph benchmarks.