# Tensor Convolutional Network for Higher-Order Interaction Prediction in Sparse Tensors

arXiv: https://arxiv.org/abs/2503.11786 · HTML: https://mlsanity.com/paper/2503.11786/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 61 references that are in the map.
- First posted on arXiv 14 Mar 2025.

## Builds on (most cited first, 22 of 22)

- [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)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [TuckER: Tensor Factorization for Knowledge Graph Completion](https://mlsanity.com/paper/1901.09590/) (2019)
- [Hypergraph Convolution and Hypergraph Attention](https://mlsanity.com/paper/1901.08150/) (2019)
- [Tensor Decompositions for temporal knowledge base completion](https://mlsanity.com/paper/2004.04926/) (2020)
- [Hyper-SAGNN: a self-attention based graph neural network for hypergraphs](https://mlsanity.com/paper/1911.02613/) (2019)
- [Anti-Symmetric DGN: a stable architecture for Deep Graph Networks](https://mlsanity.com/paper/2210.09789/) (2022)
- [Generalizing Tensor Decomposition for N-ary Relational Knowledge Bases](https://mlsanity.com/paper/2007.03988/) (2020)
- [Network of Tensor Time Series](https://mlsanity.com/paper/2102.07736/) (2021)
- [How Much and When Do We Need Higher-order Information in Hypergraphs? A Case Study on Hyperedge Prediction](https://mlsanity.com/paper/2001.11181/) (2020)
- [Scalable Tucker Factorization for Sparse Tensors - Algorithms and Discoveries](https://mlsanity.com/paper/1710.02261/) (2017)
- [AHP: Learning to Negative Sample for Hyperedge Prediction](https://mlsanity.com/paper/2204.06353/) (2022)
- [On the Persistence of Higher-Order Interactions in Real-World Hypergraphs](https://mlsanity.com/paper/2201.00972/) (2022)

## Abstract (arXiv)

Many real-world data, such as recommendation data and temporal graphs, can be represented as incomplete sparse tensors where most entries are unobserved. For such sparse tensors, identifying the top-k higher-order interactions that are most likely to occur among unobserved ones is crucial. Tensor factorization (TF) has gained significant attention in various tensor-based applications, serving as an effective method for finding these top-k potential interactions. However, existing TF methods primarily focus on effectively fusing latent vectors of entities, which limits their expressiveness. Since most entities in sparse tensors have only a few interactions, their latent representations are often insufficiently trained. In this paper, we propose TCN, an accurate and compatible tensor convolutional network that integrates seamlessly with existing TF methods for predicting higher-order interactions. We design a highly effective encoder to generate expressive latent vectors of entities. To achieve this, we propose to (1) construct a graph structure derived from a sparse tensor and (2) develop a relation-aware encoder, TCN, that learns latent representations of entities by leveraging the graph structure. Since TCN complements traditional TF methods, we seamlessly integrate TCN with existing TF methods, enhancing the performance of predicting top-k interactions. Extensive experiments show that TCN integrated with a TF method outperforms competitors, including TF methods and a hyperedge prediction method. Moreover, TCN is broadly compatible with various TF methods and GNNs (Graph Neural Networks), making it a versatile solution.