# From Latent Graph to Latent Topology Inference: Differentiable Cell Complex Module

arXiv: https://arxiv.org/abs/2305.16174 · HTML: https://mlsanity.com/paper/2305.16174/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 55 references that are in the map.
- First posted on arXiv 25 May 2023.

## Builds on (most cited first, 30 of 48)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Graph Structure Learning for Robust Graph Neural Networks](https://mlsanity.com/paper/2005.10203/) (2020)
- [Learning Discrete Structures for Graph Neural Networks](https://mlsanity.com/paper/1903.11960/) (2019)
- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [Weisfeiler and Lehman Go Cellular: CW Networks](https://mlsanity.com/paper/2106.12575/) (2021)
- [Iterative Deep Graph Learning for Graph Neural Networks: Better and Robust Node Embeddings](https://mlsanity.com/paper/2006.13009/) (2020)
- [Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs](https://mlsanity.com/paper/2202.04579/) (2022)
- [Sparse Sequence-to-Sequence Models](https://mlsanity.com/paper/1905.05702/) (2019)
- [Adaptively Sparse Transformers](https://mlsanity.com/paper/1909.00015/) (2019)
- [Simplicial Neural Networks](https://mlsanity.com/paper/2010.03633/) (2020)
- [Implicit MLE: Backpropagating Through Discrete Exponential Family Distributions](https://mlsanity.com/paper/2106.01798/) (2021)
- [Topological Deep Learning: Going Beyond Graph Data](https://mlsanity.com/paper/2206.00606/) (2022)
- [Topological Signal Processing over Simplicial Complexes](https://mlsanity.com/paper/1907.11577/) (2019)
- [Neural Algorithmic Reasoning](https://mlsanity.com/paper/2105.02761/) (2021)
- [Differentiable Graph Module (DGM) for Graph Convolutional Networks](https://mlsanity.com/paper/2002.04999/) (2020)
- [Sheaf Neural Networks](https://mlsanity.com/paper/2012.06333/) (2020)
- [Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond](https://mlsanity.com/paper/2101.05510/) (2021)
- [Principled Simplicial Neural Networks for Trajectory Prediction](https://mlsanity.com/paper/2102.10058/) (2021)
- [FairDrop: Biased Edge Dropout for Enhancing Fairness in Graph Representation Learning](https://mlsanity.com/paper/2104.14210/) (2021)
- [Cell Complex Neural Networks](https://mlsanity.com/paper/2010.00743/) (2020)

## Built on by (most cited first, 19 of 19)

- [Position: Topological Deep Learning is the New Frontier for Relational Learning](https://mlsanity.com/paper/2402.08871/) (2024)
- [TopoBench: A Framework for Benchmarking Topological Deep Learning](https://mlsanity.com/paper/2406.06642/) (2024)
- [E(n) Equivariant Topological Neural Networks](https://mlsanity.com/paper/2405.15429/) (2024)
- [Attending to Topological Spaces: The Cellular Transformer](https://mlsanity.com/paper/2405.14094/) (2024)
- [Neural Snowflakes: Universal Latent Graph Inference via Trainable Latent Geometries](https://mlsanity.com/paper/2310.15003/) (2023)
- [Representing Edge Flows on Graphs via Sparse Cell Complexes](https://mlsanity.com/paper/2309.01632/) (2023)
- [Topological Dictionary Learning](https://mlsanity.com/paper/2503.11470/) (2025)
- [ICML Topological Deep Learning Challenge 2024: Beyond the Graph Domain](https://mlsanity.com/paper/2409.05211/) (2024)
- [SPHINX: Structural Prediction using Hypergraph Inference Network](https://mlsanity.com/paper/2410.03208/) (2024)
- [Heterogeneous Graph Structure Learning through the Lens of Data-generating Processes](https://mlsanity.com/paper/2503.08760/) (2025)
- [Topological Adaptive Least Mean Squares Algorithms over Simplicial Complexes](https://mlsanity.com/paper/2505.23160/) (2025)
- [Topological Graph Signal Compression](https://mlsanity.com/paper/2308.11068/) (2023)
- [Machine Learning and Data Analysis Using Posets: A Survey](https://mlsanity.com/paper/2404.03082/) (2024)
- [Directed Semi-Simplicial Learning with Applications to Brain Activity Decoding](https://mlsanity.com/paper/2505.17939/) (2025)
- [Gumbel-MPNN: Graph Rewiring with Gumbel-Softmax](https://mlsanity.com/paper/2508.17531/) (2025)
- [Faster Inference of Cell Complexes from Flows via Matrix Factorization](https://mlsanity.com/paper/2508.21372/) (2025)
- [Weisfeiler Lehman Test on Combinatorial Complexes: Generalized Expressive Power of Topological Neural Networks](https://mlsanity.com/paper/2605.00725/) (2026)
- [Differentiable Lifting for Topological Neural Networks](https://mlsanity.com/paper/2608.01160/) (2026)
- [From topology learning to graph generation: A unifying perspective](https://mlsanity.com/paper/2609.02286/) (2026)

## Abstract (arXiv)

Latent Graph Inference (LGI) relaxed the reliance of Graph Neural Networks (GNNs) on a given graph topology by dynamically learning it. However, most of LGI methods assume to have a (noisy, incomplete, improvable, ...) input graph to rewire and can solely learn regular graph topologies. In the wake of the success of Topological Deep Learning (TDL), we study Latent Topology Inference (LTI) for learning higher-order cell complexes (with sparse and not regular topology) describing multi-way interactions between data points. To this aim, we introduce the Differentiable Cell Complex Module (DCM), a novel learnable function that computes cell probabilities in the complex to improve the downstream task. We show how to integrate DCM with cell complex message passing networks layers and train it in a end-to-end fashion, thanks to a two-step inference procedure that avoids an exhaustive search across all possible cells in the input, thus maintaining scalability. Our model is tested on several homophilic and heterophilic graph datasets and it is shown to outperform other state-of-the-art techniques, offering significant improvements especially in cases where an input graph is not provided.