# Position: Topological Deep Learning is the New Frontier for Relational Learning

arXiv: https://arxiv.org/abs/2402.08871 · HTML: https://mlsanity.com/paper/2402.08871/

## Key facts

- Cited by 66 papers in the map (data through 14 Oct 2026).
- Builds on 147 of its 250 references that are in the map.
- First posted on arXiv 14 Feb 2024.

## Builds on (most cited first, 30 of 147)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [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)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020)
- [LION: Latent Point Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2210.06978/) (2022)
- [Graph Transformer Networks](https://mlsanity.com/paper/1911.06455/) (2019)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [Parameterized Explainer for Graph Neural Network](https://mlsanity.com/paper/2011.04573/) (2020)
- [OGB-LSC: A Large-Scale Challenge for Machine Learning on Graphs](https://mlsanity.com/paper/2103.09430/) (2021)
- [Torsional Diffusion for Molecular Conformer Generation](https://mlsanity.com/paper/2206.01729/) (2022)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [Hypergraph Convolution and Hypergraph Attention](https://mlsanity.com/paper/1901.08150/) (2019)
- [SE(3) diffusion model with application to protein backbone generation](https://mlsanity.com/paper/2302.02277/) (2023)
- [Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs](https://mlsanity.com/paper/2202.04579/) (2022)
- [MeshDiffusion: Score-based Generative 3D Mesh Modeling](https://mlsanity.com/paper/2303.08133/) (2023)
- [Topology-Preserving Deep Image Segmentation](https://mlsanity.com/paper/1906.05404/) (2019)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)

## Built on by (most cited first, 30 of 66)

- [TopoBench: A Framework for Benchmarking Topological Deep Learning](https://mlsanity.com/paper/2406.06642/) (2024)
- [A Survey on Hypergraph Neural Networks: An In-Depth and Step-By-Step Guide](https://mlsanity.com/paper/2404.01039/) (2024)
- [MANTRA: The Manifold Triangulations Assemblage](https://mlsanity.com/paper/2410.02392/) (2024)
- [Copresheaf Topological Neural Networks: A Generalized Deep Learning Framework](https://mlsanity.com/paper/2505.21251/) (2025)
- [HOG-Diff: Higher-Order Guided Diffusion for Graph Generation](https://mlsanity.com/paper/2502.04308/) (2025)
- [Diss-l-ECT: Dissecting Graph Data with Local Euler Characteristic Transforms](https://mlsanity.com/paper/2410.02622/) (2024)
- [The Flood Complex: Large-Scale Persistent Homology on Millions of Points](https://mlsanity.com/paper/2509.22432/) (2025)
- [Higher-Order Topological Directionality and Directed Simplicial Neural Networks](https://mlsanity.com/paper/2409.08389/) (2024)
- [Bayesian Sheaf Neural Networks](https://mlsanity.com/paper/2410.09590/) (2024)
- [Topological Flow Matching](https://mlsanity.com/paper/2606.15897/) (2026)
- [Demystifying Higher-Order Graph Neural Networks](https://mlsanity.com/paper/2406.12841/) (2024)
- [Topology meets Machine Learning: An Introduction using the Euler Characteristic Transform](https://mlsanity.com/paper/2410.17760/) (2024)
- [Manifold Topological Deep Learning for Biomedical Data](https://mlsanity.com/paper/2503.00175/) (2025)
- [Topological Schr"odinger Bridge Matching](https://mlsanity.com/paper/2504.04799/) (2025)
- [Topological Neural Operators](https://mlsanity.com/paper/2606.09806/) (2026)
- [Persistent de Rham-Hodge Laplacians in Eulerian representation for manifold topological learning](https://mlsanity.com/paper/2408.00220/) (2024)
- [ICML Topological Deep Learning Challenge 2024: Beyond the Graph Domain](https://mlsanity.com/paper/2409.05211/) (2024)
- [Graph Classification Gaussian Processes via Hodgelet Spectral Features](https://mlsanity.com/paper/2410.10546/) (2024)
- [On topological descriptors for graph products](https://mlsanity.com/paper/2511.08846/) (2025)
- [Topology-Preserving Neural Operator Learning via Hodge Decomposition](https://mlsanity.com/paper/2605.13834/) (2026)
- [Rapid and Precise Topological Comparison with Merge Tree Neural Networks](https://mlsanity.com/paper/2404.05879/) (2024)
- [Point Cloud Synthesis Using Inner Product Transforms](https://mlsanity.com/paper/2410.18987/) (2024)
- [Topological Data Analysis Applications in Natural Language Processing: A Survey](https://mlsanity.com/paper/2411.10298/) (2024)
- [Continuous Simplicial Neural Networks](https://mlsanity.com/paper/2503.12919/) (2025)
- [Graph Persistence goes Spectral](https://mlsanity.com/paper/2506.06571/) (2025)
- [Demystifying Topological Message-Passing with Relational Structures: A Case Study on Oversquashing in Simplicial Message-Passing](https://mlsanity.com/paper/2506.06582/) (2025)
- [LEAP: Local ECT-Based Learnable Positional Encodings for Graphs](https://mlsanity.com/paper/2510.00757/) (2025)
- [MonSTeR: a Unified Model for Motion, Scene, Text Retrieval](https://mlsanity.com/paper/2510.03200/) (2025)
- [The Logical Expressiveness of Topological Neural Networks](https://mlsanity.com/paper/2604.19212/) (2026)
- [Towards Scalable Topological Regularizers](https://mlsanity.com/paper/2501.14641/) (2025)

## Abstract (arXiv)

Topological deep learning (TDL) is a rapidly evolving field that uses topological features to understand and design deep learning models. This paper posits that TDL is the new frontier for relational learning. TDL may complement graph representation learning and geometric deep learning by incorporating topological concepts, and can thus provide a natural choice for various machine learning settings. To this end, this paper discusses open problems in TDL, ranging from practical benefits to theoretical foundations. For each problem, it outlines potential solutions and future research opportunities. At the same time, this paper serves as an invitation to the scientific community to actively participate in TDL research to unlock the potential of this emerging field.