# MANTRA: The Manifold Triangulations Assemblage

arXiv: https://arxiv.org/abs/2410.02392 · HTML: https://mlsanity.com/paper/2410.02392/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 67 references that are in the map.
- First posted on arXiv 3 Oct 2024.

## Builds on (most cited first, 30 of 40)

- [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)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [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)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classification](https://mlsanity.com/paper/2009.03509/) (2020)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [A Fair Comparison of Graph Neural Networks for Graph Classification](https://mlsanity.com/paper/1912.09893/) (2019)
- [Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere](https://mlsanity.com/paper/2306.03838/) (2023)
- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [Topology Adaptive Graph Convolutional Networks](https://mlsanity.com/paper/1710.10370/) (2017)
- [Topological Deep Learning: Going Beyond Graph Data](https://mlsanity.com/paper/2206.00606/) (2022)
- [Simplicial Closure and higher-order link prediction](https://mlsanity.com/paper/1802.06916/) (2018)
- [Self-Supervised Generalisation with Meta Auxiliary Learning](https://mlsanity.com/paper/1901.08933/) (2019)
- [Topological Graph Neural Networks](https://mlsanity.com/paper/2102.07835/) (2021)
- [Where Did the Gap Go? Reassessing the Long-Range Graph Benchmark](https://mlsanity.com/paper/2309.00367/) (2023)
- [Attending to Graph Transformers](https://mlsanity.com/paper/2302.04181/) (2023)
- [Position: Topological Deep Learning is the New Frontier for Relational Learning](https://mlsanity.com/paper/2402.08871/) (2024)
- [Convolutional Learning on Simplicial Complexes](https://mlsanity.com/paper/2301.11163/) (2023)
- [Graph Neural Networks Use Graphs When They Shouldn't](https://mlsanity.com/paper/2309.04332/) (2023)
- [Geometry-aware Bayesian Optimization in Robotics using Riemannian Mat'ern Kernels](https://mlsanity.com/paper/2111.01460/) (2021)
- [TopoBench: A Framework for Benchmarking Topological Deep Learning](https://mlsanity.com/paper/2406.06642/) (2024)
- [Two's company, three (or more) is a simplex: Algebraic-topological tools for understanding higher-order structure in neural data](https://mlsanity.com/paper/1601.01704/) (2016)
- [Deep Graph Mapper: Seeing Graphs through the Neural Lens](https://mlsanity.com/paper/2002.03864/) (2020)
- [Going beyond persistent homology using persistent homology](https://mlsanity.com/paper/2311.06152/) (2023)
- [TopoX: A Suite of Python Packages for Machine Learning on Topological Domains](https://mlsanity.com/paper/2402.02441/) (2024)
- [E(n) Equivariant Topological Neural Networks](https://mlsanity.com/paper/2405.15429/) (2024)
- [On the Expressivity of Persistent Homology in Graph Learning](https://mlsanity.com/paper/2302.09826/) (2023)

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

- [HOPSE: Scalable Higher-Order Positional and Structural Encoder for Combinatorial Representations](https://mlsanity.com/paper/2505.15405/) (2025)
- [Graph Classification Gaussian Processes via Hodgelet Spectral Features](https://mlsanity.com/paper/2410.10546/) (2024)
- [Point Cloud Synthesis Using Inner Product Transforms](https://mlsanity.com/paper/2410.18987/) (2024)
- [LEAP: Local ECT-Based Learnable Positional Encodings for Graphs](https://mlsanity.com/paper/2510.00757/) (2025)
- [Have Graph -- Will Lift? The Case for Higher-Order Benchmarks](https://mlsanity.com/paper/2605.07397/) (2026)
- [Graph and Simplicial Complex Prediction Gaussian Process via the Hodgelet Representations](https://mlsanity.com/paper/2505.10877/) (2025)
- [Measuring Structure in Graph Benchmark Datasets Using Graph Invariants](https://mlsanity.com/paper/2605.06462/) (2026)
- [Directed Semi-Simplicial Learning with Applications to Brain Activity Decoding](https://mlsanity.com/paper/2505.17939/) (2025)
- [Geometry-Aware Simplicial Message Passing](https://mlsanity.com/paper/2605.06061/) (2026)
- [Diversity Curves for Graph Representation Learning](https://mlsanity.com/paper/2605.06466/) (2026)
- [No Triangulation Without Representation: Generalization in Topological Deep Learning](https://mlsanity.com/paper/2605.06467/) (2026)
- [Look Before You Lift: Visual and Quantitative Diagnostics for Topological Deep Learning](https://mlsanity.com/paper/2608.15388/) (2026)

## Abstract (arXiv)

The rising interest in leveraging higher-order interactions present in complex systems has led to a surge in more expressive models exploiting higher-order structures in the data, especially in topological deep learning (TDL), which designs neural networks on higher-order domains such as simplicial complexes. However, progress in this field is hindered by the scarcity of datasets for benchmarking these architectures. To address this gap, we introduce MANTRA, the first large-scale, diverse, and intrinsically higher-order dataset for benchmarking higher-order models, comprising over 43,000 and 250,000 triangulations of surfaces and three-dimensional manifolds, respectively. With MANTRA, we assess several graph- and simplicial complex-based models on three topological classification tasks. We demonstrate that while simplicial complex-based neural networks generally outperform their graph-based counterparts in capturing simple topological invariants, they also struggle, suggesting a rethink of TDL. Thus, MANTRA serves as a benchmark for assessing and advancing topological methods, leading the way for more effective higher-order models.