# CIN++: Enhancing Topological Message Passing

arXiv: https://arxiv.org/abs/2306.03561 · HTML: https://mlsanity.com/paper/2306.03561/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 92 references that are in the map.
- First posted on arXiv 6 Jun 2023.

## Builds on (most cited first, 30 of 53)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [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)
- [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)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [Rethinking Graph Transformers with Spectral Attention](https://mlsanity.com/paper/2106.03893/) (2021)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Provably Powerful Graph Networks](https://mlsanity.com/paper/1905.11136/) (2019)
- [Residual Gated Graph ConvNets](https://mlsanity.com/paper/1711.07553/) (2017)
- [Invariant and Equivariant Graph Networks](https://mlsanity.com/paper/1812.09902/) (2018)
- [Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting](https://mlsanity.com/paper/2006.09252/) (2020)
- [Diffusion-Convolutional Neural Networks](https://mlsanity.com/paper/1511.02136/) (2015)
- [Long Range Graph Benchmark](https://mlsanity.com/paper/2206.08164/) (2022)
- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)

## Built on by (most cited first, 14 of 14)

- [Beyond Weisfeiler-Lehman: A Quantitative Framework for GNN Expressiveness](https://mlsanity.com/paper/2401.08514/) (2024)
- [Probabilistically Rewired Message-Passing Neural Networks](https://mlsanity.com/paper/2310.02156/) (2023)
- [E(n) Equivariant Topological Neural Networks](https://mlsanity.com/paper/2405.15429/) (2024)
- [Probabilistic Graph Rewiring via Virtual Nodes](https://mlsanity.com/paper/2405.17311/) (2024)
- [Can Graph Neural Networks Learn Language with Extremely Weak Text Supervision?](https://mlsanity.com/paper/2412.08174/) (2024)
- [Return of ChebNet: Understanding and Improving an Overlooked GNN on Long Range Tasks](https://mlsanity.com/paper/2506.07624/) (2025)
- [Weisfeiler and Lehman Go Paths: Learning Topological Features via Path Complexes](https://mlsanity.com/paper/2308.06838/) (2023)
- [Can You Hear Me Now? A Benchmark for Long-Range Graph Propagation](https://mlsanity.com/paper/2512.17762/) (2025)
- [Non-backtracking Graph Neural Networks](https://mlsanity.com/paper/2310.07430/) (2023)
- [What Expressivity Theory Misses: Message Passing Complexity for GNNs](https://mlsanity.com/paper/2509.01254/) (2025)
- [Topological Neural Networks: Mitigating the Bottlenecks of Graph Neural Networks via Higher-Order Interactions](https://mlsanity.com/paper/2402.06908/) (2024)
- [Directed Semi-Simplicial Learning with Applications to Brain Activity Decoding](https://mlsanity.com/paper/2505.17939/) (2025)
- [Explainable Graph Representation Learning via Graph Pattern Analysis](https://mlsanity.com/paper/2512.04530/) (2025)
- [Scaling Higher-Order Graph Learning with Maximal Clique Complexes](https://mlsanity.com/paper/2605.31373/) (2026)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have demonstrated remarkable success in learning from graph-structured data. However, they face significant limitations in expressive power, struggling with long-range interactions and lacking a principled approach to modeling higher-order structures and group interactions. Cellular Isomorphism Networks (CINs) recently addressed most of these challenges with a message passing scheme based on cell complexes. Despite their advantages, CINs make use only of boundary and upper messages which do not consider a direct interaction between the rings present in the underlying complex. Accounting for these interactions might be crucial for learning representations of many real-world complex phenomena such as the dynamics of supramolecular assemblies, neural activity within the brain, and gene regulation processes. In this work, we propose CIN++, an enhancement of the topological message passing scheme introduced in CINs. Our message passing scheme accounts for the aforementioned limitations by letting the cells to receive also lower messages within each layer. By providing a more comprehensive representation of higher-order and long-range interactions, our enhanced topological message passing scheme achieves state-of-the-art results on large-scale and long-range chemistry benchmarks.