# What Can We Learn From MIMO Graph Convolutions?

arXiv: https://arxiv.org/abs/2505.11346 · HTML: https://mlsanity.com/paper/2505.11346/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 43 references that are in the map.
- First posted on arXiv 16 May 2025.

## Builds on (most cited first, 30 of 32)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [Rethinking Graph Transformers with Spectral Attention](https://mlsanity.com/paper/2106.03893/) (2021)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [OGB-LSC: A Large-Scale Challenge for Machine Learning on Graphs](https://mlsanity.com/paper/2103.09430/) (2021)
- [Long Range Graph Benchmark](https://mlsanity.com/paper/2206.08164/) (2022)
- [Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs](https://mlsanity.com/paper/2202.04579/) (2022)
- [CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters](https://mlsanity.com/paper/1705.07664/) (2017)
- [Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks](https://mlsanity.com/paper/2102.06462/) (2021)
- [Revisiting Heterophily For Graph Neural Networks](https://mlsanity.com/paper/2210.07606/) (2022)
- [Where Did the Gap Go? Reassessing the Long-Range Graph Benchmark](https://mlsanity.com/paper/2309.00367/) (2023)
- [Sheaf Neural Networks](https://mlsanity.com/paper/2012.06333/) (2020)
- [Gradient Gating for Deep Multi-Rate Learning on Graphs](https://mlsanity.com/paper/2210.00513/) (2022)
- [Replacing softmax with ReLU in Vision Transformers](https://mlsanity.com/paper/2309.08586/) (2023)
- [Feature Overcorrelation in Deep Graph Neural Networks: A New Perspective](https://mlsanity.com/paper/2206.07743/) (2022)
- [Rank Collapse Causes Over-Smoothing and Over-Correlation in Graph Neural Networks](https://mlsanity.com/paper/2308.16800/) (2023)
- [Transforming PageRank into an Infinite-Depth Graph Neural Network](https://mlsanity.com/paper/2207.00684/) (2022)
- [Convolutional Learning on Multigraphs](https://mlsanity.com/paper/2209.11354/) (2022)
- [Preventing Representational Rank Collapse in MPNNs by Splitting the Computational Graph](https://mlsanity.com/paper/2409.11504/) (2024)
- [Simplifying the Theory on Over-Smoothing](https://mlsanity.com/paper/2407.11876/) (2024)

## Built on by (most cited first, 1 of 1)

- [Full-Spectrum Graph Neural Networks: Expressive and Scalable](https://mlsanity.com/paper/2605.05759/) (2026)

## Abstract (arXiv)

Most graph neural networks (GNNs) utilize approximations of the general graph convolution derived in the graph Fourier domain. While GNNs are typically applied in the multi-input multi-output (MIMO) case, the approximations are performed in the single-input single-output (SISO) case. In this work, we first derive the MIMO graph convolution through the convolution theorem and approximate it directly in the MIMO case. We find the key MIMO-specific property of the graph convolution to be operating on multiple computational graphs, or equivalently, applying distinct feature transformations for each pair of nodes. As a localized approximation, we introduce localized MIMO graph convolutions (LMGCs), which generalize many linear message-passing neural networks. For almost every choice of edge weights, we prove that LMGCs with a single computational graph are injective on multisets, and the resulting representations are linearly independent when more than one computational graph is used. Our experimental results confirm that an LMGC can combine the benefits of various methods.