• Corpus ID: 222124894

Cell Complex Neural Networks

@article{Hajij2020CellCN,
  title={Cell Complex Neural Networks},
  author={Mustafa Hajij and Kyle Istvan and Ghada Zamzmi},
  journal={ArXiv},
  year={2020},
  volume={abs/2010.00743}
}
Cell complexes are topological spaces constructed from simple blocks called cells. They generalize graphs, simplicial complexes, and polyhedral complexes that form important domains for practical applications. We propose a general, combinatorial, and unifying construction for performing neural network-type computations on cell complexes. Furthermore, we introduce inter-cellular message passing schemes, message passing schemes on cell complexes that take the topology of the underlying space into… 
View PDF on arXiv
23 Citations
Highly Influential Citations
3
Background Citations
17
Methods Citations
7

Figures from this paper

23 Citations

Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks

Message Passing Simplicial Networks (MPSNs), a class of models that perform message passing on simplicial complexes (SCs) are proposed, and a Simplicial Weisfeiler-Lehman (SWL) colouring procedure is introduced for distinguishing non-isomorphic SCs.

Signal Processing On Cell Complexes

  • T. RoddenberryM. SchaubM. Hajij
  • Computer Science
    ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
  • 2022
An introduction to signal processing on (abstract) regular cell complexes, which provide a unifying framework encompassing graphs, simplicial complexes, cubical complexes and various meshes as special cases, and how appropriate Hodge Laplacians for these cell complexes can be derived.

Efficient Representation Learning for Higher-Order Data with Simplicial Complexes

It is shown that simplicial complexes with certain relaxations can more efficiently capture underlying higher-order structures than non-graph structure, regular graph, hypergraph, and traditional simplicial complex-based learning frameworks.

H IGH S KIP N ETWORKS : A H IGHER O RDER G ENERAL IZATION OF S KIP C ONNECTIONS

The preliminary results show that HSNs lead to a statistically significant improvement in the generalization error when compared to base models without high skip components.

Simplicial Complex Representation Learning

This work presents the first method that embeds a simplicial complex to a universal embedding space in a way that complex-to-complex proximity is preserved and utilizes a simplex-level embedding induced by a pre-trained simplicial autoencoder to learn an entire simplicialcomplex representation.

Convolutional Learning on Simplicial Complexes

We propose a simplicial complex convolutional neural network (SCCNN) to learn data representations on simplicial complexes. It performs convolutions based on the multi-hop simplicial adjacencies via…

Dirac signal processing of higher-order topological signals

Dirac signal processing is proposed, an adaptive, unsupervised signal processing algorithm that learns to jointly learn to jointly topological signals supported on nodes, links and triangles of simplicial complexes in a consistent way.

Semantic-Native Communication: A Simplicial Complex Perspective

Leveraging the topological nature of information, the proposed method is shown to be more reliable and efficient compared to several baselines, notably at low signal-to-noise (SNR) levels.

Pooling Strategies for Simplicial Convolutional Networks

A general formulation for a simplicial pooling layer that performs: i) local aggregation of simplicial signals; ii) principled selection of sampling sets; iii) downsampling and simplicial topology adaptation.

Weisfeiler and Leman Return with Graph Transformations

Novel graph transformations are proposed that are at least as expressive as corresponding message passing algorithms when combined with the Weisfeiler-Leman test or a sufficiently powerful graph neural network and empirically demonstrate that these transformations lead to competitive results on molecular graph datasets.

References

SHOWING 1-10 OF 56 REFERENCES

Semi-Supervised Classification with Graph Convolutional Networks

A scalable approach for semi-supervised learning on graph-structured data that is based on an efficient variant of convolutional neural networks which operate directly on graphs which outperforms related methods by a significant margin.

Algebraic Topology

The focus of this paper is a proof of the Nielsen-Schreier Theorem, stating that every subgroup of a free group is free, using tools from algebraic topology.

DeepWalk: online learning of social representations

DeepWalk is an online learning algorithm which builds useful incremental results, and is trivially parallelizable, which make it suitable for a broad class of real world applications such as network classification, and anomaly detection.

Simplicial 2-Complex Convolutional Neural Nets.

Recently, neural network architectures have been developed to accommodate when the data has the structure of a graph or, more generally, a hypergraph. While useful, graph structures can be…

K-simplex2vec: a Simplicial Extension of Node2vec

This method extends the node2vec algorithm to simplices of higher dimensions, providing insight into the structure of a simplicial complex, or into the higher-order interactions in a graph.

Simplicial Neural Networks

The SNNs are presented, a generalization of graph neural networks to data that live on a class of topological spaces called simplicial complexes, and an appropriate notion of convolution is defined that is leverage to construct the desired convolutional neural networks.

A Survey on Graph Neural Networks for Knowledge Graph Completion

This survey understands the various strengths and weaknesses of the proposed methodology and tries to find new exciting research problems in this area that require further investigation.

Improving the Accuracy, Scalability, and Performance of Graph Neural Networks with Roc

Accurate relational reasoning in edge-labeled graphs by multi-labeled random walk with restart

This paper introduces a labeled random surfer whose label indicates the relation between starting and visiting nodes, and changes the surfer’s label during random walks for multi-hop relational reasoning, and develops an iterative algorithm for computing MuRWR, which provides the best inference performance.

Deep Relational Reasoning Graph Network for Arbitrary Shape Text Detection

This paper proposes a novel unified relational reasoning graph network for arbitrary shape text detection through an innovative local graph that bridges a text proposal model via Convolutional Neural Network and a deep relational reasoning network via Graphconvolutional Network, making the network end-to-end trainable.
...