Overcoming Oversmoothness in Graph Convolutional Networks via Hybrid Scattering Networks

Wenkel, Frederik; Min, Yimeng; Hirn, Matthew; Perlmutter, Michael; Wolf, Guy

doi:10.48550/arxiv.2201.08932

Cited by 2 publications

(3 citation statements)

References 28 publications

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“…The numerical effectiveness of the graph scattering transform for tasks such as node classification, graph classification, and even graph synthesis has been demonstrated in numerous works such as [32,31,78,72,77] and [1]. However, the numerical effectiveness of the manifold scattering transform is much less well established.…”

Section: Numerical Resultsmentioning

confidence: 99%

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Geometric Scattering on Measure Spaces

Chew¹,

Hirn²,

Krishnaswamy³

et al. 2022

Preprint

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The scattering transform is a multilayered, wavelet-based transform initially introduced as a mathematical model of convolutional neural networks (CNNs) that has played a foundational role in our understanding of these networks' stability and invariance properties. In subsequent years, there has been widespread interest in extending the success of CNNs to data sets with non-Euclidean structure, such as graphs and manifolds, leading to the emerging field of geometric deep learning. In order to improve our understanding of the architectures used in this new field, several papers have proposed generalizations of the scattering transform for non-Euclidean data structures such as undirected graphs and compact Riemannian manifolds without boundary. Analogous to the original scattering transform, these works prove that these variants of the scattering transform have desirable stability and invariance properties and aim to improve our understanding of the neural networks used in geometric deep learning.In this paper, we introduce a general, unified model for geometric scattering on measure spaces. Our proposed framework includes previous work on compact Riemannian manifolds without boundary and undirected graphs as special cases but also applies to more general settings such as directed graphs, signed graphs, and manifolds with boundary. We propose a new criterion that identifies to which groups a useful representation should be invariant and show that this criterion is sufficient to guarantee that the scattering transform has desirable stability and invariance properties. Additionally, we consider finite measure spaces that are obtained from randomly sampling an unknown manifold. We propose two methods for constructing a data-driven graph on which the associated graph scattering transform approximates the scattering transform on the underlying manifold. Moreover, we use a diffusion-maps based approach to prove quantitative estimates on the rate of convergence of one of these approximations as the number of sample points tends to infinity. Lastly, we showcase the utility of our method on spherical images, a directed graph stochastic block model, and on high-dimensional single-cell data.

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Section: Numerical Resultsmentioning

confidence: 99%

“…Motivated by the so-called residual convolution operators used in [72], for improved numerical performance, we use a modified version of the windowed scattering transform given by S res…”

Section: By Construction Both L (Q)mentioning

confidence: 99%

Geometric Scattering on Measure Spaces

Chew¹,

Hirn²,

Krishnaswamy³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…The GNN used to compute p is based on the method introduced in [29]. In each layer, the network uses two types of filters: (i) low-pass filters inspired by Kipf and Welling's Graph Convolutional Network (GCN) [9] and (ii) band-pass wavelet filters inspired by the geometric scattering transform [6] (see also [5,32]).…”

Section: Inferring the Objective Functionmentioning

confidence: 99%

Inferring Metabolic States from Single Cell Transcriptomic Data via Geometric Deep Learning

Steach,

Viswanath,

et al. 2023

Preprint

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The ability to measure gene expression at single-cell resolution has elevated our understanding of how biological features emerge from complex and interdependent networks at molecular, cellular, and tissue scales. As technologies have evolved that complement scRNAseq measurements with things like single-cell proteomic, epigenomic, and genomic information, it becomes increasingly apparent how much biology exists as a product of multimodal regulation. Biological processes such as transcription, translation, and post-translational or epigenetic modification impose both energetic and specific molecular demands on a cell and are therefore implicitly constrained by the metabolic state of the cell. While metabolomics is crucial for defining a holistic model of any biological process, the chemical heterogeneity of the metabolome makes it particularly difficult to measure, and technologies capable of doing this at single-cell resolution are far behind other multiomics modalities. To address these challenges, we present GEFMAP (Gene Expression-based Flux Mapping and Metabolic Pathway Prediction), a method based on geometric deep learning for predicting flux through reactions in a global metabolic network using transcriptomics data, which we ultimately apply to scRNAseq. GEFMAP leverages the natural graph structure of metabolic networks to learn both a biological objective for each cell and estimate a mass-balanced relative flux rate for each reaction in each cell using novel deep learning models.

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Overcoming Oversmoothness in Graph Convolutional Networks via Hybrid Scattering Networks

Cited by 2 publications

References 28 publications

Geometric Scattering on Measure Spaces

Geometric Scattering on Measure Spaces

Inferring Metabolic States from Single Cell Transcriptomic Data via Geometric Deep Learning

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