Data-Driven Learning of Geometric Scattering Networks

Tong, Alexander; Wenkel, Frederik; Macdonald, Kincaid; Krishnaswamy, Smita; Wolf, Guy

doi:10.48550/arxiv.2010.02415

Cited by 2 publications

(5 citation statements)

References 17 publications

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“…Similar to Mallat [2012], the original formulations of the graph scattering transforms were fully designed networks using dyadic wavelets. However, subsequent work has incorporated learning via cross-channel convolutions [Min et al, 2020], attention mechanisms [Min et al, 2021], or by replacing dyadic-scales with scales learned from data [Tong et al, 2021]. Most closely to our work, [Zou and Lerman, 2019] and [Castro et al, 2020] have shown that the scattering transform can be incorporated into an encoder-decoder type network.…”

Section: Geometric Scatteringmentioning

confidence: 69%

“…We set the number of moments Q = 2 and the number of scales J = 4. Since our tranches ranged in molecular weight, we decided to use a learnable version of graph scattering proposed in Tong et al [2021] to individually learn diffusion scales for each tranche rather than just using dyadic powers 2 j . The learned wavelet coefficients for each of the three ZINC tranches can be seen in Figure 2.…”

Section: Resultsmentioning

confidence: 99%

“…This molecular generation network is trained with an adversarial loss as well as a latent interpolation loss that obviates the need for both the SIN and the variational training in GSAE. 3) We utilize a differentiable scattering transform Tong et al [2021] such that the scales of scattering are not fixed, but instead learned from the data. In the next section, we detail features of our network which we call GRASSY.…”

Section: Geometric Scattering Autoencodermentioning

confidence: 99%

“…Specifically, we define x Li (v j ) = 1 if the vertex v j has label L i and x Li (v j ) = 0 otherwise. We then perform multiscale wavelet transforms on each of these signals using a learnable scattering framework [Tong et al, 2021], and collect statistical moments by summing over the vertices (see Eqns. 3 and 4).…”

Section: Learned Scattering Momentsmentioning

confidence: 99%

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Molecular Graph Generation via Geometric Scattering

Bhaskar¹,

Grady²,

Perlmutter³

et al. 2021

Preprint

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Graph neural networks (GNNs) have been used extensively for addressing problems in drug design and discovery. Both ligand and target molecules are represented as graphs with node and edge features encoding information about atomic elements and bonds respectively. Although existing deep learning models perform remarkably well at predicting physicochemical properties and binding affinities, the generation of new molecules with optimized properties remains challenging. Inherently, most GNNs perform poorly in whole-graph representation due to the limitations of the message-passing paradigm. Furthermore, step-by-step graph generation frameworks that use reinforcement learning or other sequential processing can be slow and result in a high proportion of invalid molecules with substantial post-processing needed in order to satisfy the principles of stoichiometry. To address these issues, we propose a representation-first approach to molecular graph generation. We guide the latent representation of an autoencoder by capturing graph structure information with the geometric scattering transform and apply penalties that structure the representation also by molecular properties. We show that this highly structured latent space can be directly used for molecular graph generation by the use of a GAN. We demonstrate that our architecture learns meaningful representations of drug datasets and provides a platform for goal-directed drug synthesis.

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Section: Geometric Scatteringmentioning

confidence: 69%

Section: Resultsmentioning

confidence: 99%

Section: Geometric Scattering Autoencodermentioning

confidence: 99%

Section: Learned Scattering Momentsmentioning

confidence: 99%

See 2 more Smart Citations

Molecular Graph Generation via Geometric Scattering

Bhaskar¹,

Grady²,

Perlmutter³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…The practical utility of these networks has been established in [13], which primarily focuses on graph classification, and in [23], [24], [25], which used the graph scattering transform to generate molecules. Building off of these results, which use handcrafted formulations of the scattering transform, recent work [26] has proposed a framework for a datadriven tuning of the traditionally handcrafted geometric scattering design that maintains the theoretical properties from traditional designs, while also showing strong empirical results in whole-graph settings.…”

Section: Related Workmentioning

confidence: 99%

Overcoming Oversmoothness in Graph Convolutional Networks via Hybrid Scattering Networks

Wenkel¹,

Min²,

Hirn³

et al. 2022

Preprint

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Geometric deep learning (GDL) has made great strides towards generalizing the design of structure-aware neural network architectures from traditional domains to non-Euclidean ones, such as graphs. This gave rise to graph neural network (GNN) models that can be applied to graph-structured datasets arising, for example, in social networks, biochemistry, and material science. Graph convolutional networks (GCNs) in particular, inspired by their Euclidean counterparts, have been successful in processing graph data by extracting structure-aware features. However, current GNN models (and GCNs in particular) are known to be constrained by various phenomena that limit their expressive power and ability to generalize to more complex graph datasets. Most models essentially rely on low-pass filtering of graph signals via local averaging operations, thus leading to oversmoothing. Here, we propose a hybrid GNN framework that combines traditional GCN filters with band-pass filters defined via the geometric scattering transform. We further introduce an attention framework that allows the model to locally attend over the combined information from different GNN filters at the node level. Our theoretical results establish the complementary benefits of the scattering filters to leverage structural information from the graph, while our experiments show the benefits of our method on various learning tasks.

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Data-Driven Learning of Geometric Scattering Networks

Cited by 2 publications

References 17 publications

Molecular Graph Generation via Geometric Scattering

Molecular Graph Generation via Geometric Scattering

Overcoming Oversmoothness in Graph Convolutional Networks via Hybrid Scattering Networks

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