Graph Scattering beyond Wavelet Shackles
This work develops a flexible and mathematically sound framework for the design and analysis of graph scattering networks with variable branching ratios and generic functional calculus filters. Spectrally-agnostic stability guarantees for node- and graph-level perturbations are derived; the vertex-s...
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creator | Koke, Christian Kutyniok, Gitta |
description | This work develops a flexible and mathematically sound framework for the
design and analysis of graph scattering networks with variable branching ratios
and generic functional calculus filters. Spectrally-agnostic stability
guarantees for node- and graph-level perturbations are derived; the vertex-set
non-preserving case is treated by utilizing recently developed
mathematical-physics based tools. Energy propagation through the network layers
is investigated and related to truncation stability. New methods of graph-level
feature aggregation are introduced and stability of the resulting composite
scattering architectures is established. Finally, scattering transforms are
extended to edge- and higher order tensorial input. Theoretical results are
complemented by numerical investigations: Suitably chosen cattering networks
conforming to the developed theory perform better than traditional
graph-wavelet based scattering approaches in social network graph
classification tasks and significantly outperform other graph-based learning
approaches to regression of quantum-chemical energies on QM7. |
doi_str_mv | 10.48550/arxiv.2301.11456 |
format | Article |
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design and analysis of graph scattering networks with variable branching ratios
and generic functional calculus filters. Spectrally-agnostic stability
guarantees for node- and graph-level perturbations are derived; the vertex-set
non-preserving case is treated by utilizing recently developed
mathematical-physics based tools. Energy propagation through the network layers
is investigated and related to truncation stability. New methods of graph-level
feature aggregation are introduced and stability of the resulting composite
scattering architectures is established. Finally, scattering transforms are
extended to edge- and higher order tensorial input. Theoretical results are
complemented by numerical investigations: Suitably chosen cattering networks
conforming to the developed theory perform better than traditional
graph-wavelet based scattering approaches in social network graph
classification tasks and significantly outperform other graph-based learning
approaches to regression of quantum-chemical energies on QM7.</description><identifier>DOI: 10.48550/arxiv.2301.11456</identifier><language>eng</language><subject>Computer Science - Learning</subject><creationdate>2023-01</creationdate><rights>http://creativecommons.org/licenses/by-nc-nd/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2301.11456$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2301.11456$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Koke, Christian</creatorcontrib><creatorcontrib>Kutyniok, Gitta</creatorcontrib><title>Graph Scattering beyond Wavelet Shackles</title><description>This work develops a flexible and mathematically sound framework for the
design and analysis of graph scattering networks with variable branching ratios
and generic functional calculus filters. Spectrally-agnostic stability
guarantees for node- and graph-level perturbations are derived; the vertex-set
non-preserving case is treated by utilizing recently developed
mathematical-physics based tools. Energy propagation through the network layers
is investigated and related to truncation stability. New methods of graph-level
feature aggregation are introduced and stability of the resulting composite
scattering architectures is established. Finally, scattering transforms are
extended to edge- and higher order tensorial input. Theoretical results are
complemented by numerical investigations: Suitably chosen cattering networks
conforming to the developed theory perform better than traditional
graph-wavelet based scattering approaches in social network graph
classification tasks and significantly outperform other graph-based learning
approaches to regression of quantum-chemical energies on QM7.</description><subject>Computer Science - Learning</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzjsLwjAUhuEsDqL-ACc7urQmTU7SjFK8geCg4FhOm1Mt1iqxiP57r9MH7_DxMDYUPFIJAJ-gf1T3KJZcREIo0F02Xni8HoNtgW1LvmoOQU7PS-OCPd6ppjbYHrE41XTrs06J9Y0G_-2x3Xy2S5fherNYpdN1iNroEIxDBCWtsmANJyDDBaFOpLGayCnBFRV5jMo5K0ukEmJnSgHE83dNZI-Nfrdfanb11Rn9M_uQsy9ZvgDLszsX</recordid><startdate>20230126</startdate><enddate>20230126</enddate><creator>Koke, Christian</creator><creator>Kutyniok, Gitta</creator><scope>AKY</scope><scope>GOX</scope></search><sort><creationdate>20230126</creationdate><title>Graph Scattering beyond Wavelet Shackles</title><author>Koke, Christian ; Kutyniok, Gitta</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a676-57daa5439495970e5e701ea683796eed4104ecb2a4dd93faef52d7f15e0bb2a83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Computer Science - Learning</topic><toplevel>online_resources</toplevel><creatorcontrib>Koke, Christian</creatorcontrib><creatorcontrib>Kutyniok, Gitta</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Koke, Christian</au><au>Kutyniok, Gitta</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Graph Scattering beyond Wavelet Shackles</atitle><date>2023-01-26</date><risdate>2023</risdate><abstract>This work develops a flexible and mathematically sound framework for the
design and analysis of graph scattering networks with variable branching ratios
and generic functional calculus filters. Spectrally-agnostic stability
guarantees for node- and graph-level perturbations are derived; the vertex-set
non-preserving case is treated by utilizing recently developed
mathematical-physics based tools. Energy propagation through the network layers
is investigated and related to truncation stability. New methods of graph-level
feature aggregation are introduced and stability of the resulting composite
scattering architectures is established. Finally, scattering transforms are
extended to edge- and higher order tensorial input. Theoretical results are
complemented by numerical investigations: Suitably chosen cattering networks
conforming to the developed theory perform better than traditional
graph-wavelet based scattering approaches in social network graph
classification tasks and significantly outperform other graph-based learning
approaches to regression of quantum-chemical energies on QM7.</abstract><doi>10.48550/arxiv.2301.11456</doi><oa>free_for_read</oa></addata></record> |
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subjects | Computer Science - Learning |
title | Graph Scattering beyond Wavelet Shackles |
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