Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature | Paper Citation Record

Observation ad21a69c-e908-4d69-9d29-b5a1a93a5f1a · outbound

This paper cites Which graph shift operator? a spectral answer to an empirical question.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Which graph shift operator? a spectral answer to an empirical question

Reference 1

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Observation df294380-e60f-467b-848e-049e9292b110 · outbound

This paper cites Statistical mechanics of complex networks.Reviews of modern physics, 74(1):47, 2002.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Statistical mechanics of complex networks.Reviews of modern physics, 74(1):47, 2002

Reference 2

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Observation fbf0bbc5-87cc-405a-9951-f121154b7d0f · outbound

This paper cites Beyond weisfeiler– lehman with local ego-network encodings.Machine Learning and Knowledge Extraction, 5(4):1234–1265, 2023.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Beyond weisfeiler– lehman with local ego-network encodings.Machine Learning and Knowledge Extraction, 5(4):1234–1265, 2023

Reference 3

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Observation 66522bc4-0736-4f79-80d1-c041b0ecba06 · outbound

This paper cites Spectra of cayley graphs.Journal of Combinatorial Theory, Series B, 27(2):180– 189, 1979.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Spectra of cayley graphs.Journal of Combinatorial Theory, Series B, 27(2):180– 189, 1979

Reference 4

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Observation 63db0253-a883-4874-8860-c66538d3fe9c · outbound

This paper cites Constant curvature graph convo- lutional networks.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Constant curvature graph convo- lutional networks

Reference 5

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Observation 459f45ca-348c-4c86-9bf6-5cef19abfa3b · outbound

This paper cites Diffusions hypercontractives.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Diffusions hypercontractives

Reference 6

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Observation 01c18b00-82c9-43f1-bd46-d3f291734756 · outbound

This paper cites Bauer, B.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Bauer, B

Reference 7

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Observation 8f8b1feb-fbfd-41f8-8869-1e0e8520a7e9 · outbound

This paper cites Bauer, B.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Bauer, B

Reference 8

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This paper cites Bauer, Y.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Bauer, Y

Reference 9

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Observation 024724fd-764f-4154-8235-28987b2dd693 · outbound

This paper cites Laplacian eigenmaps for dimensionality reduction and data representation.Neural computation, 15(6):1373–1396, 2003.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Laplacian eigenmaps for dimensionality reduction and data representation.Neural computation, 15(6):1373–1396, 2003

Reference 10

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Observation 61fec448-713f-480c-9542-341933fe860c · outbound

This paper cites A computational fluid mechanics solution to the monge-kantorovich mass transfer problem.Numerische Mathematik, 84(3):375–393, 2000.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature A computational fluid mechanics solution to the monge-kantorovich mass transfer problem.Numerische Mathematik, 84(3):375–393, 2000

Reference 11

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Observation c6ad3e9c-c8ed-4492-9807-780c6430210d · outbound

This paper cites Unimodular random trees.Ergodic Theory Dynam.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Unimodular random trees.Ergodic Theory Dynam

Reference 12

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Observation 4d465d5f-3ed2-4f0a-a966-8c7d610c900d · outbound

This paper cites The Aldous--Lyons Conjecture I: Subgroup Tests.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature The Aldous--Lyons Conjecture I: Subgroup Tests

Reference 13

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Observation c40c02ee-b0aa-4b7a-855a-543092a66d82 · outbound

This paper cites A Note on Over-Smoothing for Graph Neural Networks.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature A Note on Over-Smoothing for Graph Neural Networks

Reference 14

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Observation ab7cb6df-4f2c-45de-8575-895ad0a338ee · outbound

This paper cites Graph neural ricci flow: Evolving feature from a curvature perspective.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Graph neural ricci flow: Evolving feature from a curvature perspective

Reference 15

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Observation 11876de1-6660-4b15-a84d-811f0844daaf · outbound

This paper cites Chung, Y.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Chung, Y

Reference 16

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Observation 7af64e36-5551-4d16-9c85-e707faf17abc · outbound

This paper cites Chung and S.-T.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Chung and S.-T

Reference 17

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This paper cites American Mathematical Soc., 1997.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature American Mathematical Soc., 1997

Reference 18

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Observation cf169a7d-90e2-43c4-9733-1ef59d55be8f · outbound

This paper cites Liouville properties.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Liouville properties

Reference 19

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Observation 10d17e7f-474d-45e8-97d1-c64eb852fe62 · outbound

This paper cites A riemannian interpolation inequality à la borell, brascamp and lieb.Inventiones mathematicae, 146(2):219– 257, 2001.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature A riemannian interpolation inequality à la borell, brascamp and lieb.Inventiones mathematicae, 146(2):219– 257, 2001

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Observation fe78bb61-71e4-4e00-ba48-0eeeaaa2d74c · outbound

This paper cites Learning parametrised graph shift operators.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Learning parametrised graph shift operators

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Observation a8a45c6d-40d9-469b-89e4-00225293c7ae · outbound

This paper cites Springer, 1992.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Springer, 1992

Reference 22

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Observation 63dfe760-3096-4ada-8c61-56f966c57309 · outbound

This paper cites Graph anisotropic diffusion for molecules.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Graph anisotropic diffusion for molecules

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Observation 81cec3c9-bafb-43ea-b175-85b6fa6d1639 · outbound

This paper cites Graph positional encoding via random feature propagation.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Graph positional encoding via random feature propagation

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Observation 470bbf62-0d25-4917-b93b-08c285e9f8ff · outbound

This paper cites Über die verteilung der wurzeln bei gewissen algebraischen gleichungen mit ganzzahligen koeffizienten.Mathematische Zeitschrift, 17(1):228–249, 1923.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Über die verteilung der wurzeln bei gewissen algebraischen gleichungen mit ganzzahligen koeffizienten.Mathematische Zeitschrift, 17(1):228–249, 1923

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Observation bf0a4b1e-04d8-4c86-a398-91131605f05c · outbound

This paper cites How powerful are k-hop message passing graph neural networks.Advances in Neural Information Processing Systems, 35:4776–4790, 2022.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature How powerful are k-hop message passing graph neural networks.Advances in Neural Information Processing Systems, 35:4776–4790, 2022

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Observation b653e357-8f46-4910-a916-f3e2116b490b · outbound

This paper cites Effective structural encodings via local curvature profiles.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Effective structural encodings via local curvature profiles

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Observation c46c99a6-9f49-4746-a2fc-3c8634aae41b · outbound

This paper cites Mitigating over-smoothing and over-squashing using aug- mentations of forman-ricci curvature.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Mitigating over-smoothing and over-squashing using aug- mentations of forman-ricci curvature

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Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Unresolved cited work

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Observation 0b391194-2b36-4ea2-bc65-5ef8b7821a4c · outbound

This paper cites Bochner’s method for cell complexes and combinatorial ricci curvature.Discrete & Computational Geometry, 29:323–374, 2003.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Bochner’s method for cell complexes and combinatorial ricci curvature.Discrete & Computational Geometry, 29:323–374, 2003

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Observation a366165a-94f3-41ad-855b-855343647ecf · outbound

This paper cites Bochner’s Method for Cell Complexes and Combinatorial Ricci Curvature.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Bochner’s Method for Cell Complexes and Combinatorial Ricci Curvature

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This paper cites Configuring random graph models with fixed degree sequences.Siam Review, 60(2):315–355, 2018.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Configuring random graph models with fixed degree sequences.Siam Review, 60(2):315–355, 2018

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Observation 446a0d77-36e4-4ac0-ae8f-ea2077b6755b · outbound

This paper cites Spectra of expansion graphs.The Electronic Journal of Linear Algebra, 6:2–10, 1999.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Spectra of expansion graphs.The Electronic Journal of Linear Algebra, 6:2–10, 1999

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Observation 3b7e67de-66e0-49cd-a3e8-993b6211368c · outbound

This paper cites On the shift operator, graph frequency, and optimal filtering in graph signal processing.IEEE Transactions on Signal Processing, 65(23):6303–6318, 2017.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature On the shift operator, graph frequency, and optimal filtering in graph signal processing.IEEE Transactions on Signal Processing, 65(23):6303–6318, 2017

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Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Unresolved cited work

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Observation 4f4cb22f-d6e9-42b4-ba29-1e1f51643968 · outbound

This paper cites Stochastic blockmodels: First steps.Social networks, 5(2):109–137, 1983.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Stochastic blockmodels: First steps.Social networks, 5(2):109–137, 1983

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Observation 0b778e4c-39ef-4cc0-8918-0f1bb2e577f7 · outbound

This paper cites Ollivier’s ricci curvature, local clustering and curvature-dimension inequalities on graphs.Discrete & Computational Geometry, 51(2):300–322, 2014.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Ollivier’s ricci curvature, local clustering and curvature-dimension inequalities on graphs.Discrete & Computational Geometry, 51(2):300–322, 2014

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This paper cites FoSR: First-order spectral rewiring for addressing oversquashing in GNNs.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature FoSR: First-order spectral rewiring for addressing oversquashing in GNNs

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Observation 725b2355-ac3e-425a-8a63-c377b58c940b · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Adam: A Method for Stochastic Optimization

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Observation c7f5d5ef-536b-4562-8c9d-17c8d4b2c926 · outbound

This paper cites Kipf and Max Welling.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Kipf and Max Welling

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This paper cites John Wiley & Sons, 1996.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature John Wiley & Sons, 1996

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This paper cites Curvature graph neural network.Information Sciences, 592:50–66, 2022.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Curvature graph neural network.Information Sciences, 592:50–66, 2022

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Observation 7bb1424e-df7d-48be-9c70-4e347470b0ab · outbound

This paper cites Deeper insights into graph convolutional networks for semi-supervised learning.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Deeper insights into graph convolutional networks for semi-supervised learning

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Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Unresolved cited work

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Observation fc957f48-2c50-4674-8384-e7f6554bb9bd · outbound

This paper cites Lin and S.-T.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Lin and S.-T

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Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Lott and C

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This paper cites Curvature-based clustering on graphs.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Curvature-based clustering on graphs

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Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Unresolved cited work

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Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Unresolved cited work

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Observation 24b4e888-dc74-472f-b129-33bd2241a46b · outbound

This paper cites TUDataset: A collection of benchmark datasets for learning with graphs.ICML 2020 GRL+ Workshop, 2020.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature TUDataset: A collection of benchmark datasets for learning with graphs.ICML 2020 GRL+ Workshop, 2020

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Observation 20509005-97d8-4e5b-8b99-abbf567a2343 · outbound

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Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Maxima for graphs and a new proof of a theorem of turán.Canadian Journal of Mathematics, 17:533–540, 1965

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Observation b4faf2c6-fafb-4a05-814a-7e65d3000384 · outbound

This paper cites Revisiting over-smoothing and over-squashing using ollivier-ricci curvature.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Revisiting over-smoothing and over-squashing using ollivier-ricci curvature

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Observation 2819f22a-f8a3-488b-9a48-63e96fdc489c · outbound

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Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Community detection on networks with ricci flow.Scientific reports, 9(1):9984, 2019

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Observation 2ab25dce-e219-4383-a1c4-6c0611537ac6 · outbound

This paper cites Springer, 2006.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Springer, 2006

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Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Ricci curvature of markov chains on metric spaces.Journal of Functional Analysis, 256(3):810–864, 2009

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Observation 17edb093-1409-4c12-8108-5b6916bf3ad1 · outbound

This paper cites Otto and C.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Otto and C

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This paper cites Master stability functions for synchronized coupled systems.Physical review letters, 80(10):2109, 1998.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Master stability functions for synchronized coupled systems.Physical review letters, 80(10):2109, 1998

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Observation e88c407e-5e73-4863-93d4-ff6312e10b50 · outbound

This paper cites Geom-gcn: Geometric graph convolutional networks.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Geom-gcn: Geometric graph convolutional networks

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Observation fb1cbd92-27cd-439a-b343-dbaa2a451e8a · outbound

This paper cites OUP Oxford, 2003.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature OUP Oxford, 2003

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Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Criteria for entropic curvature on graph spaces

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Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature V on Renesse and K.-Th

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Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Sparse expanders have negative curvature.Geom

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Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Entropic curvature on graphs along schrödinger bridges at zero temperature

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This paper cites Algorithms, graph theory, and linear equations in laplacian matrices.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Algorithms, graph theory, and linear equations in laplacian matrices

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Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Unresolved cited work

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Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Towards understanding generalization of graph neural networks

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Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Bronstein

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This paper cites The effectiveness of curvature-based rewiring and the role of hyperparameters in gnns revisited.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature The effectiveness of curvature-based rewiring and the role of hyperparameters in gnns revisited

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Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Scipy 1.0: fundamental algorithms for scientific computing in python.Nature methods, 17(3):261–272, 2020

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Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature A manifold perspective on the statistical generalization of graph neural networks

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Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature The effect of watts-strogatz and barabási-albert graphs on memory formation

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Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Revisiting semi-supervised learning with graph embeddings

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This paper cites •SBM:Stochastic Block Models representing community-structured networks [36].

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature •SBM:Stochastic Block Models representing community-structured networks [36]

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Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature reasonable

Reference 74

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Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Unresolved cited work

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Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Unresolved cited work

Reference 76

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Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature fast-decay

Reference 77

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Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature • Computation:We compute the exact ORC for every edge (u, v)in the graph using the GraphRicciCurvature library

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Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature The positional encoding is formed by the k smallest non-trivial eigenvectors of L

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This paper cites The encoding pRWPE u ∈R k is defined by the diagonal entries of the random walk diffusion matrix at various steps: pRWPE u = P1 uu,P 2 uu,.

Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature The encoding pRWPE u ∈R k is defined by the diagonal entries of the random walk diffusion matrix at various steps: pRWPE u = P1 uu,P 2 uu,

Reference 80

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Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvature Unresolved cited work

Reference 81

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