k-CCWL isomorphism tests are equivalent to TC_{k+2} topological counting logic and topological (k+2)-pebble games, characterizing the logical expressiveness of TNNs.
Architectures of Topological Deep Learning: A Survey on Topological Neural Networks, August 2023
6 Pith papers cite this work. Polarity classification is still indexing.
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Collapsed Effective Operators use Schur complement on graded Laplacians to create vertex-level operators that encode higher-order topology, preserve PSD, and improve spectral clustering and smoothing.
Cellular Sheaf Neural Operators use cell complexes, learned restriction maps, and structure-aware message passing to create discretization-aware neural surrogates that preserve constraints in multiphysics PDEs such as MHD.
Proposes sCWL, fCWL, maximal clique complex, and CliqueWalk sampling to create a scalable higher-order graph learning framework that preserves expressivity.
HetSheaf applies cellular sheaves and type-conditioned restriction maps to heterogeneous graphs, plus SheafPool for basis-invariant graph-level representations, delivering competitive accuracy with substantially reduced parameter counts.
Introduces Hodge Spectral Duality, a hybrid neural architecture that applies Hodge orthogonality and operator splitting to isolate unlearnable topological degrees of freedom from learnable geometric dynamics in solution operators on geometric meshes.
citing papers explorer
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The Logical Expressiveness of Topological Neural Networks
k-CCWL isomorphism tests are equivalent to TC_{k+2} topological counting logic and topological (k+2)-pebble games, characterizing the logical expressiveness of TNNs.
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Collapsed Effective Operators for Higher-order Structures
Collapsed Effective Operators use Schur complement on graded Laplacians to create vertex-level operators that encode higher-order topology, preserve PSD, and improve spectral clustering and smoothing.
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Cellular Sheaf Neural Operators for Structure-Preserving Surrogate Modeling of Constrained PDEs
Cellular Sheaf Neural Operators use cell complexes, learned restriction maps, and structure-aware message passing to create discretization-aware neural surrogates that preserve constraints in multiphysics PDEs such as MHD.
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Scaling Higher-Order Graph Learning with Maximal Clique Complexes
Proposes sCWL, fCWL, maximal clique complex, and CliqueWalk sampling to create a scalable higher-order graph learning framework that preserves expressivity.
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Heterogeneous Sheaf Neural Networks
HetSheaf applies cellular sheaves and type-conditioned restriction maps to heterogeneous graphs, plus SheafPool for basis-invariant graph-level representations, delivering competitive accuracy with substantially reduced parameter counts.
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Topology-Preserving Neural Operator Learning via Hodge Decomposition
Introduces Hodge Spectral Duality, a hybrid neural architecture that applies Hodge orthogonality and operator splitting to isolate unlearnable topological degrees of freedom from learnable geometric dynamics in solution operators on geometric meshes.