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.
Mathilde Papillon, Sophia Sanborn, Mustafa Hajij, and Nina Miolane
3 Pith papers cite this work. Polarity classification is still indexing.
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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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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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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.
- Topology-Preserving Neural Operator Learning via Hodge Decomposition