Public articles linked to the same research event.
arXiv Addressing the limitation that most topological deep learning approaches, being based on boundary operators and Hodge Laplacians, cannot lift or lower features and signals across more than one dimension per layer, this work proposes the adoption of cup and cap products and formulates the Cup and Cap Topological Neural Network (CCNN), a topological deep learning architecture designed to learn node-based variables (0-cochains) while accounting for many-body interactions such as triangles in the data, validated on the TopoBench datasets where it shows competitiveness with respect to other simplicial complex neural networks.
Addressing the limitation that most topological deep learning approaches, being based on boundary operators and Hodge Laplacians, cannot lift or lower features and signals across more than one dimension per layer, this work proposes the adoption of cup and cap products and formulates the Cup and Cap Topological Neural Network (CCNN), a topological deep learning architecture designed to learn node-based variables (0-cochains) while accounting for many-body interactions such as triangles in the data, validated on the TopoBench datasets where it shows competitiveness with respect to other simplicial complex neural networks.
Addressing the limitation that most topological deep learning approaches, being based on boundary operators and Hodge Laplacians, cannot lift or lower features and signals across more than one dimension per layer, this work proposes the adoption of cup and cap products and formulates the Cup and Cap Topological Neural Network (CCNN), a topological deep learning architecture designed to learn node-based variables (0-cochains) while accounting for many-body interactions such as triangles in the data, validated on the TopoBench datasets where it shows competitiveness with respect to other simplicial complex neural networks.
Addressing the limitation that most topological deep learning approaches, being based on boundary operators and Hodge Laplacians, cannot lift or lower features and signals across more than one dimension per layer, this work proposes the adoption of cup and cap products and formulates the Cup and Cap Topological Neural Network (CCNN), a topological deep learning architecture designed to learn node-based variables (0-cochains) while accounting for many-body interactions such as triangles in the data, validated on the TopoBench datasets where it shows competitiveness with respect to other simplicial complex neural networks.