Multiset Transformer: Advancing Representation Learning in Persistence Diagrams
This addresses representation learning challenges in topological data analysis for researchers working with persistence diagrams.
The authors tackled the problem of persistence diagram representation learning by proposing Multiset Transformer, the first neural network with attention mechanisms specifically designed for multisets that provides theoretical guarantees of permutation invariance. The method outperforms existing neural network approaches in this domain.
To improve persistence diagram representation learning, we propose Multiset Transformer. This is the first neural network that utilizes attention mechanisms specifically designed for multisets as inputs and offers rigorous theoretical guarantees of permutation invariance. The architecture integrates multiset-enhanced attentions with a pool-decomposition scheme, allowing multiplicities to be preserved across equivariant layers. This capability enables full leverage of multiplicities while significantly reducing both computational and spatial complexity compared to the Set Transformer. Additionally, our method can greatly benefit from clustering as a preprocessing step to further minimize complexity, an advantage not possessed by the Set Transformer. Experimental results demonstrate that the Multiset Transformer outperforms existing neural network methods in the realm of persistence diagram representation learning.