提出首个专为多重集设计的注意力网络，提升拓扑数据分析效果。
Multiset Transformer: Advancing Representation Learning in Persistence Diagrams
- 用增强型注意力机制处理多重集输入，保持元素重复性
- 相比Set Transformer，计算与空间复杂度显著降低
- 可结合聚类预处理进一步降维，适合拓扑数据学习
为改进持久性图表示学习，我们提出Multiset Transformer。这是首个针对多重集输入设计注意力机制的神经网络，并提供严格的置换不变性理论保证。该架构融合多重集增强注意力与池化-分解方案，可在等变层间保留元素重数。这一能力使模型充分挖掘重复信息的同时，相较Set Transformer显著降低计算与空间复杂度。此外，该方法可借助聚类作为预处理步骤进一步压缩复杂度，此优势是Set Transformer所不具备的。实验表明，Multiset Transformer在持久性图表示学习任务中优于现有神经网络方法。
原文摘要 · Abstract (English)
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.
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