Finding node correspondence across networks, namely multi-network alignment,
is an essential prerequisite for joint learning on multiple networks. Despite
great success in aligning networks in pairs, the literature on multi-network
alignment is sparse due to the exponentially growing solution space and lack of
high-order discrepancy measures. To fill this gap, we propose a hierarchical
multi-marginal optimal transport framework named HOT for multi-network
alignment. To handle the large solution space, multiple networks are decomposed
into smaller aligned clusters via the fused Gromov-Wasserstein (FGW)
barycenter. To depict high-order relationships across multiple networks, the
FGW distance is generalized to the multi-marginal setting, based on which
networks can be aligned jointly. A fast proximal point method is further
developed with guaranteed convergence to a local optimum. Extensive experiments
and analysis show that our proposed HOT achieves significant improvements over
the state-of-the-art in both effectiveness and scalability.

多网络对齐的多层次多边界优化传输框架（HOT）通过分解网络，使用融合的 Gromov-Wasserstein（FGW）质心来处理大规模的解空间，并基于多边界设置将 FGW 距离推广到多网络对齐中，进而开发了一种快速的邻近点方法以获得局部最优解，通过广泛的实验证明了 HOT 在效果和可扩展性方面都明显优于现有技术的成果。

网络对齐的分层多边际最优输运

Hierarchical Multi-Marginal Optimal Transport for Network Alignment

Multimodal hate detection, which aims to identify harmful content online such
as memes, is crucial for building a wholesome internet environment. Previous
work has made enlightening exploration in detecting explicit hate remarks.
However, most of their approaches neglect the analysis of implicit harm, which
is particularly challenging as explicit text markers and demographic visual
cues are often twisted or missing. The leveraged cross-modal attention
mechanisms also suffer from the distributional modality gap and lack logical
interpretability. To address these semantic gaps issues, we propose TOT: a
topology-aware optimal transport framework to decipher the implicit harm in
memes scenario, which formulates the cross-modal aligning problem as solutions
for optimal transportation plans. Specifically, we leverage an optimal
transport kernel method to capture complementary information from multiple
modalities. The kernel embedding provides a non-linear transformation ability
to reproduce a kernel Hilbert space (RKHS), which reflects significance for
eliminating the distributional modality gap. Moreover, we perceive the topology
information based on aligned representations to conduct bipartite graph path
reasoning. The newly achieved state-of-the-art performance on two publicly
available benchmark datasets, together with further visual analysis,
demonstrate the superiority of TOT in capturing implicit cross-modal alignment.

本论文提出了一种 topology-aware optimal transport (TOT) 框架，它利用最优传输计划的解决方案来解决跨模态对齐问题，从而揭示了恶意互联网违规内容的隐含危害。TOT 在两个公开数据集上取得了最新的最优性能，证明其在捕捉隐含的跨模态对齐方面具有优越性。