Latent Graph Inference (LGI) relaxed the reliance of Graph Neural Networks (GNNs) on a given graph topology by dynamically learning it. However, most of LGI methods assume to have a (noisy, incomplete, improvable, ...) input graph to rewire and can solely learn regular graph topologies. In the wake of the success of Topological Deep Learning (TDL), we study Latent Topology Inference (LTI) for learning higher-order cell complexes (with sparse and not regular topology) describing multi-way interactions between data points. To this aim, we introduce the Differentiable Cell Complex Module (DCM), a novel learnable function that computes cell probabilities in the complex to improve the downstream task. We show how to integrate DCM with cell complex message passing networks layers and train it in a end-to-end fashion, thanks to a two-step inference procedure that avoids an exhaustive search across all possible cells in the input, thus maintaining scalability. Our model is tested on several homophilic and heterophilic graph datasets and it is shown to outperform other state-of-the-art techniques, offering significant improvements especially in cases where an input graph is not provided.

本论文提出了一种基于可学习的单元概率函数和可微分单元复合模块的Latent Topology Inference（LTI）方法，用于描述点之间的多路交互，此方法在多个同质和异质图数据集上的实验证明了其优于其他现有技术的表现，可用于在没有提供输入图形的情况下提高拓扑学习的性能。

从潜在图到潜在拓扑推断：可微分的细胞复合模块