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.

翻译：潜在图推理通过动态学习拓扑结构，减轻了图神经网络对给定图拓扑的依赖。然而，大多数潜在图推理方法假设存在（含噪声、不完整、可改进的...）输入图进行重新连接，且仅能学习常规图拓扑。受拓扑深度学习成功的启发，我们研究用于学习描述数据点间多元交互的高阶胞腔复形（具有稀疏且非正则拓扑）的潜在拓扑推理。为此，我们引入可微胞腔复形模块，这是一种新型可学习函数，通过计算复形中的胞腔概率来优化下游任务。我们展示了如何将可微胞腔复形模块与胞腔复形消息传递网络层集成，并借助两步推理过程实现端到端训练——该过程避免了对输入中所有可能胞腔的穷举搜索，从而保持了可扩展性。我们的模型在多个同质性和异质性图数据集上进行了测试，结果表明其性能优于现有最优技术，尤其在未提供输入图的情况下展现出显著优势。