Membership Inference Attacks in Simplicial Complexes Neural Networks

Simplicial Complex Neural Networks (SCNs) learn from relational data with group-level structure, including triangles, cliques, loops, and higher-order interactions. Boundary operators and Hodge Laplacians support this representation learning and encode membership-relevant cues when constructed from training simplices. These construction-dependent cues create a distinctive privacy risk alongside model memorization. We present the first security study of membership inference attacks on SCNs. Our exposure-aware analysis connects higher-order utility to membership signals carried by operator construction and model responses. We introduce a Structure-Aware Black-Box attack (SA-BB) that compares a queried simplex's prediction probability with those of neighbouring candidates in a public topology. A membership classifier trained on shadow models uses these local response patterns to infer target membership through a prediction API. To mitigate this risk, we propose Dynamic Topological Pruning and Injection (DTPI), which perturbs selected high-impact topological relations during training while preserving useful higher-order structure. Our evaluation examines membership leakage and the privacy–utility trade-off across datasets, backbones, and defenses.