Stability of Flow Models for Graph Signals

Generating signals on graphs requires permutation-equivariant models that exhibit stability with respect to relative structural perturbations. While favorable stability properties of Graph Neural Networks (GNNs) have been well documented, it is unclear how structural errors propagate through the dynamics of continuous generative flow models that are gaining traction for graph signal generation. In this paper, we analyze continuous normalized flow models parameterized by GNNs and show that permutation equivariance is preserved for both the resulting continuous-time ordinary differential equations and their discrete numerical approximations used as graph signal samplers. Our primary contribution is to derive explicit stability bounds on the generated probability distributions, which quantify how relative graph perturbations affect the final sampled signals. Motivated by these theoretical bounds, we introduce a stability-promoting regularized flow matching strategy that actively penalizes the spatial Lipschitz constant of the vector field during model training. Experiments using synthetic smooth signals on stochastic block model graphs and real-world fMRI signals on brain connectomes demonstrate that this bound-oriented approach yields generative models that are more robust to structural noise, without sacrificing output quality.

Link Prediction or Perdition: the Seeds of Instability in Knowledge Graph Embeddings

Embedding models (KGEMs) constitute the main link prediction approach to complete knowledge graphs. Standard evaluation protocols emphasize rank-based metrics such as MRR or Hits@$K$, but usually overlook the influence of random seeds on result stability. Moreover, these metrics conceal potential instabilities in individual predictions and in the organization of embedding spaces. In this work, we conduct a systematic stability analysis of multiple KGEMs across several datasets. We find that high-performance models actually produce divergent predictions at the triple level and highly variable embedding spaces. By isolating stochastic factors (i.e., initialization, triple ordering, negative sampling, dropout, hardware), we show that each independently induces instability of comparable magnitude. Furthermore, for a given model, hyperparameter configurations with better MRR are not guaranteed to be more stable. Moreover, voting, albeit a known remediation mechanism, only provides a limited enhancement of stability. These findings highlight critical limitations of current benchmarking protocols, and raise concerns about the reliability of KGEMs for knowledge graph completion.