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.

Non-invasive maturity assessment of iPSC-CMs based on optical maturity characteristics using interpretable AI

Human induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) are an important resource for the identification of new therapeutic targets and cardioprotective drugs. After differentiation iPSC-CMs show an immature, fetal-like phenotype. Cultivation of iPSC-CMs in lipid-supplemented maturation medium (MM) strongly enhances their structural, metabolic and functional phenotype. Nevertheless, assessing iPSC-CM maturation state remains challenging as most methods are time consuming and go in line with cell damage or loss of the sample. To address this issue, we developed a non-invasive approach for automated classification of iPSC-CM maturity through interpretable artificial intelligence (AI)-based analysis of beat characteristics derived from video-based motion analysis. In a prospective study, we evaluated 230 video recordings of early-state, immature iPSC-CMs on day 21 after differentiation (d21) and more mature iPSC-CMs cultured in MM (d42, MM). For each recording, 10 features were extracted using Maia motion analysis software and entered into a support vector machine (SVM). The hyperparameters of the SVM were optimized in a grid search on 80 % of the data using 5-fold cross-validation. The optimized model achieved an accuracy of 99.5 $\pm$ 1.1 % on a hold-out test set. Shapley Additive Explanations (SHAP) identified displacement, relaxation-rise time and beating duration as the most relevant features for assessing maturity level. Our results suggest the use of non-invasive, optical motion analysis combined with AI-based methods as a tool to assess iPSC-CMs maturity and could be applied before performing functional readouts or drug testing. This may potentially reduce the variability and improve the reproducibility of experimental studies.

Relax and penalize: a new bilevel approach to mixed-binary hyperparameter optimization

In recent years, bilevel approaches have become very popular to efficiently estimate high-dimensional hyperparameters of machine learning models. However, to date, binary parameters are handled by continuous relaxation and rounding strategies, which could lead to inconsistent solutions. In this context, we tackle the challenging optimization of mixed-binary hyperparameters by resorting to an equivalent continuous bilevel reformulation based on an appropriate penalty term. We propose an algorithmic framework that, under suitable assumptions, is guaranteed to provide mixed-binary solutions. Moreover, the generality of the method allows to safely use existing continuous bilevel solvers within the proposed framework. We evaluate the performance of our approach for a specific machine learning problem, i.e., the estimation of the group-sparsity structure in regression problems. Reported results clearly show that our method outperforms state-of-the-art approaches based on relaxation and rounding