Let x 2 RD beadatapoint.

While the max5 function has already been used, nobody so far has shown how to deploy iteffectively, which is what the com-6 bination ofMCM and MCLoss does. In general, consider a classA with ancestors A1...An in the hierar-8 chy. The highern the more likely it is that a neural network (NN) withMCM trained withL will remain stuck9 in bad local optima. Figure 1: From left to right: (i) rectangles disposition, (ii) decision boundaries forA5 of h+MCM trained withL, and(iii)decisionboundariesforA5 ofC-HMCNN(h). Thus,allpoints19 in rectangle 3 belong to all classes, and if a datapoint20 belongs to a rectangle, then it also belongs to classA5.21

In the complex landscape of hematologic samples such as peripheral blood or bone marrow derived from flow cytometry (FC) data, cell-level prediction presents profound challenges. This work explores injecting hierarchical prior knowledge into graph neural networks (GNNs) for single-cell multi-class classification of tabular cellular data. By representing the data as graphs and encoding hierarchical relationships between classes, we propose our hierarchical plug-in method to be applied to several GNN models, namely, FCHC-GNN, and effectively designed to capture neighborhood information crucial for single-cell FC domain. Extensive experiments on our cohort of 19 distinct patients, demonstrate that incorporating hierarchical biological constraints boosts performance significantly across multiple metrics compared to baseline GNNs without such priors. The proposed approach highlights the importance of structured inductive biases for gaining improved generalization in complex biological prediction tasks.

Hierarchical multi-label classification (HMC) is a challenging classification task extending standard multi-label classification problems by imposing a hierarchy constraint on the classes. In this paper, we propose C-HMCNN(h), a novel approach for HMC problems, which, given a network h for the underlying multi-label classification problem, exploits the hierarchy information in order to produce predictions coherent with the constraint and improve performance. We conduct an extensive experimental analysis showing the superior performance of C-HMCNN(h) when compared to state-of-the-art models.