arXiv subjects

Dionisia Naddeo

Publications and source records attributed to Dionisia Naddeo.

3 recordsLinked to original sources

arXiv2026

Hierarchical Pooling for Sheaf Neural Networks

Sheaf Neural Networks (SNNs) generalize Graph Neural Networks (GNNs) by replacing scalar node signals with stalk-valued signals and by using restriction maps to measure compatibility across edges. Unlike standard graph diffusion, which encourages neighboring node features to become similar, sheaf diffusion promotes consistency through the restriction maps and can therefore model more general relationships between neighboring nodes. However, existing sheaf neural architectures mainly operate at a fixed graph resolution and do not provide a principled pooling mechanism for building hierarchical representations. In this paper, we introduce Hierarchical Sheaf Pool (HiSP), a sheaf-aware pooling framework based on local spectral coarsening. Given a partition of the graph, HiSP constructs each coarse stalk by projecting fine stalk-valued features onto the low-frequency eigenmodes of the cluster-internal sheaf Laplacian. These local modes define a cochain-level prolongation map, which allows the fine sheaf energy to be represented on the coarse space through a Galerkin operator. We further analyze the approximation induced by coarsening by separating truncation loss, due to discarded local modes, from realization loss, due to representing the projected operator as a coarse sheaf. Finally, we implement HiSP as a GNN pooling layer compatible with SNNs and provide a PyG implementation supporting batching, lifted sheaf Laplacians, and hierarchical architectures.

cs.LG↗

arXiv2026

Hyperbolic Graph Neural Networks Under the Microscope: The Role of Geometry-Task Alignment

Many complex networks exhibit hierarchical, tree-like structures, making hyperbolic space a natural candidate wherein to learn representations of them. Based on this observation, Hyperbolic Graph Neural Networks (HGNNs) have been widely adopted as a principled choice for representation learning on tree-like graphs. In this work, we question this paradigm by proposing the additional condition of geometry--task alignment, i.e., whether the metric structure of the target follows that of the input graph. We theoretically and empirically demonstrate the capability of HGNNs to recover low-distortion representations on regression problems, and show that their geometric inductive bias becomes helpful when the problem requires preserving metric structure. By jointly analyzing predictive performance and embedding distortion, we further show that HGNNs gain an advantage on link prediction, a naturally geometry-aligned task, whereas this advantage largely disappears on standard node classification benchmarks, which are typically not geometry--aligned. Overall, our findings shift the focus from only asking "Is the graph hyperbolic?" to also questioning "Is the task aligned with hyperbolic geometry?", showing that HGNNs consistently outperform Euclidean models under such alignment, while their advantage vanishes otherwise.

cs.LG↗

arXiv2024

NbTi: a nontrivial puzzle for the conventional theory of superconductivity

We present the first $ab$-$initio$ study of superconductivity in NbTi, the workhorse for many applications. Despite its apparent simplicity, NbTi turns out to be a major challenge for computational superconductivity. In fact, anharmonic effects are crucial to obtain dynamically stable phonons for the ordered bcc phase, unstable at the harmonic level, and beyond-Morel Anderson effects in the Coulomb interaction reduce the Tc by more than 20%. Lattice disorder causes an additional large discrepancy in $T_c$ compared to experiment. Our results imply that a quantitative description of technologically-relevant superconductors requires methodological developments beyond the current standards.

cond-mat.supr-con↗