Frédéric Giroire

Davide Ferre', Frédéric Giroire, Frederik Mallmann-Trenn et al.

The Strong Lottery Ticket Hypothesis (SLTH) posits that large, randomly initialized neural networks contain sparse subnetworks capable of approximating a target function at initialization without training, suggesting that pruning alone is sufficient. Pruning methods are typically classified as unstructured, where individual weights can be removed from the network, and structured, where parameters are removed according to specific patterns, as in neuron pruning. Existing theoretical results supporting the SLTH rely almost exclusively on unstructured pruning, showing that logarithmic overparameterization suffices to approximate simple target networks. In contrast, neuron pruning has received limited theoretical attention. In this work, we consider the problem of approximating a single bias-free ReLU neuron using a randomly initialized bias-free two-layer ReLU network, thereby isolating the intrinsic limitations of neuron pruning. We show that neuron pruning requires a starting network with $Ω(d/\varepsilon)$ hidden neurons to $\varepsilon$-approximate a target ReLU neuron. In contrast, weight pruning achieves $\varepsilon$-approximation with only $O(d\log(1/\varepsilon))$ neurons, establishing an exponential separation between the two pruning paradigms.

Justin Dachille, Aurora Rossi, Sunil Kumar Maurya et al.

Computing node importance in networks is a long-standing fundamental problem that has driven extensive study of various centrality measures. A particularly well-known centrality measure is betweenness centrality, which becomes computationally prohibitive on large-scale networks. Graph Neural Network (GNN) models have thus been proposed to predict node rankings according to their relative betweenness centrality. However, state-of-the-art methods fail to generalize to high-diameter graphs such as road networks. We propose BRAVA-GNN, a lightweight GNN architecture that leverages the empirically observed correlation linking betweenness centrality to degree-based quantities, in particular multi-hop degree mass. This correlation motivates the use of degree masses as size-invariant node features and synthetic training graphs that closely match the degree distributions of real networks. Furthermore, while previous work relies on scale-free synthetic graphs, we leverage the hyperbolic random graph model, which reproduces power-law exponents outside the scale-free regime, better capturing the structure of real-world graphs like road networks. This design enables BRAVA-GNN to generalize across diverse graph families while using 54x fewer parameters than the most lightweight existing GNN baseline. Extensive experiments on 19 real-world networks, spanning social, web, email, and road graphs, show that BRAVA-GNN achieves up to 214% improvement in Kendall-Tau correlation and up to 70x speedup in inference time over state-of-the-art GNN-based approaches, particularly on challenging road networks.