Abstract
Hyperbolic geometry explains many structural features of real-world networks, yet existing hyperbolic generative network models with community organization such as the nonuniform popularity-similarity optimization (nPSO) are restricted to unipartite graphs. Here we introduce a bipartite extension of the nPSO model called nBPSO, motivated by the prevalence of community organization in real-world bipartite networks and the emerging evidence of hyperbolic hierarchical connectivity in trained sparse neural networks. nBPSO provides explicit control over link density, degree distribution, average clustering, and community organization. We engineer the model to generate consecutive and concatenated bipartite layers, enabling initialization of dynamic sparse training multilayer perceptron neural networks with tunable hyperbolic organization for each layer. We find that task-agnostic (unaligned with the task) hyperbolic random network initialization degrades the performance of sparse neural networks compared with uniform random initialization. This degradation arises because the hyperbolic random initialization imposes an arbitrary hierarchical prior into the sparse topology. Dynamic sparse training may then need to optimize the weights and reorganize this arbitrary task-agnostic hierarchy into a task-driven one. By contrast, a uniform random initialization imposes at start less structural bias and may therefore be easier to reconfigure during training toward the hierarchical topology suited to the task. This work motivates the need for data-informed hyperbolic initialization methods which generate sparse topologies with a hierarchical prior closer to the task, facilitating the further learning of a task-oriented hierarchical organization during dynamic sparse training. In addition, nBPSO represents the first hyperbolic bipartite network generative model that allows the mesoscale community structure to be explicitly controlled through model parameters, making it a useful tool for broader complex systems applications where community organization is central to accurate and interpretable modeling.