Strengthening Policy Coherence to Link Healthy Hydration with Water Security in the United States.

Modularity is a fundamental principle in neuroscience, shaping our understanding of neural architecture, dynamics, and function. The brain is not a homogeneous system, but a complex network, composed of distinct yet interacting modules. In network neuroscience, modularity is a defining feature of brain organization, manifesting in the segregation of structural and functional subnetworks that support specialized processing. These notions echo a deeply rooted principle in cognitive science, which suggests that cognitive processes operate within informationally encapsulated domains, highlighting modularity as a key characteristic of mental architecture. More recent perspectives suggest that cognition emerges from a hierarchy of increasingly polyfunctional nested circuits, dynamically recruited to support both domain-specific and integrative processes. Thus, understanding modularity is essential not only for characterizing the brain’s structural and functional topology but also for elucidating the computational principles that underlie human cognition. Beyond neurobiological organization, modularity is also increasingly studied in artificial intelligence, both as a network feature and as a design principle. In this context, a module can consist of any neural architecture component, from a layer to a whole network as part of an ensemble. In deep learning, modular systems leverage intrinsic or imposed modularity in data and tasks via routing functions to select relevant modules and aggregation functions to combine their outputs. Such approaches have been shown to offer key advantages such as enhanced interpretability, efficiency, and generalization, enabling systems to decompose complex tasks and recombine learned solutions. Related ideas also appear in reservoir computing, where modular or hierarchical architectures, such as deep echo state networks, stack multiple reservoirs to enable sequential processing and generate multiscale temporal representations. In contrast, the present work investigates topological modularity and hierarchy in a single recurrent neural network. In a network, small densely connected modules can be embedded into higher-order modules, leading to hierarchical modularity. Such a multi-scale organization has been hypothesized to maintain a balance between information segregation in specialized communities and global integration via intermodular communication. Previous work has focused on characterizing the dynamical effects of hierarchical modularity in synthetic neural networks. Notably, using both simple spreading models and spiking neural networks, it was found that hierarchical modularity supports criticality, a dynamical regime characterized by advantageous computational properties. Hierarchical modular networks have also been associated with increased functional diversity, but only as derived from functional connectivity. Yet, how hierarchical modularity shapes cognitive function remains unclear.