The hippocampus as a small-world cognitive map

When a mouse perceives a hawk's shadow, it may have only seconds to decide where to run, yet the safest refuge is often neither visible nor nearby. To survive, it must search its cognitive map quickly enough to choose among many possibilities, and accurately enough to avoid dead ends and hazards along the way. But what counts as "safe" changes over minutes to days as paths, refuges, and threats shift, so a cognitive map must be searchable not only over places but also over time. This highlights a core design problem: cognitive maps must preserve fine local structure for reliable action, yet remain globally searchable so that distant, useful solutions can be found efficiently in both space and time. The hippocampus is thought to support such maps, with population activity representing world states and their transitions--yet how these representations remain locally faithful while enabling efficient global search is not well understood. Here, we used a novel geometry-regularized autoencoder to model longitudinal calcium imaging from thousands of hippocampal CA1 neurons in mice learning a memory-guided navigation task. We discovered that the hippocampal population code achieves both local fidelity and global searchability through complementary mechanisms operating at different scales, yielding small-world network structure in the space of neural representations, with strong local clustering and a sparse set of long-range shortcuts that enable rapid access to distant states. At the population level, helical (rotation-plus-drift) dynamics of neural representations relative to past experience build new maps that preserve information about nearby positions in space and time while remaining distinguishable from earlier representations. At the cellular level, neurons with coordinated multi-field activity spanning distant representations create sparse, long-range shortcuts through the space of possible states. During synchronous population events in immobility, decoded activity often jumps to distant states in space, time, and task conditions, suggesting these shortcuts are engaged during offline processing. This functional organization, with implications for both neuroscience and artificial intelligence, sheds light on how hippocampal representations may be optimized for a fundamental challenge faced by intelligent systems: efficiently searching through accurate internal models of the world.