Highlights d Human brains map abstract relationships among entities from piecemeal learning d Separately learnt dimensions are combined and represented in a 2D social hierarchy d To make novel inferences, HC reinstates a hub that connects two social hierarchies d EC and vmPFC encode Euclidean distances of inferred vectors for novel inferences

Abstract. The three-dimensional P and S velocity (from VF/V s ratios) distribution and improved hypocenters for the Yellowstone volcanic field have been determined from inversion of first arrival times from 7942 local earthquakes and 16 controlled-source explosions. The P velocity model has an rms residual of ñ 0.09 s, whereas the Vp/Vs ratio model (calculated from 511 earthquakes) has an rms residual of ñ 0.29 s. High P and S velocities outside the Yellowstone caldera represent thermally undisturbed basement and sedimentary rocks. A caldera-wide 15% decrease from regional P velocities at depths of 6 to 12 km is coincident with a -60 mGal gravity anomaly and is interpreted as a hot, subsolidus, granitic batholith with a quasi-plastic rheology. Localized 30% reductions from regional seismic velocities and higher Vp/Vs ratios 8 km beneath Yellowstone's resurgent domes are interpreted as partial melts and vestigial magma systems associated with youthful (less than 2 Ma) silicic volcanism. Additional low seismic velocities and Vp/Vs ratios and a 20 mGal gravity low less than 4 km beneath the northeast caldera rim are interpreted as a hydrothermal fracture zone thermally driven by underlying partial melt. Hypocenters relocated with the three-dimensional P velocity model show subparallel alignment with NW-SE trending postcaldera volcanic vents and normal faults northwest of the caldera. Focal depths of relocated earthquakes decrease from more than 11 km outside the caldera to less than 6 km within the caldera, reflecting thinning and heating of the seismogenic crust.

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Generalizing experiences to guide decision making in novel situations is a hallmark of flexible behavior. It has been hypothesized such flexibility depends on a cognitive map of an environment or task, but directly linking the two has proven elusive. Here, we find that discretely sampled abstract relationships between entities in an unseen two-dimensional (2-D) social hierarchy are reconstructed into a unitary 2-D cognitive map in the hippocampus and entorhinal cortex. We further show that humans utilize a grid-like code in several brain regions, including entorhinal cortex and medial prefrontal cortex, for inferred direct trajectories between entities in the reconstructed abstract space during discrete decisions.Moreover, these neural grid-like codes in the entorhinal cortex predict neural decision value computations in the medial prefrontal cortex and temporoparietal junction area during choice.Collectively, these findings show that grid-like codes are used by the human brain to infer novel solutions, even in abstract and discrete problems, and suggest a general mechanism underpinning flexible decision making and generalization.