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The nature of the Fermi surface observed in the recently discovered family ofunconventional insulators starting with SmB$_6$ and subsequently YbB$_{12}$ isa subject of intense inquiry. Here we shed light on this question by comparingquantum oscillations between the high magnetic field-induced metallic regime inYbB$_{12}$ and the unconventional insulating regime. In the field-inducedmetallic regime beyond 47 T, we find prominent quantum oscillations in thecontactless resistivity characterised by multiple frequencies up to at least3000 T and heavy effective masses up to at least 17 $m_\text{e}$,characteristic of an $f$-electron hybridised metallic Fermi surface. The growthof quantum oscillation amplitude at low temperatures in electrical transportand magnetic torque in insulating YbB$_{12}$ is closely similar to theLifshitz-Kosevich low temperature growth of quantum oscillation amplitude infield-induced metallic YbB$_{12}$, pointing to an origin of quantumoscillations in insulating YbB$_{12}$ from in-gap neutral low energyexcitations. The field-induced metallic regime of YbB$_{12}$ is characterisedby more Fermi surface sheets of heavy quasiparticle effective mass that emergein addition to the heavy Fermi surface sheets yielding multiple quantumoscillation frequencies below 1000 T observed in both insulating and metallicregimes. We thus observe a heavy multi-component Fermi surface in which$f$-electron hybridisation persists from the unconventional insulating to thefield-induced metallic regime of YbB$_{12}$, which is in distinct contrast tothe unhybridised conduction electron Fermi surface observed in the case of theunconventional insulator SmB$_6$. Our findings require a different theoreticalmodel of neutral in-gap low energy excitations in which the $f$-electronhybridisation is retained in the case of the unconventional insulatorYbB$_{12}$.

$f$-electron hybridised metallic Fermi surface in magnetic field-induced metallic YbB$_{12}$