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Multilevel, high-resistance resistive random access memory (RRAM) devices are desirable for neuromorphic computing applications because of their ability to represent synaptic weights and support energy-efficient computing. High resistance operation is also beneficial for scalability as it reduces parasitic resistances from interconnects in crossbar arrays, which can result in inference errors that increase with array size. Here, we present Al2O3/TiO2 bilayer RRAM devices with ultrahigh resistance values (up to 2 G \Omega) and multilevel programmability, demonstrating the writing of eight states with a standard deviation of separation and a dynamic range spanning three orders of magnitude. These capabilities, combined with long retention times, highlight their potential for implementation in artificial neural networks. To gain insight into their performance, we examine their switching behavior, which exhibits traits characteristic of both filamentary and filament-free metal-oxide RRAM. Initial voltage application induces changes in current that span multiple orders of magnitude, indicating the formation of conductive filaments composed of oxygen vacancies, typical of filamentary RRAM. In contrast, low-frequency noise analysis suggests that switching is governed by the collective movement of oxygen vacancies rather than the closing and rupture of individual filaments. We infer that the conduction in our devices is governed by filaments with a broad spatial distribution of gap distances between filament ends and the electrode, enabling reliable switching of states within an exceptionally high resistance regime.