Oxide-based resistive memory systems have high near-term promise for use in nonvolatile memory. Here we introduce a memory system employing a three-dimensional (3D) networked nanoporous (NP) Ta2O5-x structure and graphene for ultrahigh density storage. The devices exhibit a self-embedded highly nonlinear I-V switching behavior with an extremely low leakage current (on the order of pA) and good endurance. Calculations indicated that this memory architecture could be scaled up to a ∼162 Gbit crossbar array without the need for selectors or diodes normally used in crossbar arrays. In addition, we demonstrate that the voltage point for a minimum current is systematically controlled by the applied set voltage, thereby offering a broad range of switching characteristics. The potential switching mechanism is suggested based upon the transformation from Schottky to Ohmic-like contacts, and vice versa, depending on the movement of oxygen vacancies at the interfaces induced by the voltage polarity, and the formation of oxygen ions in the pores by the electric field.