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Resistive switching memory (RRAM) devices generally rely on the formation/dissolution of conductive filaments through insulating materials, such as metal oxides and chalcogenide glasses. Understanding the mechanisms for filament formation and disruption in resistive switching materials is a critical step toward the development of reliable and controllable RRAM for future-generation storage. In particular, the capability to control the filament resistance and the reset current through the compliance current during filament formation may provide a key signature to clarify the switching mechanism. This paper provides a physically based explanation for the universal resistance switching in bipolar RRAM devices. A numerical model of filament growth based on thermally activated ion migration accounts for the resistance switching characteristics. The same physical picture is extended to numerically model the reset transition. The impact of migration parameters and experimental setup on the set/reset characteristics is discussed through numerical simulations.