The learning and inference efficiencies of an artificial neural network represented by a cross‐point synaptic memristor array can be achieved using a selector, with high selectivity (Ion/Ioff) and sufficient death region, stacked vertically on a synaptic memristor. This can prevent a sneak current in the memristor array. A selector with multiple jar‐shaped conductive Cu filaments in the resistive switching layer is precisely fabricated by designing the Cu ion concentration depth profile of the CuGeSe layer as a filament source, TiN diffusion barrier layer, and Ge3Se7 switching layer. The selector performs super‐linear‐threshold‐switching with a selectivity of > 107, death region of −0.70–0.65 V, holding time of 300 ns, switching speed of 25 ns, and endurance cycle of > 106. In addition, the mechanism of switching is proven by the formation of conductive Cu filaments between the CuGeSe and Ge3Se7 layers under a positive bias on the top Pt electrode and an automatic rupture of the filaments after the holding time. Particularly, a spiking deep neural network using the designed one‐selector‐one‐memory cross‐point array improves the Modified National Institute of Standards and Technology classification accuracy by ≈3.8% by eliminating the sneak current in the cross‐point array during the inference process.