As a synaptic device candidate for artificial neural networks (ANNs), memristors hold great promise for efficient neuromorphic computing. However, commonly used filamentary memristors normally exhibit large cyclic variations due to the stochastic nature of filament formation and ablation, which will inevitably degrade the computing accuracy. Here we demonstrate, in nanoscale Ag2S-based memristors that resistance-switching (RS) at the contact interface can be a promising solution to reduce cyclic variations. When the Ag2S memristor is operated with a filament-free interface RS via Schottky barrier height modification at the contact interface, it shows an ultra-small cycle-to-cycle variation of 1.4% during 104 switching cycles. This is in direct contrast to the variation of (28.9%) of the RS filament extracted from the same device. Interface RS can also emulate synaptic functions and psychological behavior. Its improved learning ability over a filament RS, with a higher saturated accuracy approaching 99.6%, is finally demonstrated in a simplified ANN.