AbstractMemristive crossbar architectures are evolving as powerful in-memory computing engines for artificial neural networks. However, the limited number of non-volatile conductance states offered by state-of-the-art memristors is a concern for their hardware implementation since trained weights must be rounded to the nearest conductance states, introducing error which can significantly limit inference accuracy. Moreover, the incapability of precise weight updates can lead to convergence problems and slowdown of on-chip training. In this article, we circumvent these challenges by introducing graphene-based multi-level (>16) and non-volatile memristive synapses with arbitrarily programmable conductance states. We also show desirable retention and programming endurance. Finally, we demonstrate that graphene memristors enable weight assignment based on k-means clustering, which offers greater computing accuracy when compared with uniform weight quantization for vector matrix multiplication, an essential component for any artificial neural network.