Resistive Random Access Memories (ReRAM) arrays provides a promising basement to deploy neural network accelerators based on near or in memory computing. However most popular accelerators rely on Ohm’s and Kirchhoff’s laws to achieve multiply and accumulate, and thus are prone to ReRAM variability and voltage drop in the memory array, and thus need sophisticated readout circuits. Here we propose a robust binary neural network, based on fully differential capacitive neurons and ReRAM synapses, used in a resistive bridge fashion. We fabricated a network layer with up to 23 inputs that we extrapolated to large numbers of inputs through simulation. Defining proper programming and reading conditions, we demonstrate the high resilience of this solution with a minimal accuracy drop, compared to a software baseline, on image classification tasks. Moreover, our solution can achieve a peak energy efficiency, comparable with the state of the art, when projected to a 22 nanometer technology.