Building blocks for implementing Vector-by-Matrix Multiplication (VMM) are implemented with analog circuitry including non-volatile memory devices (flash transistors) and using in-memory computation. In one example, improved performance and more accurate VMM is achieved in arrays including multi-gate flash transistors when computation uses a control gate or the combination of control gate and word line (instead of using the word line alone). In another example, very fast weight programming of the arrays is achieved using a novel programming protocol. In yet another example, higher density and faster array programming is achieved when the gate(s) responsible for erasing devices, or the source line, are re-routed across different rows, e.g., in a zigzag form. In yet another embodiment a neural network is provided with nonlinear synaptic weights implemented with nonvolatile memory devices.