In this paper, we present a novel neural network (NN) adaptive control architecture with guaranteed transient performance. With this new architecture, both input and output signals of an uncertain nonlinear system follow a desired linear system during the transient phase, in addition to stable tracking. This new architecture uses a low-pass filter in the feedback loop, which consequently enables to enforce the desired transient performance by increasing the adaptation gain. For the guaranteed transient performance of both input and output signals of the uncertain nonlinear system, the L1 gain of a cascaded system, comprised of the low-pass filter and the closed-loop desired reference model, is required to be less than the inverse of the Lipschitz constant of the unknown nonlinearities in the system. The tools from this paper can be used to develop a theoretically justified verification and validation framework for NN adaptive controllers. Simulation results illustrate the theoretical findings.