Multirotors are widely used in applications ranging from surveillance to precision agriculture, yet conventional designs remain limited by their under-actuation. Tilt-rotor configurations overcome this limitation by enabling full actuation. This paper investigates neural-network-based control strategies for a fully actuated tilt-rotor system with four thrust-vectoring inputs. Our work is structured in two parts. First, we deliberately present a negative result by evaluating a direct input-output control approach. In this method, multilayer perceptrons (MLPs), long short-term memory (LSTM) networks, and transformer models are trained to map system states and their desired values directly to control signals. We show that this strategy fails to stabilize the system, highlighting the inherent difficulty of applying direct input-output learning to highly unstable plants. Second, as the main contribution, we propose a neural-network-enhanced sliding mode controller (SMC). The method decomposes the system dynamics into input-independent and input-dependent components, with the former learned from a small dataset using lightweight networks, thereby reducing real-time computational demands. Moreover, the proposed method can be trained using flight logs collected from low-performance controllers, and the resulting dynamic model learned from real-world data can be used in simulation. We further compare MLP- and LSTM-based implementations under model uncertainties and external disturbances, demonstrating the robustness and effectiveness of the proposed approach; in particular, the controller with the LSTM plant dynamics predictor achieves superior performance to its MLP-based counterpart while also exhibiting lower runtime.