<p>How to process higher dimensional data and more complex dynamic systems on the basis of general memristive neural networks, and accelerate their synchronization time, has become one of the key bottlenecks in the future progress of neural networks. This paper investigates the finite-time synchronization (FNTS) and fixed-time synchronization (FXTS) problems of multidimension-valued memristive neural networks (MVMNNs). First, MVMNNs can be established and transformed into corresponding multidimensional systems by assigning different real, complex, or quaternion values to the state variables or connection weights of neural networks to meet the needs of different types of signal processing. The flexibility of this model enables it to efficiently handle high-dimensional data processing. Unlike traditional methods of dividing the real and imaginary parts, there is no need to separate the real and imaginary parts of MVMNNs. A new form of Lyapunov–Krasovskii functional is constructed and a novel nonlinear state feedback controller is designed. The controller combines adjustable coefficients to ensure the stability of MVMNNs. The FNTS/FXTS criterions in MVMNNs are obtained by applying the expanded Cauchy-Schwartz inequality and the distributional derivative of the absolute-valued function. Finally, two numerical cases are presented to demonstrate the validity of the results.</p>