Constructing a computing circuit in three dimensions (3D) is a necessary step to enable the massive connections and efficient communications required in complex neural networks. 3D circuits based on conventional complementary metal–oxide–semiconductor transistors are, however, difficult to build because of challenges involved in growing or stacking multilayer single-crystalline silicon channels. Here we report a 3D circuit composed of eight layers of monolithically integrated memristive devices. The vertically aligned input and output electrodes in our 3D structure make it possible to directly map and implement complex neural networks. As a proof-of-concept demonstration, we programmed parallelly operated kernels into the 3D array, implemented a convolutional neural network and achieved software-comparable accuracy in recognizing handwritten digits from the Modified National Institute of Standard and Technology database. We also demonstrated the edge detection of moving objects in videos by applying groups of Prewitt filters in the 3D array to process pixels in parallel.

在三维（3D）中构建计算电路是实现复杂神经网络所需的大量连接和有效通信的必要步骤。但是，基于传统的互补金属氧化物半导体晶体管的3D电路很难构建，因为在生长或堆叠多层单晶硅通道方面存在挑战。在这里，我们报告一个由八层单片集成忆阻器件层组成的3D电路。我们3D结构中垂直对齐的输入和输出电极使直接映射和实现复杂的神经网络成为可能。作为概念验证的演示，我们将并行操作的内核编程到3D阵列中，实现了卷积神经网络，并在修改后的美国国家标准技术研究院数据库中识别手写数字时达到了软件可比的准确性。我们还通过在3D阵列中应用Prewitt滤镜组并行处理像素，演示了视频中运动对象的边缘检测。