Analogue in-memory computing (AIMC) with resistive memory devices could reduce the latency and energy consumption of deep neural network inference tasks by directly performing computations within memory. However, to achieve end-to-end improvements in latency and energy consumption, AIMC must be combined with on-chip digital operations and on-chip communication. Here we report a multicore AIMC chip designed and fabricated in 14 nm complementary metal–oxide–semiconductor technology with backend-integrated phase-change memory. The fully integrated chip features 64 AIMC cores interconnected via an on-chip communication network. It also implements the digital activation functions and additional processing involved in individual convolutional layers and long short-term memory units. With this approach, we demonstrate near-software-equivalent inference accuracy with ResNet and long short-term memory networks, while implementing all the computations associated with the weight layers and the activation functions on the chip. For 8-bit input/output matrix–vector multiplications, in the four-phase (high-precision) or one-phase (low-precision) operational read mode, the chip can achieve a maximum throughput of 16.1 or 63.1 tera-operations per second at an energy efficiency of 2.48 or 9.76 tera-operations per second per watt, respectively.