Neuromorphic computing based on two-dimensional materials represents a promising hardware approach for data-intensive applications. Central to this new paradigm are memristive devices, which serve as the essential components in synaptic kernels. However, large-scale implementation of synaptic matrix using two-dimensional materials is hindered by challenges related to random component variation and array-level integration. Here, we develop a 16 × 16 computing kernel based on two-transistor-two-resistor unit with three-dimensional heterogeneous integration compatibility to boost energy efficiency and computing performance. We demonstrate the 4-bit weight characteristics of artificial synapses with low stochasticity. The synaptic array demonstration validates the practicality of utilizing emerging two-dimensional materials for monolithic three-dimensional heterogeneous integration. Additionally, we introduce the Gaussian noise quantization weight-training scheme alongside the ConvMixer convolution architecture to achieve image dataset identification with high accuracy. Our findings indicate that the synaptic kernel can significantly improve detection accuracy and inference performance on the CIFAR-10 dataset.