This paper presents a novel parallel convolution-self-attention neural network (PCSANN) based calibration scheme for Pipelined and Pipelined-SAR ADCs. Combining convolution neural network (CNN) and self-attention neural network (SANN), the proposed architecture jointly calibrates various nonlinearities in ADCs as a black box, including comparator offsets, inter-stage gain error (IGE), inter-stage nonlinearity, digital-to-analog converter (DAC) errors, memory effect (ME), etc. This proposed calibration scheme is validated with a fabricated 12-bit 150MSps pipelined ADC prototype and a fabricated 12-bit 750MSps pipelined-SAR ADC prototype. Measurement results show that the spurious-free dynamic range (SFDR) of the pipelined ADC is improved by 14.17dB from 64.98dB to 79.15dB, and the pipelined-SAR ADC achieves a 7.60dB improvement in SFDR from 63.00dB to 70.60dB.