A lightweight two-stage convolutional (deep) neural network (CNN) based modulation format identification (MFI) scheme is proposed and demonstrated for the polarization domain multiplexing (PDM) fiber communication system with probabilistically shaped (PS) modulation formats. The scheme is tested on a PDM system at a symbol rate of 28 GBaud. Six probabilistically shaped (PS) modulation formats (of 3 bit/symbol PS-16QAM, PS-32QAM, and PS-64QAM, of 4 bit/symbol PS-32QAM and PS-64QAM, and of 5 bit/symbol PS-64QAM) along with six standard modulation formats (BPSK, QPSK, 8PSK and three uniformly shaped (US) QAM: US-16QAM, US-32QAM and US-64QAM) are identified by the trained CNN. By taking advantage of computer vision, the results show that the proposed scheme can provide very high accuracy and significantly improve the identification performance over the existing techniques. The influences of the learning rate of the CNN are also discussed. INDEX TERMS Optical fiber communication, modulation format identification, convolutional neural networks.