## 1 Introduction  
To meet the growing demand for support for diverse data services, such as the Internet of Things, Big Data, cloud computing and video streaming, spectrum-sliced elastic optical networks (EONs) [1] were proposed. These have attracted considerable interest from the telecommunications R&D community worldwide [2]. A key focal point has been addressing the developing trend, in optical networks, of evolving from fixed network architectures to flexible and elastic ones [3, 4]. According to different transmission link conditions and various quality of service requirements, transceivers involved in EONs have to be capable of dynamically adjusting their operation parameters--including, for example, modulation formats, symbol rates and transmission power--in order to maximize their signal transmission capacities and spectral/power utilization efficiency. In traditional optical networks, these parameters are delivered to the corresponding receivers by the supervisory control layer of the optical networks. However, if the supervisory channel is disrupted and/or does not respond to the dynamic traffic demands with sufficient speed, the digital coherent receivers may fail to work appropriately [5; 6; 7]. In addition, both the cross-layer communications and end-to-end handshaking have been regarded as major factors limiting the flexibility of next-generation optical networks. Therefore, it is highly desirable that digital coherent receivers be able to autonomously identify these transmission parameters without assistance from the supervisory control layer. Of the aforementioned parameters, the modulation format is one of the most important. It is crucial to identify and monitor the modulation format in real time in communication scenarios with timing-varying channel characteristics, where adaptive signal modulation format variations must be implemented. The use of MFI techniques would eliminate the transmissions of signal modulation format information between the transceivers, thus considerably reducing unwanted overhead. The MFI algorithm could be applied before modulation format-dependent algorithms, including polarization demultiplexing, frequency offset compensation and carrier phase recovery [8], ensuring optimal system performance. The previously-reported MFI schemes for optical fiber communications were roughly classified into the following three categories: (1) data-aided schemes [9; 10; 11], in which additional pilot information is introduced and the computational complexity of the MFI scheme is low (at the cost of reduced spectral efficiency); (2) schemes based on Stokes space [7; 8; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23], which are not sensitive to carrier phase noise, frequency offset or polarization mixing; (3) schemes based on signal characteristics arising from constant modulus algorithm (CMA) equalization [24; 25; 26; 27; 28; 29; 30; 31; 32; 33], which are based on CMA-equalized signals and do not require any space mapping. Meanwhile, CMA can also compensate for residual chromatic dispersion (CD) and polarization mode dispersion (PMD). However, these schemes face a significant challenge, in that modulation format features are ambiguous under the effects of noise and other transmission impairments. In recent years, due to the power of ambiguous information identification, machine learning technologies have been widely employed for the identification of CMA equalized signals. These have included convolutional neural networks (CNN) [2], binarized neural networks (BNN) [3], support vector machine learning (SVM) [5], random forest methods [6], and deep neural networks (DNN) [34; 35]. Assisted by the powerful properties of machine learning, these schemes have been able to achieve high MFI performances. However, in order to obtain the desired optimal performances, these schemes require a large number of training samples, high computational resources and a complex training process.