## 1 Introduction  
From streaming 4 K/8 K videos to accessing cloud-based Internet services, the need for high-speed and reliable Internet connectivity is on the rise. To satisfy these bandwidth demands, high-capacity optical transmission technologies are required. Recently, 800 Gbit/s systems were proposed utilizing eight lanes of 50 Gbaud four-level pulse amplitude modulation (PAM4) (i.e., 8 \(\times\) 100 Gbit/s/\(\lambda\)) or by utilizing four lanes of 100 Gbaud PAM4 (i.e., 4 \(\times\) 200 Gbit/s/\(\lambda\)) [1, 2]. It was also reported that an aggregate data rate of 1.6 Tbit/s transceiver (TRx) was realized by utilizing eight lanes of 200 Gbit/s [3]. For beyond 1 Tbit/s transmission [4], a single-lane data rate at or beyond 200 Gbit/s is required with improved power and space efficiencies [5]. Nowadays, silicon photonics (SiPh) is widely considered as one of the important optical integration technologies for the next generation data center optical networks and optical interconnects [6, 7, 8, 9, 10, 11]. SiPh devices consume less power and produce less heat than conventional electronic circuits, offering great advantages of energy-efficient bandwidth upgrade. In addition, SiPh is compatible with the mature, complementary metal-oxide-semiconductor (CMOS) fabrication technologies, which potentially allow integration of photonic and electronic devices at mass volume cost effectively. Recently, different high-speed SiPh modulators have been reported [12]. Although SiPh-based modulators provide many merits, such as low power consumption and a small footprint, there are still many challenges for data center interconnect applications [13]. One is the limited electrical-to-optical (EO) bandwidth (i.e., 50-60 Gbaud) and limited extinction ratio (ER) of the SiPh modulators. Hence, different digital signal processing (DSP) techniques are employed to further enhance the data rates, such as Volterraequalization [14], feed-forward equalization (FFE), and decision feedback equalization (DFE) [15], as well as machine learning approaches, including long short-term memory neural network (LSTMNN) [16], recurrent neural network (RNN) [17], etc. As discussed before, machine learning approaches have been successfully applied in optical communications and networking [18; 19]. Neuromorphics is an attempt to migrate the elements in machine learning algorithms to a hardware platform [20]. This could lead to much faster and more energy efficient data processing [21]. Thanks to the advancements in photonics technologies, bringing together neuromorphics and photonics could offer a high-bandwidth and low-power-consumption operation when compared with electronics [22]. An optical neural network (ONN) enables the running of machine learning algorithms more efficiently [23]. Once an ONN is trained, its architecture could be passive, and the computation using optical signals will be operated without the need of additional power consumption. ONNs can be implemented using free-space optics, which can provide the advantages of negligible crosstalk with lower losses [24]. Recently, many researchers have explored ONNs using an integrated approach with programmable silicon interferometers for matrix and vector multiplications [25; 26]. This enables chip-scale parameter calculations in neural networks. The basic component is the Mach-Zehnder Interferometer (MZI), which is utilized to manipulate both power coupling ratio and phase. The multiple MZI configuration can achieve a transmission matrix that resembles a fully connected layer in a neural network. Besides the MZI-based ONN, microring-based ONN [27] and phase change material-based ONN [28] are also promising. In this work, we propose and demonstrate an ONN to regenerate the four-level pulse amplitude modulation (PAM4) signal with high inter-symbol interference (ISI) generated experimentally by a silicon microring modulator (SiMRM). The proposed ONN has a multiple MZI configuration achieving a transmission matrix that resembles a fully connected layer in a neural network.