Jaroslaw E. Prilepsky

Pedro J. Freire, Antonio Napoli, Diego Arguello Ron et al.

In this paper, a new methodology is proposed that allows for the low-complexity development of neural network (NN) based equalizers for the mitigation of impairments in high-speed coherent optical transmission systems. In this work, we provide a comprehensive description and comparison of various deep model compression approaches that have been applied to feed-forward and recurrent NN designs. Additionally, we evaluate the influence these strategies have on the performance of each NN equalizer. Quantization, weight clustering, pruning, and other cutting-edge strategies for model compression are taken into consideration. In this work, we propose and evaluate a Bayesian optimization-assisted compression, in which the hyperparameters of the compression are chosen to simultaneously reduce complexity and improve performance. In conclusion, the trade-off between the complexity of each compression approach and its performance is evaluated by utilizing both simulated and experimental data in order to complete the analysis. By utilizing optimal compression approaches, we show that it is possible to design an NN-based equalizer that is simpler to implement and has better performance than the conventional digital back-propagation (DBP) equalizer with only one step per span. This is accomplished by reducing the number of multipliers used in the NN equalizer after applying the weighted clustering and pruning algorithms. Furthermore, we demonstrate that an equalizer based on NN can also achieve superior performance while still maintaining the same degree of complexity as the full electronic chromatic dispersion compensation block. We conclude our analysis by highlighting open questions and existing challenges, as well as possible future research directions.

Pedro J. Freire, Sasipim Srivallapanondh, Michael Anderson et al.

In this work, we demonstrate the offline FPGA realization of both recurrent and feedforward neural network (NN)-based equalizers for nonlinearity compensation in coherent optical transmission systems. First, we present a realization pipeline showing the conversion of the models from Python libraries to the FPGA chip synthesis and implementation. Then, we review the main alternatives for the hardware implementation of nonlinear activation functions. The main results are divided into three parts: a performance comparison, an analysis of how activation functions are implemented, and a report on the complexity of the hardware. The performance in Q-factor is presented for the cases of bidirectional long-short-term memory coupled with convolutional NN (biLSTM + CNN) equalizer, CNN equalizer, and standard 1-StpS digital back-propagation (DBP) for the simulation and experiment propagation of a single channel dual-polarization (SC-DP) 16QAM at 34 GBd along 17x70km of LEAF. The biLSTM+CNN equalizer provides a similar result to DBP and a 1.7 dB Q-factor gain compared with the chromatic dispersion compensation baseline in the experimental dataset. After that, we assess the Q-factor and the impact of hardware utilization when approximating the activation functions of NN using Taylor series, piecewise linear, and look-up table (LUT) approximations. We also show how to mitigate the approximation errors with extra training and provide some insights into possible gradient problems in the LUT approximation. Finally, to evaluate the complexity of hardware implementation to achieve 200G and 400G throughput, fixed-point NN-based equalizers with approximated activation functions are developed and implemented in an FPGA.

Sasipim Srivallapanondh, Pedro J. Freire, Bernhard Spinnler et al.

To circumvent the non-parallelizability of recurrent neural network-based equalizers, we propose knowledge distillation to recast the RNN into a parallelizable feedforward structure. The latter shows 38\% latency decrease, while impacting the Q-factor by only 0.5dB.

Pedro J. Freire, Michael Anderson, Bernhard Spinnler et al.

For the first time, recurrent and feedforward neural network-based equalizers for nonlinearity compensation are implemented in an FPGA, with a level of complexity comparable to that of a dispersion equalizer. We demonstrate that the NN-based equalizers can outperform a 1 step-per-span DBP.

Vladislav Neskorniuk, Andrea Carnio, Domenico Marsella et al.

Autoencoder-based deep learning is applied to jointly optimize geometric and probabilistic constellation shaping for optical coherent communication. The optimized constellation shaping outperforms the 256 QAM Maxwell-Boltzmann probabilistic distribution with extra 0.05 bits/4D-symbol mutual information for 64 GBd transmission over 170 km SMF link.

Sasipim Srivallapanondh, Pedro J. Freire, Ashraful Alam et al.

For the first time, multi-task learning is proposed to improve the flexibility of NN-based equalizers in coherent systems. A "single" NN-based equalizer improves Q-factor by up to 4 dB compared to CDC, without re-training, even with variations in launch power, symbol rate, or transmission distance.

Pedro Freire, Egor Manuylovich, Jaroslaw E. Prilepsky et al.

This tutorial-review on applications of artificial neural networks in photonics targets a broad audience, ranging from optical research and engineering communities to computer science and applied mathematics. We focus here on the research areas at the interface between these disciplines, attempting to find the right balance between technical details specific to each domain and overall clarity. First, we briefly recall key properties and peculiarities of some core neural network types, which we believe are the most relevant to photonics, also linking the layer's theoretical design to some photonics hardware realizations. After that, we elucidate the question of how to fine-tune the selected model's design to perform the required task with optimized accuracy. Then, in the review part, we discuss recent developments and progress for several selected applications of neural networks in photonics, including multiple aspects relevant to optical communications, imaging, sensing, and the design of new materials and lasers. In the following section, we put a special emphasis on how to accurately evaluate the complexity of neural networks in the context of the transition from algorithms to hardware implementation. The introduced complexity characteristics are used to analyze the applications of neural networks in optical communications, as a specific, albeit highly important example, comparing those with some benchmark signal processing methods. We combine the description of the well-known model compression strategies used in machine learning, with some novel techniques introduced recently in optical applications of neural networks. It is important to stress that although our focus in this tutorial-review is on photonics, we believe that the methods and techniques presented here can be handy in a much wider range of scientific and engineering applications.

Bilal Khalid, Pedro Freire, Sergei K. Turitsyn et al.

Kolmogorov-Arnold Networks (KANs) have recently emerged as a powerful architecture for various machine learning applications. However, their unique structure raises significant concerns regarding their computational overhead. Existing studies primarily evaluate KAN complexity in terms of Floating-Point Operations (FLOPs) required for GPU-based training and inference. However, in many latency-sensitive and power-constrained deployment scenarios, such as neural network-driven non-linearity mitigation in optical communications or channel state estimation in wireless communications, training is performed offline and dedicated hardware accelerators are preferred over GPUs for inference. Recent hardware implementation studies report KAN complexity using platform-specific resource consumption metrics, such as Look-Up Tables, Flip-Flops, and Block RAMs. However, these metrics require a full hardware design and synthesis stage that limits their utility for early-stage architectural decisions and cross-platform comparisons. To address this, we derive generalized, platform-independent formulae for evaluating the hardware inference complexity of KANs in terms of Real Multiplications (RM), Bit Operations (BOP), and Number of Additions and Bit-Shifts (NABS). We extend our analysis across multiple KAN variants, including B-spline, Gaussian Radial Basis Function (GRBF), Chebyshev, and Fourier KANs. The proposed metrics can be computed directly from the network structure and enable a fair and straightforward inference complexity comparison between KAN and other neural network architectures.

Geraldo Gomes, Pedro Freire, Jaroslaw E. Prilepsky et al.

Power efficiency remains a significant challenge in modern optical fiber communication systems, driving efforts to reduce the computational complexity of digital signal processing, particularly in chromatic dispersion compensation (CDC) algorithms. While various strategies for complexity reduction have been proposed, many lack the necessary hardware implementation to validate their benefits. This paper provides a theoretical analysis of the tap overlapping effect in CDC filters for coherent receivers, introduces a novel Time-Domain Clustered Equalizer (TDCE) technique based on this concept, and presents a Field-Programmable Gate Array (FPGA) implementation for validation. We developed an innovative parallelization method for TDCE, implementing it in hardware for fiber lengths up to 640 km. A fair comparison with the state-of-the-art frequency domain equalizer (FDE) under identical conditions is also conducted. Our findings highlight that implementation strategies, including parallelization and memory management, are as crucial as computational complexity in determining hardware complexity and energy efficiency. The proposed TDCE hardware implementation achieves up to 70.7\% energy savings and 71.4\% multiplier usage savings compared to FDE, despite its higher computational complexity.

Pedro Freire, Sasipim Srivallapanondh, Antonio Napoli et al.

In this paper, we provide a systematic approach for assessing and comparing the computational complexity of neural network layers in digital signal processing. We provide and link four software-to-hardware complexity measures, defining how the different complexity metrics relate to the layers' hyper-parameters. This paper explains how to compute these four metrics for feed-forward and recurrent layers, and defines in which case we ought to use a particular metric depending on whether we characterize a more soft- or hardware-oriented application. One of the four metrics, called `the number of additions and bit shifts (NABS)', is newly introduced for heterogeneous quantization. NABS characterizes the impact of not only the bitwidth used in the operation but also the type of quantization used in the arithmetical operations. We intend this work to serve as a baseline for the different levels (purposes) of complexity estimation related to the neural networks' application in real-time digital signal processing, aiming at unifying the computational complexity estimation.

Yousuf Moiz Ali, Jaroslaw E. Prilepsky, João Pedro et al.

We present a novel online learning-based approach for concept drift adaptation in optical network failure detection, achieving up to a 70% improvement in performance over conventional static models while maintaining low latency.

Yousuf Moiz Ali, Jaroslaw E. Prilepsky, Nicola Sambo et al.

Machine learning-based failure management in optical networks has gained significant attention in recent years. However, severe class imbalance, where normal instances vastly outnumber failure cases, remains a considerable challenge. While pre- and in-processing techniques have been widely studied, post-processing methods are largely unexplored. In this work, we present a direct comparison of pre-, in-, and post-processing approaches for class imbalance mitigation in failure detection and identification using an experimental dataset. For failure detection, post-processing methods-particularly Threshold Adjustment-achieve the highest F1 score improvement (up to 15.3%), while Random Under-Sampling provides the fastest inference. In failure identification, GenAI methods deliver the most substantial performance gains (up to 24.2%), whereas post-processing shows limited impact in multi-class settings. When class overlap is present and latency is critical, over-sampling methods such as the SMOTE are most effective; without latency constraints, Meta-Learning yields the best results. In low-overlap scenarios, Generative AI approaches provide the highest performance with minimal inference time.

Yousuf Moiz Ali, Jaroslaw E. Prilepsky, Nicola Sambo et al.

We compare pre-, in-, and post-processing techniques for class imbalance mitigation in optical network failure detection. Threshold Adjustment achieves the highest F1 gain (15.3%), while Random Under-sampling (RUS) offers the fastest inference, highlighting a key performance-complexity trade-off.

Sasipim Srivallapanondh, Pedro J. Freire, Antonio Napoli et al.

To reduce the complexity of the hardware implementation of neural network-based optical channel equalizers, we demonstrate that the performance of the biLSTM equalizer with approximated activation functions is close to that of the original model.

Pedro J. Freire, Bernhard Spinnler, Daniel Abode et al.

We introduce the domain adaptation and randomization approach for calibrating neural network-based equalizers for real transmissions, using synthetic data. The approach renders up to 99\% training process reduction, which we demonstrate in three experimental setups.

Pedro J. Freire, Yevhenii Osadchuk, Antonio Napoli et al.

Addressing the neural network-based optical channel equalizers, we quantify the trade-off between their performance and complexity by carrying out the comparative analysis of several neural network architectures, presenting the results for TWC and SSMF set-ups.

Vladislav Neskorniuk, Andrea Carnio, Vinod Bajaj et al.

We present a novel end-to-end autoencoder-based learning for coherent optical communications using a "parallelizable" perturbative channel model. We jointly optimized constellation shaping and nonlinear pre-emphasis achieving mutual information gain of 0.18 bits/sym./pol. simulating 64 GBd dual-polarization single-channel transmission over 30x80 km G.652 SMF link with EDFAs.