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This paper introduces a novel methodology for developing low-complexity neural network (NN) based equalizers to address impairments in high-speed coherent optical transmission systems. We present a comprehensive exploration and comparison of deep model compression techniques applied to feed-forward and recurrent NN designs, assessing their impact on equalizer performance. Our investigation encompasses quantization, weight clustering, pruning, and other cutting-edge compression strategies. We propose and evaluate a Bayesian optimization-assisted compression approach that optimizes hyperparameters to simultaneously enhance performance and reduce complexity. Additionally, we introduce four distinct metrics (RMpS, BoP, NABS, and NLGs) to quantify computing complexity in various compression algorithms. These metrics serve as benchmarks for evaluating the relative effectiveness of NN …