The nonlinear Shannon capacity limit has been identified as the fundamental barrier to the maximum rate of transmitted information in optical communications. In long-haul high-bandwidth optical networks, this limit is mainly attributed to deterministic Kerr-induced fiber nonlinearities and from the interaction of amplified spontaneous emission noise from cascaded optical amplifiers with fiber nonlinearity: the stochastic parametric noise amplification. Unlike earlier impractical approaches that compensate solely deterministic nonlinearities, here we demonstrate a novel electronic-based deep neural network with multiple-inputs and outputs (MIMO) that tackles the interplay of deterministic and stochastic nonlinearity manifestation in coherent optical signals. Our demonstration shows that MIMO deep learning can compensate nonlinear inter-carrier crosstalk effects even in the presence of frequency stochastic variations, which has hitherto been considered impossible. Our solution significantly outperforms conventional machine learning and gold-standard nonlinear equalizers without sacrificing computational complexity, leading to record-breaking transmission performance for up to 40 Gbit/sec high-spectral-efficient optical signals.