Multicarrier transmissions, such as orthogonal frequency/chirp division multiplexing (OF/CDM), offer high spectral efficiency and low complexity equalization in multipath fading channels at the cost of high peak-to-average power ratio (PAPR). High peak powers can occur randomly and may drive the power amplifier (PA) into saturation, resulting in non-linear distortion. In this work, we propose a novel tensor-train (TT) deep neural network (DNN) architecture combined with soft clipping to reduce the PAPR to a deterministic level and minimize in-band distortion, while also satisfying spectral mask constraints. The proposed solution requires modifications only at the transmitter and there is no loss of spectral efficiency. Employing the TT decomposition allows for significant reduction in parameters. Results show that the proposed solution allows for significant reduction in PAPR with minimal performance loss. Furthermore, an upper bound for the PAPR is also derived which allows for the prediction of the required input power back off (IBO) without extensive simulations and trial-and-error.