Due to the non-Gaussian natureNon-Gaussian distribution of erratic noiseErratic noise, traditional Gaussian-based denoising techniquesGaussian denoising methods face significant difficulties in effectively suppressing this type of noise. To address this issue, various state-of-the-art (SOTA) approaches, such as robust low-rank approximation (LRA)Low-rank approximation (LRA) and deep learning (DLDeep learning (DL)) techniques, have been proposed and have demonstrated encouraging results in mitigating erratic noiseErratic noise. However, the majority of these SOTA methods are grounded in matrix-based representations, which do not sufficiently capture the spatial correlations between erratic noiseErratic noise and valid signals, leading to suboptimal performance. To overcome these limitations, this study introduces a robust tensor-based deep learning (RTDL) approach for unsupervised 3D seismic erratic noiseErratic noise suppression, leveraging a combination of tensor sparse representation (SR)Tensor sparse representationSparse representation (SR) and a tensor neural network (tNN)Tensor neural network (t-NN). The core of the RTDL method lies in the incorporation of a robust tensor sparse norm designed to thoroughly utilize the tubular sparse structure of erratic noiseErratic noise in 3D space. By integrating this tensor sparse norm into the tNNTensor neural network (t-NN), a novel data-driven model is formed, which effectively enhances 3D erratic noiseErratic noise reduction. To optimize the parameters of this model, an efficient tensor optimization strategy based on alternating minimization (Alt) is employed, solving two subproblems in a sequential manner: tensor SR and the tNNTensor neural network (t-NN). Extensive experiments on both synthetic and real-world datasets demonstrate that the proposed RTDL method achieves superior results compared to existing SOTA techniques.