<p>Tensor network is a fundamental data modeling approach to discover the hidden low-rank patterns in tensors and has attracted significant attention in many fields. This paper investigates the generalized tensor network (GTN) decomposition, which allows various famous loss functions. We develop a fast and accurate framework of all-at-once optimization for computing the generalized decomposition. It includes a unified way to find gradient and Hessian approximation as well as a more efficient method for the latter devised by exploiting the sparsity and multilinear structure. Further, the framework also incorporates a unified way with two accelerated techniques for implicitly estimating Hessian approximations for large-scale tensors. To facilitate understanding, we obtain the corresponding results for some specific GTN decompositions as examples. The adaptability and flexibility of GTN decomposition and the effectiveness of our framework are demonstrated on synthetic data and real-world problems. The acceleration of efficient methods for Hessian approximation is also evaluated via synthetic data.</p>