Hot-rolled strip products have diverse applications, and enhancing the detection, diagnostics, and prognostics of product quality during hot rolling is essential. Nevertheless, the multivariable, strong coupling, nonlinear, and time-varying nature of the production process poses a rigorous challenge for accurate hot-rolled prognostics. This paper implements a progressive layered extraction (PLE) multi-task learning (MTL) framework to simultaneously estimate multiple quality indicators, such as strip crown, center line deviation, exit temperature, wedge, width, and symmetry flatness. Additionally, the paper proposes the implements of Hybrid Bayesian Neural Network (HBNN) experts and a gating network with attention mechanism to integrate private and shared task features. It also puts forth an auxiliary task involving a Variational Autoencoder with Generative Adversarial Networks (VAE-GAN) to extract latent states from the original sequence. Moreover, an adaptive joint loss optimization is employed to update the weight of individual task losses for MTL training problems, and three sets of field hot-rolled datasets are used for model evaluation. In the experimental validation, considering the noisy field data and limited conditions in the real hot rolled production, comparative experiments are conducted to demonstrate the improved generalization and robustness of the proposed MTL approach. These experiments involve different percentages of the total data, ranging from 5% to 20%, and various prediction horizons ranging from 1 to 50 steps for model establishment. In addition, the paper discusses the interpretation of the model and strategies for further enhancing model performance.