Dependable service-oriented computing relies on multiple Quality-of-Service (QoS) parameters to assess service performance. However, real-world QoS data are often sparse, noisy, and shaped by hierarchical dependencies arising from QoS interactions, geographical constraints, and network-level factors, making accurate prediction challenging. Existing deep learning-based methods often predict each QoS parameter separately, requiring multiple similar models, which increases computational overhead and limits their suitability for applications requiring joint decisions across multiple QoS parameters. Although recent joint QoS prediction studies employ shared architectures, differences in numerical ranges across QoS parameters can lead to task imbalance and negative transfer, while inadequate representation learning and suboptimal joint optimization can degrade prediction accuracy. We present SHARP-QoS, a joint QoS prediction framework with three components. First, hyperbolic graph and hypergraph convolutions in the Poincaré ball extract hierarchical features from QoS invocation and contextual graphs. Second, sparsely gated sub-network routing selectively shares contextual and cross-QoS features, and a gated fusion module combines them with the structural features. Third, an EMA-based loss-balancing strategy smooths short-term fluctuations in task losses to provide less fluctuating task weights. Experiments on three multi-QoS datasets covering two, three, and four QoS parameters show that SHARP-QoS achieves lower prediction errors than existing joint QoS prediction methods. Because its contextual branch relies only on public region and AS attributes, it supports prediction for new users and services. Ablation, hyperparameter, outlier, and scalability analyses further assess its performance, highlighting the trade-off between prediction accuracy and computational cost.

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