###### Abstract  
Alzheimer's disease (AD) is an irreversible neurodegenerative disease. Providing trustworthy AD progression predictions for at-risk individuals contributes to early identification of AD patients and holds significant value in discovering effective treatments and empowering the patient in taking proactive care. Recently, although numerous disease progression models based on machine learning have emerged, they often focus solely on enhancing predictive accuracy and ignore the measurement of result reliability. Consequently, this oversight adversely affects the recognition and acceptance of these models in clinical applications. To address these problems, we propose a multi-task evidential sequence learning model for the trustworthy prediction of disease progression. Specifically, we incorporate evidential deep learning into the multi-task learning framework based on recurrent neural networks. We simultaneously perform AD clinical diagnosis and cognitive score predictions while quantifying the uncertainty of each prediction without incurring additional computational costs by leveraging the Dirichlet and Normal-Inverse-Gamma distributions. Moreover, an adaptive weighting scheme is introduced to automatically balance between tasks for more effective training. Finally, experimental results on the TADPOLE dataset validate that our model not only has a comparable predictive performance to similar models but also offers reliable quantification of prediction uncertainties, providing a crucial supplementary factor for risk-sensitive AD progression prediction applications. Alzheimer's disease; disease progression prediction; deep sequence learning; trustworthy evidential learning; adaptive weighting scheme 202310390  
cognitive score prediction holds a particular significance in clinical practice, as it enables physicians to make more accurate assessments of disease progression and provide patients with better treatment plans. Recently, the rapid progress of deep learning has attracted a growing number of researchers to explore its applications in the diagnosis of AD and the prediction of cognitive scores. [PERSON] et al. [3] utilized recurrent neural networks (RNNs) with LSTM cells to predict future cognitive scores. [PERSON] et al. and [PERSON] et al. [4; 5] employed variants of RNNs to predict AD diagnosis. Although both achieved promising results in their respective tasks, they focused solely on completing individual prediction tasks, disregarding the existing correlations among different tasks. Studies investigated by [PERSON] et al. [6] and [PERSON] et al. [7] have demonstrated that the simultaneous learning of multiple tasks during the AD disease modeling process benefits the model's ability to capture underlying disease characteristics and enhances the generalization performance of each task. Therefore, establishing a multi-task learning model that simultaneously handles disease diagnosis and cognitive score prediction proves to be an effective strategy for improving model performance. However, determining the appropriate loss weights for each task becomes a new unresolved issue when introducing multi-task learning. The allocation of loss weights directly impacts the model's performance and generalization ability across different tasks. Currently, most AD progression prediction models overlook the significance of loss weights among tasks and either assign equal weights or rely on laborious manual adjustments. Hence, there is a need to explore more effective methods for adjusting loss weights to construct superior multi-task learning models. Meanwhile, despite the high accuracy of existing AD clinical diagnosis and cognitive score prediction models, their recognition and acceptance in clinical applications remain limited. Trust in the outcomes of deep learning models is hindered in the healthcare domain due to their complex and black-box characteristics, presenting a challenge for decision makers.