Deep neural networks achieve impressive results across diverse applications, yet their overconfidence on unseen inputs necessitates reliable epistemic uncertainty modeling. Existing methods for uncertainty modeling face a fundamental dilemma: Bayesian approaches provide principled estimates but remain computationally prohibitive, while efficient second-order predictors lack rigorous connections between their specific objectives and epistemic uncertainty quantification. To resolve this dilemma, we introduce Dirichlet-approximated possibilistic posterior predictions (DAPPr), a principled framework grounded in possibility theory. We define a possibilistic posterior over parameters, project it to the prediction space via supremum operators, and approximate the projected posterior using learnable Dirichlet possibility functions. This projection-and-approximation strategy yields a simple training objective with closed-form solutions. Despite its simplicity, extensive experiments across diverse benchmarks show that DAPPr achieves competitive or superior uncertainty quantification performance over state-of-the-art second-order predictors while maintaining both principled derivation and computational efficiency. Code is available at https://github.com/MaxwellYaoNi/DAPPr.

翻译：深度神经网络在各类应用中取得了令人瞩目的成果，但其对未见输入的过度自信需要可靠的认知不确定性建模。现有不确定性建模方法面临根本性困境：贝叶斯方法能提供原则性估计但计算成本高昂，而高效的二阶预测器在特定目标与认知不确定性量化之间缺乏严谨的理论联系。为破解这一困境，我们提出狄利克雷近似可能性后验预测（DAPPr），这是一个基于可能性理论的原则性框架。我们定义参数上的可能性后验，通过上确界算子将其投影到预测空间，并利用可学习的狄利克雷可能性函数近似投影后的后验。这种投影-近似策略产生了具有闭式解的简洁训练目标。尽管方法简洁，但在多样化基准上的广泛实验表明，DAPPr在保持理论严谨性和计算效率的同时，其不确定性量化性能达到或超越当前最先进的二阶预测器。代码已开源至 https://github.com/MaxwellYaoNi/DAPPr。