Building robust, interpretable, and secure artificial intelligence system requires some degree of quantifying and representing uncertainty via a probabilistic perspective, as it allows to mimic human cognitive abilities. However, probabilistic computation presents significant challenges due to its inherent complexity. In this paper, we develop an efficient and interpretable probabilistic computation framework by truncating the probabilistic representation up to its first two moments, i.e., mean and covariance. We instantiate the framework by training a deterministic surrogate of a stochastic network that learns the complex probabilistic representation via combinations of simple activations, encapsulating the non-linearities coupling of the mean and covariance. We show that when the mean is supervised for optimizing the task objective, the unsupervised covariance spontaneously emerging from the non-linear coupling with the mean faithfully captures the uncertainty associated with model predictions. Our research highlights the inherent computability and simplicity of probabilistic computation, enabling its wider application in large-scale settings.

翻译：构建鲁棒、可解释且安全的人工智能系统，需要从概率视角出发，对不确定性进行一定程度的量化与表征，因为这可以模拟人类认知能力。然而，概率计算因其固有的复杂性而面临重大挑战。本文通过将概率表征截断至前两阶矩，即均值与协方差，开发了一个高效且可解释的概率计算框架。我们通过训练一个随机网络的确定性替代模型来实例化该框架，该模型通过简单激活函数的组合学习复杂的概率表征，并封装了均值与协方差之间的非线性耦合关系。研究表明，当均值受任务目标监督优化时，通过均值与协方差间的非线性耦合自动涌现出的无监督协方差，能够忠实地捕捉模型预测相关的不确定性。本文凸显了概率计算固有的可计算性与简洁性，使其得以在更大规模场景中广泛应用。