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：构建稳健、可解释且安全的人工智能系统需要在一定程度上通过概率视角量化并表征不确定性，因为这种方法能够模拟人类的认知能力。然而，概率计算因其固有的复杂性而面临重大挑战。本文提出了一种高效且可解释的概率计算框架，通过将概率表示截断至其前两阶矩（即均值和协方差）来实现。我们通过训练一个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示，并封装了均值与协方差之间的非线性耦合。研究表明，当均值受监督以优化任务目标时，由均值-协方差非线性耦合自发涌现的无监督协方差，能够忠实地捕获与模型预测相关的不确定性。我们的研究凸显了概率计算的固有可计算性与简洁性，从而使其能够更广泛地应用于大规模场景。