Probabilistic computation and uncertainty quantification with emerging covariance
This work addresses the need for robust and interpretable AI systems by enabling uncertainty quantification, though it appears incremental as it builds on existing probabilistic methods.
The paper tackles the challenge of probabilistic computation in neural networks by developing a moment neural network that truncates probabilistic representation to mean and covariance, revealing that unsupervised covariance emerges from nonlinear coupling with the mean to capture prediction uncertainty.
Building robust, interpretable, and secure AI system requires quantifying and representing uncertainty under a probabilistic perspective to mimic human cognitive abilities. However, probabilistic computation presents significant challenges for most conventional artificial neural network, as they are essentially implemented in a deterministic manner. In this paper, we develop an efficient probabilistic computation framework by truncating the probabilistic representation of neural activation up to its mean and covariance and construct a moment neural network that encapsulates the nonlinear coupling between the mean and covariance of the underlying stochastic network. We reveal that when only the mean but not the covariance is supervised during gradient-based learning, the unsupervised covariance spontaneously emerges from its nonlinear coupling with the mean and faithfully captures the uncertainty associated with model predictions. Our findings highlight the inherent simplicity of probabilistic computation by seamlessly incorporating uncertainty into model prediction, paving the way for integrating it into large-scale AI systems.