There has recently been a concerted effort to derive mechanisms in vision and machine learning systems to offer uncertainty estimates of the predictions they make. Clearly, there are benefits to a system that is not only accurate but also has a sense for when it is not. Existing proposals center around Bayesian interpretations of modern deep architectures – these are effective but can often be computationally demanding. We show how classical ideas in the literature on exponential families on probabilistic networks provide an excellent starting point to derive uncertainty estimates in Gated Recurrent Units (GRU). Our proposal directly quantifies uncertainty deterministically, without the need for costly sampling-based estimation. We show that while uncertainty is quite useful by itself in computer vision and machine learning, we also demonstrate that it can play a key role in enabling statistical analysis with deep networks in neuroimaging studies with normative modeling methods. To our knowledge, this is the first result describing sampling-free uncertainty estimation for powerful sequential models such as GRUs.