Christian Henning

Learning a sequence of tasks without access to i.i.d. observations is a widely studied form of continual learning (CL) that remains challenging. In principle, Bayesian learning directly applies to this setting, since recursive and one-off Bayesian updates yield the same result. In practice, however, recursive updating often leads to poor trade-off solutions across tasks because approximate inference is necessary for most models of interest. Here, we describe an alternative Bayesian approach where task-conditioned parameter distributions are continually inferred from data. We offer a practical deep learning implementation of our framework based on probabilistic task-conditioned hypernetworks, an approach we term posterior meta-replay. Experiments on standard benchmarks show that our probabilistic hypernetworks compress sequences of posterior parameter distributions with virtually no forgetting. We obtain considerable performance gains compared to existing Bayesian CL methods, and identify task inference as our major limiting factor. This limitation has several causes that are independent of the considered sequential setting, opening up new avenues for progress in CL.

The question whether inputs are valid for the problem a neural network is trying to solve has sparked interest in out-of-distribution (OOD) detection. It is widely assumed that Bayesian neural networks (BNNs) are well suited for this task, as the endowed epistemic uncertainty should lead to disagreement in predictions on outliers. In this paper, we question this assumption and show that proper Bayesian inference with function space priors induced by neural networks does not necessarily lead to good OOD detection. To circumvent the use of approximate inference, we start by studying the infinite-width case, where Bayesian inference can be exact due to the correspondence with Gaussian processes. Strikingly, the kernels derived from common architectural choices lead to function space priors which induce predictive uncertainties that do not reflect the underlying input data distribution and are therefore unsuited for OOD detection. Importantly, we find the OOD behavior in this limiting case to be consistent with the corresponding finite-width case. To overcome this limitation, useful function space properties can also be encoded in the prior in weight space, however, this can currently only be applied to a specified subset of the domain and thus does not inherently extend to OOD data. Finally, we argue that a trade-off between generalization and OOD capabilities might render the application of BNNs for OOD detection undesirable in practice. Overall, our study discloses fundamental problems when naively using BNNs for OOD detection and opens interesting avenues for future research.

Natural intelligence has the ability to continuously learn from its environment, an environment that is constantly changing and thus induces uncertainties that need to be coped with to ensure survival. By contrast, artificial intelligence (AI) commonly learns from data only once during a particular training phase, and rarely explicitly represents or utilizes uncertainties. In this thesis, we contribute towards improving AI in these regards by designing and understanding neural network-based models that learn continually and that explicitly represent several sources of uncertainty, with the ultimate goal of obtaining models that are useful, reliable and practical. We start by setting this research into a broader context and providing an introduction to the fields of uncertainty estimation and continual learning. This detailed review can constitute an entry point for those interested in familiarizing themselves with these topics. After laying this foundation, we dive into the specific question of how to learn a set of tasks continually and present our approach for solving this problem based on a system of neural networks. More specifically, we train a meta-network to generate task-specific parameters for an inference model and show that, in this setting, forgetting can be prevented using a simple regularization at the meta-level. Due to the existence of task-specific solutions, the problem arises of having to infer the task to which an unseen input belongs. We investigate two major ways for solving this \emphtask-inference problem: (i) replay-based and (ii) uncertainty-based. While replay-based task-inference exhibits remarkable performance on simple benchmarks, our implementation of this method relies on generative modelling, which becomes disproportionately difficult with increased task complexity. Uncertainty-based task-inference, on the other hand, does not rely on external models and scales more easily to complex scenarios. Because calibrating the uncertainties required for task-inference is difficult, in practice, one often resorts to models that should \emphknow what they don’t know. This can in theory be achieved through a Bayesian treatment of model parameters. However, due to the difficulty in interpreting the prior knowledge given to a neural network-based model, it also becomes difficult to interpret what it is that the model \emphknows not to know. This realization has implications beyond continual learning, and more generally affects how current machine learning models handle unseen inputs. We discuss the intricacies associated with choosing prior knowledge in neural networks and show that common choices often lead to uncertainties that do not intrinsically reflect certain desiderata such as detecting unseen inputs that the model should not generalize to. Overall, this thesis compactly summarizes and contributes to the advancement of two important topics in nowadays deep learning research, uncertainty estimation and continual learning, while disclosing existing challenges, evaluating novel approaches and identifying promising avenues for future research.