Although neural networks are powerful function approximators, the underlying modelling assumptions ultimately define the likelihood and thus the hypothesis class they are parameterizing. In classification, these assumptions are minimal as the commonly employed softmax is capable of representing any categorical distribution. In regression, however, restrictive assumptions on the type of continuous distribution to be realized are typically placed, like the dominant choice of training via mean-squared error and its underlying Gaussianity assumption. Recently, modelling advances allow to be agnostic to the type of continuous distribution to be modelled, granting regression the flexibility of classification models. While past studies stress the benefit of such flexible regression models in terms of performance, here we study the effect of the model choice on uncertainty estimation. We highlight that under model misspecification, aleatoric uncertainty is not properly captured, and that a Bayesian treatment of a misspecified model leads to unreliable epistemic uncertainty estimates. Overall, our study provides an overview on how modelling choices in regression may influence uncertainty estimation and thus any downstream decision making process.

The need to avoid confident predictions on unfamiliar data 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 induced under common architectural choices lead to uncertainties that do not reflect the underlying data generating process and are therefore unsuited for OOD detection. Importantly, we find this OOD behavior to be consistent with the corresponding finite-width networks. Desirable function space properties can be encoded in the prior in weight space, however, this currently only applies 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.

The need to avoid confident predictions on unfamiliar data has sparked interest in out-of-distribution (OOD) detection. It is widely assumed that Bayesian neural networks (BNN) 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 provide empirical evidence that proper Bayesian inference with common neural network architectures 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 considering the corresponding Gaussian process. Strikingly, the kernels induced under common architectural choices lead to uncertainties that do not reflect the underlying data generating process and are therefore unsuited for OOD detection. Finally, we study finite-width networks using HMC, and observe OOD behavior that is consistent with the infinite-width case. Overall, our study discloses fundamental problems when naively using BNNs for OOD detection and opens interesting avenues for future research.

Continual Learning (CL) algorithms have recently received a lot of attention as they attempt to overcome the need to train with an i.i.d. sample from some unknown target data distribution. Building on prior work, we study principled ways to tackle the CL problem by adopting a Bayesian perspective and focus on continually learning a task-specific posterior distribution via a shared meta-model, a task-conditioned hypernetwork. This approach, which we term Posterior-replay CL, is in sharp contrast to most Bayesian CL approaches that focus on the recursive update of a single posterior distribution. The benefits of our approach are (1) an increased flexibility to model solutions in weight space and therewith less susceptibility to task dissimilarity, (2) access to principled task-specific predictive uncertainty estimates, that can be used to infer task identity during test time and to detect task boundaries during training, and (3) the ability to revisit and update task-specific posteriors in a principled manner without requiring access to past data. The proposed framework is versatile, which we demonstrate using simple posterior approximations (such as Gaussians) as well as powerful, implicit distributions modelled via a neural network. We illustrate the conceptual advance of our framework on low-dimensional problems and show performance gains on computer vision benchmarks.

While a diverse collection of continual learning (CL) methods has been proposed to prevent catastrophic forgetting, a thorough investigation of their effectiveness for processing sequential data with recurrent neural networks (RNNs) is lacking. Here, we provide the first comprehensive evaluation of established CL methods on a variety of sequential data benchmarks. Specifically, we shed light on the particularities that arise when applying weight-importance methods, such as elastic weight consolidation, to RNNs. In contrast to feedforward networks, RNNs iteratively reuse a shared set of weights and require working memory to process input samples. We show that the performance of weight-importance methods is not directly affected by the length of the processed sequences, but rather by high working memory requirements, which lead to an increased need for stability at the cost of decreased plasticity for learning subsequent tasks. We additionally provide theoretical arguments supporting this interpretation by studying linear RNNs. Our study shows that established CL methods can be successfully ported to the recurrent case, and that a recent regularization approach based on hypernetworks outperforms weight-importance methods, thus emerging as a promising candidate for CL in RNNs. Overall, we provide insights on the differences between CL in feedforward networks and RNNs, while guiding towards effective solutions to tackle CL on sequential data.

The largely successful method of training neural networks is to learn their weights using some variant of stochastic gradient descent (SGD). Here, we show that the solutions found by SGD can be further improved by ensembling a subset of the weights in late stages of learning. At the end of learning, we obtain back a single model by taking a spatial average in weight space. To avoid incurring increased computational costs, we investigate a family of low-dimensional late-phase weight models which interact multiplicatively with the remaining parameters. Our results show that augmenting standard models with late-phase weights improves generalization in established benchmarks such as CIFAR-10/100, ImageNet and enwik8. These findings are complemented with a theoretical analysis of a noisy quadratic problem which provides a simplified picture of the late phases of neural network learning. Neural networks trained with SGD generalize remarkably well on a wide range of problems. A classic technique to further improve generalization is to ensemble many such models (Lakshminarayanan et al., 2017). At test time, the predictions made by each model are combined, usually through a simple average. Although largely successful, this technique is costly both during learning and inference. This has prompted the development of ensembling methods with reduced complexity, for example by collecting models along an optimization path generated by SGD (Huang et al., 2017), by performing interpolations in weight space (Garipov et al., 2018), or by tying a subset of the weights over the ensemble (Lee et al., 2015; Wen et al., 2020). An alternative line of work explores the use of ensembles to guide the optimization of a single model (Zhang et al., 2015; Pittorino et al., 2020). We join these efforts and develop a method that fine-tunes the behavior of SGD using late-phase weights: late in training, we replicate a subset of the weights of a neural network and randomly initialize them in a small neighborhood.

Artificial neural networks suffer from catastrophic forgetting when they are sequentially trained on multiple tasks. To overcome this problem, we present a novel approach based on task-conditioned hypernetworks, i.e., networks that generate the weights of a target model based on task identity. Continual learning (CL) is less difficult for this class of models thanks to a simple key observation: instead of relying on recalling the input-output relations of all previously seen data, task-conditioned hypernetworks only require rehearsing previous weight realizations, which can be maintained in memory using a simple regularizer. Besides achieving good performance on standard CL benchmarks, additional experiments on long task sequences reveal that task-conditioned hypernetworks display an unprecedented capacity to retain previous memories. Notably, such long memory lifetimes are achieved in a compressive regime, when the number of trainable weights is comparable or smaller than target network size. We provide insight into the structure of low-dimensional task embedding spaces (the input space of the hypernetwork) and show that task-conditioned hypernetworks demonstrate transfer learning properties. Finally, forward information transfer is further supported by empirical results on a challenging CL benchmark based on the CIFAR-10/100 image datasets.