Ensembles of neural networks achieve superior performance compared to stand-alone networks not only in terms of accuracy on in-distribution data but also on data with distributional shift alongside improved uncertainty calibration. Diversity among networks in an ensemble is believed to be key for building strong ensembles, but typical approaches only ensemble different weight vectors of a fixed architecture. Instead, we investigate neural architecture search (NAS) for explicitly constructing ensembles to exploit diversity among networks of varying architectures and to achieve robustness against distributional shift. By directly optimizing ensemble performance, our methods implicitly encourage diversity among networks, without the need to explicitly define diversity. We find that the resulting ensembles are more diverse compared to ensembles composed of a fixed architecture and are therefore also more powerful. We show significant improvements in ensemble performance on image classification tasks both for in-distribution data and during distributional shift with better uncertainty calibration.
Feature allocation models are popular models used in different applications such as unsupervised learning or network modeling. In particular, the Indian buffet process is a flexible and simple one-parameter feature allocation model where the number of features grows unboundedly with the number of objects. The Indian buffet process, like most feature allocation models, satisfies a symmetry property of exchangeability: the distribution is invariant under permutation of the objects. While this property is desirable in some cases, it has some strong implications. Importantly, the number of objects sharing a particular feature grows linearly with the number of objects. In this article, we describe a class of non-exchangeable feature allocation models where the number of objects sharing a given feature grows sublinearly, where the rate can be controlled by a tuning parameter. We derive the asymptotic properties of the model, and show that such model provides a better fit and better predictive performances on various datasets.
We propose a method for training a deterministic deep model that can find and reject out of distribution data points at test time with a single forward pass. Our approach, deterministic uncertainty quantification (DUQ), builds upon ideas of RBF networks. We scale training in these with a novel loss function and centroid updating scheme. By enforcing detectability of changes in the input using a gradient penalty, we are able to reliably detect out of distribution data. Our uncertainty quantification scales well to large datasets, and using a single model, we improve upon or match Deep Ensembles on notable difficult dataset pairs such as FashionMNIST vs. MNIST, and CIFAR-10 vs. SVHN, while maintaining competitive accuracy.
Overparameterized neural networks display state-of-the art performance. However, there is a growing need for smaller, energy-efficient, neural networks to be able to use machine learning applications on devices with limited computational resources. A popular approach consists of using pruning techniques. While these techniques have traditionally focused on pruning pre-trained neural networks (e.g. LeCun et al. (1990) and Hassabi et al. (1993)), recent work by Lee et al. (2018) showed promising results where pruning is performed at initialization. However, such procedures remain unsatisfactory as the resulting pruned networks can be difficult to train and, for instance, these procedures do not prevent one layer being fully pruned. In this paper we provide a comprehensive theoretical analysis of pruning at initialization and training sparse architectures. This analysis allows us to propose novel principled approaches which we validate experimentally on a variety of network architectures. We particularly show that we can prune up to 99.9% of the weights while keeping the model trainable.
Stochastic gradient descent with momentum (SGDm) is one of the most popular optimization algorithms in deep learning. While there is a rich theory of SGDm for convex problems, the theory is considerably less developed in the context of deep learning where the problem is non-convex and the gradient noise might exhibit a heavy-tailed behavior, as empirically observed in recent studies. In this study, we consider a \emph{continuous-time} variant of SGDm, known as the underdamped Langevin dynamics (ULD), and investigate its asymptotic properties under heavy-tailed perturbations. Supported by recent studies from statistical physics, we argue both theoretically and empirically that the heavy-tails of such perturbations can result in a bias even when the step-size is small, in the sense that \emph{the optima of stationary distribution} of the dynamics might not match \emph{the optima of the cost function to be optimized}. As a remedy, we develop a novel framework, which we coin as \emph{fractional} ULD (FULD), and prove that FULD targets the so-called Gibbs distribution, whose optima exactly match the optima of the original cost. We observe that the Euler discretization of FULD has noteworthy algorithmic similarities with \emph{natural gradient} methods and \emph{gradient clipping}, bringing a new perspective on understanding their role in deep learning. We support our theory with experiments conducted on a synthetic model and neural networks.
Few-shot supervised learning leverages experience from previous learning tasks to solve new tasks where only a few labelled examples are available. One successful line of approach to this problem is to use an encoder-decoder meta-learning pipeline, whereby labelled data in a task is encoded to produce task representation, and this representation is used to condition the decoder to make predictions on unlabelled data. We propose an approach that uses this pipeline with two important features. 1) We use infinite-dimensional functional representations of the task rather than fixed-dimensional representations. 2) We iteratively apply functional updates to the representation. We show that our approach can be interpreted as extending functional gradient descent, and delivers performance that is comparable to or outperforms previous state-of-the-art on few-shot classification benchmarks such as miniImageNet and tieredImageNet.
Existing approaches to amortized inference in probabilistic programs with unbounded loops can produce estimators with infinite variance. An instance of this is importance sampling inference in programs that explicitly include rejection sampling as part of the user-programmed generative procedure. In this paper we develop a new and efficient amortized importance sampling estimator. We prove finite variance of our estimator and empirically demonstrate our method's correctness and efficiency compared to existing alternatives on generative programs containing rejection sampling loops and discuss how to implement our method in a generic probabilistic programming framework.
We introduce a fully stochastic gradient based approach to Bayesian optimal experimental design (BOED). This is achieved through the use of variational lower bounds on the expected information gain (EIG) of an experiment that can be simultaneously optimized with respect to both the variational and design parameters. This allows the design process to be carried out through a single unified stochastic gradient ascent procedure, in contrast to existing approaches that typically construct an EIG estimator on a pointwise basis, before passing this estimator to a separate optimizer. We show that this, in turn, leads to more efficient BOED schemes and provide a number of a different variational objectives suited to different settings. Furthermore, we show that our gradient-based approaches are able to provide effective design optimization in substantially higher dimensional settings than existing approaches.
Continual learning aims to improve the ability of modern learning systems to deal with non-stationary distributions, typically by attempting to learn a series of tasks sequentially. Prior art in the field has largely considered supervised or reinforcement learning tasks, and often assumes full knowledge of task labels and boundaries. In this work, we propose an approach (CURL) to tackle a more general problem that we will refer to as unsupervised continual learning. The focus is on learning representations without any knowledge about task identity, and we explore scenarios when there are abrupt changes between tasks, smooth transitions from one task to another, or even when the data is shuffled. The proposed approach performs task inference directly within the model, is able to dynamically expand to capture new concepts over its lifetime, and incorporates additional rehearsal-based techniques to deal with catastrophic forgetting. We demonstrate the efficacy of CURL in an unsupervised learning setting with MNIST and Omniglot, where the lack of labels ensures no information is leaked about the task. Further, we demonstrate strong performance compared to prior art in an i.i.d setting, or when adapting the technique to supervised tasks such as incremental class learning.
Universal probabilistic programming systems (PPSs) provide a powerful and expressive framework for specifying rich and complex probabilistic models. However, this expressiveness comes at the cost of substantially complicating the process of drawing inferences from the model. In particular, inference can become challenging when the support of the model varies between executions. Though general-purpose inference engines have been designed to operate in such settings, they are typically highly inefficient, often relying on proposing from the prior to make transitions. To address this, we introduce a new inference framework: Divide, Conquer, and Combine (DCC). DCC divides the program into separate straight-line sub-programs, each of which has a fixed support allowing more powerful inference algorithms to be run locally, before recombining their outputs in a principled fashion. We show how DCC can be implemented as an automated and general-purpose PPS inference engine, and empirically confirm that it can provide substantial performance improvements over previous approaches.