Erik Daxberger

Erik Daxberger, Floris Weers, Bowen Zhang et al.

Sparse Mixture-of-Experts models (MoEs) have recently gained popularity due to their ability to decouple model size from inference efficiency by only activating a small subset of the model parameters for any given input token. As such, sparse MoEs have enabled unprecedented scalability, resulting in tremendous successes across domains such as natural language processing and computer vision. In this work, we instead explore the use of sparse MoEs to scale-down Vision Transformers (ViTs) to make them more attractive for resource-constrained vision applications. To this end, we propose a simplified and mobile-friendly MoE design where entire images rather than individual patches are routed to the experts. We also propose a stable MoE training procedure that uses super-class information to guide the router. We empirically show that our sparse Mobile Vision MoEs (V-MoEs) can achieve a better trade-off between performance and efficiency than the corresponding dense ViTs. For example, for the ViT-Tiny model, our Mobile V-MoE outperforms its dense counterpart by 3.39% on ImageNet-1k. For an even smaller ViT variant with only 54M FLOPs inference cost, our MoE achieves an improvement of 4.66%.

Javier Antorán, David Janz, James Urquhart Allingham et al.

The linearised Laplace method for estimating model uncertainty has received renewed attention in the Bayesian deep learning community. The method provides reliable error bars and admits a closed-form expression for the model evidence, allowing for scalable selection of model hyperparameters. In this work, we examine the assumptions behind this method, particularly in conjunction with model selection. We show that these interact poorly with some now-standard tools of deep learning--stochastic approximation methods and normalisation layers--and make recommendations for how to better adapt this classic method to the modern setting. We provide theoretical support for our recommendations and validate them empirically on MLPs, classic CNNs, residual networks with and without normalisation layers, generative autoencoders and transformers.

Erik Daxberger, Eric Nalisnick, James Urquhart Allingham et al.

The Bayesian paradigm has the potential to solve core issues of deep neural networks such as poor calibration and data inefficiency. Alas, scaling Bayesian inference to large weight spaces often requires restrictive approximations. In this work, we show that it suffices to perform inference over a small subset of model weights in order to obtain accurate predictive posteriors. The other weights are kept as point estimates. This subnetwork inference framework enables us to use expressive, otherwise intractable, posterior approximations over such subsets. In particular, we implement subnetwork linearized Laplace as a simple, scalable Bayesian deep learning method: We first obtain a MAP estimate of all weights and then infer a full-covariance Gaussian posterior over a subnetwork using the linearized Laplace approximation. We propose a subnetwork selection strategy that aims to maximally preserve the model's predictive uncertainty. Empirically, our approach compares favorably to ensembles and less expressive posterior approximations over full networks. Our proposed subnetwork (linearized) Laplace method is implemented within the laplace PyTorch library at https://github.com/AlexImmer/Laplace.

Runa Eschenhagen, Erik Daxberger, Philipp Hennig et al.

Deep neural networks are prone to overconfident predictions on outliers. Bayesian neural networks and deep ensembles have both been shown to mitigate this problem to some extent. In this work, we aim to combine the benefits of the two approaches by proposing to predict with a Gaussian mixture model posterior that consists of a weighted sum of Laplace approximations of independently trained deep neural networks. The method can be used post hoc with any set of pre-trained networks and only requires a small computational and memory overhead compared to regular ensembles. We theoretically validate that our approach mitigates overconfidence "far away" from the training data and empirically compare against state-of-the-art baselines on standard uncertainty quantification benchmarks.

Erik Daxberger, Agustinus Kristiadi, Alexander Immer et al.

Bayesian formulations of deep learning have been shown to have compelling theoretical properties and offer practical functional benefits, such as improved predictive uncertainty quantification and model selection. The Laplace approximation (LA) is a classic, and arguably the simplest family of approximations for the intractable posteriors of deep neural networks. Yet, despite its simplicity, the LA is not as popular as alternatives like variational Bayes or deep ensembles. This may be due to assumptions that the LA is expensive due to the involved Hessian computation, that it is difficult to implement, or that it yields inferior results. In this work we show that these are misconceptions: we (i) review the range of variants of the LA including versions with minimal cost overhead; (ii) introduce "laplace", an easy-to-use software library for PyTorch offering user-friendly access to all major flavors of the LA; and (iii) demonstrate through extensive experiments that the LA is competitive with more popular alternatives in terms of performance, while excelling in terms of computational cost. We hope that this work will serve as a catalyst to a wider adoption of the LA in practical deep learning, including in domains where Bayesian approaches are not typically considered at the moment.

Austin Tripp, Erik Daxberger, José Miguel Hernández-Lobato

Many important problems in science and engineering, such as drug design, involve optimizing an expensive black-box objective function over a complex, high-dimensional, and structured input space. Although machine learning techniques have shown promise in solving such problems, existing approaches substantially lack sample efficiency. We introduce an improved method for efficient black-box optimization, which performs the optimization in the low-dimensional, continuous latent manifold learned by a deep generative model. In contrast to previous approaches, we actively steer the generative model to maintain a latent manifold that is highly useful for efficiently optimizing the objective. We achieve this by periodically retraining the generative model on the data points queried along the optimization trajectory, as well as weighting those data points according to their objective function value. This weighted retraining can be easily implemented on top of existing methods, and is empirically shown to significantly improve their efficiency and performance on synthetic and real-world optimization problems.

Erik Daxberger, José Miguel Hernández-Lobato

Despite their successes, deep neural networks may make unreliable predictions when faced with test data drawn from a distribution different to that of the training data, constituting a major problem for AI safety. While this has recently motivated the development of methods to detect such out-of-distribution (OoD) inputs, a robust solution is still lacking. We propose a new probabilistic, unsupervised approach to this problem based on a Bayesian variational autoencoder model, which estimates a full posterior distribution over the decoder parameters using stochastic gradient Markov chain Monte Carlo, instead of fitting a point estimate. We describe how information-theoretic measures based on this posterior can then be used to detect OoD inputs both in input space and in the model's latent space. We empirically demonstrate the effectiveness of our proposed approach.

Yunpu Ma, Volker Tresp, Erik Daxberger

In recent years a number of large-scale triple-oriented knowledge graphs have been generated and various models have been proposed to perform learning in those graphs. Most knowledge graphs are static and reflect the world in its current state. In reality, of course, the state of the world is changing: a healthy person becomes diagnosed with a disease and a new president is inaugurated. In this paper, we extend models for static knowledge graphs to temporal knowledge graphs. This enables us to store episodic data and to generalize to new facts (inductive learning). We generalize leading learning models for static knowledge graphs (i.e., Tucker, RESCAL, HolE, ComplEx, DistMult) to temporal knowledge graphs. In particular, we introduce a new tensor model, ConT, with superior generalization performance. The performances of all proposed models are analyzed on two different datasets: the Global Database of Events, Language, and Tone (GDELT) and the database for Integrated Conflict Early Warning System (ICEWS). We argue that temporal knowledge graph embeddings might be models also for cognitive episodic memory (facts we remember and can recollect) and that a semantic memory (current facts we know) can be generated from episodic memory by a marginalization operation. We validate this episodic-to-semantic projection hypothesis with the ICEWS dataset.