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Vincent Fortuin

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20 papers

2 author rows

ICML Conference 2025 Conference Paper

Can Transformers Learn Full Bayesian Inference in Context?

Arik Reuter
Tim G. J. Rudner
Vincent Fortuin
David Rügamer

Transformers have emerged as the dominant architecture in the field of deep learning, with a broad range of applications and remarkable in-context learning (ICL) capabilities. While not yet fully understood, ICL has already proved to be an intriguing phenomenon, allowing transformers to learn in context—without requiring further training. In this paper, we further advance the understanding of ICL by demonstrating that transformers can perform full Bayesian inference for commonly used statistical models in context. More specifically, we introduce a general framework that builds on ideas from prior fitted networks and continuous normalizing flows and enables us to infer complex posterior distributions for models such as generalized linear models and latent factor models. Extensive experiments on real-world datasets demonstrate that our ICL approach yields posterior samples that are similar in quality to state-of-the-art MCMC or variational inference methods that do not operate in context. The source code for this paper is available at https: //github. com/ArikReuter/ICL_for_Full_Bayesian_Inference

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TMLR Journal 2025 Journal Article

On the Challenges and Opportunities in Generative AI

Laura Manduchi
Clara Meister
Kushagra Pandey
Robert Bamler
Ryan Cotterell
Sina Däubener
Sophie Fellenz
Asja Fischer

The field of deep generative modeling has grown rapidly in the last few years. With the availability of massive amounts of training data coupled with advances in scalable unsupervised learning paradigms, recent large-scale generative models show tremendous promise in synthesizing high-resolution images and text, as well as structured data such as videos and molecules. However, we argue that current large-scale generative AI models exhibit several fundamental shortcomings that hinder their widespread adoption across domains. In this work, our objective is to identify these issues and highlight key unresolved challenges in modern generative AI paradigms that should be addressed to further enhance their capabilities, versatility, and reliability. By identifying these challenges, we aim to provide researchers with insights for exploring fruitful research directions, thus fostering the development of more robust and accessible generative AI solutions.

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NeurIPS Conference 2025 Conference Paper

ProSpero: Active Learning for Robust Protein Design Beyond Wild-Type Neighborhoods

Michal Kmicikiewicz
Vincent Fortuin
Ewa Szczurek

Designing protein sequences of both high fitness and novelty is a challenging task in data-efficient protein engineering. Exploration beyond wild-type neighborhoods often leads to biologically implausible sequences or relies on surrogate models that lose fidelity in novel regions. Here, we propose ProSpero, an active learning framework in which a frozen pre-trained generative model is guided by a surrogate updated from oracle feedback. By integrating fitness-relevant residue selection with biologically-constrained Sequential Monte Carlo sampling, our approach enables exploration beyond wild-type neighborhoods while preserving biological plausibility. We show that our framework remains effective even when the surrogate is misspecified. ProSpero consistently outperforms or matches existing methods across diverse protein engineering tasks, retrieving sequences of both high fitness and novelty.

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NeurIPS Conference 2024 Conference Paper

FSP-Laplace: Function-Space Priors for the Laplace Approximation in Bayesian Deep Learning

Tristan Cinquin
Marvin Pförtner
Vincent Fortuin
Philipp Hennig
Robert Bamler

Laplace approximations are popular techniques for endowing deep networks with epistemic uncertainty estimates as they can be applied without altering the predictions of the trained network, and they scale to large models and datasets. While the choice of prior strongly affects the resulting posterior distribution, computational tractability and lack of interpretability of the weight space typically limit the Laplace approximation to isotropic Gaussian priors, which are known to cause pathological behavior as depth increases. As a remedy, we directly place a prior on function space. More precisely, since Lebesgue densities do not exist on infinite-dimensional function spaces, we recast training as finding the so-called weak mode of the posterior measure under a Gaussian process (GP) prior restricted to the space of functions representable by the neural network. Through the GP prior, one can express structured and interpretable inductive biases, such as regularity or periodicity, directly in function space, while still exploiting the implicit inductive biases that allow deep networks to generalize. After model linearization, the training objective induces a negative log-posterior density to which we apply a Laplace approximation, leveraging highly scalable methods from matrix-free linear algebra. Our method provides improved results where prior knowledge is abundant (as is the case in many scientific inference tasks). At the same time, it stays competitive for black-box supervised learning problems, where neural networks typically excel.

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ICML Conference 2024 Conference Paper

Improving Neural Additive Models with Bayesian Principles

Kouroche Bouchiat
Alexander Immer
Hugo Yèche
Gunnar Rätsch
Vincent Fortuin

Neural additive models (NAMs) enhance the transparency of deep neural networks by handling input features in separate additive sub-networks. However, they lack inherent mechanisms that provide calibrated uncertainties and enable selection of relevant features and interactions. Approaching NAMs from a Bayesian perspective, we augment them in three primary ways, namely by a) providing credible intervals for the individual additive sub-networks; b) estimating the marginal likelihood to perform an implicit selection of features via an empirical Bayes procedure; and c) facilitating the ranking of feature pairs as candidates for second-order interaction in fine-tuned models. In particular, we develop Laplace-approximated NAMs (LA-NAMs), which show improved empirical performance on tabular datasets and challenging real-world medical tasks.

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TMLR Journal 2024 Journal Article

Incorporating Unlabelled Data into Bayesian Neural Networks

Mrinank Sharma
Tom Rainforth
Yee Whye Teh
Vincent Fortuin

Conventional Bayesian Neural Networks (BNNs) are unable to leverage unlabelled data to improve their predictions. To overcome this limitation, we introduce Self-Supervised Bayesian Neural Networks, which use unlabelled data to learn models with suitable prior predictive distributions. This is achieved by leveraging contrastive pretraining techniques and optimising a variational lower bound. We then show that the prior predictive distributions of self-supervised BNNs capture problem semantics better than conventional BNN priors. In turn, our approach offers improved predictive performance over conventional BNNs, especially in low-budget regimes.

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ICML Conference 2024 Conference Paper

Position: Bayesian Deep Learning is Needed in the Age of Large-Scale AI

Theodore Papamarkou
Maria Skoularidou
Konstantina Palla
Laurence Aitchison
Julyan Arbel
David B. Dunson
Maurizio Filippone
Vincent Fortuin

In the current landscape of deep learning research, there is a predominant emphasis on achieving high predictive accuracy in supervised tasks involving large image and language datasets. However, a broader perspective reveals a multitude of overlooked metrics, tasks, and data types, such as uncertainty, active and continual learning, and scientific data, that demand attention. Bayesian deep learning (BDL) constitutes a promising avenue, offering advantages across these diverse settings. This paper posits that BDL can elevate the capabilities of deep learning. It revisits the strengths of BDL, acknowledges existing challenges, and highlights some exciting research avenues aimed at addressing these obstacles. Looking ahead, the discussion focuses on possible ways to combine large-scale foundation models with BDL to unlock their full potential.

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NeurIPS Conference 2024 Conference Paper

Shaving Weights with Occam's Razor: Bayesian Sparsification for Neural Networks using the Marginal Likelihood

Rayen Dhahri
Alexander Immer
Betrand Charpentier
Stephan Günnemann
Vincent Fortuin

Neural network sparsification is a promising avenue to save computational time and memory costs, especially in an age where many successful AI models are becoming too large to naively deploy on consumer hardware. While much work has focused on different weight pruning criteria, the overall sparsifiability of the network, i. e. , its capacity to be pruned without quality loss, has often been overlooked. We present Sparsifiability via the Marginal likelihood (SpaM), a sparsification framework that highlights the effectiveness of using the Bayesian marginal likelihood in conjunction with sparsity-inducing priors for making neural networks more sparsifiable. Our approach implements an automatic Occam's razor that selects the most sparsifiable model that still explains the data well, both for structured and unstructured sparsification. In addition, we demonstrate that the pre-computed posterior precision from the Laplace approximation can be re-used to define a cheap pruning criterion, which outperforms many existing (more expensive) approaches. We demonstrate the effectiveness of our framework, especially at high sparsity levels, across a range of different neural network architectures and datasets.

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UAI Conference 2024 Conference Paper

Understanding Pathologies of Deep Heteroskedastic Regression

Eliot Wong-Toi
Alex Boyd
Vincent Fortuin
Stephan Mandt

Deep, overparameterized regression models are notorious for their tendency to overfit. This problem is exacerbated in heteroskedastic models, which predict both mean and residual noise for each data point. At one extreme, these models fit all training data perfectly, eliminating residual noise entirely; at the other, they overfit the residual noise while predicting a constant, uninformative mean. We observe a lack of middle ground, suggesting a phase transition dependent on model regularization strength. Empirical verification supports this conjecture by fitting numerous models with varying mean and variance regularization. To explain the transition, we develop a theoretical framework based on a statistical field theory, yielding qualitative agreement with experiments. As a practical consequence, our analysis simplifies hyperparameter tuning from a two-dimensional to a one-dimensional search, substantially reducing the computational burden. Experiments on diverse datasets, including UCI datasets and the large-scale ClimSim climate dataset, demonstrate significantly improved performance in various calibration tasks.

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JMLR Journal 2023 Journal Article

Scalable PAC-Bayesian Meta-Learning via the PAC-Optimal Hyper-Posterior: From Theory to Practice

Jonas Rothfuss
Martin Josifoski
Vincent Fortuin
Andreas Krause

Meta-Learning aims to speed up the learning process on new tasks by acquiring useful inductive biases from datasets of related learning tasks. While, in practice, the number of related tasks available is often small, most of the existing approaches assume an abundance of tasks; making them unrealistic and prone to overfitting. A central question in the meta-learning literature is how to regularize to ensure generalization to unseen tasks. In this work, we provide a theoretical analysis using the PAC-Bayesian theory and present a generalization bound for meta-learning, which was first derived by Rothfuss et al. (2021). Crucially, the bound allows us to derive the closed form of the optimal hyper-posterior, referred to as PACOH, which leads to the best performance guarantees. We provide a theoretical analysis and empirical case study under which conditions and to what extent these guarantees for meta-learning improve upon PAC-Bayesian per-task learning bounds. The closed-form PACOH inspires a practical meta-learning approach that avoids the reliance on bi-level optimization, giving rise to a stochastic optimization problem that is amenable to standard variational methods that scale well. Our experiments show that, when instantiating the PACOH with Gaussian processes and Bayesian Neural Networks models, the resulting methods are more scalable, and yield state-of-the-art performance, both in terms of predictive accuracy and the quality of uncertainty estimates. [abs] [ pdf ][ bib ] &copy JMLR 2023. ( edit, beta )

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ICLR Conference 2022 Conference Paper

Isotropic Gaussian priors are the de facto standard for modern Bayesian neural network inference. However, it is unclear whether these priors accurately reflect our true beliefs about the weight distributions or give optimal performance. To find better priors, we study summary statistics of neural network weights in networks trained using stochastic gradient descent (SGD). We find that convolutional neural network (CNN) and ResNet weights display strong spatial correlations, while fully connected networks (FCNNs) display heavy-tailed weight distributions. We show that building these observations into priors can lead to improved performance on a variety of image classification datasets. Surprisingly, these priors mitigate the cold posterior effect in FCNNs, but slightly increase the cold posterior effect in ResNets.

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UAI Conference 2022 Conference Paper

Data augmentation in Bayesian neural networks and the cold posterior effect

Seth Nabarro
Stoil Ganev
Adrià Garriga-Alonso
Vincent Fortuin
Mark van der Wilk
Laurence Aitchison

Bayesian neural networks that incorporate data augmentation implicitly use a “randomly perturbed log-likelihood [which] does not have a clean interpretation as a valid likelihood function” (Izmailov et al. 2021). Here, we provide several approaches to developing principled Bayesian neural networks incorporating data augmentation. We introduce a “finite orbit” setting which allows valid likelihoods to be computed exactly, and for the more usual “full orbit” setting we derive multi-sample bounds tighter than those used previously. These models cast light on the origin of the cold posterior effect. In particular, we find that the cold posterior effect persists even in these principled models incorporating data augmentation. This suggests that the cold posterior effect cannot be dismissed as an artifact of data augmentation using incorrect likelihoods.

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TMLR Journal 2022 Journal Article

Deep Classifiers with Label Noise Modeling and Distance Awareness

Vincent Fortuin
Mark Collier
Florian Wenzel
James Urquhart Allingham
Jeremiah Zhe Liu
Dustin Tran
Balaji Lakshminarayanan
Jesse Berent

Uncertainty estimation in deep learning has recently emerged as a crucial area of interest to advance reliability and robustness in safety-critical applications. While there have been many proposed methods that either focus on distance-aware model uncertainties for out-of-distribution detection or on input-dependent label uncertainties for in-distribution calibration, both of these types of uncertainty are often necessary. In this work, we propose the HetSNGP method for jointly modeling the model and data uncertainty. We show that our proposed model affords a favorable combination between these two types of uncertainty and thus outperforms the baseline methods on some challenging out-of-distribution datasets, including CIFAR-100C, ImageNet-C, and ImageNet-A. Moreover, we propose HetSNGP Ensemble, an ensembled version of our method which additionally models uncertainty over the network parameters and outperforms other ensemble baselines.

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NeurIPS Conference 2022 Conference Paper

Invariance Learning in Deep Neural Networks with Differentiable Laplace Approximations

Alexander Immer
Tycho van der Ouderaa
Gunnar Rätsch
Vincent Fortuin
Mark van der Wilk

Data augmentation is commonly applied to improve performance of deep learning by enforcing the knowledge that certain transformations on the input preserve the output. Currently, the data augmentation parameters are chosen by human effort and costly cross-validation, which makes it cumbersome to apply to new datasets. We develop a convenient gradient-based method for selecting the data augmentation without validation data during training of a deep neural network. Our approach relies on phrasing data augmentation as an invariance in the prior distribution on the functions of a neural network, which allows us to learn it using Bayesian model selection. This has been shown to work in Gaussian processes, but not yet for deep neural networks. We propose a differentiable Kronecker-factored Laplace approximation to the marginal likelihood as our objective, which can be optimised without human supervision or validation data. We show that our method can successfully recover invariances present in the data, and that this improves generalisation and data efficiency on image datasets.

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TMLR Journal 2022 Journal Article

Sparse MoEs meet Efficient Ensembles

James Urquhart Allingham
Florian Wenzel
Zelda E Mariet
Basil Mustafa
Joan Puigcerver
Neil Houlsby
Ghassen Jerfel
Vincent Fortuin

Machine learning models based on the aggregated outputs of submodels, either at the activation or prediction levels, often exhibit strong performance compared to individual models. We study the interplay of two popular classes of such models: ensembles of neural networks and sparse mixture of experts (sparse MoEs). First, we show that the two approaches have complementary features whose combination is beneficial. This includes a comprehensive evaluation of sparse MoEs in uncertainty related benchmarks. Then, we present efficient ensemble of experts (E$^3$), a scalable and simple ensemble of sparse MoEs that takes the best of both classes of models, while using up to 45% fewer FLOPs than a deep ensemble. Extensive experiments demonstrate the accuracy, log-likelihood, few-shot learning, robustness, and uncertainty improvements of E$^3$ over several challenging vision Transformer-based baselines. E$^3$ not only preserves its efficiency while scaling to models with up to 2.7B parameters, but also provides better predictive performance and uncertainty estimates for larger models.

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ICML Conference 2021 Conference Paper

PACOH: Bayes-Optimal Meta-Learning with PAC-Guarantees

Jonas Rothfuss
Vincent Fortuin
Martin Josifoski
Andreas Krause 0001

Meta-learning can successfully acquire useful inductive biases from data. Yet, its generalization properties to unseen learning tasks are poorly understood. Particularly if the number of meta-training tasks is small, this raises concerns about overfitting. We provide a theoretical analysis using the PAC-Bayesian framework and derive novel generalization bounds for meta-learning. Using these bounds, we develop a class of PAC-optimal meta-learning algorithms with performance guarantees and a principled meta-level regularization. Unlike previous PAC-Bayesian meta-learners, our method results in a standard stochastic optimization problem which can be solved efficiently and scales well. When instantiating our PAC-optimal hyper-posterior (PACOH) with Gaussian processes and Bayesian Neural Networks as base learners, the resulting methods yield state-of-the-art performance, both in terms of predictive accuracy and the quality of uncertainty estimates. Thanks to their principled treatment of uncertainty, our meta-learners can also be successfully employed for sequential decision problems.

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NeurIPS Conference 2021 Conference Paper

Repulsive Deep Ensembles are Bayesian

Francesco D'Angelo
Vincent Fortuin

Deep ensembles have recently gained popularity in the deep learning community for their conceptual simplicity and efficiency. However, maintaining functional diversity between ensemble members that are independently trained with gradient descent is challenging. This can lead to pathologies when adding more ensemble members, such as a saturation of the ensemble performance, which converges to the performance of a single model. Moreover, this does not only affect the quality of its predictions, but even more so the uncertainty estimates of the ensemble, and thus its performance on out-of-distribution data. We hypothesize that this limitation can be overcome by discouraging different ensemble members from collapsing to the same function. To this end, we introduce a kernelized repulsive term in the update rule of the deep ensembles. We show that this simple modification not only enforces and maintains diversity among the members but, even more importantly, transforms the maximum a posteriori inference into proper Bayesian inference. Namely, we show that the training dynamics of our proposed repulsive ensembles follow a Wasserstein gradient flow of the KL divergence with the true posterior. We study repulsive terms in weight and function space and empirically compare their performance to standard ensembles and Bayesian baselines on synthetic and real-world prediction tasks.

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ICML Conference 2021 Conference Paper

Scalable Marginal Likelihood Estimation for Model Selection in Deep Learning

Alexander Immer
Matthias Bauer 0001
Vincent Fortuin
Gunnar Rätsch
Mohammad Emtiyaz Khan

Marginal-likelihood based model-selection, even though promising, is rarely used in deep learning due to estimation difficulties. Instead, most approaches rely on validation data, which may not be readily available. In this work, we present a scalable marginal-likelihood estimation method to select both hyperparameters and network architectures, based on the training data alone. Some hyperparameters can be estimated online during training, simplifying the procedure. Our marginal-likelihood estimate is based on Laplace’s method and Gauss-Newton approximations to the Hessian, and it outperforms cross-validation and manual tuning on standard regression and image classification datasets, especially in terms of calibration and out-of-distribution detection. Our work shows that marginal likelihoods can improve generalization and be useful when validation data is unavailable (e. g. , in nonstationary settings).

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ICLR Conference 2020 Conference Paper

Conservative Uncertainty Estimation By Fitting Prior Networks

Kamil Ciosek
Vincent Fortuin
Ryota Tomioka
Katja Hofmann
Richard E. Turner

Obtaining high-quality uncertainty estimates is essential for many applications of deep neural networks. In this paper, we theoretically justify a scheme for estimating uncertainties, based on sampling from a prior distribution. Crucially, the uncertainty estimates are shown to be conservative in the sense that they never underestimate a posterior uncertainty obtained by a hypothetical Bayesian algorithm. We also show concentration, implying that the uncertainty estimates converge to zero as we get more data. Uncertainty estimates obtained from random priors can be adapted to any deep network architecture and trained using standard supervised learning pipelines. We provide experimental evaluation of random priors on calibration and out-of-distribution detection on typical computer vision tasks, demonstrating that they outperform deep ensembles in practice.

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AAAI Conference 2018 Conference Paper

InspireMe: Learning Sequence Models for Stories

Vincent Fortuin
Romann Weber
Sasha Schriber
Diana Wotruba
Markus Gross

We present a novel approach to modeling stories using recurrent neural networks. Different story features are extracted using natural language processing techniques and used to encode the stories as sequences. These sequences can be learned by deep neural networks, in order to predict the next story events. The predictions can be used as an inspiration for writers who experience a writer’s block. We further assist writers in their creative process by generating visualizations of the character interactions in the story. We show that suggestions from our model are rated as highly as the real scenes from a set of ﬁlms and that our visualizations can help people in gaining deeper story understanding.

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