David Rügamer

Jonas Gregor Wiese, Lisa Wimmer, Theodore Papamarkou et al.

Bayesian inference in deep neural networks is challenging due to the high-dimensional, strongly multi-modal parameter posterior density landscape. Markov chain Monte Carlo approaches asymptotically recover the true posterior but are considered prohibitively expensive for large modern architectures. Local methods, which have emerged as a popular alternative, focus on specific parameter regions that can be approximated by functions with tractable integrals. While these often yield satisfactory empirical results, they fail, by definition, to account for the multi-modality of the parameter posterior. In this work, we argue that the dilemma between exact-but-unaffordable and cheap-but-inexact approaches can be mitigated by exploiting symmetries in the posterior landscape. Such symmetries, induced by neuron interchangeability and certain activation functions, manifest in different parameter values leading to the same functional output value. We show theoretically that the posterior predictive density in Bayesian neural networks can be restricted to a symmetry-free parameter reference set. By further deriving an upper bound on the number of Monte Carlo chains required to capture the functional diversity, we propose a straightforward approach for feasible Bayesian inference. Our experiments suggest that efficient sampling is indeed possible, opening up a promising path to accurate uncertainty quantification in deep learning.

Emanuel Sommer, Kangning Diao, Jakob Robnik et al.

Scaling inference methods such as Markov chain Monte Carlo to high-dimensional models remains a central challenge in Bayesian deep learning. A promising recent proposal, microcanonical Langevin Monte Carlo, has shown state-of-the-art performance across a wide range of problems. However, its reliance on full-dataset gradients makes it prohibitively expensive for large-scale problems. This paper addresses a fundamental question: Can microcanonical dynamics effectively leverage mini-batch gradient noise? We provide the first systematic study of this problem, establishing a novel continuous-time theoretical analysis of stochastic-gradient microcanonical dynamics. We reveal two critical failure modes: a theoretically derived bias due to anisotropic gradient noise and numerical instabilities in complex high-dimensional posteriors. To tackle these issues, we propose a principled gradient noise preconditioning scheme shown to significantly reduce this bias and develop a novel, energy-variance-based adaptive tuner that automates step size selection and dynamically informs numerical guardrails. The resulting algorithm is a robust and scalable microcanonical Monte Carlo sampler that achieves state-of-the-art performance on challenging high-dimensional inference tasks like Bayesian neural networks. Combined with recent ensemble techniques, our work unlocks a new class of stochastic microcanonical Langevin ensemble (SMILE) samplers for large-scale Bayesian inference.

Tobias Weber, Michael Ingrisch, Bernd Bischl et al.

While recent advances in large-scale foundational models show promising results, their application to the medical domain has not yet been explored in detail. In this paper, we progress into the realms of large-scale modeling in medical synthesis by proposing Cheff - a foundational cascaded latent diffusion model, which generates highly-realistic chest radiographs providing state-of-the-art quality on a 1-megapixel scale. We further propose MaCheX, which is a unified interface for public chest datasets and forms the largest open collection of chest X-rays up to date. With Cheff conditioned on radiological reports, we further guide the synthesis process over text prompts and unveil the research area of report-to-chest-X-ray generation.

Daniel Dold, Emanuel Sommer, Julius Kobialka et al.

While parameter-efficient fine-tuning methods like low-rank adaptation (LoRA) are standard for large language models, principled estimation of epistemic uncertainty remains challenging. Recent results in the LoRA regime suggest that discrete multi-mode approaches such as deep ensembles offer little benefit over single-mode methods. This contradicts broader observations in deep learning, where ensembling independent optima typically improves generalization, and linking these modes through continuous low-loss valleys further enhances Bayesian model averaging (BMA). Whether such structure exists in the LoRA space and whether it yields functional diversity missed by local or discrete methods has not been studied. We introduce LoRA-Curve, a segmented Bézier curve parameterization in the LoRA space, with two variants: a free configuration that jointly optimizes all control points, and an anchored configuration that connects independently fine-tuned LoRA optima. We prove pathwise continuity and Lipschitz regularity of the loss along the curve and empirically show, across reasoning and classification benchmarks with Qwen2.5 7B, that linear interpolation encounters loss barriers, while our anchored multi-segment curves connect independent optima through continuous low-loss valleys. Combined with flat-minima perturbations and a Jensen-Shannon divergence regularizer, LoRA-Curve yields measurably higher mutual information of the predictive distribution without sacrificing performance, and links continuous parameter-space traversal to functional diversity.

Felix Ott, David Rügamer, Lucas Heublein et al.

The performance of a machine learning model degrades when it is applied to data from a similar but different domain than the data it has initially been trained on. To mitigate this domain shift problem, domain adaptation (DA) techniques search for an optimal transformation that converts the (current) input data from a source domain to a target domain to learn a domain-invariant representation that reduces domain discrepancy. This paper proposes a novel supervised DA based on two steps. First, we search for an optimal class-dependent transformation from the source to the target domain from a few samples. We consider optimal transport methods such as the earth mover's distance, Sinkhorn transport and correlation alignment. Second, we use embedding similarity techniques to select the corresponding transformation at inference. We use correlation metrics and higher-order moment matching techniques. We conduct an extensive evaluation on time-series datasets with domain shift including simulated and various online handwriting datasets to demonstrate the performance.

David Rügamer

Epistemic uncertainty is often viewed as a reducible uncertainty that vanishes with increasing data. This perspective implicitly assumes parameter identifiability and equates epistemic uncertainty with predictive variability. In overparametrized neural networks, however, model parameters are typically non-identifiable due to symmetries and redundant representations. As a consequence, substantial parameter uncertainty can persist even when the underlying function is fully identified. In this work, we analyze epistemic uncertainty through the lens of non-identifiability and characterize both discrete and continuous sources of residual uncertainty. Focusing on one-hidden-layer ReLU networks, we thoroughly analyze the resulting posterior structure and validate our theoretical insights through empirical studies.

Felix Ott, Nisha Lakshmana Raichur, David Rügamer et al.

Visual-inertial localization is a key problem in computer vision and robotics applications such as virtual reality, self-driving cars, and aerial vehicles. The goal is to estimate an accurate pose of an object when either the environment or the dynamics are known. Absolute pose regression (APR) techniques directly regress the absolute pose from an image input in a known scene using convolutional and spatio-temporal networks. Odometry methods perform relative pose regression (RPR) that predicts the relative pose from a known object dynamic (visual or inertial inputs). The localization task can be improved by retrieving information from both data sources for a cross-modal setup, which is a challenging problem due to contradictory tasks. In this work, we conduct a benchmark to evaluate deep multimodal fusion based on pose graph optimization and attention networks. Auxiliary and Bayesian learning are utilized for the APR task. We show accuracy improvements for the APR-RPR task and for the RPR-RPR task for aerial vehicles and hand-held devices. We conduct experiments on the EuRoC MAV and PennCOSYVIO datasets and record and evaluate a novel industry dataset.

Andreas Klaß, Sven M. Lorenz, Martin W. Lauer-Schmaltz et al.

For many applications, analyzing the uncertainty of a machine learning model is indispensable. While research of uncertainty quantification (UQ) techniques is very advanced for computer vision applications, UQ methods for spatio-temporal data are less studied. In this paper, we focus on models for online handwriting recognition, one particular type of spatio-temporal data. The data is observed from a sensor-enhanced pen with the goal to classify written characters. We conduct a broad evaluation of aleatoric (data) and epistemic (model) UQ based on two prominent techniques for Bayesian inference, Stochastic Weight Averaging-Gaussian (SWAG) and Deep Ensembles. Next to a better understanding of the model, UQ techniques can detect out-of-distribution data and domain shifts when combining right-handed and left-handed writers (an underrepresented group).

David Rügamer, Andreas Bender, Simon Wiegrebe et al.

Recommender Systems (RS) pervade many aspects of our everyday digital life. Proposed to work at scale, state-of-the-art RS allow the modeling of thousands of interactions and facilitate highly individualized recommendations. Conceptually, many RS can be viewed as instances of statistical regression models that incorporate complex feature effects and potentially non-Gaussian outcomes. Such structured regression models, including time-aware varying coefficients models, are, however, limited in their applicability to categorical effects and inclusion of a large number of interactions. Here, we propose Factorized Structured Regression (FaStR) for scalable varying coefficient models. FaStR overcomes limitations of general regression models for large-scale data by combining structured additive regression and factorization approaches in a neural network-based model implementation. This fusion provides a scalable framework for the estimation of statistical models in previously infeasible data settings. Empirical results confirm that the estimation of varying coefficients of our approach is on par with state-of-the-art regression techniques, while scaling notably better and also being competitive with other time-aware RS in terms of prediction performance. We illustrate FaStR's performance and interpretability on a large-scale behavioral study with smartphone user data.

Felix Ott, Lucas Heublein, David Rügamer et al.

The localization of objects is a crucial task in various applications such as robotics, virtual and augmented reality, and the transportation of goods in warehouses. Recent advances in deep learning have enabled the localization using monocular visual cameras. While structure from motion (SfM) predicts the absolute pose from a point cloud, absolute pose regression (APR) methods learn a semantic understanding of the environment through neural networks. However, both fields face challenges caused by the environment such as motion blur, lighting changes, repetitive patterns, and feature-less structures. This study aims to address these challenges by incorporating additional information and regularizing the absolute pose using relative pose regression (RPR) methods. RPR methods suffer under different challenges, i.e., motion blur. The optical flow between consecutive images is computed using the Lucas-Kanade algorithm, and the relative pose is predicted using an auxiliary small recurrent convolutional network. The fusion of absolute and relative poses is a complex task due to the mismatch between the global and local coordinate systems. State-of-the-art methods fusing absolute and relative poses use pose graph optimization (PGO) to regularize the absolute pose predictions using relative poses. In this work, we propose recurrent fusion networks to optimally align absolute and relative pose predictions to improve the absolute pose prediction. We evaluate eight different recurrent units and construct a simulation environment to pre-train the APR and RPR networks for better generalized training. Additionally, we record a large database of different scenarios in a challenging large-scale indoor environment that mimics a warehouse with transportation robots. We conduct hyperparameter searches and experiments to show the effectiveness of our recurrent fusion method compared to PGO.

Rama Kassoumeh, David Rügamer, Henning Oppel

The increasing frequency of heavy rainfall events, which are a major cause of urban flooding, underscores the urgent need for accurate precipitation forecasting - particularly in urban areas where localized events often go undetected by ground-based sensors. In Germany, only 17.3% of hourly heavy rain events between 2001 and 2018 were recorded by rain gauges, highlighting the limitations of traditional monitoring systems. Radar data are another source that effectively tracks ongoing precipitation; however, forecasting the development of heavy rain using radar alone remains challenging due to the brief and unpredictable nature of such events. Our focus is on evaluating the effectiveness of fusing satellite and radar data for nowcasting. We develop a multimodal nowcasting model that combines both radar and satellite imagery for predicting precipitation at lead times of 5, 15, and 30 minutes. We demonstrate that this multimodal strategy significantly outperforms radar-only approaches. Experimental results show that integrating satellite data improves prediction accuracy, particularly for intense precipitation. The proposed model increases the Critical Success Index for heavy rain by 4% and for violent rain by 3% at a 5-minute lead time. Moreover, it maintains higher predictive skill at longer lead times, where radar-only performance declines. A qualitative analysis of the severe flooding event in the state of North Rhine-Westphalia, Germany in 2021 further illustrates the superior performance of the multimodal model. Unlike the radar-only model, which captures general precipitation patterns, the multimodal model yields more detailed and accurate forecasts for regions affected by heavy rain. This improved precision enables timely, reliable, life-saving warnings. Implementation available at https://github.com/RamaKassoumeh/Multimodal_heavy_rain

Thomas Nagler, David Rügamer

Prior-data fitted networks (PFNs) have emerged as promising foundation models for prediction from tabular datasets, achieving state-of-the-art performance on small to moderate data sizes without tuning. While PFNs are motivated by Bayesian ideas, they do not provide any uncertainty quantification for predictive means, quantiles, or similar quantities. We propose a principled, efficient, and tuning-free sampling procedure to construct Bayesian posteriors for such estimates based on martingale posteriors, and prove its convergence. Several simulated and real-world data examples showcase the efficiency and calibration of our method in inference applications.

Chris Kolb, Christian L. Müller, Bernd Bischl et al.

We present a framework for smooth optimization of explicitly regularized objectives for (structured) sparsity. These non-smooth and possibly non-convex problems typically rely on solvers tailored to specific models and regularizers. In contrast, our method enables fully differentiable and approximation-free optimization and is thus compatible with the ubiquitous gradient descent paradigm in deep learning. The proposed optimization transfer comprises an overparameterization of selected parameters and a change of penalties. In the overparametrized problem, smooth surrogate regularization induces non-smooth, sparse regularization in the base parametrization. We prove that the surrogate objective is equivalent in the sense that it not only has identical global minima but also matching local minima, thereby avoiding the introduction of spurious solutions. Additionally, our theory establishes results of independent interest regarding matching local minima for arbitrary, potentially unregularized, objectives. We comprehensively review sparsity-inducing parametrizations across different fields that are covered by our general theory, extend their scope, and propose improvements in several aspects. Numerical experiments further demonstrate the correctness and effectiveness of our approach on several sparse learning problems ranging from high-dimensional regression to sparse neural network training.

Felix Ott, David Rügamer, Lucas Heublein et al.

The performance of a machine learning model degrades when it is applied to data from a similar but different domain than the data it has initially been trained on. The goal of domain adaptation (DA) is to mitigate this domain shift problem by searching for an optimal feature transformation to learn a domain-invariant representation. Such a domain shift can appear in handwriting recognition (HWR) applications where the motion pattern of the hand and with that the motion pattern of the pen is different for writing on paper and on tablet. This becomes visible in the sensor data for online handwriting (OnHW) from pens with integrated inertial measurement units. This paper proposes a supervised DA approach to enhance learning for OnHW recognition between tablet and paper data. Our method exploits loss functions such as maximum mean discrepancy and correlation alignment to learn a domain-invariant feature representation (i.e., similar covariances between tablet and paper features). We use a triplet loss that takes negative samples of the auxiliary domain (i.e., paper samples) to increase the amount of samples of the tablet dataset. We conduct an evaluation on novel sequence-based OnHW datasets (i.e., words) and show an improvement on the paper domain with an early fusion strategy by using pairwise learning.

Patrick Kaiser, Christoph Kern, David Rügamer

Both industry and academia have made considerable progress in developing trustworthy and responsible machine learning (ML) systems. While critical concepts like fairness and explainability are often addressed, the safety of systems is typically not sufficiently taken into account. By viewing data-driven decision systems as socio-technical systems, we draw on the uncertainty in ML literature to show how fairML systems can also be safeML systems. We posit that a fair model needs to be an uncertainty-aware model, e.g. by drawing on distributional regression. For fair decisions, we argue that a safe fail option should be used for individuals with uncertain categorization. We introduce semi-structured deep distributional regression as a modeling framework which addresses multiple concerns brought against standard ML models and show its use in a real-world example of algorithmic profiling of job seekers.

Emanuel Sommer, David Rügamer

The practical adoption of sampling-based inference (SAI) in Bayesian neural networks (BNNs) remains limited, partly due to persistent misconceptions about the feasibility and efficiency of sampling. This position paper argues that SAI has achieved computational parity with optimization-based methods and is at the verge of superseding such methods for effective and efficient inference in BNNs. This development should be in the interest of the whole community, promoting BNNs as a principled paradigm with its long-standing yet unfulfilled promise of providing principled uncertainty quantification for neural networks. SAI can even do more -- yielding superior prediction performance through model averaging, serving as the foundation for a plethora of possible downstream tasks, and providing crucial insights into the landscape of BNNs. In order to make such a change happen and unfold the potential of sampling, overcoming current misconceptions is a necessary first step. The next step is to realign research efforts toward addressing remaining challenges in SAI. In particular, the community must focus on two core problems: sufficient exploration of the posterior landscape and high-fidelity distillation of posterior samples for efficient downstream inference. By addressing conceptual and practical obstacles, we can unlock the full potential of SAI and establish it as a central tool in Bayesian deep learning.

Zheyu Zhang, Han Yang, Bolei Ma et al.

Large Language Models (LLMs) demonstrate remarkable performance on a variety of natural language understanding (NLU) tasks, primarily due to their in-context learning ability. This ability could be applied to building babylike models, i.e. models at small scales, improving training efficiency. In this paper, we propose a "CoThought" pipeline, which efficiently trains smaller "baby" language models (BabyLMs) by leveraging the Chain of Thought prompting of LLMs. Our pipeline restructures a dataset of less than 100M in size using GPT-3.5-turbo, transforming it into task-oriented, human-readable texts that are comparable to the school texts for language learners. The BabyLM is then pretrained on this restructured dataset in a RoBERTa fashion. In evaluations across 4 benchmarks, our BabyLM outperforms the vanilla RoBERTa in 10 linguistic, NLU, and question-answering tasks by more than 3 points, showing a superior ability to extract contextual information. These results suggest that compact LMs pretrained on small, LLM-restructured data can better understand tasks and achieve improved performance.

David Köhler, David Rügamer, Matthias Schmid

Machine learning (ML) has seen significant growth in both popularity and importance. The high prediction accuracy of ML models is often achieved through complex black-box architectures that are difficult to interpret. This interpretability problem has been hindering the use of ML in fields like medicine, ecology and insurance, where an understanding of the inner workings of the model is paramount to ensure user acceptance and fairness. The need for interpretable ML models has boosted research in the field of interpretable machine learning (IML). Here we propose a novel approach for the functional decomposition of black-box predictions, which is considered a core concept of IML. The idea of our method is to replace the prediction function by a surrogate model consisting of simpler subfunctions. Similar to additive regression models, these functions provide insights into the direction and strength of the main feature contributions and their interactions. Our method is based on a novel concept termed stacked orthogonality, which ensures that the main effects capture as much functional behavior as possible and do not contain information explained by higher-order interactions. Unlike earlier functional IML approaches, it is neither affected by extrapolation nor by hidden feature interactions. To compute the subfunctions, we propose an algorithm based on neural additive modeling and an efficient post-hoc orthogonalization procedure.

Philipp Schiele, Christoph Berninger, David Rügamer

The autoregressive moving average (ARMA) model is a classical, and arguably one of the most studied approaches to model time series data. It has compelling theoretical properties and is widely used among practitioners. More recent deep learning approaches popularize recurrent neural networks (RNNs) and, in particular, Long Short-Term Memory (LSTM) cells that have become one of the best performing and most common building blocks in neural time series modeling. While advantageous for time series data or sequences with long-term effects, complex RNN cells are not always a must and can sometimes even be inferior to simpler recurrent approaches. In this work, we introduce the ARMA cell, a simpler, modular, and effective approach for time series modeling in neural networks. This cell can be used in any neural network architecture where recurrent structures are present and naturally handles multivariate time series using vector autoregression. We also introduce the ConvARMA cell as a natural successor for spatially-correlated time series. Our experiments show that the proposed methodology is competitive with popular alternatives in terms of performance while being more robust and compelling due to its simplicity

Emanuel Sommer, Rickmer Schulte, Sarah Deubner et al.

Bayesian Deep Ensembles (BDEs) represent a powerful approach for uncertainty quantification in deep learning, combining the robustness of Deep Ensembles (DEs) with flexible multi-chain MCMC. While DEs are affordable in most deep learning settings, (long) sampling of Bayesian neural networks can be prohibitively costly. Yet, adding sampling after optimizing the DEs has been shown to yield significant improvements. This leaves a critical practical question: How long should the sequential sampling process continue to yield significant improvements over the initial optimized DE baseline? To tackle this question, we propose a stopping rule based on E-values. We formulate the ensemble construction as a sequential anytime-valid hypothesis test, providing a principled way to decide whether or not to reject the null hypothesis that MCMC offers no improvement over a strong baseline, to early stop the sampling. Empirically, we study this approach for diverse settings. Our results demonstrate the efficacy of our approach and reveal that only a fraction of the full-chain budget is often required.

Tobias Weber, Michael Ingrisch, Bernd Bischl et al.

Purpose: To analyze and remove protected feature effects in chest radiograph embeddings of deep learning models. Methods: An orthogonalization is utilized to remove the influence of protected features (e.g., age, sex, race) in CXR embeddings, ensuring feature-independent results. To validate the efficacy of the approach, we retrospectively study the MIMIC and CheXpert datasets using three pre-trained models, namely a supervised contrastive, a self-supervised contrastive, and a baseline classifier model. Our statistical analysis involves comparing the original versus the orthogonalized embeddings by estimating protected feature influences and evaluating the ability to predict race, age, or sex using the two types of embeddings. Results: Our experiments reveal a significant influence of protected features on predictions of pathologies. Applying orthogonalization removes these feature effects. Apart from removing any influence on pathology classification, while maintaining competitive predictive performance, orthogonalized embeddings further make it infeasible to directly predict protected attributes and mitigate subgroup disparities. Conclusion: The presented work demonstrates the successful application and evaluation of the orthogonalization technique in the domain of chest X-ray image classification.

Daniel Schalk, Bernd Bischl, David Rügamer

Various privacy-preserving frameworks that respect the individual's privacy in the analysis of data have been developed in recent years. However, available model classes such as simple statistics or generalized linear models lack the flexibility required for a good approximation of the underlying data-generating process in practice. In this paper, we propose an algorithm for a distributed, privacy-preserving, and lossless estimation of generalized additive mixed models (GAMM) using component-wise gradient boosting (CWB). Making use of CWB allows us to reframe the GAMM estimation as a distributed fitting of base learners using the $L_2$-loss. In order to account for the heterogeneity of different data location sites, we propose a distributed version of a row-wise tensor product that allows the computation of site-specific (smooth) effects. Our adaption of CWB preserves all the important properties of the original algorithm, such as an unbiased feature selection and the feasibility to fit models in high-dimensional feature spaces, and yields equivalent model estimates as CWB on pooled data. Next to a derivation of the equivalence of both algorithms, we also showcase the efficacy of our algorithm on a distributed heart disease data set and compare it with state-of-the-art methods.

Arik Reuter, Tim G. J. Rudner, Vincent Fortuin et al.

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.

Rickmer Schulte, David Rügamer

The analysis of neural representation has become an integral part of research aiming to better understand the inner workings of neural networks. While there are many different approaches to investigate neural representations, an important line of research has focused on doing so through the lens of intrinsic dimensions (IDs). Although this perspective has provided valuable insights and stimulated substantial follow-up research, important limitations of this approach have remained largely unaddressed. In this paper, we highlight a crucial discrepancy between theory and practice of IDs in neural representations, theoretically and empirically showing that common ID estimators are, in fact, not tracking the true underlying ID of the representation. We contrast this negative result with an investigation of the underlying factors that may drive commonly reported ID-related results on neural representation in the literature. Building on these insights, we offer a new perspective on ID estimation in neural representations.

Qiwen Xu, David Rügamer, Holger Wenz et al.

Digital subtraction angiography (DSA) plays a central role in the diagnosis and treatment of cerebrovascular disease, yet its invasive nature and high acquisition cost severely limit large-scale data collection and public data sharing. Therefore, we developed a semantically conditioned latent diffusion model (LDM) that synthesizes arterial-phase cerebral DSA frames under explicit control of anatomical circulation (anterior vs.\ posterior) and canonical C-arm positions. We curated a large single-centre DSA dataset of 99,349 frames and trained a conditional LDM using text embeddings that encoded anatomy and acquisition geometry. To assess clinical realism, four medical experts, including two neuroradiologists, one neurosurgeon, and one internal medicine expert, systematically rated 400 synthetic DSA images using a 5-grade Likert scale for evaluating proximal large, medium, and small peripheral vessels. The generated images achieved image-wise overall Likert scores ranging from 3.1 to 3.3, with high inter-rater reliability (ICC(2,k) = 0.80--0.87). Distributional similarity to real DSA frames was supported by a low median Fréchet inception distance (FID) of 15.27. Our results indicate that semantically controlled LDMs can produce realistic synthetic DSAs suitable for downstream algorithm development, research, and training.

David Rundel, Julius Kobialka, Constantin von Crailsheim et al.

The recently developed Prior-Data Fitted Networks (PFNs) have shown very promising results for applications in low-data regimes. The TabPFN model, a special case of PFNs for tabular data, is able to achieve state-of-the-art performance on a variety of classification tasks while producing posterior predictive distributions in mere seconds by in-context learning without the need for learning parameters or hyperparameter tuning. This makes TabPFN a very attractive option for a wide range of domain applications. However, a major drawback of the method is its lack of interpretability. Therefore, we propose several adaptations of popular interpretability methods that we specifically design for TabPFN. By taking advantage of the unique properties of the model, our adaptations allow for more efficient computations than existing implementations. In particular, we show how in-context learning facilitates the estimation of Shapley values by avoiding approximate retraining and enables the use of Leave-One-Covariate-Out (LOCO) even when working with large-scale Transformers. In addition, we demonstrate how data valuation methods can be used to address scalability challenges of TabPFN. Our proposed methods are implemented in a package tabpfn_iml and made available at https://github.com/david-rundel/tabpfn_iml.

Vyron Arvanitis, Angelos Aslanidis, Emanuel Sommer et al.

bde is a user-friendly Python package for Bayesian Deep Ensembles with a particular focus on tabular data. Built on an efficient JAX implementation of the sampling-based inference method Microcanonical Langevin Ensembles (MILE), it provides scikit-learn compatible estimators for fast training, efficient Markov Chain Monte Carlo sampling, and uncertainty quantification in both regression and classification tasks.

Yawei Li, David Rügamer, Bernd Bischl et al.

Fine-tuned large language models (LLMs) often exhibit overconfidence, particularly when trained on small datasets, resulting in poor calibration and inaccurate uncertainty estimates. Evidential Deep Learning (EDL), an uncertainty-aware approach, enables uncertainty estimation in a single forward pass, making it a promising method for calibrating fine-tuned LLMs. However, despite its computational efficiency, EDL is prone to overfitting, as its training objective can result in overly concentrated probability distributions. To mitigate this, we propose regularizing EDL by incorporating an information bottleneck (IB). Our approach IB-EDL suppresses spurious information in the evidence generated by the model and encourages truly predictive information to influence both the predictions and uncertainty estimates. Extensive experiments across various fine-tuned LLMs and tasks demonstrate that IB-EDL outperforms both existing EDL and non-EDL approaches. By improving the trustworthiness of LLMs, IB-EDL facilitates their broader adoption in domains requiring high levels of confidence calibration. Code is available at https://github.com/sandylaker/ib-edl.

David Rügamer

In the age of big data and interpretable machine learning, approaches need to work at scale and at the same time allow for a clear mathematical understanding of the method's inner workings. While there exist inherently interpretable semi-parametric regression techniques for large-scale applications to account for non-linearity in the data, their model complexity is still often restricted. One of the main limitations are missing interactions in these models, which are not included for the sake of better interpretability, but also due to untenable computational costs. To address this shortcoming, we derive a scalable high-order tensor product spline model using a factorization approach. Our method allows to include all (higher-order) interactions of non-linear feature effects while having computational costs proportional to a model without interactions. We prove both theoretically and empirically that our methods scales notably better than existing approaches, derive meaningful penalization schemes and also discuss further theoretical aspects. We finally investigate predictive and estimation performance both with synthetic and real data.

Ludwig Bothmann, Sven Strickroth, Giuseppe Casalicchio et al.

Education should not be a privilege but a common good. It should be openly accessible to everyone, with as few barriers as possible; even more so for key technologies such as Machine Learning (ML) and Data Science (DS). Open Educational Resources (OER) are a crucial factor for greater educational equity. In this paper, we describe the specific requirements for OER in ML and DS and argue that it is especially important for these fields to make source files publicly available, leading to Open Source Educational Resources (OSER). We present our view on the collaborative development of OSER, the challenges this poses, and first steps towards their solutions. We outline how OSER can be used for blended learning scenarios and share our experiences in university education. Finally, we discuss additional challenges such as credit assignment or granting certificates.

David Rügamer

Recent advances to combine structured regression models and deep neural networks for better interpretability, more expressiveness, and statistically valid uncertainty quantification demonstrate the versatility of semi-structured neural networks (SSNs). We show that techniques to properly identify the contributions of the different model components in SSNs, however, lead to suboptimal network estimation, slower convergence, and degenerated or erroneous predictions. In order to solve these problems while preserving favorable model properties, we propose a non-invasive post-hoc orthogonalization (PHO) that guarantees identifiability of model components and provides better estimation and prediction quality. Our theoretical findings are supported by numerical experiments, a benchmark comparison as well as a real-world application to COVID-19 infections.

Theodore Papamarkou, Maria Skoularidou, Konstantina Palla et al.

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.

Moritz Herrmann, F. Julian D. Lange, Katharina Eggensperger et al.

We warn against a common but incomplete understanding of empirical research in machine learning that leads to non-replicable results, makes findings unreliable, and threatens to undermine progress in the field. To overcome this alarming situation, we call for more awareness of the plurality of ways of gaining knowledge experimentally but also of some epistemic limitations. In particular, we argue most current empirical machine learning research is fashioned as confirmatory research while it should rather be considered exploratory.

Chris Kolb, Tobias Weber, Bernd Bischl et al.

Sparse regularization techniques are well-established in machine learning, yet their application in neural networks remains challenging due to the non-differentiability of penalties like the $L_1$ norm, which is incompatible with stochastic gradient descent. A promising alternative is shallow weight factorization, where weights are decomposed into two factors, allowing for smooth optimization of $L_1$-penalized neural networks by adding differentiable $L_2$ regularization to the factors. In this work, we introduce deep weight factorization, extending previous shallow approaches to more than two factors. We theoretically establish equivalence of our deep factorization with non-convex sparse regularization and analyze its impact on training dynamics and optimization. Due to the limitations posed by standard training practices, we propose a tailored initialization scheme and identify important learning rate requirements necessary for training factorized networks. We demonstrate the effectiveness of our deep weight factorization through experiments on various architectures and datasets, consistently outperforming its shallow counterpart and widely used pruning methods.

Samuel Müller, Arik Reuter, Noah Hollmann et al.

Training neural networks on randomly generated artificial datasets yields Bayesian models that capture the prior defined by the dataset-generating distribution. Prior-data Fitted Networks (PFNs) are a class of methods designed to leverage this insight. In an era of rapidly increasing computational resources for pre-training and a near stagnation in the generation of new real-world data in many applications, PFNs are poised to play a more important role across a wide range of applications. They enable the efficient allocation of pre-training compute to low-data scenarios. Originally applied to small Bayesian modeling tasks, the field of PFNs has significantly expanded to address more complex domains and larger datasets. This position paper argues that PFNs and other amortized inference approaches represent the future of Bayesian inference, leveraging amortized learning to tackle data-scarce problems. We thus believe they are a fruitful area of research. In this position paper, we explore their potential and directions to address their current limitations.

Emanuel Sommer, Jakob Robnik, Giorgi Nozadze et al.

Despite recent advances, sampling-based inference for Bayesian Neural Networks (BNNs) remains a significant challenge in probabilistic deep learning. While sampling-based approaches do not require a variational distribution assumption, current state-of-the-art samplers still struggle to navigate the complex and highly multimodal posteriors of BNNs. As a consequence, sampling still requires considerably longer inference times than non-Bayesian methods even for small neural networks, despite recent advances in making software implementations more efficient. Besides the difficulty of finding high-probability regions, the time until samplers provide sufficient exploration of these areas remains unpredictable. To tackle these challenges, we introduce an ensembling approach that leverages strategies from optimization and a recently proposed sampler called Microcanonical Langevin Monte Carlo (MCLMC) for efficient, robust and predictable sampling performance. Compared to approaches based on the state-of-the-art No-U-Turn Sampler, our approach delivers substantial speedups up to an order of magnitude, while maintaining or improving predictive performance and uncertainty quantification across diverse tasks and data modalities. The suggested Microcanonical Langevin Ensembles and modifications to MCLMC additionally enhance the method's predictability in resource requirements, facilitating easier parallelization. All in all, the proposed method offers a promising direction for practical, scalable inference for BNNs.

David Rügamer

In the current era of vast data and transparent machine learning, it is essential for techniques to operate at a large scale while providing a clear mathematical comprehension of the internal workings of the method. Although there already exist interpretable semi-parametric regression methods for large-scale applications that take into account non-linearity in the data, the complexity of the models is still often limited. One of the main challenges is the absence of interactions in these models, which are left out for the sake of better interpretability but also due to impractical computational costs. To overcome this limitation, we propose a new approach using a factorization method to derive a highly scalable higher-order tensor product spline model. Our method allows for the incorporation of all (higher-order) interactions of non-linear feature effects while having computational costs proportional to a model without interactions. We further develop a meaningful penalization scheme and examine the induced optimization problem. We conclude by evaluating the predictive and estimation performance of our method.

Lucas Kook, Chris Kolb, Philipp Schiele et al.

Neural network representations of simple models, such as linear regression, are being studied increasingly to better understand the underlying principles of deep learning algorithms. However, neural representations of distributional regression models, such as the Cox model, have received little attention so far. We close this gap by proposing a framework for distributional regression using inverse flow transformations (DRIFT), which includes neural representations of the aforementioned models. We empirically demonstrate that the neural representations of models in DRIFT can serve as a substitute for their classical statistical counterparts in several applications involving continuous, ordered, time-series, and survival outcomes. We confirm that models in DRIFT empirically match the performance of several statistical methods in terms of estimation of partial effects, prediction, and aleatoric uncertainty quantification. DRIFT covers both interpretable statistical models and flexible neural networks opening up new avenues in both statistical modeling and deep learning.

Tobias Weber, Jakob Dexl, David Rügamer et al.

We address the computational barrier of deploying advanced deep learning segmentation models in clinical settings by studying the efficacy of network compression through tensor decomposition. We propose a post-training Tucker factorization that enables the decomposition of pre-existing models to reduce computational requirements without impeding segmentation accuracy. We applied Tucker decomposition to the convolutional kernels of the TotalSegmentator (TS) model, an nnU-Net model trained on a comprehensive dataset for automatic segmentation of 117 anatomical structures. Our approach reduced the floating-point operations (FLOPs) and memory required during inference, offering an adjustable trade-off between computational efficiency and segmentation quality. This study utilized the publicly available TS dataset, employing various downsampling factors to explore the relationship between model size, inference speed, and segmentation performance. The application of Tucker decomposition to the TS model substantially reduced the model parameters and FLOPs across various compression rates, with limited loss in segmentation accuracy. We removed up to 88% of the model's parameters with no significant performance changes in the majority of classes after fine-tuning. Practical benefits varied across different graphics processing unit (GPU) architectures, with more distinct speed-ups on less powerful hardware. Post-hoc network compression via Tucker decomposition presents a viable strategy for reducing the computational demand of medical image segmentation models without substantially sacrificing accuracy. This approach enables the broader adoption of advanced deep learning technologies in clinical practice, offering a way to navigate the constraints of hardware capabilities.

Richard D. Paul, Johannes Seiffarth, David Rügamer et al.

Cell tracking is a key computational task in live-cell microscopy, but fully automated analysis of high-throughput imaging requires reliable and, thus, uncertainty-aware data analysis tools, as the amount of data recorded within a single experiment exceeds what humans are able to overlook. We here propose and benchmark various methods to reason about and quantify uncertainty in linear assignment-based cell tracking algorithms. Our methods take inspiration from statistics and machine learning, leveraging two perspectives on the cell tracking problem explored throughout this work: Considering it as a Bayesian inference problem and as a classification problem. Our methods admit a framework-like character in that they equip any frame-to-frame tracking method with uncertainty quantification. We demonstrate this by applying it to various existing tracking algorithms including the recently presented Transformer-based trackers. We demonstrate empirically that our methods yield useful and well-calibrated tracking uncertainties.

Rickmer Schulte, David Rügamer, Thomas Nagler

There is growing interest in extending average treatment effect (ATE) estimation to incorporate non-tabular data, such as images and text, which may act as sources of confounding. Neglecting these effects risks biased results and flawed scientific conclusions. However, incorporating non-tabular data necessitates sophisticated feature extractors, often in combination with ideas of transfer learning. In this work, we investigate how latent features from pre-trained neural networks can be leveraged to adjust for sources of confounding. We formalize conditions under which these latent features enable valid adjustment and statistical inference in ATE estimation, demonstrating results along the example of double machine learning. We discuss critical challenges inherent to latent feature learning and downstream parameter estimation arising from the high dimensionality and non-identifiability of representations. Common structural assumptions for obtaining fast convergence rates with additive or sparse linear models are shown to be unrealistic for latent features. We argue, however, that neural networks are largely insensitive to these issues. In particular, we show that neural networks can achieve fast convergence rates by adapting to intrinsic notions of sparsity and dimension of the learning problem.

Daniel Dold, David Rügamer, Beate Sick et al.

Semi-structured regression models enable the joint modeling of interpretable structured and complex unstructured feature effects. The structured model part is inspired by statistical models and can be used to infer the input-output relationship for features of particular importance. The complex unstructured part defines an arbitrary deep neural network and thereby provides enough flexibility to achieve competitive prediction performance. While these models can also account for aleatoric uncertainty, there is still a lack of work on accounting for epistemic uncertainty. In this paper, we address this problem by presenting a Bayesian approximation for semi-structured regression models using subspace inference. To this end, we extend subspace inference for joint posterior sampling from a full parameter space for structured effects and a subspace for unstructured effects. Apart from this hybrid sampling scheme, our method allows for tunable complexity of the subspace and can capture multiple minima in the loss landscape. Numerical experiments validate our approach's efficacy in recovering structured effect parameter posteriors in semi-structured models and approaching the full-space posterior distribution of MCMC for increasing subspace dimension. Further, our approach exhibits competitive predictive performance across simulated and real-world datasets.

Daniel Dold, Julius Kobialka, Nicolai Palm et al.

Understanding the structure of neural network loss surfaces, particularly the emergence of low-loss tunnels, is critical for advancing neural network theory and practice. In this paper, we propose a novel approach to directly embed loss tunnels into the loss landscape of neural networks. Exploring the properties of these loss tunnels offers new insights into their length and structure and sheds light on some common misconceptions. We then apply our approach to Bayesian neural networks, where we improve subspace inference by identifying pitfalls and proposing a more natural prior that better guides the sampling procedure.

David Rügamer, Chris Kolb, Tobias Weber et al.

The complexity of black-box algorithms can lead to various challenges, including the introduction of biases. These biases present immediate risks in the algorithms' application. It was, for instance, shown that neural networks can deduce racial information solely from a patient's X-ray scan, a task beyond the capability of medical experts. If this fact is not known to the medical expert, automatic decision-making based on this algorithm could lead to prescribing a treatment (purely) based on racial information. While current methodologies allow for the "orthogonalization" or "normalization" of neural networks with respect to such information, existing approaches are grounded in linear models. Our paper advances the discourse by introducing corrections for non-linearities such as ReLU activations. Our approach also encompasses scalar and tensor-valued predictions, facilitating its integration into neural network architectures. Through extensive experiments, we validate our method's effectiveness in safeguarding sensitive data in generalized linear models, normalizing convolutional neural networks for metadata, and rectifying pre-existing embeddings for undesired attributes.

Chris Kolb, Laetitia Frost, Bernd Bischl et al.

Structured sparsity regularization offers a principled way to compact neural networks, but its non-differentiability breaks compatibility with conventional stochastic gradient descent and requires either specialized optimizers or additional post-hoc pruning without formal guarantees. In this work, we propose $D$-Gating, a fully differentiable structured overparameterization that splits each group of weights into a primary weight vector and multiple scalar gating factors. We prove that any local minimum under $D$-Gating is also a local minimum using non-smooth structured $L_{2,2/D}$ penalization, and further show that the $D$-Gating objective converges at least exponentially fast to the $L_{2,2/D}$-regularized loss in the gradient flow limit. Together, our results show that $D$-Gating is theoretically equivalent to solving the original group sparsity problem, yet induces distinct learning dynamics that evolve from a non-sparse regime into sparse optimization. We validate our theory across vision, language, and tabular tasks, where $D$-Gating consistently delivers strong performance-sparsity tradeoffs and outperforms both direct optimization of structured penalties and conventional pruning baselines.

Enes Özeren, Alexander Ulbrich, Sascha Filimon et al.

A comprehensive understanding of traffic accidents is essential for improving city safety and informing policy decisions. In this study, we analyze traffic incidents in Munich to identify patterns and characteristics that distinguish different types of accidents. The dataset consists of both structured tabular features, such as location, time, and weather conditions, as well as unstructured free-text descriptions detailing the circumstances of each accident. Each incident is categorized into one of seven predefined classes. To assess the reliability of these labels, we apply NLP methods, including topic modeling and few-shot learning, which reveal inconsistencies in the labeling process. These findings highlight potential ambiguities in accident classification and motivate a refined predictive approach. Building on these insights, we develop a classification model that achieves high accuracy in assigning accidents to their respective categories. Our results demonstrate that textual descriptions contain the most informative features for classification, while the inclusion of tabular data provides only marginal improvements. These findings emphasize the critical role of free-text data in accident analysis and highlight the potential of transformer-based models in improving classification reliability.

Tobias Pielok, Bernd Bischl, David Rügamer

Semi-implicit variational inference (SIVI) is a powerful framework for approximating complex posterior distributions, but training with the Kullback-Leibler (KL) divergence can be challenging due to high variance and bias in high-dimensional settings. While current state-of-the-art semi-implicit variational inference methods, particularly Kernel Semi-Implicit Variational Inference (KSIVI), have been shown to work in high dimensions, training remains moderately expensive. In this work, we propose a kernelized KL divergence estimator that stabilizes training through nonparametric smoothing. To further reduce the bias, we introduce an importance sampling correction. We provide a theoretical connection to the amortized version of the Stein variational gradient descent, which estimates the score gradient via Stein's identity, showing that both methods minimize the same objective, but our semi-implicit approach achieves lower gradient variance. In addition, our method's bias in function space is benign, leading to more stable and efficient optimization. Empirical results demonstrate that our method outperforms or matches state-of-the-art SIVI methods in both performance and training efficiency.

Tobias Pielok, Bernd Bischl, David Rügamer

Recent years have witnessed growing interest in semi-implicit variational inference (SIVI) methods due to their ability to rapidly generate samples from complex distributions. However, since the likelihood of these samples is non-trivial to estimate in high dimensions, current research focuses on finding effective SIVI training routines. Although unbiased implicit variational inference (UIVI) has largely been dismissed as imprecise and computationally prohibitive because of its inner MCMC loop, we revisit this method and show that UIVI's MCMC loop can be effectively replaced via importance sampling and the optimal proposal distribution can be learned stably by minimizing an expected forward Kullback-Leibler divergence without bias. Our refined approach demonstrates superior performance or parity with state-of-the-art methods on established SIVI benchmarks.

Vishwa Mohan Singh, Alberto Gaston Villagran Asiares, Luisa Sophie Schuhmacher et al.

Diffusion Tensor Imaging (DTI) tractography offers detailed insights into the structural connectivity of the brain, but presents challenges in effective representation and interpretation in deep learning models. In this work, we propose a novel 2D representation of DTI tractography that encodes tract-level fractional anisotropy (FA) values into a 9x9 grayscale image. This representation is processed through a Beta-Total Correlation Variational Autoencoder with a Spatial Broadcast Decoder to learn a disentangled and interpretable latent embedding. We evaluate the quality of this embedding using supervised and unsupervised representation learning strategies, including auxiliary classification, triplet loss, and SimCLR-based contrastive learning. Compared to the 1D Group deep neural network (DNN) baselines, our approach improves the F1 score in a downstream sex classification task by 15.74% and shows a better disentanglement than the 3D representation.

Marcel Arpogaus, Thomas Kneib, Thomas Nagler et al.

Density regression models allow a comprehensive understanding of data by modeling the complete conditional probability distribution. While flexible estimation approaches such as normalizing flows (NF) work particularly well in multiple dimensions, interpreting the input-output relationship of such models is often difficult, due to the black-box character of deep learning models. In contrast, existing statistical methods for multivariate outcomes such as multivariate conditional transformation models (MCTM) are restricted in flexibility and are often not expressive enough to represent complex multivariate probability distributions. In this paper, we combine MCTM with state-of-the-art and autoregressive NF to leverage the transparency of MCTM for modeling interpretable feature effects on the marginal distributions in the first step and the flexibility of neural-network-based NF techniques to account for complex and non-linear relationships in the joint data distribution. We demonstrate our method's versatility in various numerical experiments and compare it with MCTM and other NF models on both simulated and real-world data.