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Sebastian J. Vollmer

Publications and source records attributed to Sebastian J. Vollmer.

At least 19 recordsLinked to original sources
arXiv2026

Walking the Score Manifold: Continuous-time Generative Dynamics on Learned Data Manifolds

Generative modeling of time-dependent data is typically formulated on a discrete temporal grid, restricting supervision to the observed timestamps in the training data. We instead frame generation as continuous-time evolution on a learned data manifold. To this end, we leverage pretrained score-based models as geometric priors and learn a vector field that evolves data along score-induced interpolation paths. Because these dynamics follow transitions that respect the geometry learned by the score model, they support generation at arbitrary timestamps and temporal super-resolution beyond the discretization of the training data. Moreover, this geometric formulation allows us to train the vector field simulation-free through a regression objective. To improve long-horizon rollout robustness, we introduce an objective that promotes path-relative transverse exponential stability. While motivated by stability theory, it admits a practical interpretation as denoising score matching transverse to the interpolation path. Further, we extend the framework to a probabilistic setting that models a distribution over plausible future trajectories. We demonstrate the method on natural video and scientific dynamical data, including temporal super-resolution, PDE-based spatiotemporal fields, and molecular dynamics. Our results show that score-based priors provide a strong foundation for learning stochastic continuous-time generative dynamics.

cs.LG↗
arXiv2026

CLAM: Causal Spatial Disaggregation to Infer Local Effects From Coarse Data

Learning fine-grained spatial patterns from coarse-resolution data is challenging, especially in causal settings where high-resolution effects must be inferred from aggregated interventions and outcomes. We introduce CLAM, a method for estimating localized causal effects from coarse observations by exploiting high-resolution contextual covariates that modulate these effects. By jointly learning the causal mechanism and a disaggregation mapping, CLAM captures interactions that are missed when addressing these problems independently. The method supports localized effect estimation, counterfactual reasoning, and principled outcome disaggregation, and reliably captures spatially varying causal effects across diverse settings. This is particularly relevant for applications such as public health and environmental policy, where decisions are made at broad scales despite substantial local heterogeneity. Code is available at https://github.com/gerritgr/clam

cs.LG↗
arXiv2026

Orca: Neural Operators for Causal Reasoning in Continuous Time

Structural causal models are the standard language for reasoning about interventions and counterfactuals, but they describe static variables, typically measured once, and usually forbid cyclic dependencies. Many systems we care about, such as patients, climates, and economies, instead evolve continuously in time, are observed at irregular time points, and contain feedback loops. We argue that neural operator learning provides a natural foundation for causal reasoning in this setting, and propose Orca, a framework in which each node of the causal graph is a function of time and each mechanism is a learned map between function spaces. We extend existing neural operator architectures to express causal mechanisms: a mechanism computes the function value of a node from its parent nodes by taking several parent functions as input, respects the arrow of time, and treats latent exogenous noise as a function that can be inferred and reused for counterfactuals. We formalize the model class and demonstrate counterfactual reasoning on synthetic continuous-time examples. Code is available at https://github.com/gerritgr/orca

cs.AI↗
arXiv2026

Physics-Constrained Fine-Tuning of Flow-Matching Models for Generation and Inverse Problems

We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems. Starting from a model trained on low-fidelity or observational data, we apply a differentiable post-training procedure that minimizes weak-form residuals of governing partial differential equations (PDEs), promoting physical consistency and adherence to boundary conditions without distorting the underlying learned distribution. To infer unknown physical inputs, such as source terms, material parameters, or boundary data, we augment the generative process with a learnable latent parameter predictor and propose a joint optimization strategy. The resulting model produces physically valid field solutions alongside plausible estimates of hidden parameters, effectively addressing ill-posed inverse problems in a data-driven yet physicsaware manner. We validate our method on canonical PDE benchmarks, demonstrating improved satisfaction of PDE constraints and accurate recovery of latent coefficients. Our approach bridges generative modelling and scientific inference, opening new avenues for simulation-augmented discovery and data-efficient modelling of physical systems.

cs.LG↗
arXiv2026

Calibrated Preference Learning: The Case of Label Ranking

Calibration, the alignment of predicted probabilities with true outcome frequencies, is essential for reliable decision-making. While extensively studied for classification and regression, calibration has not been formally addressed for probabilistic label ranking, where the goal is to predict a distribution over orderings of a label set. Naively treating rankings as classes ignores their structure and fails to capture important modalities such as pairwise and top-k predictions. We formalize calibration for label ranking and develop a hierarchy of notions covering full rankings, sub-rankings, and top-k rankings. We prove that full-rank calibration implies the others but not conversely, and sub-ranking and top-k calibration are incomparable. Empirically, we find popular label ranking models are often poorly calibrated, with substantial differences between sub-ranking and top-k metrics. Applying our framework to RLHF reward models, we find that calibration correlates strongly but not perfectly with benchmark accuracy, suggesting it captures a meaningful quality dimension beyond top-1 accuracy. These findings motivate future work on understanding the downstream effects of miscalibration and developing methods to correct it.

cs.LG↗
arXiv2025

Decomposing Visual Classification: Assessing Tree-Based Reasoning in VLMs

Vision language models (VLMs) excel at zero-shot visual classification, but their performance on fine-grained tasks and large hierarchical label spaces is understudied. This paper investigates whether structured, tree-based reasoning can enhance VLM performance. We introduce a framework that decomposes classification into interpretable decisions using decision trees and evaluates it on fine-grained (GTSRB) and coarse-grained (CIFAR-10) datasets. Although the model achieves 98.2% accuracy in understanding the tree knowledge, tree-based reasoning consistently underperforms standard zero-shot prompting. We also explore enhancing the tree prompts with LLM-generated classes and image descriptions to improve alignment. The added description enhances the performance of the tree-based and zero-shot methods. Our findings highlight limitations of structured reasoning in visual classification and offer insights for designing more interpretable VLM systems.

cs.CV↗
arXiv2025

Automated Visualization Makeovers with LLMs

Making a good graphic that accurately and efficiently conveys the desired message to the audience is both an art and a science, typically not taught in the data science curriculum. Visualisation makeovers are exercises where the community exchange feedback to improve charts and data visualizations. Can multi-modal large language models (LLMs) emulate this task? Given a plot in the form of an image file, or the code used to generate it, an LLM, primed with a list of visualization best practices, is employed to semi-automatically generate constructive criticism to produce a better plot. Our system is centred around prompt engineering of a pre-trained model, relying on a combination of userspecified guidelines and any latent knowledge of data visualization practices that might lie within an LLMs training corpus. Unlike other works, the focus is not on generating valid visualization scripts from raw data or prompts, but on educating the user how to improve their existing data visualizations according to an interpretation of best practices. A quantitative evaluation is performed to measure the sensitivity of the LLM agent to various plotting issues across different chart types. We make the tool available as a simple self-hosted applet with an accessible Web interface.

cs.HC↗
arXiv2025

The Power of Stories: Narrative Priming Shapes How LLM Agents Collaborate and Compete

According to Yuval Noah Harari, large-scale human cooperation is driven by shared narratives that encode common beliefs and values. This study explores whether such narratives can similarly nudge LLM agents toward collaboration. We use a finitely repeated public goods game in which LLM agents choose either cooperative or egoistic spending strategies. We prime agents with stories highlighting teamwork to different degrees and test how this influences negotiation outcomes. Our experiments explore four questions:(1) How do narratives influence negotiation behavior? (2) What differs when agents share the same story versus different ones? (3) What happens when the agent numbers grow? (4) Are agents resilient against self-serving negotiators? We find that story-based priming significantly affects negotiation strategies and success rates. Common stories improve collaboration, benefiting each agent. By contrast, priming agents with different stories reverses this effect, and those agents primed toward self-interest prevail. We hypothesize that these results carry implications for multi-agent system design and AI alignment.

cs.AI↗
arXiv2023

Energy Discrepancies: A Score-Independent Loss for Energy-Based Models

Energy-based models are a simple yet powerful class of probabilistic models, but their widespread adoption has been limited by the computational burden of training them. We propose a novel loss function called Energy Discrepancy (ED) which does not rely on the computation of scores or expensive Markov chain Monte Carlo. We show that ED approaches the explicit score matching and negative log-likelihood loss under different limits, effectively interpolating between both. Consequently, minimum ED estimation overcomes the problem of nearsightedness encountered in score-based estimation methods, while also enjoying theoretical guarantees. Through numerical experiments, we demonstrate that ED learns low-dimensional data distributions faster and more accurately than explicit score matching or contrastive divergence. For high-dimensional image data, we describe how the manifold hypothesis puts limitations on our approach and demonstrate the effectiveness of energy discrepancy by training the energy-based model as a prior of a variational decoder model.

stat.ML↗
arXiv2020

Flexible model composition in machine learning and its implementation in MLJ

A graph-based protocol called `learning networks' which combine assorted machine learning models into meta-models is described. Learning networks are shown to overcome several limitations of model composition as implemented in the dominant machine learning platforms. After illustrating the protocol in simple examples, a concise syntax for specifying a learning network, implemented in the MLJ framework, is presented. Using the syntax, it is shown that learning networks are are sufficiently flexible to include Wolpert's model stacking, with out-of-sample predictions for the base learners.

cs.LG↗
arXiv2020

MLJ: A Julia package for composable machine learning

MLJ (Machine Learing in Julia) is an open source software package providing a common interface for interacting with machine learning models written in Julia and other languages. It provides tools and meta-algorithms for selecting, tuning, evaluating, composing and comparing those models, with a focus on flexible model composition. In this design overview we detail chief novelties of the framework, together with the clear benefits of Julia over the dominant multi-language alternatives.

cs.LG↗
arXiv2018

Measuring Sample Quality with Diffusions

Stein's method for measuring convergence to a continuous target distribution relies on an operator characterizing the target and Stein factor bounds on the solutions of an associated differential equation. While such operators and bounds are readily available for a diversity of univariate targets, few multivariate targets have been analyzed. We introduce a new class of characterizing operators based on Ito diffusions and develop explicit multivariate Stein factor bounds for any target with a fast-coupling Ito diffusion. As example applications, we develop computable and convergence-determining diffusion Stein discrepancies for log-concave, heavy-tailed, and multimodal targets and use these quality measures to select the hyperparameters of biased Markov chain Monte Carlo (MCMC) samplers, compare random and deterministic quadrature rules, and quantify bias-variance tradeoffs in approximate MCMC. Our results establish a near-linear relationship between diffusion Stein discrepancies and Wasserstein distances, improving upon past work even for strongly log-concave targets. The exposed relationship between Stein factors and Markov process coupling may be of independent interest.

stat.ML↗
arXiv2017

An iterative technique for bounding derivatives of solutions of Stein equations

We introduce a simple iterative technique for bounding derivatives of solutions of Stein equations $Lf=h-\mathbb{E}h(Z)$, where $L$ is a linear differential operator and $Z$ is the limit random variable. Given bounds on just the solutions or certain lower order derivatives of the solution, the technique allows one to deduce bounds for derivatives of any order, in terms of supremum norms of derivatives of the test function $h$. This approach can be readily applied to many Stein equations from the literature. We consider a number of applications; in particular, we derive bounds for derivatives of any order of the solution of the general variance-gamma Stein equation.

math.PR↗
arXiv2017

The True Cost of Stochastic Gradient Langevin Dynamics

The problem of posterior inference is central to Bayesian statistics and a wealth of Markov Chain Monte Carlo (MCMC) methods have been proposed to obtain asymptotically correct samples from the posterior. As datasets in applications grow larger and larger, scalability has emerged as a central problem for MCMC methods. Stochastic Gradient Langevin Dynamics (SGLD) and related stochastic gradient Markov Chain Monte Carlo methods offer scalability by using stochastic gradients in each step of the simulated dynamics. While these methods are asymptotically unbiased if the stepsizes are reduced in an appropriate fashion, in practice constant stepsizes are used. This introduces a bias that is often ignored. In this paper we study the mean squared error of Lipschitz functionals in strongly log- concave models with i.i.d. data of growing data set size and show that, given a batchsize, to control the bias of SGLD the stepsize has to be chosen so small that the computational cost of reaching a target accuracy is roughly the same for all batchsizes. Using a control variate approach, the cost can be reduced dramatically. The analysis is performed by considering the algorithms as noisy discretisations of the Langevin SDE which correspond to the Euler method if the full data set is used. An important observation is that the 1scale of the step size is determined by the stability criterion if the accuracy is required for consistent credible intervals. Experimental results confirm our theoretical findings.

stat.ME↗
arXiv2017

Note on A. Barbour's paper on Stein's method for diffusion approximations

In (Barbour, 1990) foundations for diffusion approximation via Stein's method are laid. This paper has been cited more than 130 times and is a cornerstone in the area of Stein's method. A semigroup argument is used therein to solve a Stein equation for Gaussian diffusion approximation. We prove that, contrary to the claim in (Barbour, 1990), the semigroup considered therein is not strongly continuous on the Banach space of continuous, real-valued functions on D[0,1] growing slower than a cubic, equipped with an appropriate norm. We also provide a proof of the exact formulation of the solution to the Stein equation of interest, which does not require the aforementioned strong continuity. This shows that the main results of (Barbour, 1990) hold true.

math.PR↗
arXiv2017

Multilevel Monte Carlo for Reliability Theory

As the size of engineered systems grows, problems in reliability theory can become computationally challenging, often due to the combinatorial growth in the cut sets. In this paper we demonstrate how Multilevel Monte Carlo (MLMC) - a simulation approach which is typically used for stochastic differential equation models - can be applied in reliability problems by carefully controlling the bias-variance tradeoff in approximating large system behaviour. In this first exposition of MLMC methods in reliability problems we address the canonical problem of estimating the expectation of a functional of system lifetime and show the computational advantages compared to classical Monte Carlo methods. The difference in computational complexity can be orders of magnitude for very large or complicated system structures.

stat.CO↗
arXiv2017

The Bouncy Particle Sampler: A Non-Reversible Rejection-Free Markov Chain Monte Carlo Method

Markov chain Monte Carlo methods have become standard tools in statistics to sample from complex probability measures. Many available techniques rely on discrete-time reversible Markov chains whose transition kernels build up over the Metropolis-Hastings algorithm. We explore and propose several original extensions of an alternative approach introduced recently in Peters and de With (2012) where the target distribution of interest is explored using a continuous-time Markov process. In the Metropolis-Hastings algorithm, a trial move to a region of lower target density, equivalently "higher energy", than the current state can be rejected with positive probability. In this alternative approach, a particle moves along straight lines continuously around the space and, when facing a high energy barrier, it is not rejected but its path is modified by bouncing against this barrier. The resulting non-reversible Markov process provides a rejection-free MCMC sampling scheme. We propose several original techniques to simulate this continuous-time process exactly in a wide range of scenarios of interest to statisticians. When the target distribution factorizes as a product of factors involving only subsets of variables, such as the posterior distribution associated to a probabilistic graphical model, it is possible to modify the original algorithm to exploit this structure and update in parallel variables within each clique. We present several extensions by proposing methods to sample mixed discrete-continuous distributions and distributions restricted to a connected smooth domain. We also show that it is possible to move the particle using a general flow instead of straight lines. We demonstrate the efficiency of this methodology through simulations on a variety of applications and show that it can outperform Hybrid Monte Carlo schemes in interesting scenarios.

stat.ME↗