arXiv subjects

Thomas B. Schön

Publications and source records attributed to Thomas B. Schön.

At least 19 recordsLinked to original sources

arXiv2026

Funnel planning and control for manipulators using neural Signed Configuration Distance Functions

Robust motion planning and control for manipulators is the problem of guaranteeing safe execution and collision-free motion under disturbances. The Kinodynamic Motion Planning via Funnel Control (KDF) is a recently proposed planner that comes with robustness guarantees and is particularly attractive for collision-free control as it guarantees closed-loop evolution inside a funnel, i.e., a collision-free region around a nominal trajectory. Despite its attractive theoretical properties, the current approach for computing funnels is computationally demanding, which limits its expressiveness and performance. We address its current limitations by proposing a novel funnel planning and control solution. Our key tool to enable this is a neural Signed Configuration Distance Function (nSCDF) which allows us to estimate collision-free balls and gradients in a computationally efficient way. We use the nSCDF in our planner to compute a nominal trajectory, where path length and clearance are balanced. To track the trajectory with collision-avoidance guarantees, we design a funnel controller that exploits the geometric information from the nSCDF. From numerical experiments, we observe that our planner produces nominal paths $2$ times faster, while at the same time obtaining $20 \%$ shorter path length and $5$ times the clearance. Finally, we also observe improved motion performance and robustness properties when using the nSCDF for funnel control.

cs.RO↗

arXiv2026

Safe learning-based control via function-based uncertainty quantification

Uncertainty quantification is essential when deploying learning-based control methods in safety-critical systems. This is commonly realized by constructing uncertainty tubes that enclose the unknown function of interest, e.g., the reward and constraint functions or the underlying dynamics model, with high probability. However, existing approaches for uncertainty quantification typically rely on restrictive assumptions that encode smoothness properties of the unknown function, such as a known norm in a function space. Moreover, these methods usually struggle with discontinuities. In this paper, we model the unknown function as a random function from which independent and identically distributed realizations can be generated. We then construct uncertainty tubes via the scenario approach that hold with high probability. Our uncertainty tubes rely solely on sampled realizations and can therefore accommodate discontinuities represented by the sampling model. We integrate these uncertainty tubes into a safe Bayesian optimization algorithm with which we safely tune control parameters on a real Furuta pendulum.

eess.SY↗

arXiv2026

On the role of the tokenizer in ECG transformer models

Tokenization determines both the physiological content presented to an ECG Transformer and the sequence over which attention operates. We compare eight tokenization strategies across Transformer, Informer, Reformer, and FEDformer on the nine-label CPSC2018 classification task. The input projection and principal backbone capacity are controlled to isolate the effect of token construction. Median-beat and HeartLang tokenization achieve mean macro-AUCs of 0.893 and 0.889 across the four backbones, compared with 0.822 and 0.824 for point-wise and patch-wise tokenization. Pooling the two physiology-aware representations yields an 8.2% relative improvement in macro-AUC. They also reduce mean sequence length from 1,250 to 158 tokens and mean peak training memory from 5.21 to 0.27 GB. The results show that aligning tokens with ECG morphology can improve both predictive performance and memory efficiency without increasing backbone capacity. The source code is available on https://github.com/LeeJarvis996/ecg_tokenizer.

cs.LG↗

arXiv2026

Efficient Image Restoration with State-Dependent Forward Diffusion

This paper proposes to perform image restoration through a state-dependent mean-reverting forward diffusion (FoD) process. In contrast to traditional diffusion-based approaches that rely on a coupled forward-backward diffusion scheme, FoD directly learns image restoration through a single forward diffusion process, yielding a simple yet efficient framework. The core of FoD is a state-dependent stochastic differential equation (SDE) that involves a mean-reverting term in both the drift and diffusion functions. This mean-reverting structure drives the low-quality data toward the clean endpoint with controlled stochastic variation, therefore simulating a stochastic interpolation between source and target distributions. More importantly, FoD is analytically tractable and is trained using a simple stochastic flow matching objective, enabling few-step sampling during inference. The proposed FoD model, despite its simplicity, achieves strong overall performance on various image restoration tasks compared to representative diffusion, diffusion bridge, and flow matching approaches. The code is available at https://github.com/Algolzw/FoD.

cs.LG↗

arXiv2026

Robust Convex Model Predictive Control with collision avoidance guarantees for robot manipulators

Industrial manipulators typically operate in cluttered environments, where safe motion planning is critical. However, model uncertainties further complicate this task, which leads to conservative speed limits to reduce the influence of disturbances. Hence, there is a need for control methods that can guarantee safe motions which are executed fast. We address this by suggesting a novel model predictive control (MPC) solution for manipulators, where our two main components are a robust tube MPC and a corridor planning algorithm to obtain collision-free motion. Our solution results in a convex MPC formulation, which we can solve fast, making our method practically useful. We demonstrate the efficacy of our method in a simulated environment with a 6 DOF industrial robot operating in cluttered environments with uncertain model parameters. We outperform benchmark methods by tolerating higher levels of model uncertainty while achieving faster motion.

cs.RO↗

arXiv2026

Is Supervised Learning Really That Different from Unsupervised?

We demonstrate how supervised learning can be decomposed into a two-stage procedure, where (1) all model parameters are selected in an unsupervised manner, and (2) the outputs y are added to the model, without changing the parameter values. This is achieved by a new model selection criterion that - in contrast to cross-validation - can be used also without access to y. For linear ridge regression, we bound the asymptotic out-of-sample risk of our method in terms of the optimal asymptotic risk. We also demonstrate that versions of linear and kernel ridge regression, smoothing splines, k-nearest neighbors, random forests, and neural networks, trained without access to y, perform similarly to their standard y-based counterparts. Hence, our results suggest that the difference between supervised and unsupervised learning is less fundamental than it may appear.

stat.ML↗

arXiv2026

A neural signed configuration distance function for path planning of picking manipulators

Picking manipulators are task specific robots, with fewer degrees of freedom compared to general-purpose manipulators, and are heavily used in industry. The efficiency of the picking robots is highly dependent on the path planning solution, which is commonly based on sampling-based multi-query methods. The planner is robustly able to solve the problem, but its heavy use of collision-detection limits the planning capabilities for online use. We approach this problem by presenting a novel implicit obstacle representation for path planning, a neural signed configuration distance function (nSCDF), which allows us to form collision-free balls in the configuration space. We use the ball representation to re-formulate a state of the art multi-query path planner, i.e., instead of points, we use balls in the graph. Our planner returns a collision-free corridor, which allows us to use convex programming to produce optimized paths. From our numerical experiments, we observe that our planner produces paths that are close to those from an asymptotically optimal path planner, in significantly less time.

cs.RO↗

arXiv2026

A Rigorous, Tractable Measure of Model Complexity

An accurate assessment of a model's complexity is crucial for topics such as interpretation, generalization, and model selection. However, most existing complexity measures either rely on heuristic assumptions or are computationally prohibitive. In this paper, we present a mathematically rigorous yet easy-to-compute measure of model complexity that is based on the similarities between the model gradients across inputs. It is thus well-defined for any parametric model, but also for kernel-based non-parametric models. We prove that our measure of complexity generalizes model-specific complexity measures such as polynomial degree (for polynomial regression), kernel length scale (for Matérn kernels), number of neighbors (for k-nearest neighbors), number of splits (for decision trees), and number of trees (for random forests). We also use our measure to obtain new insights into the double descent phenomenon for random Fourier features, random forests, neural networks, and gradient boosting.

stat.ML↗

arXiv2026

How Do Electrocardiogram Models Scale?

While scaling laws have established a fundamental framework for foundation models in natural language processing, their applicability to electrocardiogram (ECG) models remains poorly characterized. Indeed, recent studies do not always yield consistent downstream gains as one increases the model size or pre-training dataset size of ECG models, leaving the exact roles of architectural inductive biases, pre-training paradigms, and expected improvements with size largely unanswered. In this work, we systematically investigate neural and loss-to-loss scaling laws within the ECG domain. By pre-training over $120$ models (ranging from $20$K to $200$M parameters) on the large-scale CODE dataset ($2.3$M records), we decouple the effects of model architecture (ResNet vs. Transformer) and pre-training paradigm, namely supervised learning (SL) versus self-supervised learning (SSL). We found that (i) SL models are data-bottlenecked in-distribution, whereas SSL models scale robustly across both model and data sizes; (ii) for out-of-distribution (OOD) generalization, ResNets are $1.3$ to $2.5$ times more parameter-efficient than Transformers, while SSL is up to $16$ times more data-efficient and achieves up to $7.6$ times higher transfer efficiency than SL on unseen clinical tasks; (iii) across the observed scales, ResNet-based models generally achieve the lowest OOD loss, with SSL dominating on unseen clinical tasks and self-supervised Transformers overtaking at very large model sizes. Our results suggest that the path to effective ECG foundation models lies in the strategic alignment of architecture and paradigm rather than brute-force scaling.

cs.LG↗

arXiv2026

Simultaneous State Estimation and Online Model Learning in a Soft Robotic System

Operating complex real-world systems, such as soft robots, can benefit from precise predictive control schemes that require accurate state and model knowledge. This knowledge is typically not available in practical settings and must be inferred from noisy measurements. In particular, it is challenging to simultaneously estimate unknown states and learn a model online from sequentially arriving measurements. In this paper, we show how a recently proposed gray-box system identification tool enables the estimation of a soft robot's current pose while at the same time learning a bending stiffness model. For estimation and learning, we only need a nominal constant-curvature robot model and measurements of the robot's base reactions (e.g., base forces). The estimation scheme -- relying on a marginalized particle filter -- allows us to conveniently interface nominal constant-curvature equations with a Gaussian Process (GP) bending stiffness model to be learned. This, in contrast to estimation via a random walk over stiffness values, enables prediction of bending stiffness and improves overall model quality. We demonstrate, using a real-world soft robot, that the method learns a bending-stiffness model online while accurately estimating the robot's pose. Notably, reduced error in multi-step forward predictions indicates that the learned bending-stiffness GP improves overall model quality.

eess.SY↗

arXiv2026

Structure-Preserving Gaussian Processes Via Discrete Euler-Lagrange Equations

In this paper, we propose Lagrangian Gaussian Processes (LGPs) for probabilistic and data-efficient learning of dynamics via discrete forced Euler-Lagrange equations. Importantly, the geometric structure of the Lagrange-d'Alembert principle, which governs the motion of dynamical systems, is preserved by construction in the absence of external forces. This allows learning physically consistent models that overcome erroneous drift in the system's energy, thereby providing stable long-term predictions. At the core of our approach lie linear operators for Gaussian process conditioning, constructed from discrete forced Euler-Lagrange equations and variational discretization schemes. Thereby and unlike prior work, the method enables learning dynamics from discrete position snapshots, i.e., without access to a system's velocities or momenta. This is particularly relevant for a large class of practical scenarios where only position measurements are available, for instance, in motion capture or visual servoing applications. We demonstrate the data-efficiency and generalization capabilities of the LGPs in various synthetic and real-world case studies, including a real-world soft robot with hysteresis. The experimental results underscore that the LGPs learn physically consistent dynamics with uncertainty quantification solely from sparse positional data and enable stable long-term predictions.

cs.LG↗

arXiv2026

Learning Dynamics from Input-Output Data with Hamiltonian Gaussian Processes

Embedding non-restrictive prior knowledge, such as energy conservation laws, into learning methods is a key motive to construct physically consistent dynamics models from limited data, relevant for, e.g., model-based control. Recent work incorporates Hamiltonian dynamics into Gaussian Processes (GPs) to obtain uncertainty-quantifying, energy-consistent models, but these methods rely on -- rarely available -- velocity or momentum data. In this paper, we study dynamics learning using Hamiltonian GPs and focus on learning solely from input-output data, without relying on velocity or momentum measurements. Adopting a non-conservative formulation, energy exchange with the environment, e.g., through external forces or dissipation, can be captured. We provide a fully Bayesian scheme for estimating probability densities of unknown hidden states, GP hyperparameters, as well as structural hyperparameters, such as damping coefficients. The proposed method is evaluated in a nonlinear simulation case study and compared to a state-of-the-art approach that relies on momentum measurements.

cs.LG↗

arXiv2026

Ergodicity in reinforcement learning

In reinforcement learning, we typically aim to optimize the expected value of the sum of rewards an agent collects over a trajectory. However, if the process generating these rewards is non-ergodic, the expected value, i.e., the average over infinitely many trajectories with a given policy, is uninformative for the average over a single, but infinitely long trajectory. Thus, if we care about how the individual agent performs during deployment, the expected value is not a good optimization objective. In this paper, we discuss the impact of non-ergodic reward processes on reinforcement learning agents through an instructive example, relate the notion of ergodic reward processes to more widely used notions of ergodic Markov chains, and present existing solutions that optimize long-term performance of individual trajectories under non-ergodic reward dynamics.

cs.LG↗

arXiv2026

Self-Rewarding Sequential Monte Carlo for Masked Diffusion Language Models

This work presents self-rewarding sequential Monte Carlo (SMC), an inference-time scaling algorithm enabling effective sampling of masked diffusion language models (MDLMs). Our algorithm stems from the observation that most existing MDLMs rely on a confidence-based sampling strategy, where only tokens with the highest prediction confidence are preserved at each step. This restricts the generation to a noise-sensitive, greedy decoding paradigm, resulting in an inevitable collapse in the diversity of possible paths. We address this problem by launching multiple interacting diffusion processes in parallel, referred to as particles, for trajectory exploration. Importantly, we introduce the trajectory-level confidence as a self-rewarding signal for assigning particle importance weights. During sampling, particles are iteratively weighted and resampled to systematically steer generation towards globally confident, high-quality samples. Our self-rewarding SMC is verified on various masked diffusion language models and benchmarks, achieving significant improvement without extra training or reward guidance, while effectively converting parallel inference capacity into improved sampling quality. Our code is available at https://github.com/Algolzw/self-rewarding-smc.

cs.LG↗

arXiv2025

Safe Bayesian optimization across noise models via scenario programming

Safe Bayesian optimization (BO) with Gaussian processes is an effective tool for tuning control policies in safety-critical real-world systems, specifically due to its sample efficiency and safety guarantees. However, most safe BO algorithms assume homoscedastic sub-Gaussian measurement noise, an assumption that does not hold in many relevant applications. In this article, we propose a straightforward yet rigorous approach for safe BO across noise models, including homoscedastic sub-Gaussian and heteroscedastic heavy-tailed distributions. We provide a high-probability bound on the measurement noise via the scenario approach, integrate these bounds into high probability confidence intervals, and prove safety and optimality for our proposed safe BO algorithm. We deploy our algorithm in synthetic examples and in tuning a controller for the Franka Emika manipulator in simulation.

math.OC↗

arXiv2025

CODE-II: A large-scale dataset for artificial intelligence in ECG analysis

Data-driven methods for electrocardiogram (ECG) interpretation are rapidly progressing. Large datasets have enabled advances in artificial intelligence (AI) based ECG analysis, yet limitations in annotation quality, size, and scope remain major challenges. Here we present CODE-II, a large-scale real-world dataset of 2,735,269 12-lead ECGs from 2,093,807 adult patients collected by the Telehealth Network of Minas Gerais (TNMG), Brazil. Each exam was annotated using standardized diagnostic criteria and reviewed by cardiologists. A defining feature of CODE-II is a set of 66 clinically meaningful diagnostic classes, developed with cardiologist input and routinely used in telehealth practice. We additionally provide an open available subset: CODE-II-open, a public subset of 15,000 patients, and the CODE-II-test, a non-overlapping set of 8,475 exams reviewed by multiple cardiologists for blinded evaluation. A neural network pre-trained on CODE-II achieved superior transfer performance on external benchmarks (PTB-XL and CPSC 2018) and outperformed alternatives trained on larger datasets.

eess.SP↗

arXiv2025

Kernel Learning with Adversarial Features: Numerical Efficiency and Adaptive Regularization

Adversarial training has emerged as a key technique to enhance model robustness against adversarial input perturbations. Many of the existing methods rely on computationally expensive min-max problems that limit their application in practice. We propose a novel formulation of adversarial training in reproducing kernel Hilbert spaces, shifting from input to feature-space perturbations. This reformulation enables the exact solution of inner maximization and efficient optimization. It also provides a regularized estimator that naturally adapts to the noise level and the smoothness of the underlying function. We establish conditions under which the feature-perturbed formulation is a relaxation of the original problem and propose an efficient optimization algorithm based on iterative kernel ridge regression. We provide generalization bounds that help to understand the properties of the method. We also extend the formulation to multiple kernel learning. Empirical evaluation shows good performance in both clean and adversarial settings.

stat.ML↗

arXiv2025

Taming Diffusion Models for Image Restoration: A Review

Diffusion models have achieved remarkable progress in generative modelling, particularly in enhancing image quality to conform to human preferences. Recently, these models have also been applied to low-level computer vision for photo-realistic image restoration (IR) in tasks such as image denoising, deblurring, dehazing, etc. In this review paper, we introduce key constructions in diffusion models and survey contemporary techniques that make use of diffusion models in solving general IR tasks. Furthermore, we point out the main challenges and limitations of existing diffusion-based IR frameworks and provide potential directions for future work.

cs.CV↗