arXiv subjects

Matthias Althoff

Publications and source records attributed to Matthias Althoff.

At least 19 recordsLinked to original sources

arXiv2026

RAM: Reachability Across Morphologies

Many stages of the robotic lifecycle, from morphology synthesis to operation, rely fundamentally on the reachable workspace. However, current methods for approximating workspaces are slow, imprecise, or tied to a single morphology. We introduce Reachability Across Morphologies (RAM): a morphology-conditioned, implicit neural representation that acts as a fast, differentiable surrogate for pose reachability, generalising to unseen morphologies while inherently accounting for self-collisions. To train RAM, we publish a large-scale dataset of $3\cdot10^{10}$ samples generated solely from forward kinematics. Experiments show that our model achieves an $ F_1$-score of $86\%$ at nanosecond inference, outperforming the baseline by $14\%$ while reducing inference time by three orders of magnitude. We further demonstrate speed-ups of one and two orders of magnitude for gradient-based morphology and trajectory optimisation, respectively. Website: https://timwalter.github.io/ram.

cs.RO↗

arXiv2026

Multi-Variable Conformal Prediction: Optimizing Prediction Sets without Data Splitting

Conformal prediction constructs prediction sets with finite-sample coverage guarantees, but its calibration stage is structurally constrained to a scalar score function and a single threshold variable - forcing shapes of prediction sets to be fixed before calibration, typically through data splitting. We introduce multi-variable conformal prediction (MCP), a framework that extends conformal prediction to vector-valued score functions with multiple simultaneous calibration variables. Building on scenario theory as a principled framework for certifying data-driven decisions, MCP unifies prediction set design and calibration into a single optimization problem, eliminating data splitting without sacrificing coverage guarantees. We propose two computationally efficient variants: RemMCP, grounded in constrained optimization with constraint removal, which admits a clean generalization of split conformal prediction; and RelMCP, based on iterative optimization with constraint relaxation, which supports non-convex score functions at the cost of possibly greater conservatism. Through numerical experiments on ellipsoidal and multi-modal prediction sets, we demonstrate that RemMCP and RelMCP consistently meet the target coverage with prediction set sizes smaller than or comparable to those of baselines with data split, while considerably reducing variance across calibration runs - a direct consequence of using all available data for shape optimization and calibration simultaneously.

stat.ML↗

arXiv2026

Formally Verifying Analog Neural Networks Under Process Variations Using Polynomial Zonotopes

Analog neural networks are gaining attention due to their efficiency in terms of power consumption and processing speed. However, since analog neural networks are implemented as physical circuits, they are highly sensitive to manufacturing process variations, which can cause large deviations from the nominal model. We present a polynomial-based model that resembles the performance of the neuron circuit under process variations. This model is formally verified via reachability analysis using polynomial zonotopes, thus avoiding conventional, time-consuming Monte Carlo simulations. We evaluate our proposed verification approach on three different datasets and on fully-connected and convolutional analog neural networks. Our experimental results confirm the effectiveness of our verification approach by reducing the verification time from up to a day to seconds while enclosing up to 99% of the variation samples.

cs.LG↗

arXiv2026

Learning Image-Adaptive Scale Fields for Metric Depth Recovery

Monocular depth estimation (MDE) typically produces depth estimations that are defined up to an unknown scale or shift. When only sparse metric anchors are available, recovering accurate metric depth becomes challenging yet necessary for practical applications. We address this problem by formulating metric depth recovery as image-adaptive scale field modeling. Instead of directly correcting the depth, we reformulate the correction as a low-dimensional linear combination of image-adaptive basis maps. These maps are derived from semantic and geometric cues encoded in the MDE estimations and intermediate representations. The weights of basis maps are efficiently determined from sparse metric anchors via a least-squares problem. This formulation yields improved metric depth accuracy, strong robustness under extreme anchor sparsity, and an interpretable decomposition of spatial scale variations. Extensive experiments across multiple datasets and representative MDE models demonstrate the effectiveness and general applicability of our approach.

cs.CV↗

arXiv2026

Set-Based Training of Neural Barrier Certificates for Safety Verification of Dynamical Systems

Barrier certificates are scalar functions over the state space of dynamical systems that separate all unsafe states from all reachable states. The existence of a barrier certificate formally verifies the safety of the dynamical system. Recent approaches synthesize barrier certificates by iteratively training a neural network. In each iteration, the candidate is formally verified - if successful, the barrier certificate is found. Instead, we propose a set-based training approach that tightly integrates verification into training via a set-based loss function that soundly encodes all barrier certificate properties. A loss of zero formally proves the validity of the barrier certificate, collapsing the iterative training and verification into a single training procedure. Our experiments demonstrate that our set-based training approach scales well with the system dimension and naturally handles complex nonlinear dynamics.

eess.SY↗

arXiv2026

Lexicographic Minimum-Violation Motion Planning using Signal Temporal Logic

Motion planning for autonomous vehicles often requires satisfying multiple conditionally conflicting specifications. In situations where not all specifications can be met simultaneously, minimum-violation motion planning maintains system operation by minimizing violations of specifications in accordance with their priorities. Signal temporal logic (STL) provides a formal language for rigorously defining these specifications and enables the quantitative evaluation of their violations. However, a total ordering of specifications yields a lexicographic optimization problem, which is typically computationally expensive to solve using standard methods. We address this problem by discretizing the multi-objective lexicographic optimization problem via non-uniform quantization and transforming it into a single-objective optimization problem using bit-shifting. Specifically, we extend a deterministic model predictive path integral (MPPI) solver to efficiently solve optimization problems without quadratic input cost. Additionally, a novel predicate robustness measure that combines spatial and temporal violations is introduced. Our results show that the proposed method offers an interpretable and scalable solution for lexicographic STL minimum-violation motion planning using a single-objective solver.

cs.RO↗

arXiv2026

Vision-Based Safe Human-Robot Collaboration with Uncertainty Guarantees

We propose a framework for vision-based human pose estimation and motion prediction that gives conformal prediction guarantees for certifiably safe human-robot collaboration. Our framework combines aleatoric uncertainty estimation with OOD detection for high probabilistic confidence. To integrate our pipeline in certifiable safety frameworks, we propose conformal prediction sets for human motion predictions with high, valid confidence. We evaluate our pipeline on recorded human motion data and a real-world human-robot collaboration setting.

cs.RO↗

arXiv2026

Divide and Discard: Fast Tightening of Guaranteed State Bounds for Nonlinear Systems

We propose a simple yet effective divide-and-discard (DD) approach to guaranteed state estimation for nonlinear discrete-time systems. Our method iteratively subdivides interval enclosures of the state and propagates them forward in time using a mean-value enclosure. The central idea is to rely on repeated refinement of simple sets rather than on more complex set representations, yielding an observer that is straightforward to implement and easy to integrate into existing frameworks. Our divide-and-discard strategy exploits that many sets can be discarded early and limits the number of maintained sets, resulting in low computational cost with complexity that scales only quadratically in the state dimension. The proposed method is evaluated on nonlinear benchmark problems previously used to compare guaranteed observers, where it outperforms state-of-the-art approaches in terms of both computational efficiency and enclosure tightness.

eess.SY↗

arXiv2026

To Learn or Not to Learn: A Litmus Test for Using Reinforcement Learning in Control

Reinforcement learning (RL) can be a powerful alternative to classical control methods when standard model-based control is insufficient, e.g., when deriving a suitable model is intractable or impossible. In many cases, however, the choice between model-based and RL-based control is not obvious. Due to the high computational costs of training RL agents, RL-based control should be limited to cases where it is expected to yield superior results compared to model-based control. To the best of our knowledge, there exists no approach to quantify the benefit of RL-based control that does not require RL training. In this work, we present a computationally efficient, purely simulation-based litmus test predicting whether RL-based control is superior to model-based control. Our test evaluates the suitability of the given model for model-based control by analyzing the impact of model uncertainties on the control problem. For this, we use reachset-conformant model identification combined with simulation-based analysis. This is followed by a learnability evaluation of the uncertainties based on correlation analysis. This two-part analysis enables an informed decision on the suitability of RL for a control problem without training an RL agent. We apply our test to several benchmarks, demonstrating its applicability to a wide range of control problems and highlight the potential to save computational resources.

eess.SY↗

arXiv2026

Provably Explaining Neural Additive Models

Despite significant progress in post-hoc explanation methods for neural networks, many remain heuristic and lack provable guarantees. A key approach for obtaining explanations with provable guarantees is by identifying a cardinally-minimal subset of input features which by itself is provably sufficient to determine the prediction. However, for standard neural networks, this task is often computationally infeasible, as it demands a worst-case exponential number of verification queries in the number of input features, each of which is NP-hard. In this work, we show that for Neural Additive Models (NAMs), a recent and more interpretable neural network family, we can efficiently generate explanations with such guarantees. We present a new model-specific algorithm for NAMs that generates provably cardinally-minimal explanations using only a logarithmic number of verification queries in the number of input features, after a parallelized preprocessing step with logarithmic runtime in the required precision is applied to each small univariate NAM component. Our algorithm not only makes the task of obtaining cardinally-minimal explanations feasible, but even outperforms existing algorithms designed to find the relaxed variant of subset-minimal explanations - which may be larger and less informative but easier to compute - despite our algorithm solving a much more difficult task. Our experiments demonstrate that, compared to previous algorithms, our approach provides provably smaller explanations than existing works and substantially reduces the computation time. Moreover, we show that our generated provable explanations offer benefits that are unattainable by standard sampling-based techniques typically used to interpret NAMs.

cs.LG↗

arXiv2026

Perception with Guarantees: Certified Pose Estimation via Reachability Analysis

Agents in cyber-physical systems are increasingly entrusted with safety-critical tasks. Ensuring safety of these agents often requires localizing the pose for subsequent actions. Pose estimates can, e.g., be obtained from various combinations of lidar sensors, cameras, and external services such as GPS. Crucially, in safety-critical domains, a rough estimate is insufficient to formally determine safety, i.e., guaranteeing safety even in the worst-case scenario, and external services might additionally not be trustworthy. We address this problem by presenting a certified pose estimation in 3D solely from a camera image and a well-known target geometry. This is realized by formally bounding the pose, which is computed by leveraging recent results from reachability analysis and formal neural network verification. Our experiments demonstrate that our approach efficiently and accurately localizes agents in both synthetic and real-world experiments.

cs.CV↗

arXiv2026

A Comparison of Set-Based Observers for Nonlinear Systems

Set-based state estimation computes sets of states consistent with a system model given bounded sets of disturbances and noise. Bounding the set of states is crucial for safety-critical applications so that one can ensure that all specifications are met. While numerous approaches have been proposed for nonlinear discrete-time systems, a unified evaluation under comparable conditions is lacking. This paper reviews and implements a representative selection of set-based observers within the CORA framework. To provide an objective comparison, the methods are evaluated on common benchmarks, and we examine computational effort, scalability, and the conservatism of the resulting state bounds. This study highlights characteristic trade-offs between observer categories and set representations, as well as practical considerations arising in their implementation. All implementations are made publicly available to support reproducibility and future development. This paper thereby offers the first broad, tool-supported comparison of guaranteed state estimators for nonlinear discrete-time systems.

eess.SY↗

arXiv2026

BSAT: B-Spline Adaptive Tokenizer for Long-Term Time Series Forecasting

Long-term time series forecasting using transformers is hampered by the quadratic complexity of self-attention and the rigidity of uniform patching, which may be misaligned with the data's semantic structure. In this paper, we introduce the \textit{B-Spline Adaptive Tokenizer (BSAT)}, a novel, parameter-free method that adaptively segments a time series by fitting it with B-splines. BSAT algorithmically places tokens in high-curvature regions and represents each variable-length basis function as a fixed-size token, composed of its coefficient and position. Further, we propose a hybrid positional encoding that combines a additive learnable positional encoding with Rotary Positional Embedding featuring a layer-wise learnable base: L-RoPE. This allows each layer to attend to different temporal dependencies. Our experiments on several public benchmarks show that our model is competitive with strong performance at high compression rates. This makes it particularly well-suited for use cases with strong memory constraints.

cs.LG↗

arXiv2025

Results of the 2024 CommonRoad Motion Planning Competition for Autonomous Vehicles

Over the past decade, a wide range of motion planning approaches for autonomous vehicles has been developed to handle increasingly complex traffic scenarios. However, these approaches are rarely compared on standardized benchmarks, limiting the assessment of relative strengths and weaknesses. To address this gap, we present the setup and results of the 4th CommonRoad Motion Planning Competition held in 2024, conducted using the CommonRoad benchmark suite. This annual competition provides an open-source and reproducible framework for benchmarking motion planning algorithms. The benchmark scenarios span highway and urban environments with diverse traffic participants, including passenger cars, buses, and bicycles. Planner performance is evaluated along four dimensions: efficiency, safety, comfort, and compliance with selected traffic rules. This report introduces the competition format and provides a comparison of representative high-performing planners from the 2023 and 2024 editions.

cs.RO↗

arXiv2025

Improving Stochastic Action-Constrained Reinforcement Learning via Truncated Distributions

In reinforcement learning (RL), it is often advantageous to consider additional constraints on the action space to ensure safety or action relevance. Existing work on such action-constrained RL faces challenges regarding effective policy updates, computational efficiency, and predictable runtime. Recent work proposes to use truncated normal distributions for stochastic policy gradient methods. However, the computation of key characteristics, such as the entropy, log-probability, and their gradients, becomes intractable under complex constraints. Hence, prior work approximates these using the non-truncated distributions, which severely degrades performance. We argue that accurate estimation of these characteristics is crucial in the action-constrained RL setting, and propose efficient numerical approximations for them. We also provide an efficient sampling strategy for truncated policy distributions and validate our approach on three benchmark environments, which demonstrate significant performance improvements when using accurate estimations.

cs.LG↗

arXiv2025

From Demonstrations to Safe Deployment: Path-Consistent Safety Filtering for Diffusion Policies

Diffusion policies (DPs) achieve state-of-the-art performance on complex manipulation tasks by learning from large-scale demonstration datasets, often spanning multiple embodiments and environments. However, they cannot guarantee safe behavior, requiring external safety mechanisms. These, however, alter actions in ways unseen during training, causing unpredictable behavior and performance degradation. To address these problems, we propose path-consistent safety filtering (PACS) for DPs. Our approach performs path-consistent braking on a trajectory computed from the sequence of generated actions. In this way, we keep the execution consistent with the training distribution of the policy, maintaining the learned, task-completing behavior. To enable real-time deployment and handle uncertainties, we verify safety using set-based reachability analysis. Our experimental evaluation in simulation and on three challenging real-world human-robot interaction tasks shows that PACS (a) provides formal safety guarantees in dynamic environments, (b) preserves task success rates, and (c) outperforms reactive safety approaches, such as control barrier functions, by up to 68 % in terms of task success. Videos are available at our project website: https://tum-lsy.github.io/pacs.

cs.RO↗

arXiv2025

SanDRA: Safe Large-Language-Model-Based Decision Making for Automated Vehicles Using Reachability Analysis

Large language models (LLMs) have been widely applied to knowledge-driven decision-making for automated vehicles due to their strong generalization and reasoning capabilities. However, the safety of the resulting decisions cannot be ensured due to possible hallucinations and the lack of integrated vehicle dynamics. To address this issue, we propose SanDRA, the first safe large-language-model-based decision making framework for automated vehicles using reachability analysis. Our approach starts with a comprehensive description of the driving scenario to prompt LLMs to generate and rank feasible driving actions. These actions are translated into temporal logic formulas that incorporate formalized traffic rules, and are subsequently integrated into reachability analysis to eliminate unsafe actions. We validate our approach in both open-loop and closed-loop driving environments using off-the-shelf and finetuned LLMs, showing that it can provide provably safe and, where possible, legally compliant driving actions, even under high-density traffic conditions. To ensure transparency and facilitate future research, all code and experimental setups are publicly available at github.com/CommonRoad/SanDRA.

cs.RO↗

arXiv2025

Falsification-driven reinforcement learning for maritime motion planning

Compliance with maritime traffic rules is essential for the safe operation of autonomous vessels, yet training reinforcement learning (RL) agents to adhere to them is challenging. The behavior of RL agents is shaped by the training scenarios they encounter, but creating scenarios that capture the complexity of maritime navigation is non-trivial, and real-world data alone is insufficient. To address this, we propose a falsification-driven RL approach that generates adversarial training scenarios in which the vessel under test violates maritime traffic rules, which are expressed as signal temporal logic specifications. Our experiments on open-sea navigation with two vessels demonstrate that the proposed approach provides more relevant training scenarios and achieves more consistent rule compliance.

eess.SY↗