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Researcher profile

Matthias Althoff

Matthias Althoff contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Machine LearningRoboticsArtificial Intelligenceeess.SYSystems and ControlComputer VisionComputational GeometryComputer Science and Game Theoryeess.SPHuman-Computer Interactionmath.NANumerical Analysis

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Trust 21 - EmergingVerification L1Unclaimed author
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Published work

11 published item(s)

preprint2026arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

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. Then, we formally verify the behavior of the circuit-level model using reachability analysis with polynomial zonotopes, thus, avoiding conventional, time-consuming Monte Carlo simulations. We evaluate our proposed verification approach on three different datasets, verifying both fully-connected and convolutional analog neural networks. Our experimental results confirm the effectiveness of our verification approach by reducing the verification time from days to seconds while enclosing 99% of the variation samples.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

On Computing the Minkowski Difference of Zonotopes

Zonotopes are becoming an increasingly popular set representation for formal verification techniques. This is mainly due to their efficient representation and their favorable computational complexity of important operations in high-dimensional spaces. In particular, zonotopes are closed under Minkowski addition and linear maps, which can be very efficiently implemented. Unfortunately, zonotopes are not closed under Minkowski difference for dimensions greater than two. However, we present an algorithm that efficiently computes a halfspace representation of the Minkowski difference of two zonotopes. In addition, we present an efficient algorithm that computes an approximation of the Minkowski difference in generator representation. The efficiency of the proposed solution is demonstrated by numerical experiments. These experiments show a reduced computation time in comparison to that when first the halfspace representation of zonotopes is obtained and the Minkowski difference is performed subsequently.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Provably Safe Deep Reinforcement Learning for Robotic Manipulation in Human Environments

Deep reinforcement learning (RL) has shown promising results in the motion planning of manipulators. However, no method guarantees the safety of highly dynamic obstacles, such as humans, in RL-based manipulator control. This lack of formal safety assurances prevents the application of RL for manipulators in real-world human environments. Therefore, we propose a shielding mechanism that ensures ISO-verified human safety while training and deploying RL algorithms on manipulators. We utilize a fast reachability analysis of humans and manipulators to guarantee that the manipulator comes to a complete stop before a human is within its range. Our proposed method guarantees safety and significantly improves the RL performance by preventing episode-ending collisions. We demonstrate the performance of our proposed method in simulation using human motion capture data.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Event-Triggered Diffusion Kalman Filters

Distributed state estimation strongly depends on collaborative signal processing, which often requires excessive communication and computation to be executed on resource-constrained sensor nodes. To address this problem, we propose an event-triggered diffusion Kalman filter, which collects measurements and exchanges messages between nodes based on a local signal indicating the estimation error. On this basis, we develop an energy-aware state estimation algorithm that regulates the resource consumption in wireless networks and ensures the effectiveness of every consumed resource. The proposed algorithm does not require the nodes to share its local covariance matrices, and thereby allows considerably reducing the number of transmission messages. To confirm its efficiency, we apply the proposed algorithm to the distributed simultaneous localization and time synchronization problem and evaluate it on a physical testbed of a mobile quadrotor node and stationary custom ultra-wideband wireless devices. The obtained experimental results indicate that the proposed algorithm allows saving 86% of the communication overhead associated with the original diffusion Kalman filter while causing deterioration of performance by 16% only. We make the Matlab code and the real testing data available online.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Pedestrian Models for Autonomous Driving Part I: Low-Level Models, from Sensing to Tracking

Autonomous vehicles (AVs) must share space with pedestrians, both in carriageway cases such as cars at pedestrian crossings and off-carriageway cases such as delivery vehicles navigating through crowds on pedestrianized high-streets. Unlike static obstacles, pedestrians are active agents with complex, interactive motions. Planning AV actions in the presence of pedestrians thus requires modelling of their probable future behaviour as well as detecting and tracking them. This narrative review article is Part I of a pair, together surveying the current technology stack involved in this process, organising recent research into a hierarchical taxonomy ranging from low-level image detection to high-level psychology models, from the perspective of an AV designer. This self-contained Part I covers the lower levels of this stack, from sensing, through detection and recognition, up to tracking of pedestrians. Technologies at these levels are found to be mature and available as foundations for use in high-level systems, such as behaviour modelling, prediction and interaction control.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Pedestrian Models for Autonomous Driving Part II: High-Level Models of Human Behavior

Autonomous vehicles (AVs) must share space with pedestrians, both in carriageway cases such as cars at pedestrian crossings and off-carriageway cases such as delivery vehicles navigating through crowds on pedestrianized high-streets. Unlike static obstacles, pedestrians are active agents with complex, interactive motions. Planning AV actions in the presence of pedestrians thus requires modelling of their probable future behaviour as well as detecting and tracking them. This narrative review article is Part II of a pair, together surveying the current technology stack involved in this process, organising recent research into a hierarchical taxonomy ranging from low-level image detection to high-level psychological models, from the perspective of an AV designer. This self-contained Part II covers the higher levels of this stack, consisting of models of pedestrian behaviour, from prediction of individual pedestrians' likely destinations and paths, to game-theoretic models of interactions between pedestrians and autonomous vehicles. This survey clearly shows that, although there are good models for optimal walking behaviour, high-level psychological and social modelling of pedestrian behaviour still remains an open research question that requires many conceptual issues to be clarified. Early work has been done on descriptive and qualitative models of behaviour, but much work is still needed to translate them into quantitative algorithms for practical AV control.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Reachability Analysis of Large Linear Systems with Uncertain Inputs in the Krylov Subspace

One often wishes for the ability to formally analyze large-scale systems---typically, however, one can either formally analyze a rather small system or informally analyze a large-scale system. This work tries to further close this performance gap for reachability analysis of linear systems. Reachability analysis can capture the whole set of possible solutions of a dynamic system and is thus used to prove that unsafe states are never reached; this requires full consideration of arbitrarily varying uncertain inputs, since sensor noise or disturbances usually do not follow any patterns. We use Krylov methods in this work to compute reachable sets for large-scale linear systems. While Krylov methods have been used before in reachability analysis, we overcome the previous limitation that inputs must be (piecewise) constant. As a result, we can compute reachable sets of systems with several thousand state variables for bounded, but arbitrarily varying inputs.

0 citations0 reviewsNo code linkedOpen access