Anomaly Detection for Sparse and Irregular Multivariate Time Series with Latent SDEs

Multivariate time series anomaly detection (MTSAD) is critical for a wide range of application areas, such as industrial monitoring, cybersecurity, or healthcare. Real-world data is often sparse, irregularly sampled or partially observed, yet existing methods assume uniformly sampled time series. We propose a generative approach based on Latent SDEs that projects the observed time series on a continuous-time stochastic dynamical system, directly being able to handle missing observations and irregular sampling, while also naturally capturing possible cyclic behavior that many real-world use cases inherently possess. Experiments on six anomaly benchmark datasets show that our proposed method ranks first among state-of-the-art baselines. We further demonstrate that our method remains robust under severe data sparsity, while performance significantly degrades for the tested baseline methods. These results highlight latent SDEs as a natural inductive bias for anomaly detection in multivariate time series, especially in presence of real-world irregularities.

Federated Learning for Multivariate Time Series Anomaly Detection in Industrial Automation

Federated learning (FL) has broadened the horizon for multivariate time series anomaly detection (MTSAD). However, benchmarking such anomaly detection methods within FL paradigm poses data-centric challenges. The existing datasets do not counteract these challenges since they do not simultaneously provide sufficient scale, accurate labels, and freedom from common flaws. In addition, the role of cyclic process behavior, which is common in discrete industrial automation, remains underexplored for MTSAD for the current state of research. This paper aims to shed more light on the literature and address these gaps by introducing a dataset designed with cyclic dynamics arising from the repetitive nature of discrete automation processes and evaluates selected MTSAD methods on both the proposed dataset and a public benchmark dataset.

Chebyshev Policies and the Mountain Car Problem: Reinforcement Learning for Low-Dimensional Control Tasks

We analytically solve the Mountain Car problem, a canonical benchmark in RL, and derive an optimal control solution, closing a gap after 36 years. This enables us to reveal two surprising insights: The optimal control is quite simple, yet modern RL agents display a large gap to optimality. Motivated by the analysis of the optimal control, we introduce Chebyshev policies as a universal (i.e. dense) class of RL policies from first principles. They can be trained as drop-in replacements of neural nets, reducing the regret by a factor of 4.18, while requiring 277 times fewer parameters, fostering sample efficiency, explainability and realtime capability. Chebyshev policies are evaluated on further RL tasks, including a real-world nonlinear motion control testbed. They consistently improve performance over neural nets with PPO, ARS and REINFORCE. Our results demonstrate how Chebyshev policies offer a compelling and lightweight alternative or addition to neural nets for low-dimensional control tasks.

Generative Modeling of Approximately Periodic Time Series by a Posterior-Weighted Gaussian Process

Discrete automated processes in industrial and cyber-physical systems often exhibit a repetitive structure in which successive repetitions follow a common trajectory while differing in duration, amplitude, and fine-scale dynamics. Such \emph{approximately periodic} behavior poses a challenge for Gaussian Processes (GP) modeling: strictly periodic models suppress inter-repetition variability, while non-periodic models fail to capture the strong structural regularities required for generation. In this work, we propose a stochastic generative model for approximately periodic time series. The model is based on a GP whose posterior is modulated by a novel kernel. Our approach decouples intra-repetition structure from inter-repetition variability through a two-stage construction which yields a generative distribution with a identical mean function across repetitions, while allowing smooth variation between repetitions. The modeling choices are supported by an implementation in which realistic synthetic trajectories are generated from toy datasets.

Topologically Stable Hough Transform

We propose an alternative formulation of the well-known Hough transform to detect lines in point clouds. Replacing the discretized voting scheme of the classical Hough transform by a continuous score function, its persistent features in the sense of persistent homology give a set of candidate lines. We also devise and implement an algorithm to efficiently compute these candidate lines.

Mechanisms of AI Protein Folding in ESMFold

How do protein structure prediction models fold proteins? We investigate this question by tracing how ESMFold folds a beta hairpin, a prevalent structural motif. Through counterfactual interventions on model latents, we identify two computational stages in the folding trunk. In the first stage, early blocks initialize pairwise biochemical signals: residue identities and associated biochemical features such as charge flow from sequence representations into pairwise representations. In the second stage, late blocks develop pairwise spatial features: distance and contact information accumulate in the pairwise representation. We demonstrate that the mechanisms underlying structural decisions of ESMFold can be localized, traced through interpretable representations, and manipulated with strong causal effects.

Embedding the MLOps Lifecycle into OT Reference Models

Machine Learning Operations (MLOps) practices are increas- ingly adopted in industrial settings, yet their integration with Opera- tional Technology (OT) systems presents significant challenges. This pa- per analyzes the fundamental obstacles in combining MLOps with OT en- vironments and proposes a systematic approach to embed MLOps prac- tices into established OT reference models. We evaluate the suitability of the Reference Architectural Model for Industry 4.0 (RAMI 4.0) and the International Society of Automation Standard 95 (ISA-95) for MLOps integration and present a detailed mapping of MLOps lifecycle compo- nents to RAMI 4.0 exemplified by a real-world use case. Our findings demonstrate that while standard MLOps practices cannot be directly transplanted to OT environments, structured adaptation using existing reference models can provide a pathway for successful integration.

The Flood Complex: Large-Scale Persistent Homology on Millions of Points

We consider the problem of computing persistent homology (PH) for large-scale Euclidean point cloud data, aimed at downstream machine learning tasks, where the exponential growth of the most widely-used Vietoris-Rips complex imposes serious computational limitations. Although more scalable alternatives such as the Alpha complex or sparse Rips approximations exist, they often still result in a prohibitively large number of simplices. This poses challenges in the complex construction and in the subsequent PH computation, prohibiting their use on large-scale point clouds. To mitigate these issues, we introduce the Flood complex, inspired by the advantages of the Alpha and Witness complex constructions. Informally, at a given filtration value $r\geq 0$, the Flood complex contains all simplices from a Delaunay triangulation of a small subset of the point cloud $X$ that are fully covered by balls of radius $r$ emanating from $X$, a process we call flooding. Our construction allows for efficient PH computation, possesses several desirable theoretical properties, and is amenable to GPU parallelization. Scaling experiments on 3D point cloud data show that we can compute PH of up to dimension 2 on several millions of points. Importantly, when evaluating object classification performance on real-world and synthetic data, we provide evidence that this scaling capability is needed, especially if objects are geometrically or topologically complex, yielding performance superior to other PH-based methods and neural networks for point cloud data.

Topology-driven identification of repetitions in multi-variate time series

Many multi-variate time series obtained in the natural sciences and engineering possess a repetitive behavior, as for instance state-space trajectories of industrial machines in discrete automation. Recovering the times of recurrence from such a multi-variate time series is of a fundamental importance for many monitoring and control tasks. For a periodic time series this is equivalent to determining its period length. In this work we present a persistent homology framework to estimate recurrence times in multi-variate time series with different generalizations of cyclic behavior (periodic, repetitive, and recurring). To this end, we provide three specialized methods within our framework that are provably stable and validate them using real-world data, including a new benchmark dataset from an injection molding machine.

Persistence-based Hough Transform for Line Detection

The Hough transform is a popular and classical technique in computer vision for the detection of lines (or more general objects). It maps a pixel into a dual space -- the Hough space: each pixel is mapped to the set of lines through this pixel, which forms a curve in Hough space. The detection of lines then becomes a voting process to find those lines that received many votes by pixels. However, this voting is done by thresholding, which is susceptible to noise and other artifacts. In this work, we present an alternative voting technique to detect peaks in the Hough space based on persistent homology, which very naturally addresses limitations of simple thresholding. Experiments on synthetic data show that our method significantly outperforms the original method, while also demonstrating enhanced robustness. This work seeks to inspire future research in two key directions. First, we highlight the untapped potential of Topological Data Analysis techniques and advocate for their broader integration into existing methods, including well-established ones. Secondly, we initiate a discussion on the mathematical stability of the Hough transform, encouraging exploration of mathematically grounded improvements to enhance its robustness.