arXiv subjects

Roland Kwitt

Publications and source records attributed to Roland Kwitt.

At least 19 recordsLinked to original sources

arXiv2026

Exploring Zero-Shot Foundation Models for Multivariate Time Series Anomaly Detection

Multivariate Time Series Anomaly Detection (MTSAD) is essential for reliability and safety in domains such as industrial process monitoring and financial risk management, yet conventional approaches rely on application-specific models that are costly to train and hard to scale. Foundation Models (FMs), pre-trained on broad data with strong zero-shot generalization, have recently become available for univariate time series forecasting, raising the question of whether they can address MTSAD without task-specific training. We investigate the zero-shot application of a univariate forecasting FM, TimesFM, to industrial MTSAD on the Secure Water Treatment (SWaT) benchmark, evaluating two strategies: treating the FM as a per-feature forecaster with thresholded prediction errors, and as an embedder whose intermediate representations feed standard outlier detectors. Neither of our proposed setups is competitive with established baselines; embeddings reveal only partial separation between normal and anomalous segments, insufficient for reliable detection. The cause is that the FM is too effective at capturing temporal dynamics, yielding low error even within fully anomalous windows, so persistent anomalies become indistinguishable from normal behavior. However, these observations yield valuable insights: the error peaks at anomaly boundaries, indicating FMs reliably detect distribution changes. We conclude that the proposed naive zero-shot FMs are unsuitable for MTSAD but promising for change-point detection.

cs.LG↗

arXiv2026

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.

cs.LG↗

arXiv2026

Learning Topological Representations for Molecular Dynamics

Molecular dynamics (MD) simulations generate trajectories in a high-dimensional configuration space whose analysis critically depends on molecular descriptors, typically handcrafted observables or learned kinetic embeddings. Designing descriptors that are both expressive and broadly applicable, however, remains challenging. We study persistent homology (PH) as a general-purpose representation for MD and introduce the masked Flood complex, a protein-tailored modification of a recently introduced simplicial complex construction that emphasizes inter-residue structure at low computational cost. Vectorized persistence diagrams then provide information-rich, geometry-aware summaries of protein conformations, which we evaluate on protein class prediction, frame-level observable regression, and Markov state model (MSM) estimation from learned low-dimensional coordinates in a single shared representation space. Results on the mdCATH dataset show that PH-based descriptors are competitive across tasks, with masked Flood PH yielding the most consistent overall performance. Further, when using topologically-informed MSMs as a drop-in replacement within the recent MarS-FM framework for generative modeling of protein conformations, we obtain consistently better ensemble statistics than MSMs based on physical observables. Finally, we explore the transferability of the generative model to qualitatively different, fast folding, proteins.

q-bio.BM↗

arXiv2026

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. Source code and datasets are available on https://github.com/plus-rkwitt/flooder.

cs.LG↗

arXiv2025

CARL: A Framework for Equivariant Image Registration

Image registration estimates spatial correspondences between a pair of images. These estimates are typically obtained via numerical optimization or regression by a deep network. A desirable property of such estimators is that a correspondence estimate (e.g., the true oracle correspondence) for an image pair is maintained under deformations of the input images. Formally, the estimator should be equivariant to a desired class of image transformations. In this work, we present careful analyses of the desired equivariance properties in the context of multi-step deep registration networks. Based on these analyses we 1) introduce the notions of $[U,U]$ equivariance (network equivariance to the same deformations of the input images) and $[W,U]$ equivariance (where input images can undergo different deformations); we 2) show that in a suitable multi-step registration setup it is sufficient for overall $[W,U]$ equivariance if the first step has $[W,U]$ equivariance and all others have $[U,U]$ equivariance; we 3) show that common displacement-predicting networks only exhibit $[U,U]$ equivariance to translations instead of the more powerful $[W,U]$ equivariance; and we 4) show how to achieve multi-step $[W,U]$ equivariance via a coordinate-attention mechanism combined with displacement-predicting refinement layers (CARL). Overall, our approach obtains excellent practical registration performance on several 3D medical image registration tasks and outperforms existing unsupervised approaches for the challenging problem of abdomen registration.

cs.CV↗

arXiv2025

multiGradICON: A Foundation Model for Multimodal Medical Image Registration

Modern medical image registration approaches predict deformations using deep networks. These approaches achieve state-of-the-art (SOTA) registration accuracy and are generally fast. However, deep learning (DL) approaches are, in contrast to conventional non-deep-learning-based approaches, anatomy-specific. Recently, a universal deep registration approach, uniGradICON, has been proposed. However, uniGradICON focuses on monomodal image registration. In this work, we therefore develop multiGradICON as a first step towards universal *multimodal* medical image registration. Specifically, we show that 1) we can train a DL registration model that is suitable for monomodal *and* multimodal registration; 2) loss function randomization can increase multimodal registration accuracy; and 3) training a model with multimodal data helps multimodal generalization. Our code and the multiGradICON model are available at https://github.com/uncbiag/uniGradICON.

eess.IV↗

arXiv2024

Neural Persistence Dynamics

We consider the problem of learning the dynamics in the topology of time-evolving point clouds, the prevalent spatiotemporal model for systems exhibiting collective behavior, such as swarms of insects and birds or particles in physics. In such systems, patterns emerge from (local) interactions among self-propelled entities. While several well-understood governing equations for motion and interaction exist, they are notoriously difficult to fit to data, as most prior work requires knowledge about individual motion trajectories, i.e., a requirement that is challenging to satisfy with an increasing number of entities. To evade such confounding factors, we investigate collective behavior from a $\textit{topological perspective}$, but instead of summarizing entire observation sequences (as done previously), we propose learning a latent dynamical model from topological features $\textit{per time point}$. The latter is then used to formulate a downstream regression task to predict the parametrization of some a priori specified governing equation. We implement this idea based on a latent ODE learned from vectorized (static) persistence diagrams and show that a combination of recent stability results for persistent homology justifies this modeling choice. Various (ablation) experiments not only demonstrate the relevance of each model component but provide compelling empirical evidence that our proposed model - $\textit{Neural Persistence Dynamics}$ - substantially outperforms the state-of-the-art across a diverse set of parameter regression tasks.

cs.LG↗

arXiv2024

Position: Topological Deep Learning is the New Frontier for Relational Learning

Topological deep learning (TDL) is a rapidly evolving field that uses topological features to understand and design deep learning models. This paper posits that TDL is the new frontier for relational learning. TDL may complement graph representation learning and geometric deep learning by incorporating topological concepts, and can thus provide a natural choice for various machine learning settings. To this end, this paper discusses open problems in TDL, ranging from practical benefits to theoretical foundations. For each problem, it outlines potential solutions and future research opportunities. At the same time, this paper serves as an invitation to the scientific community to actively participate in TDL research to unlock the potential of this emerging field.

cs.LG↗

arXiv2024

uniGradICON: A Foundation Model for Medical Image Registration

Conventional medical image registration approaches directly optimize over the parameters of a transformation model. These approaches have been highly successful and are used generically for registrations of different anatomical regions. Recent deep registration networks are incredibly fast and accurate but are only trained for specific tasks. Hence, they are no longer generic registration approaches. We therefore propose uniGradICON, a first step toward a foundation model for registration providing 1) great performance \emph{across} multiple datasets which is not feasible for current learning-based registration methods, 2) zero-shot capabilities for new registration tasks suitable for different acquisitions, anatomical regions, and modalities compared to the training dataset, and 3) a strong initialization for finetuning on out-of-distribution registration tasks. UniGradICON unifies the speed and accuracy benefits of learning-based registration algorithms with the generic applicability of conventional non-deep-learning approaches. We extensively trained and evaluated uniGradICON on twelve different public datasets. Our code and the uniGradICON model are available at https://github.com/uncbiag/uniGradICON.

cs.CV↗

arXiv2024

Latent SDEs on Homogeneous Spaces

We consider the problem of variational Bayesian inference in a latent variable model where a (possibly complex) observed stochastic process is governed by the solution of a latent stochastic differential equation (SDE). Motivated by the challenges that arise when trying to learn an (almost arbitrary) latent neural SDE from data, such as efficient gradient computation, we take a step back and study a specific subclass instead. In our case, the SDE evolves on a homogeneous latent space and is induced by stochastic dynamics of the corresponding (matrix) Lie group. In learning problems, SDEs on the unit n-sphere are arguably the most relevant incarnation of this setup. Notably, for variational inference, the sphere not only facilitates using a truly uninformative prior, but we also obtain a particularly simple and intuitive expression for the Kullback-Leibler divergence between the approximate posterior and prior process in the evidence lower bound. Experiments demonstrate that a latent SDE of the proposed type can be learned efficiently by means of an existing one-step geometric Euler-Maruyama scheme. Despite restricting ourselves to a less rich class of SDEs, we achieve competitive or even state-of-the-art results on various time series interpolation/classification problems.

cs.LG↗

arXiv2023

$\texttt{GradICON}$: Approximate Diffeomorphisms via Gradient Inverse Consistency

We present an approach to learning regular spatial transformations between image pairs in the context of medical image registration. Contrary to optimization-based registration techniques and many modern learning-based methods, we do not directly penalize transformation irregularities but instead promote transformation regularity via an inverse consistency penalty. We use a neural network to predict a map between a source and a target image as well as the map when swapping the source and target images. Different from existing approaches, we compose these two resulting maps and regularize deviations of the $\bf{Jacobian}$ of this composition from the identity matrix. This regularizer -- $\texttt{GradICON}$ -- results in much better convergence when training registration models compared to promoting inverse consistency of the composition of maps directly while retaining the desirable implicit regularization effects of the latter. We achieve state-of-the-art registration performance on a variety of real-world medical image datasets using a single set of hyperparameters and a single non-dataset-specific training protocol.

cs.CV↗

arXiv2023

Inverse Consistency by Construction for Multistep Deep Registration

Inverse consistency is a desirable property for image registration. We propose a simple technique to make a neural registration network inverse consistent by construction, as a consequence of its structure, as long as it parameterizes its output transform by a Lie group. We extend this technique to multi-step neural registration by composing many such networks in a way that preserves inverse consistency. This multi-step approach also allows for inverse-consistent coarse to fine registration. We evaluate our technique on synthetic 2-D data and four 3-D medical image registration tasks and obtain excellent registration accuracy while assuring inverse consistency.

cs.CV↗

arXiv2023

Dissecting Supervised Contrastive Learning

Minimizing cross-entropy over the softmax scores of a linear map composed with a high-capacity encoder is arguably the most popular choice for training neural networks on supervised learning tasks. However, recent works show that one can directly optimize the encoder instead, to obtain equally (or even more) discriminative representations via a supervised variant of a contrastive objective. In this work, we address the question whether there are fundamental differences in the sought-for representation geometry in the output space of the encoder at minimal loss. Specifically, we prove, under mild assumptions, that both losses attain their minimum once the representations of each class collapse to the vertices of a regular simplex, inscribed in a hypersphere. We provide empirical evidence that this configuration is attained in practice and that reaching a close-to-optimal state typically indicates good generalization performance. Yet, the two losses show remarkably different optimization behavior. The number of iterations required to perfectly fit to data scales superlinearly with the amount of randomly flipped labels for the supervised contrastive loss. This is in contrast to the approximately linear scaling previously reported for networks trained with cross-entropy.

stat.ML↗

arXiv2023

On Measuring Excess Capacity in Neural Networks

We study the excess capacity of deep networks in the context of supervised classification. That is, given a capacity measure of the underlying hypothesis class - in our case, empirical Rademacher complexity - to what extent can we (a priori) constrain this class while retaining an empirical error on a par with the unconstrained regime? To assess excess capacity in modern architectures (such as residual networks), we extend and unify prior Rademacher complexity bounds to accommodate function composition and addition, as well as the structure of convolutions. The capacity-driving terms in our bounds are the Lipschitz constants of the layers and an (2, 1) group norm distance to the initializations of the convolution weights. Experiments on benchmark datasets of varying task difficulty indicate that (1) there is a substantial amount of excess capacity per task, and (2) capacity can be kept at a surprisingly similar level across tasks. Overall, this suggests a notion of compressibility with respect to weight norms, complementary to classic compression via weight pruning. Source code is available at https://github.com/rkwitt/excess_capacity.

cs.LG↗

arXiv2021

Comparing object recognition in humans and deep convolutional neural networks -- An eye tracking study

Deep convolutional neural networks (DCNNs) and the ventral visual pathway share vast architectural and functional similarities in visual challenges such as object recognition. Recent insights have demonstrated that both hierarchical cascades can be compared in terms of both exerted behavior and underlying activation. However, these approaches ignore key differences in spatial priorities of information processing. In this proof-of-concept study, we demonstrate a comparison of human observers (N = 45) and three feedforward DCNNs through eye tracking and saliency maps. The results reveal fundamentally different resolutions in both visualization methods that need to be considered for an insightful comparison. Moreover, we provide evidence that a DCNN with biologically plausible receptive field sizes called vNet reveals higher agreement with human viewing behavior as contrasted with a standard ResNet architecture. We find that image-specific factors such as category, animacy, arousal, and valence have a direct link to the agreement of spatial object recognition priorities in humans and DCNNs, while other measures such as difficulty and general image properties do not. With this approach, we try to open up new perspectives at the intersection of biological and computer vision research.

cs.CV↗

arXiv2021

Topological Attention for Time Series Forecasting

The problem of (point) forecasting $ \textit{univariate} $ time series is considered. Most approaches, ranging from traditional statistical methods to recent learning-based techniques with neural networks, directly operate on raw time series observations. As an extension, we study whether $\textit{local topological properties}$, as captured via persistent homology, can serve as a reliable signal that provides complementary information for learning to forecast. To this end, we propose $\textit{topological attention}$, which allows attending to local topological features within a time horizon of historical data. Our approach easily integrates into existing end-to-end trainable forecasting models, such as $\texttt{N-BEATS}$, and in combination with the latter exhibits state-of-the-art performance on the large-scale M4 benchmark dataset of 100,000 diverse time series from different domains. Ablation experiments, as well as a comparison to a broad range of forecasting methods in a setting where only a single time series is available for training, corroborate the beneficial nature of including local topological information through an attention mechanism.

cs.LG↗

arXiv2021

ICON: Learning Regular Maps Through Inverse Consistency

Learning maps between data samples is fundamental. Applications range from representation learning, image translation and generative modeling, to the estimation of spatial deformations. Such maps relate feature vectors, or map between feature spaces. Well-behaved maps should be regular, which can be imposed explicitly or may emanate from the data itself. We explore what induces regularity for spatial transformations, e.g., when computing image registrations. Classical optimization-based models compute maps between pairs of samples and rely on an appropriate regularizer for well-posedness. Recent deep learning approaches have attempted to avoid using such regularizers altogether by relying on the sample population instead. We explore if it is possible to obtain spatial regularity using an inverse consistency loss only and elucidate what explains map regularity in such a context. We find that deep networks combined with an inverse consistency loss and randomized off-grid interpolation yield well behaved, approximately diffeomorphic, spatial transformations. Despite the simplicity of this approach, our experiments present compelling evidence, on both synthetic and real data, that regular maps can be obtained without carefully tuned explicit regularizers, while achieving competitive registration performance.

cs.CV↗

arXiv2021

Graph Filtration Learning

We propose an approach to learning with graph-structured data in the problem domain of graph classification. In particular, we present a novel type of readout operation to aggregate node features into a graph-level representation. To this end, we leverage persistent homology computed via a real-valued, learnable, filter function. We establish the theoretical foundation for differentiating through the persistent homology computation. Empirically, we show that this type of readout operation compares favorably to previous techniques, especially when the graph connectivity structure is informative for the learning problem.

cs.LG↗