arXiv subjects

Carola-Bibiane Schönlieb

Publications and source records attributed to Carola-Bibiane Schönlieb.

At least 73 records · Page 4Linked to original sources

arXiv2025

D2SA: Dual-Stage Distribution and Slice Adaptation for Efficient Test-Time Adaptation in MRI Reconstruction

Variations in Magnetic resonance imaging (MRI) scanners and acquisition protocols cause distribution shifts that degrade reconstruction performance on unseen data. Test-time adaptation (TTA) offers a promising solution to address this discrepancies. However, previous single-shot TTA approaches are inefficient due to repeated training and suboptimal distributional models. Self-supervised learning methods may risk over-smoothing in scarce data scenarios. To address these challenges, we propose a novel Dual-Stage Distribution and Slice Adaptation (D2SA) via MRI implicit neural representation (MR-INR) to improve MRI reconstruction performance and efficiency, which features two stages. In the first stage, an MR-INR branch performs patient-wise distribution adaptation by learning shared representations across slices and modelling patient-specific shifts with mean and variance adjustments. In the second stage, single-slice adaptation refines the output from frozen convolutional layers with a learnable anisotropic diffusion module, preventing over-smoothing and reducing computation. Experiments across five MRI distribution shifts demonstrate that our method can integrate well with various self-supervised learning (SSL) framework, improving performance and accelerating convergence under diverse conditions.

eess.IV↗

arXiv2025

Pullback Flow Matching on Data Manifolds

We propose Pullback Flow Matching (PFM), a novel framework for generative modeling on data manifolds. Unlike existing methods that assume or learn restrictive closed-form manifold mappings for training Riemannian Flow Matching (RFM) models, PFM leverages pullback geometry and isometric learning to preserve the underlying manifold's geometry while enabling efficient generation and precise interpolation in latent space. This approach not only facilitates closed-form mappings on the data manifold but also allows for designable latent spaces, using assumed metrics on both data and latent manifolds. By enhancing isometric learning through Neural ODEs and proposing a scalable training objective, we achieve a latent space more suitable for interpolation, leading to improved manifold learning and generative performance. We demonstrate PFM's effectiveness through applications in synthetic data, protein dynamics and protein sequence data, generating novel proteins with specific properties. This method shows strong potential for drug discovery and materials science, where generating novel samples with specific properties is of great interest.

cs.LG↗

arXiv2025

G-Adaptivity: optimised graph-based mesh relocation for finite element methods

We present a novel, and effective, approach to achieve optimal mesh relocation in finite element methods (FEMs). The cost and accuracy of FEMs is critically dependent on the choice of mesh points. Mesh relocation (r-adaptivity) seeks to optimise the mesh geometry to obtain the best solution accuracy at given computational budget. Classical r-adaptivity relies on the solution of a separate nonlinear "meshing" PDE to determine mesh point locations. This incurs significant cost at remeshing, and relies on estimates that relate interpolation- and FEM-error. Recent machine learning approaches have focused on the construction of fast surrogates for such classical methods. Instead, our new approach trains a graph neural network (GNN) to determine mesh point locations by directly minimising the FE solution error from the PDE system Firedrake to achieve higher solution accuracy. Our GNN architecture closely aligns the mesh solution space to that of classical meshing methodologies, thus replacing classical estimates for optimality with a learnable strategy. This allows for rapid and robust training and results in an extremely efficient and effective GNN approach to online r-adaptivity. Our method outperforms both classical, and prior ML, approaches to r-adaptive meshing. In particular, it achieves lower FE solution error, whilst retaining the significant speed-up over classical methods observed in prior ML work.

cs.LG↗

arXiv2025

Data-driven approaches to inverse problems

Inverse problems are concerned with the reconstruction of unknown physical quantities using indirect measurements and are fundamental across diverse fields such as medical imaging, remote sensing, and material sciences. These problems serve as critical tools for visualizing internal structures beyond what is visible to the naked eye, enabling quantification, diagnosis, prediction, and discovery. However, most inverse problems are ill-posed, necessitating robust mathematical treatment to yield meaningful solutions. While classical approaches provide mathematically rigorous and computationally stable solutions, they are constrained by the ability to accurately model solution properties and implement them efficiently. A more recent paradigm considers deriving solutions to inverse problems in a data-driven manner. Instead of relying on classical mathematical modeling, this approach utilizes highly over-parameterized models, typically deep neural networks, which are adapted to specific inverse problems using carefully selected training data. Current approaches that follow this new paradigm distinguish themselves through solution accuracy paired with computational efficiency that was previously inconceivable. These notes offer an introduction to this data-driven paradigm for inverse problems. The first part of these notes will provide an introduction to inverse problems, discuss classical solution strategies, and present some applications. The second part will delve into modern data-driven approaches, with a particular focus on adversarial regularization and provably convergent linear plug-and-play denoisers. Throughout the presentation of these methodologies, their theoretical properties will be discussed, and numerical examples will be provided. The lecture series will conclude with a discussion of open problems and future perspectives in the field.

math.NA↗

arXiv2025

Generalized Lie Symmetries in Physics-Informed Neural Operators

Physics-informed neural operators (PINOs) have emerged as powerful tools for learning solution operators of partial differential equations (PDEs). Recent research has demonstrated that incorporating Lie point symmetry information can significantly enhance the training efficiency of PINOs, primarily through techniques like data, architecture, and loss augmentation. In this work, we focus on the latter, highlighting that point symmetries oftentimes result in no training signal, limiting their effectiveness in many problems. To address this, we propose a novel loss augmentation strategy that leverages evolutionary representatives of point symmetries, a specific class of generalized symmetries of the underlying PDE. These generalized symmetries provide a richer set of generators compared to standard symmetries, leading to a more informative training signal. We demonstrate that leveraging evolutionary representatives enhances the performance of neural operators, resulting in improved data efficiency and accuracy during training.

cs.LG↗

arXiv2025

Bridging Annotation Gaps: Transferring Labels to Align Object Detection Datasets

Combining multiple object detection datasets offers a path to improved generalisation but is hindered by inconsistencies in class semantics and bounding box annotations. Some methods to address this assume shared label taxonomies and address only spatial inconsistencies; others require manual relabelling, or produce a unified label space, which may be unsuitable when a fixed target label space is required. We propose Label-Aligned Transfer (LAT), a label transfer framework that systematically projects annotations from diverse source datasets into the label space of a target dataset. LAT begins by training dataset-specific detectors to generate pseudo-labels, which are then combined with ground-truth annotations via a Privileged Proposal Generator (PPG) that replaces the region proposal network in two-stage detectors. To further refine region features, a Semantic Feature Fusion (SFF) module injects class-aware context and features from overlapping proposals using a confidence-weighted attention mechanism. This pipeline preserves dataset-specific annotation granularity while enabling many-to-one label space transfer across heterogeneous datasets, resulting in a semantically and spatially aligned representation suitable for training a downstream detector. LAT thus jointly addresses both class-level misalignments and bounding box inconsistencies without relying on shared label spaces or manual annotations. Across multiple benchmarks, LAT demonstrates consistent improvements in target-domain detection performance, achieving gains of up to +4.8AP over semi-supervised baselines.

cs.CV↗

arXiv2025

Generative Unordered Flow for Set-Structured Data Generation

Flow-based generative models have demonstrated promising performance across a broad spectrum of data modalities (e.g., image and text). However, there are few works exploring their extension to unordered data (e.g., spatial point set), which is not trivial because previous models are mostly designed for vector data that are naturally ordered. In this paper, we present unordered flow, a type of flow-based generative model for set-structured data generation. Specifically, we convert unordered data into an appropriate function representation, and learn the probability measure of such representations through function-valued flow matching. For the inverse map from a function representation to unordered data, we propose a method similar to particle filtering, with Langevin dynamics to first warm-up the initial particles and gradient-based search to update them until convergence. We have conducted extensive experiments on multiple real-world datasets, showing that our unordered flow model is very effective in generating set-structured data and significantly outperforms previous baselines.

cs.LG↗

arXiv2025

Enhancing Fourier Neural Operators with Local Spatial Features

Partial Differential Equation (PDE) problems often exhibit strong local spatial structures, and effectively capturing these structures is critical for approximating their solutions. Recently, the Fourier Neural Operator (FNO) has emerged as an efficient approach for solving these PDE problems. By using parametrization in the frequency domain, FNOs can efficiently capture global patterns. However, this approach inherently overlooks the critical role of local spatial features, as frequency-domain parameterized convolutions primarily emphasize global interactions without encoding comprehensive localized spatial dependencies. Although several studies have attempted to address this limitation, their extracted Local Spatial Features (LSFs) remain insufficient, and computational efficiency is often compromised. To address this limitation, we introduce a convolutional neural network (CNN)-based feature pre-extractor to capture LSFs directly from input data, resulting in a hybrid architecture termed \textit{Conv-FNO}. Furthermore, we introduce two novel resizing schemes to make our Conv-FNO resolution invariant. In this work, we focus on demonstrating the effectiveness of incorporating LSFs into FNOs by conducting both a theoretical analysis and extensive numerical experiments. Our findings show that this simple yet impactful modification enhances the representational capacity of FNOs and significantly improves performance on challenging PDE benchmarks.

cs.LG↗

arXiv2025

DiTASK: Multi-Task Fine-Tuning with Diffeomorphic Transformations

Pre-trained Vision Transformers now serve as powerful tools for computer vision. Yet, efficiently adapting them for multiple tasks remains a challenge that arises from the need to modify the rich hidden representations encoded by the learned weight matrices, without inducing interference between tasks. Current parameter-efficient methods like LoRA, which apply low-rank updates, force tasks to compete within constrained subspaces, ultimately degrading performance. We introduce DiTASK a novel Diffeomorphic Multi-Task Fine-Tuning approach that maintains pre-trained representations by preserving weight matrix singular vectors, while enabling task-specific adaptations through neural diffeomorphic transformations of the singular values. By following this approach, DiTASK enables both shared and task-specific feature modulations with minimal added parameters. Our theoretical analysis shows that DITASK achieves full-rank updates during optimization, preserving the geometric structure of pre-trained features, and establishing a new paradigm for efficient multi-task learning (MTL). Our experiments on PASCAL MTL and NYUD show that DiTASK achieves state-of-the-art performance across four dense prediction tasks, using 75% fewer parameters than existing methods. Our code is available [here](https://github.com/ipsitmantri/DiTASK).

cs.CV↗

arXiv2025

Smooth Model Compression without Fine-Tuning

Compressing and pruning large machine learning models has become a critical step towards their deployment in real-world applications. Standard pruning and compression techniques are typically designed without taking the structure of the network's weights into account, limiting their effectiveness. We explore the impact of smooth regularization on neural network training and model compression. By applying nuclear norm, first- and second-order derivative penalties of the weights during training, we encourage structured smoothness while preserving predictive performance on par with non-smooth models. We find that standard pruning methods often perform better when applied to these smooth models. Building on this observation, we apply a Singular-Value-Decomposition-based compression method that exploits the underlying smooth structure and approximates the model's weight tensors by smaller low-rank tensors. Our approach enables state-of-the-art compression without any fine-tuning - reaching up to $91\%$ accuracy on a smooth ResNet-18 on CIFAR-10 with $70\%$ fewer parameters.

cs.LG↗

arXiv2025

Score-based Pullback Riemannian Geometry: Extracting the Data Manifold Geometry using Anisotropic Flows

Data-driven Riemannian geometry has emerged as a powerful tool for interpretable representation learning, offering improved efficiency in downstream tasks. Moving forward, it is crucial to balance cheap manifold mappings with efficient training algorithms. In this work, we integrate concepts from pullback Riemannian geometry and generative models to propose a framework for data-driven Riemannian geometry that is scalable in both geometry and learning: score-based pullback Riemannian geometry. Focusing on unimodal distributions as a first step, we propose a score-based Riemannian structure with closed-form geodesics that pass through the data probability density. With this structure, we construct a Riemannian autoencoder (RAE) with error bounds for discovering the correct data manifold dimension. This framework can naturally be used with anisotropic normalizing flows by adopting isometry regularization during training. Through numerical experiments on diverse datasets, including image data, we demonstrate that the proposed framework produces high-quality geodesics passing through the data support, reliably estimates the intrinsic dimension of the data manifold, and provides a global chart of the manifold. To the best of our knowledge, this is the first scalable framework for extracting the complete geometry of the data manifold.

cs.LG↗

arXiv2025

Blessing of Dimensionality for Approximating Sobolev Classes on Manifolds

The manifold hypothesis says that natural high-dimensional data lie on or around a low-dimensional manifold. The recent success of statistical and learning-based methods in very high dimensions empirically supports this hypothesis, suggesting that typical worst-case analysis does not provide practical guarantees. A natural step for analysis is thus to assume the manifold hypothesis and derive bounds that are independent of any ambient dimensions that the data may be embedded in. Theoretical implications in this direction have recently been explored in terms of generalization of ReLU networks and convergence of Langevin methods. In this work, we consider optimal uniform approximations with functions of finite statistical complexity. While upper bounds on uniform approximation exist in the literature using ReLU neural networks, we consider the opposite: lower bounds to quantify the fundamental difficulty of approximation on manifolds. In particular, we demonstrate that the statistical complexity required to approximate a class of bounded Sobolev functions on a compact manifold is bounded from below, and moreover that this bound is dependent only on the intrinsic properties of the manifold, such as curvature, volume, and injectivity radius.

cs.LG↗

arXiv2025

You KAN Do It in a Single Shot: Plug-and-Play Methods with Single-Instance Priors

The use of Plug-and-Play (PnP) methods has become a central approach for solving inverse problems, with denoisers serving as regularising priors that guide optimisation towards a clean solution. In this work, we introduce KAN-PnP, an optimisation framework that incorporates Kolmogorov-Arnold Networks (KANs) as denoisers within the Plug-and-Play (PnP) paradigm. KAN-PnP is specifically designed to solve inverse problems with single-instance priors, where only a single noisy observation is available, eliminating the need for large datasets typically required by traditional denoising methods. We show that KANs, based on the Kolmogorov-Arnold representation theorem, serve effectively as priors in such settings, providing a robust approach to denoising. We prove that the KAN denoiser is Lipschitz continuous, ensuring stability and convergence in optimisation algorithms like PnP-ADMM, even in the context of single-shot learning. Additionally, we provide theoretical guarantees for KAN-PnP, demonstrating its convergence under key conditions: the convexity of the data fidelity term, Lipschitz continuity of the denoiser, and boundedness of the regularisation functional. These conditions are crucial for stable and reliable optimisation. Our experimental results show, on super-resolution and joint optimisation, that KAN-PnP outperforms exiting methods, delivering superior performance in single-shot learning with minimal data. The method exhibits strong convergence properties, achieving high accuracy with fewer iterations.

cs.CV↗

arXiv2025

Brain Foundation Models with Hypergraph Dynamic Adapter for Brain Disease Analysis

Brain diseases, such as Alzheimer's disease and brain tumors, present profound challenges due to their complexity and societal impact. Recent advancements in brain foundation models have shown significant promise in addressing a range of brain-related tasks. However, current brain foundation models are limited by task and data homogeneity, restricted generalization beyond segmentation or classification, and inefficient adaptation to diverse clinical tasks. In this work, we propose SAM-Brain3D, a brain-specific foundation model trained on over 66,000 brain image-label pairs across 14 MRI sub-modalities, and Hypergraph Dynamic Adapter (HyDA), a lightweight adapter for efficient and effective downstream adaptation. SAM-Brain3D captures detailed brain-specific anatomical and modality priors for segmenting diverse brain targets and broader downstream tasks. HyDA leverages hypergraphs to fuse complementary multi-modal data and dynamically generate patient-specific convolutional kernels for multi-scale feature fusion and personalized patient-wise adaptation. Together, our framework excels across a broad spectrum of brain disease segmentation and classification tasks. Extensive experiments demonstrate that our method consistently outperforms existing state-of-the-art approaches, offering a new paradigm for brain disease analysis through multi-modal, multi-scale, and dynamic foundation modeling.

cs.CV↗

arXiv2025

Nested Bregman Iterations for Decomposition Problems

We consider the task of image reconstruction while simultaneously decomposing the reconstructed image into components with different features. A commonly used tool for this is a variational approach with an infimal convolution of appropriate functions as a regularizer. Especially for noise corrupted observations, incorporating these functionals into the classical method of Bregman iterations provides a robust method for obtaining an overall good approximation of the true image, by stopping early the iteration according to a discrepancy principle. However, crucially, the quality of the separate components depends further on the proper choice of the regularization weights associated to the infimally convoluted functionals. Here, we propose the method of Nested Bregman iterations to improve a decomposition in a structured way. This allows to transform the task of choosing the weights into the problem of stopping the iteration according to a meaningful criterion based on normalized cross-correlation. We discuss the well-definedness and the convergence behavior of the proposed method, and illustrate its strength numerically with various image decomposition tasks employing infimal convolution functionals.

math.NA↗

arXiv2025

Parameter choices in HaarPSI for IQA with medical images

When developing machine learning models, image quality assessment (IQA) measures are a crucial component for the evaluation of obtained output images. However, commonly used full-reference IQA (FR-IQA) measures have been primarily developed and optimized for natural images. In many specialized settings, such as medical images, this poses an often overlooked problem regarding suitability. In previous studies, the FR-IQA measure HaarPSI showed promising behavior regarding generalizability. The measure is based on Haar wavelet representations and the framework allows optimization of two parameters. So far, these parameters have been aligned for natural images. Here, we optimize these parameters for two medical image data sets, a photoacoustic and a chest X-ray data set, with IQA expert ratings. We observe that they lead to similar parameter values, different to the natural image data, and are more sensitive to parameter changes. We denote the novel optimized setting as HaarPSI$_{MED}$, which improves the performance of the employed medical images significantly (p<0.05). Additionally, we include an independent CT test data set that illustrates the generalizability of HaarPSI$_{MED}$, as well as visual examples that qualitatively demonstrate the improvement. The results suggest that adapting common IQA measures within their frameworks for medical images can provide a valuable, generalizable addition to employment of more specific task-based measures.

eess.IV↗

arXiv2025

SurvSurf: a partially monotonic neural network for first-hitting time prediction of intermittently observed discrete and continuous sequential events

We propose a neural-network based survival model (SurvSurf) specifically designed for direct and simultaneous probabilistic prediction of the first hitting time of sequential events from baseline. Unlike existing models, SurvSurf is theoretically guaranteed to never violate the monotonic relationship between the cumulative incidence functions of sequential events, while allowing nonlinear influence from predictors. It also incorporates implicit truths for unobserved intermediate events in model fitting, and supports both discrete and continuous time and events. We also identified a variant of the Integrated Brier Score (IBS) that showed robust correlation with the mean squared error (MSE) between the true and predicted probabilities by accounting for implied truths about the missing intermediate events. We demonstrated the superiority of SurvSurf compared to modern and traditional predictive survival models in two simulated datasets and two real-world datasets, using MSE, the more robust IBS and by measuring the extent of monotonicity violation.

stat.ML↗

arXiv2025

Stochastic Primal-Dual Three Operator Splitting Algorithm with Extension to Equivariant Regularization-by-Denoising

In this work we propose a stochastic primal-dual three-operator splitting algorithm (TOS-SPDHG) for solving a class of convex three-composite optimization problems. Our proposed scheme is a direct three-operator splitting extension of the SPDHG algorithm [Chambolle et al. 2018]. We provide theoretical convergence analysis showing ergodic $O(1/K)$ convergence rate, and demonstrate the effectiveness of our approach in imaging inverse problems. Moreover, we further propose TOS-SPDHG-RED and TOS-SPDHG-eRED which utilizes the regularization-by-denoising (RED) framework to leverage pretrained deep denoising networks as priors.

math.OC↗