arXiv subjects

Johannes Schwab

Publications and source records attributed to Johannes Schwab.

At least 19 recordsLinked to original sources

arXiv2026

Scaling Point-in-Time Language Models

Large language models trained on unrestricted internet corpora inevitably embed information from the future, introducing lookahead bias that compromises the validity of backtests and causal inference in finance and the social sciences. Point-in-time language models--trained exclusively on text available up to each calendar date--eliminate this leakage by construction, but existing efforts typically produce models that lag substantially behind their unconstrained counterparts. We show that this performance gap can be substantially narrowed through scale. Training decoder-only transformers with up to 4 billion parameters on 1 trillion chronologically filtered tokens from FineWeb, we construct a sequence of monthly model checkpoints spanning 2013-2024. Across a range of common-sense reasoning and language understanding benchmarks, our models approach the performance of leading open-weight models of comparable size (e.g., Gemma-3-4B and LLaMA-7B) trained on temporally unrestricted data, although a performance gap remains on several tasks. Instruction fine-tuning via LoRA further improves downstream usability. We release the complete pipeline--including dataset construction, training infrastructure, and evaluation code--to enable reproducible point-in-time language modeling and to support research applications that require strict temporal validity.

cs.CL↗

arXiv2026

Design Choices in Splitting-Based Self-Supervised Sparse-View CT Reconstruction

Self-supervised data splitting has emerged as a promising paradigm for sparse-view CT reconstruction, enabling training from incomplete measurements without fully sampled ground truth. However, the influence of key design choices, including partitioning strategy, preprocessing, and inference, remains insufficiently understood. In this work, we introduce a unified framework that decomposes splitting-based reconstruction into these three components, enabling controlled comparison of existing methods and two incremental extensions: multi-partition splitting and an alternative inference strategy. Experiments on simulated LoDoPaB-CT data under independent and correlated noise, together with validation on the real-world 2DeteCT dataset, show that the optimal partitioning strategy strongly depends on the measurement noise structure. Lattice-based splitting performs favorably under independent noise, whereas angular masking is more robust under correlated noise and real measured data. Multi-partition splitting consistently improves over pure projection-wise splitting in several settings. Complementary perceptual and structural metrics, including LPIPS and HaarPSI, reveal differences between masking strategies that are less apparent from PSNR and SSIM alone. These results provide practical guidelines for designing self-supervised sparse-view CT reconstruction methods and highlight the limitations of common independence assumptions in realistic imaging environments.

cs.CV↗

arXiv2026

Visible Lagrangians for Hitchin Systems and Pillowcase Covers

We study complex Lagrangians in Hitchin systems that factor through a proper subvariety of the Hitchin base non-trivially intersecting the regular locus. This gives a general framework for several examples in the literature. We compute the fiber-wise Fourier-Mukai transform of flat line bundles on visible Lagrangians. This proposes a construction of mirror dual branes to visible Lagrangians. Finally, we study a new example of visible Lagrangians in detail. Such visible Lagrangian exists whenever the underlying Riemann surface is a pillowcase cover. The proposed mirror dual brane turns out to be closely related to Hausel's toy model.

math.AG↗

arXiv2026

Learning Regularization Functionals for Inverse Problems: A Comparative Study

In recent years, a variety of learned regularization frameworks for solving inverse problems in imaging have emerged. These offer flexible modeling together with mathematical insights. The proposed methods differ in their architectural design and training strategies, making direct comparison challenging due to non-modular implementations. We address this gap by collecting and unifying the available code into a common framework. This unified view allows us to systematically compare the approaches and highlight their strengths and limitations, providing valuable insights into their future potential. We also provide concise descriptions of each method, complemented by practical guidelines.

cs.LG↗

arXiv2026

HyDRA: Hybrid Denoising Regularization for Measurement-Only DEQ Training

Solving image reconstruction problems of the form $\mathbf{A} \mathbf{x} = \mathbf{y}$ remains challenging due to ill-posedness and the lack of large-scale supervised datasets. Deep Equilibrium (DEQ) models have been used successfully but typically require supervised pairs $(\mathbf{x},\mathbf{y})$. In many practical settings, only measurements $\mathbf{y}$ are available. We introduce HyDRA (Hybrid Denoising Regularization Adaptation), a measurement-only framework for DEQ training that combines measurement consistency with an adaptive denoising regularization term, together with a data-driven early stopping criterion. Experiments on sparse-view CT demonstrate competitive reconstruction quality and fast inference.

cs.CV↗

arXiv2025

Training NTK to Generalize with KARE

The performance of the data-dependent neural tangent kernel (NTK; Jacot et al. (2018)) associated with a trained deep neural network (DNN) often matches or exceeds that of the full network. This implies that DNN training via gradient descent implicitly performs kernel learning by optimizing the NTK. In this paper, we propose instead to optimize the NTK explicitly. Rather than minimizing empirical risk, we train the NTK to minimize its generalization error using the recently developed Kernel Alignment Risk Estimator (KARE; Jacot et al. (2020)). Our simulations and real data experiments show that NTKs trained with KARE consistently match or significantly outperform the original DNN and the DNN- induced NTK (the after-kernel). These results suggest that explicitly trained kernels can outperform traditional end-to-end DNN optimization in certain settings, challenging the conventional dominance of DNNs. We argue that explicit training of NTK is a form of over-parametrized feature learning.

cs.LG↗

arXiv2025

Noisier2Inverse: Self-Supervised Learning for Image Reconstruction with Correlated Noise

We propose Noisier2Inverse, a correction-free self-supervised deep learning approach for general inverse problems. The proposed method learns a reconstruction function without the need for ground truth samples and is applicable in cases where measurement noise is statistically correlated. This includes computed tomography, where detector imperfections or photon scattering create correlated noise patterns, as well as microscopy and seismic imaging, where physical interactions during measurement introduce dependencies in the noise structure. Similar to Noisier2Noise, a key step in our approach is the generation of noisier data from which the reconstruction network learns. However, unlike Noisier2Noise, the proposed loss function operates in measurement space and is trained to recover an extrapolated image instead of the original noisy one. This eliminates the need for an extrapolation step during inference, which would otherwise suffer from ill-posedness. We numerically demonstrate that our method clearly outperforms previous self-supervised approaches that account for correlated noise.

cs.CV↗

arXiv2025

Chern classes of linear submanifolds with application to spaces of k-differentials and ball quotients

We provide formulas for the Chern classes of linear submanifolds of the moduli spaces of Abelian differentials and hence for their Euler characteristic. This includes as special case the moduli spaces of k-differentials, for which we set up the full intersection theory package and implement it in the sage-program diffstrata. As an application, we give an algebraic proof of the theorems of Deligne-Mostow and Thurston that suitable compactifications of moduli spaces of k-differentials on the 5-punctured projective line with weights satisfying the INT-condition are quotients of the complex two-ball.

math.AG↗

arXiv2024

Realizability of tropical pluri-canonical divisors

Consider a pair consisting of an abstract tropical curve and an effective divisor from the linear system associated to $k$ times the canonical divisor for $k \in \mathbb{Z}_{\geq 1}$. In this article we give a purely combinatorial criterion to determine if such a pair arises as the tropicalization of a pair consisting of a smooth algebraic curve over a non-Archimedean field with algebraically closed residue field of characteristic 0 together with an effective pluri-canonical divisor. To do so, we introduce tropical normalized covers as special instances of tropical Hurwitz covers and reduce the realizability problem for pluri-canonical divisors to the realizability problem for normalized covers. Our main result generalizes the work of Möller-Ulirsch-Werner on realizability of tropical canonical divisors and incorporates the recent progress on compactifications of strata of $k$-differentials in the work of Bainbridge-Chen-Gendron-Grushevsky-Möller.

math.AG↗

arXiv2024

Self2Seg: Single-Image Self-Supervised Joint Segmentation and Denoising

We develop Self2Seg, a self-supervised method for the joint segmentation and denoising of a single image. To this end, we combine the advantages of variational segmentation with self-supervised deep learning. One major benefit of our method lies in the fact, that in contrast to data-driven methods, where huge amounts of labeled samples are necessary, Self2Seg segments an image into meaningful regions without any training database. Moreover, we demonstrate that self-supervised denoising itself is significantly improved through the region-specific learning of Self2Seg. Therefore, we introduce a novel self-supervised energy functional in which denoising and segmentation are coupled in a way that both tasks benefit from each other. We propose a unified optimisation strategy and numerically show that for noisy microscopy images our proposed joint approach outperforms its sequential counterpart as well as alternative methods focused purely on denoising or segmentation.

cs.CV↗

arXiv2024

Sparse2Inverse: Self-supervised inversion of sparse-view CT data

Sparse-view computed tomography (CT) enables fast and low-dose CT imaging, an essential feature for patient-save medical imaging and rapid non-destructive testing. In sparse-view CT, only a few projection views are acquired, causing standard reconstructions to suffer from severe artifacts and noise. To address these issues, we propose a self-supervised image reconstruction strategy. Specifically, in contrast to the established Noise2Inverse, our proposed training strategy uses a loss function in the projection domain, thereby bypassing the otherwise prescribed nullspace component. We demonstrate the effectiveness of the proposed method in reducing stripe-artifacts and noise, even from highly sparse data.

eess.IV↗

arXiv2023

Lifting-based variational multiclass segmentation algorithm: design, convergence analysis, and implementation with applications in medical imaging

We propose, analyze and realize a variational multiclass segmentation scheme that partitions a given image into multiple regions exhibiting specific properties. Our method determines multiple functions that encode the segmentation regions by minimizing an energy functional combining information from different channels. Multichannel image data can be obtained by lifting the image into a higher dimensional feature space using specific multichannel filtering or may already be provided by the imaging modality under consideration, such as an RGB image or multimodal medical data. Experimental results show that the proposed method performs well in various scenarios. In particular, promising results are presented for two medical applications involving classification of brain abscess and tumor growth, respectively. As main theoretical contributions, we prove the existence of global minimizers of the proposed energy functional and show its stability and convergence with respect to noisy inputs. In particular, these results also apply to the special case of binary segmentation, and these results are also novel in this particular situation.

cs.CV↗

arXiv2023

Variational multichannel multiclass segmentation using unsupervised lifting with CNNs

We propose an unsupervised image segmentation approach, that combines a variational energy functional and deep convolutional neural networks. The variational part is based on a recent multichannel multiphase Chan-Vese model, which is capable to extract useful information from multiple input images simultaneously. We implement a flexible multiclass segmentation method that divides a given image into $K$ different regions. We use convolutional neural networks (CNNs) targeting a pre-decomposition of the image. By subsequently minimising the segmentation functional, the final segmentation is obtained in a fully unsupervised manner. Special emphasis is given to the extraction of informative feature maps serving as a starting point for the segmentation. The initial results indicate that the proposed method is able to decompose and segment the different regions of various types of images, such as texture and medical images and compare its performance with another multiphase segmentation method.

cs.CV↗

arXiv2022

Regularization of Inverse Problems by Filtered Diagonal Frame Decomposition

The characteristic feature of inverse problems is their instability with respect to data perturbations. In order to stabilize the inversion process, regularization methods have to be developed and applied. In this work we introduce and analyze the concept of filtered diagonal frame decomposition which extends the standard filtered singular value decomposition to the frame case. Frames as generalized singular system allows to better adapt to a given class of potential solutions. In this paper, we show that filtered diagonal frame decomposition yield a convergent regularization method. Moreover, we derive convergence rates under source type conditions and prove order optimality under the assumption that the considered frame is a Riesz-basis.

math.NA↗

arXiv2021

Augmented NETT Regularization of Inverse Problems

We propose aNETT (augmented NETwork Tikhonov) regularization as a novel data-driven reconstruction framework for solving inverse problems. An encoder-decoder type network defines a regularizer consisting of a penalty term that enforces regularity in the encoder domain, augmented by a penalty that penalizes the distance to the data manifold. We present a rigorous convergence analysis including stability estimates and convergence rates. For that purpose, we prove the coercivity of the regularizer used without requiring explicit coercivity assumptions for the networks involved. We propose a possible realization together with a network architecture and a modular training strategy. Applications to sparse-view and low-dose CT show that aNETT achieves results comparable to state-of-the-art deep-learning-based reconstruction methods. Unlike learned iterative methods, aNETT does not require repeated application of the forward and adjoint models, which enables the use of aNETT for inverse problems with numerically expensive forward models. Furthermore, we show that aNETT trained on coarsely sampled data can leverage an increased sampling rate without the need for retraining.

math.NA↗

arXiv2020

Sparse aNETT for Solving Inverse Problems with Deep Learning

We propose a sparse reconstruction framework (aNETT) for solving inverse problems. Opposed to existing sparse reconstruction techniques that are based on linear sparsifying transforms, we train an autoencoder network $D \circ E$ with $E$ acting as a nonlinear sparsifying transform and minimize a Tikhonov functional with learned regularizer formed by the $\ell^q$-norm of the encoder coefficients and a penalty for the distance to the data manifold. We propose a strategy for training an autoencoder based on a sample set of the underlying image class such that the autoencoder is independent of the forward operator and is subsequently adapted to the specific forward model. Numerical results are presented for sparse view CT, which clearly demonstrate the feasibility, robustness and the improved generalization capability and stability of aNETT over post-processing networks.

math.NA↗

arXiv2020

Data-consistent neural networks for solving nonlinear inverse problems

Data assisted reconstruction algorithms, incorporating trained neural networks, are a novel paradigm for solving inverse problems. One approach is to first apply a classical reconstruction method and then apply a neural network to improve its solution. Empirical evidence shows that such two-step methods provide high-quality reconstructions, but they lack a convergence analysis. In this paper we formalize the use of such two-step approaches with classical regularization theory. We propose data-consistent neural networks that we combine with classical regularization methods. This yields a data-driven regularization method for which we provide a full convergence analysis with respect to noise. Numerical simulations show that compared to standard two-step deep learning methods, our approach provides better stability with respect to structural changes in the test set, while performing similarly on test data similar to the training set. Our method provides a stable solution of inverse problems that exploits both the known nonlinear forward model as well as the desired solution manifold from data.

math.NA↗

arXiv2020

Deep synthesis regularization of inverse problems

Recently, a large number of efficient deep learning methods for solving inverse problems have been developed and show outstanding numerical performance. For these deep learning methods, however, a solid theoretical foundation in the form of reconstruction guarantees is missing. In contrast, for classical reconstruction methods, such as convex variational and frame-based regularization, theoretical convergence and convergence rate results are well established. In this paper, we introduce deep synthesis regularization (DESYRE) using neural networks as nonlinear synthesis operator bridging the gap between these two worlds. The proposed method allows to exploit the deep learning benefits of being well adjustable to available training data and on the other hand comes with a solid mathematical foundation. We present a complete convergence analysis with convergence rates for the proposed deep synthesis regularization. We present a strategy for constructing a synthesis network as part of an analysis-synthesis sequence together with an appropriate training strategy. Numerical results show the plausibility of our approach.

math.NA↗