Tootfinder

Resummation of Cosmological Correlators and their UV-Regularization
Matthias Nowinski, Ivo Sachs
https://arxiv.org/abs/2507.21224 https://arxiv.org/pdf/250…

Resummation of Cosmological Correlators and their UV-Regularization
Cosmological correlators are important observables in cosmology. They are often approximated by de Sitter space correlators. In this paper, we give a first precise diagrammatical computation of higher loop diagrams to all orders for a conformally coupled scalar in four dimensions. We show that, in contrast to flat space, diagrams of necklace topology do not resum using the natural application of de Sitter-invariant regularization and are thus hard to evaluate. We propose a modification to the U…

Assessing local deformation and computing scalar curvature with nonlinear conformal regularization of decoders
Benjamin Cou\'eraud, Vikram Sunkara, Christof Sch\"utte
https://arxiv.org/abs/2508.20413

Assessing local deformation and computing scalar curvature with nonlinear conformal regularization of decoders
One aim of dimensionality reduction is to discover the main factors that explain the data, and as such is paramount to many applications. When working with high dimensional data, autoencoders offer a simple yet effective approach to learn low-dimensional representations. The two components of a general autoencoder consist first of an encoder that maps the observed data onto a latent space; and second a decoder that maps the latent space back to the original observation space, which allows to le…

An inherent regularization approach to parameter-free preconditioning for nearly incompressible linear poroelasticity and elasticity
Weizhang Huang, Zhuoran Wang
https://arxiv.org/abs/2507.22334

An inherent regularization approach to parameter-free preconditioning for nearly incompressible linear poroelasticity and elasticity
An inherent regularization strategy and block Schur complement preconditioning are studied for linear poroelasticity problems discretized using the lowest-order weak Galerkin FEM in space and the implicit Euler scheme in time. At each time step, the resulting saddle point system becomes nearly singular in the locking regime, where the solid is nearly incompressible. This near-singularity stems from the leading block, which corresponds to a linear elasticity system. To enable efficient iterative…

Constructive Quantum Field Theory on Curved Surfaces and Related Topics
Jiasheng Lin
https://arxiv.org/abs/2507.21655 https://arxiv.org/pdf/2507.21655

Constructive Quantum Field Theory on Curved Surfaces and Related Topics
This is the Ph.D. thesis of the author. In this thesis, we construct the $ P(ϕ)_2 $ Quantum Field Theory (QFT) model on curved surfaces and show that it satisfies Segal's axioms (arXiv:2403.12804). An important ingredient in this construction is the use of a local regularization procedure to define the interaction as a random variable with respect to the Gaussian Free Field (GFF). We provide a counterexample demonstrating that spectral truncation regularization violates locality (arXiv:2312.15…

A Self-scaled Approximate $\ell_0$ Regularization Robust Model for Outlier Detection
Pengyang Song, Jue Wang
https://arxiv.org/abs/2506.22277 https://

A Self-scaled Approximate $\ell_0$ Regularization Robust Model for Outlier Detection
Robust regression models in the presence of outliers have significant practical relevance in areas such as signal processing, financial econometrics, and energy management. Many existing robust regression methods, either grounded in statistical theory or sparse signal recovery, typically rely on the explicit or implicit assumption of outlier sparsity to filter anomalies and recover the underlying signal or data. However, these methods often suffer from limited robustness or high computational c…

PBiLoss: Popularity-Aware Regularization to Improve Fairness in Graph-Based Recommender Systems
Mohammad Naeimi, Mostafa Haghir Chehreghani
https://arxiv.org/abs/2507.19067 http…

PBiLoss: Popularity-Aware Regularization to Improve Fairness in Graph-Based Recommender Systems
Recommender systems, especially those based on graph neural networks (GNNs), have achieved remarkable success in capturing user-item interaction patterns. However, they remain susceptible to popularity bias--the tendency to over-recommend popular items--resulting in reduced content diversity and compromised fairness. In this paper, we propose PBiLoss, a novel regularization-based loss function designed to counteract popularity bias in graph-based recommender models explicitly. PBiLoss augments …

On Policy Stochasticity in Mutual Information Optimal Control of Linear Systems
Shoju Enami, Kenji Kashima
https://arxiv.org/abs/2507.21543 https://arxiv.o…

On Policy Stochasticity in Mutual Information Optimal Control of Linear Systems
In recent years, mutual information optimal control has been proposed as an extension of maximum entropy optimal control. Both approaches introduce regularization terms to render the policy stochastic, and it is important to theoretically clarify the relationship between the temperature parameter (i.e., the coefficient of the regularization term) and the stochasticity of the policy. Unlike in maximum entropy optimal control, this relationship remains unexplored in mutual information optimal con…

Replaced article(s) found for cs.CL. https://arxiv.org/list/cs.CL/new
[2/5]:
- Self-Regularization with Sparse Autoencoders for Controllable LLM-based Classification
Xuansheng Wu, Wenhao Yu, Xiaoming Zhai, Ninghao Liu

Bayesian symbolic regression: Automated equation discovery from a physicists' perspective
Roger Guimera, Marta Sales-Pardo
https://arxiv.org/abs/2507.19540 https://

Bayesian symbolic regression: Automated equation discovery from a physicists' perspective
Symbolic regression automates the process of learning closed-form mathematical models from data. Standard approaches to symbolic regression, as well as newer deep learning approaches, rely on heuristic model selection criteria, heuristic regularization, and heuristic exploration of model space. Here, we discuss the probabilistic approach to symbolic regression, an alternative to such heuristic approaches with direct connections to information theory and statistical physics. We show how the prob…

Dimensional Regularization of Bubble Diagrams in de Sitter Spacetime
Hongyu Zhang
https://arxiv.org/abs/2507.19318 https://arxiv.org/pdf/2507.19318

Dimensional Regularization of Bubble Diagrams in de Sitter Spacetime
Correlators of large-scale fluctuations produced during cosmic inflation are major observables of inflationary cosmology. In cosmological collider physics, many interesting correlators are generated through loop processes. However, ultraviolet divergences often appear when computing the loop correlators, and a regularization is required. In this work, Källén-Lehmann representation and dimensional regularization are used to analytically compute various correlators with a bubble loop of massive…

Momentum Equation-Based Regularization and Image Registration for Two-Dimensional Ultrasound Elasticity Imaging
Olalekan A. Babaniyi, Rebecca Rodrigues, Michael S. Richards
https://arxiv.org/abs/2508.19086

Momentum Equation-Based Regularization and Image Registration for Two-Dimensional Ultrasound Elasticity Imaging
Objective: Evaluate and compare multiple mechanics-based and traditional regularization strategies within a variational image registration framework for quasi-static ultrasound elastography. Methods:We reformulate a previously proposed momentum-equation-based post-processing method (SPREME) as a regularization term directly integrated into an image registration energy functional. Four regularization types are implemented and compared: a strain magnitude ($\R_ε$), a strain magnitude with incomp…

Local Wellposedness and Global Weak Solutions of the Pauli-Darwin/Poisswell Equations
Pierre Germain, Norbert J. Mauser, Jakob M\"oller
https://arxiv.org/abs/2506.22333

Local Wellposedness and Global Weak Solutions of the Pauli-Darwin/Poisswell Equations
We construct local (in time) strong solutions in $H^s(\mathbb{R}^3)$, $s>3/2$ and global weak solutions with finite energy for the Pauli-Darwin equation and the Pauli-Poisswell equation. These are the first rigorous results on these two models, which couple a 2-spinor with an electromagnetic field. The proofs rely on energy estimates for the strong solutions and compactness with an appropriate regularization for the weak solutions.

H\"older estimates for degenerate complex Monge-Amp\`ere equations
Bin Guo, Slawomir Kolodziej, Jian Song, Jacob Sturm
https://arxiv.org/abs/2508.20933 https://

Hölder estimates for degenerate complex Monge-Ampère equations
Uniform $L^\infty$ and Hölder estimates were proved by the Kolodziej for complex Monge-Ampère equations on compact Kähler manifolds with $L^p$ volume measure with $p>1$. On the other hand, establishing Hölder estimates on singular Kähler varieties has remained open. In this paper, we establish uniform Hölder continuity for a family of complex Monge-Ampère equations on Kähler varieties, by developing a geometric regularization based on the partial $C^0$ estimate, i.e., quantitive Kodaira…

Higher-genus multiple zeta values
Konstantin Baune, Johannes Broedel, Egor Im, Zhexian Ji, Yannis Moeckli
https://arxiv.org/abs/2507.21765 https://arxiv.or…

Higher-genus multiple zeta values
Multiple zeta values arise as special values of polylogarithms defined on Riemann surfaces of various genera. Building on the vast knowledge for classical and elliptic multiple zeta values, we explore a canonical extension of the formalism to Riemann surfaces of higher genera, which yields higher-genus multiple zeta values. We provide a regularization prescription for higher-genus polylogarithms, which we extend to higher-genus multiple zeta values. Our regularization uses the Schottky uniformi…

Replaced article(s) found for physics.atom-ph. https://arxiv.org/list/physics.atom-ph/new
[1/1]:
- Relativistic corrections of order $m\alpha^6$: singular operators and regularization
Vladimir I Korobov

Sparse-mode Dynamic Mode Decomposition for Disambiguating Local and Global Structures
Sara M. Ichinaga, Steven L. Brunton, Aleksandr Y. Aravkin, J. Nathan Kutz
https://arxiv.org/abs/2507.19787

Sparse-mode Dynamic Mode Decomposition for Disambiguating Local and Global Structures
The dynamic mode decomposition (DMD) is a data-driven approach that extracts the dominant features from spatiotemporal data. In this work, we introduce sparse-mode DMD, a new variant of the optimized DMD framework that specifically leverages sparsity-promoting regularization in order to approximate DMD modes which have localized spatial structure. The algorithm maintains the noise-robust properties of optimized DMD while disambiguating between modes which are spatially local versus global in na…

Papanicolaou Stain Unmixing for RGB Image Using Weighted Nucleus Sparsity and Total Variation Regularization
Nanxin Gong, Saori Takeyama, Masahiro Yamaguchi, Takumi Urata, Fumikazu Kimura, Keiko Ishii
https://arxiv.org/abs/2506.20450

Papanicolaou Stain Unmixing for RGB Image Using Weighted Nucleus Sparsity and Total Variation Regularization
The Papanicolaou stain, consisting of eosin Y, hematoxylin, light Green SF yellowish, orange G, and Bismarck brown Y, provides extensive color information essential for cervical cancer screening in cytopathology. However, the visual observation of these colors is subjective and difficult to characterize. In digital image analysis, the RGB intensities are affected by staining and imaging variations, hindering direct quantification of color in Papanicolaou-stained samples. Stain unmixing is a pro…

Relaxed Total Generalized Variation Regularized Piecewise Smooth Mumford-Shah Model for Triangulated Surface Segmentation
Huayan Zhang, Shanqiang Wang, Xiaochao Wang
https://arxiv.org/abs/2507.19284

Relaxed Total Generalized Variation Regularized Piecewise Smooth Mumford-Shah Model for Triangulated Surface Segmentation
The Mumford-Shah (MS) model is an important technique for mesh segmentation. Many existing researches focus on piecewise constant MS mesh segmentation model with total variation regularization, which pursue the shortest length of boundaries. Different from previous efforts, in this article, we propose a novel piecewise smooth MS mesh segmentation model by utilizing the relaxed total generalized variation regularization (rTGV). The new model assumes that the feature function of a mesh can be app…

Regularized Extragradient Methods for Solving Equilibrium Problems on Hadamard Manifolds
Shikher Sharmaa, Pankaj Gautam, Simeon Reich
https://arxiv.org/abs/2506.22391

Regularized Extragradient Methods for Solving Equilibrium Problems on Hadamard Manifolds
Employing two distinct types of regularization terms, we propose two regularized extragradient methods for solving equilibrium problems on Hadamard manifolds. The sequences generated by these extragradient algorithms converge to a solution of the equilibrium problem without requiring the Lipschitz continuity of the bifunction or imposing additional conditions on the parameters. We establish convergence results for both algorithms and derive global error bounds along with $R$-linear convergence …

Enhancing Generalization of Spiking Neural Networks Through Temporal Regularization
Boxuan Zhang, Zhen Xu, Kuan Tao
https://arxiv.org/abs/2506.19256 https:…

Enhancing Generalization of Spiking Neural Networks Through Temporal Regularization
Spiking Neural Networks (SNNs) have received widespread attention due to their event-driven and low-power characteristics, making them particularly effective for processing event-based neuromorphic data. Recent studies have shown that directly trained SNNs suffer from severe overfitting issues due to the limited scale of neuromorphic datasets and the gradient mismatching problem, which fundamentally constrain their generalization performance. In this paper, we propose a temporal regularization …

Precision Matrix Regularization in Sufficient Dimension Reduction for Improved Quadratic Discriminant Classification
Derik T. Boonstra, Rakheon Kim, Dean M. Young
https://arxiv.org/abs/2506.19192

Precision Matrix Regularization in Sufficient Dimension Reduction for Improved Quadratic Discriminant Classification
Sufficient dimension reduction (SDR) methods, which often rely on class precision matrices, are widely used in supervised statistical classification problems. However, when class-specific sample sizes are small relative to the original feature-space dimension, precision matrix estimation becomes unstable and, as a result, increases the variability of the linear dimension reduction (LDR) matrix. Ultimately, this fact causes suboptimal supervised classification. To address this problem, we develo…

Medium effects on the electromagnetic form factors of $\rho$ meson
Parada T. P. Hutauruk, Terry Mart, Kazuo Tsushima
https://arxiv.org/abs/2508.20501 https://

Medium effects on the electromagnetic form factors of $ρ$ meson
The dynamics of partons inside the light $ρ$ meson is found to be essential for its properties and internal structure, both in free space and in the nuclear medium. In this paper, we systematically investigate the in-medium structure changes of $ρ^+$ mesons within the covariant Nambu-Jona-Lasinio (NJL) model, utilizing the Schwinger proper-time regularization scheme. We solve the Bethe-Salpeter equations to guarantee the bound meson-state condition. At the quark level, the nuclear medium effe…

MOVER: Multimodal Optimal Transport with Volume-based Embedding Regularization
Haochen You, Baojing Liu
https://arxiv.org/abs/2508.12149 https://arxiv.org/…

MOVER: Multimodal Optimal Transport with Volume-based Embedding Regularization
Recent advances in multimodal learning have largely relied on pairwise contrastive objectives to align different modalities, such as text, video, and audio, in a shared embedding space. While effective in bi-modal setups, these approaches struggle to generalize across multiple modalities and often lack semantic structure in high-dimensional spaces. In this paper, we propose MOVER, a novel framework that combines optimal transport-based soft alignment with volume-based geometric regularization t…

Studying Effective String Theory using deep generative models
Michele Caselle, Elia Cellini, Alessandro Nada
https://arxiv.org/abs/2508.20610 https://arxiv…

Studying Effective String Theory using deep generative models
Effective String Theory (EST) offers a robust non-perturbative framework for describing confinement in Yang-Mills theory by treating the confining flux tube between a static quark-antiquark pair as a thin, vibrating string. While EST calculations are typically carried out using zeta-function regularization, certain problems-such as determining the flux tube width-are too complex to solve analytically. However, recent studies have demonstrated that EST can be explored numerically by employing de…

Modification of a Numerical Method Using FIR Filters in a Time-dependent SIR Model for COVID-19
Felipe Rog\'erio Pimentel, Rafael Gustavo Alves
https://arxiv.org/abs/2506.21739

Modification of a Numerical Method Using FIR Filters in a Time-dependent SIR Model for COVID-19
Authors Yi-Cheng Chen, Ping-En Lu, Cheng-Shang Chang, and Tzu-Hsuan Liu use the Finite Impulse Response (FIR) linear system filtering method to track and predict the number of people infected and recovered from COVID-19, in a pandemic context in which there was still no vaccine and the only way to avoid contagion was isolation. To estimate the coefficients of these FIR filters, Chen et al. used machine learning methods through a classical optimization problem with regularization (ridge regressi…

A Reinforcement Learning Framework for Some Singular Stochastic Control Problems
Zongxia Liang, Xiaodong Luo, Xiang Yu
https://arxiv.org/abs/2506.22203 htt…

A Reinforcement Learning Framework for Some Singular Stochastic Control Problems
We develop a continuous-time reinforcement learning framework for a class of singular stochastic control problems without entropy regularization. The optimal singular control is characterized as the optimal singular control law, which is a pair of regions of time and the augmented states. The goal of learning is to identify such an optimal region via the trial-and-error procedure. In this context, we generalize the existing policy evaluation theories with regular controls to learn our optimal s…

HuBERT-VIC: Improving Noise-Robust Automatic Speech Recognition of Speech Foundation Model via Variance-Invariance-Covariance Regularization
Hyebin Ahn, Kangwook Jang, Hoirin Kim
https://arxiv.org/abs/2508.12292

HuBERT-VIC: Improving Noise-Robust Automatic Speech Recognition of Speech Foundation Model via Variance-Invariance-Covariance Regularization
Noise robustness in speech foundation models (SFMs) has been a critical challenge, as most models are primarily trained on clean data and experience performance degradation when the models are exposed to noisy speech. To address this issue, we propose HuBERT-VIC, a noise-robust SFM with variance, in-variance, and covariance regularization (VICReg) objectives. These objectives adjust the statistics of noisy speech representations, enabling the model to capture diverse acoustic characteristics an…

Domain Generalization and Adaptation in Intensive Care with Anchor Regression
Malte Londschien, Manuel Burger, Gunnar R\"atsch, Peter B\"uhlmann
https://arxiv.org/abs/2507.21783

Domain Generalization and Adaptation in Intensive Care with Anchor Regression
The performance of predictive models in clinical settings often degrades when deployed in new hospitals due to distribution shifts. This paper presents a large-scale study of causality-inspired domain generalization on heterogeneous multi-center intensive care unit (ICU) data. We apply anchor regression and introduce anchor boosting, a novel, tree-based nonlinear extension, to a large dataset comprising 400,000 patients from nine distinct ICU databases. The anchor regularization consistently im…

Canard cycles of non-linearly regularized piecewise smooth vector fields
Peter De Maesschalck, Renato Huzak, Otavio Henrique Perez
https://arxiv.org/abs/2506.18099

Canard cycles of non-linearly regularized piecewise smooth vector fields
The main purpose of this paper is to study limit cycles in non-linear regularizations of planar piecewise smooth systems with fold points (or more degenerate tangency points) and crossing regions. We deal with a slow fast Hopf point after non-linear regularization and blow-up. We give a simple criterion for upper bounds and the existence of limit cycles of canard type, expressed in terms of zeros of the slow divergence integral. Using the criterion we can construct a quadratic regularization of…

Weakly-Convex Regularization for Magnetic Resonance Image Denoising
Akash Prabakar, Abhishek Shreekant Bhandiwad, Abijith Jagannath Kamath, Chandra Sekhar Seelamantula
https://arxiv.org/abs/2508.14438 …

Weakly-Convex Regularization for Magnetic Resonance Image Denoising
Regularization for denoising in magnetic resonance imaging (MRI) is typically achieved using convex regularization functions. Recently, deep learning techniques have been shown to provide superior denoising performance. However, this comes at the price of lack of explainability, interpretability and stability, which are all crucial to MRI. In this work, we present a constructive approach for designing weakly-convex regularization functions for MR image denoising. We show that our technique perf…

Ambiguities in the generation of CFJ-terms in a 5-dimensional extension of QED in one loop
H. G. Fargnoli, J. C. C. Felipe, G. Gazzola
https://arxiv.org/abs/2506.20961

Ambiguities in the generation of CFJ-terms in a 5-dimensional extension of QED in one loop
In this paper, we investigate a Lorentz symmetry breaking extension of Quantum Electrodynamics (QED), incorporating 5-dimensional CPT-odd terms at the one-loop level. Employing an independent regularization method, we systematically separate the divergences into regularization-independent contributions and regularization-dependent (surface terms). We demonstrate that these surface terms, potentially contributing to the radiative generation of Carroll-Field-Jackiw (CFJ) terms, remain undetermine…

Solving Mean-Field Games with Monotonicity Methods in Banach Spaces?
Rita Ferreira, Diogo Gomes, Melih Ucer
https://arxiv.org/abs/2506.21212 https://

Solving Mean-Field Games with Monotonicity Methods in Banach Spaces?
This paper develops a unified framework for proving the existence of solutions to stationary first-order mean-field games (MFGs) based on the theory of monotone operators in Banach spaces. We cast the coupled MFG system as a variational inequality, overcoming the limitations of prior Hilbert-space approaches that relied on high-order regularization and typically yielded only weak solutions in the monotone operator sense. In contrast, with our low-order regularization, we obtain strong solutions…

$\ell_{1}^{2}-\eta\ell_{2}^{2}$ sparsity regularization for nonlinear ill-posed problems
Long Li, Liang Ding
https://arxiv.org/abs/2508.16163 https://arxiv…

$\ell_{1}^{2}-η\ell_{2}^{2}$ sparsity regularization for nonlinear ill-posed problems
In this study, we investigate the $\left\|\cdot\right\|_{\ell_{1}}^{2}-η\left\|\cdot\right\|_{\ell_{2}}^{2}$ sparsity regularization with $0< η\leq 1$, in the context of nonlinear ill-posed inverse problems. We focus on the examination of the well-posedness associated with this regularization approach. Notably, the case where $η=1$ presents weaker theoretical outcomes than $0< η<1$, primarily due to the absence of coercivity and the Radon-Riesz property associated with t…

FlatCAD: Fast Curvature Regularization of Neural SDFs for CAD Models
Haotian Yin, Aleksander Plocharski, Michal Jan Wlodarczyk, Mikolaj Kida, Przemyslaw Musialski
https://arxiv.org/abs/2506.16627

FlatCAD: Fast Curvature Regularization of Neural SDFs for CAD Models
Neural signed-distance fields (SDFs) have become a versatile backbone for geometric learning, yet enforcing developable, CAD-style behavior still hinges on Gaussian curvature penalties that require full Hessian evaluation and second-order automatic differentiation, both of which are costly in memory and runtime. We present a curvature proxy that regularizes only the mixed second-order term (Weingarten term), allowing the two principal curvatures to adapt freely to data while suppressing unwante…

Active-set Newton-MR methods for nonconvex optimization problems with bound constraints
Ernesto G. Birgin, Geovani N. Grapiglia, Diaulas S. Marcondes
https://arxiv.org/abs/2508.20967

Active-set Newton-MR methods for nonconvex optimization problems with bound constraints
This paper presents active-set methods for minimizing nonconvex twice-continuously differentiable functions subject to bound constraints. Within the faces of the feasible set, we employ descent methods with Armijo line search, utilizing approximated Newton directions obtained through the Minimum Residual (MINRES) method. To escape the faces, we investigate the use of the Spectral Projected Gradient (SPG) method and a tailored variant of the Cubic Regularization of Newton's method for bound-cons…

The Stationary Klein-Gordon Equation with a Delta-like Source: A Generalized Function Approach
J. P. Ferreira, F. E. Barone, F. A. Barone
https://arxiv.org/abs/2508.18329 https:…

The Stationary Klein-Gordon Equation with a Delta-like Source: A Generalized Function Approach
This work aims to initiate a discussion on finding solutions to non-homoge\-neous differential equations in terms of generalized functions. For simplicity, we conduct the analysis within the specific context of the stationary Klein-Gordon equation with a point-like source, identifying a generalized function that solves such an equation and aligns with the solution obtained through the Fourier approach with dimensional regularization. In addition to being regular at the source singularity, a not…

Frequency Response Identification of Low-Order Systems: Finite-Sample Analysis
Arya Honarpisheh, Mario Sznaier
https://arxiv.org/abs/2508.17142 https://arx…

Frequency Response Identification of Low-Order Systems: Finite-Sample Analysis
This paper proposes a frequency-domain system identification method for learning low-order systems. The identification problem is formulated as the minimization of the l2 norm between the identified and measured frequency responses, with the nuclear norm of the Loewner matrix serving as a regularization term. This formulation results in an optimization problem that can be efficiently solved using standard convex optimization techniques. We derive an upper bound on the sampled-frequency complexi…

Replaced article(s) found for cs.NE. https://arxiv.org/list/cs.NE/new
[1/1]:
- Enhancing Generalization of Spiking Neural Networks Through Temporal Regularization
Boxuan Zhang, Zhen Xu, Kuan Tao

Chiral restoration temperature at finite spin density in QCD
Pracheta Singha, Victor E. Ambrus, Sergiu Busuioc, Aritra Bandyopadhyay, Maxim N. Chernodub
https://arxiv.org/abs/2508.20237

Chiral restoration temperature at finite spin density in QCD
We investigate the impact of a uniform spin density on the critical temperature of the chiral phase transition in finite-temperature QCD in the scope of the linear sigma model. We demonstrate that at a finite spin potential $μ_Σ$, corresponding to a finite spin density, the predictive power of the model is challenged by an ambiguity associated with a contribution of the vacuum renormalization term to the free energy. Eliminating the regularization freedom through comparison with recent low-$�…

Operator-differential expressions: regularization and completeness of the root functions
Sergey Buterin
https://arxiv.org/abs/2507.14545 https://

Operator-differential expressions: regularization and completeness of the root functions
We consider an operator-differential expression of the form $$ \ell y=\frac{d^m}{dx^m}\Big(By^{(n)}+Cy\Big), \quad 0

Introduction to Regularization and Learning Methods for Inverse Problems
Danielle Bednarski, Tim Roith
https://arxiv.org/abs/2508.18178 https://arxiv.org/p…

Introduction to Regularization and Learning Methods for Inverse Problems
These lecture notes evolve around mathematical concepts arising in inverse problems. We start by introducing inverse problems through examples such as differentiation, deconvolution, computed tomography and phase retrieval. This then leads us to the framework of well-posedness and first considerations regarding reconstruction and inversion approaches. The second chapter then first deals with classical regularization theory of inverse problems in Hilbert spaces. After introducing the pseudo-inve…

Improving U-Net Confidence on TEM Image Data with L2-Regularization, Transfer Learning, and Deep Fine-Tuning
Aiden Ochoa, Xinyuan Xu, Xing Wang
https://arxiv.org/abs/2507.16779

Improving U-Net Confidence on TEM Image Data with L2-Regularization, Transfer Learning, and Deep Fine-Tuning
With ever-increasing data volumes, it is essential to develop automated approaches for identifying nanoscale defects in transmission electron microscopy (TEM) images. However, compared to features in conventional photographs, nanoscale defects in TEM images exhibit far greater variation due to the complex contrast mechanisms and intricate defect structures. These challenges often result in much less labeled data and higher rates of annotation errors, posing significant obstacles to improving ma…

The Chapman-Enskog Divergence Problem in Plasma Transport: Structural Limitations and a Practical Regularization Approach
Justo Karell
https://arxiv.org/abs/2508.12390 https://

The Chapman-Enskog Divergence Problem in Plasma Transport: Structural Limitations and a Practical Regularization Approach
We calculate transport coefficients from the Chapman--Enskog expansion with BGK collision operators, obtaining exactly $κ= \frac{5nT}{2mν}$, and show that maximum entropy closure yields identical results when applied with the same collision operator. Through structural arguments, we suggest that this $1/ν$ divergence extends to other local collision operators of the form $\mathcal{L} = ν\hat{L}$, making the divergence fundamental to the Chapman--Enskog approach rather than a closure artifac…

On zero-order consistency residue and background pressure for the conservative SPH fluid dynamics
Feng Wang, Xiangyu Hu
https://arxiv.org/abs/2507.18210 https://

On zero-order consistency residue and background pressure for the conservative SPH fluid dynamics
As one of the major challenges for the conservative smoothed particle hydrodynamics (SPH) method, the zero-order consistency issue, although thought to be mitigated by the particle regularization scheme, such as the transport velocity formulation, significantly damps the flow in a long channel for both laminar and turbulent simulations. Building on this finding, this paper not only thoroughly analyzes the damping reason in this pressure-driven channel flow, but also relates this problem with th…

DeCRED: Decoder-Centric Regularization for Encoder-Decoder Based Speech Recognition
Alexander Polok, Santosh Kesiraju, Karel Bene\v{s}, Bolaji Yusuf, Luk\'a\v{s} Burget, Jan \v{C}ernock\'y
https://arxiv.org/abs/2508.08938

DeCRED: Decoder-Centric Regularization for Encoder-Decoder Based Speech Recognition
This paper presents a simple yet effective regularization for the internal language model induced by the decoder in encoder-decoder ASR models, thereby improving robustness and generalization in both in- and out-of-domain settings. The proposed method, Decoder-Centric Regularization in Encoder-Decoder (DeCRED), adds auxiliary classifiers to the decoder, enabling next token prediction via intermediate logits. Empirically, DeCRED reduces the mean internal LM BPE perplexity by 36.6% relative to 11…

Load-Balanced Diffusion Monte Carlo Method with Lattice Regularization
Kousuke Nakano, Sandro Sorella, Michele Casula
https://arxiv.org/abs/2508.12033 https://

Load-Balanced Diffusion Monte Carlo Method with Lattice Regularization
Ab initio quantum Monte Carlo (QMC) is a stochastic approach for solving the many-body Schrödinger equation without resorting to one-body approximations. QMC algorithms are readily parallelizable via ensembles of $N_w$ walkers, making them well suited to large-scale high-performance computing. Among the QMC techniques, Diffusion Monte Carlo (DMC) is widely regarded as the most reliable, since it provides the projection onto the ground state of a given Hamiltonian under the fixed-node approxima…

Quantifying and Visualizing Sim-to-Real Gaps: Physics-Guided Regularization for Reproducibility
Yuta Kawachi
https://arxiv.org/abs/2507.23445 https://arxiv…

Quantifying and Visualizing Sim-to-Real Gaps: Physics-Guided Regularization for Reproducibility
Simulation-to-real transfer using domain randomization for robot control often relies on low-gear-ratio, backdrivable actuators, but these approaches break down when the sim-to-real gap widens. Inspired by the traditional PID controller, we reinterpret its gains as surrogates for complex, unmodeled plant dynamics. We then introduce a physics-guided gain regularization scheme that measures a robot's effective proportional gains via simple real-world experiments. Then, we penalize any deviation o…

Robust Convolution Neural ODEs via Contractivity-promoting regularization
Muhammad Zakwan, Liang Xu, Giancarlo Ferrari-Trecate
https://arxiv.org/abs/2508.11432 https://

Robust Convolution Neural ODEs via Contractivity-promoting regularization
Neural networks can be fragile to input noise and adversarial attacks. In this work, we consider Convolutional Neural Ordinary Differential Equations (NODEs), a family of continuous-depth neural networks represented by dynamical systems, and propose to use contraction theory to improve their robustness. For a contractive dynamical system two trajectories starting from different initial conditions converge to each other exponentially fast. Contractive Convolutional NODEs can enjoy increase…

Scattered point measurement-based regularization for backward problems for fractional wave equations
Dakang Cen, Zhiyuan Li, Wenlong Zhang
https://arxiv.org/abs/2506.17575

Scattered point measurement-based regularization for backward problems for fractional wave equations
In this work, we are devoted to the reconstruction of an unknown initial value from the terminal data. The asymptotic and root-distribution properties of Mittag-Leffler functions are used to establish stability of the backward problem. Furthermore, we introduce a regularization method that effectively handles scattered point measurements contaminated with stochastic noise. Furthermore, we prove the stochastic convergence of our proposed regularization and provide an iterative algorithm to find …

Regularization of Nonlinear Inverse Problems -- From Functional Analysis to Data-Driven Approaches
Clemens Kirisits, Bochra Mejri, Sergei Pereverzev, Otmar Scherzer, Cong Shi
https://arxiv.org/abs/2506.17465

Regularization of Nonlinear Inverse Problems -- From Functional Analysis to Data-Driven Approaches
The focus of this book is on the analysis of regularization methods for solving \emph{nonlinear inverse problems}. Specifically, we place a strong emphasis on techniques that incorporate supervised or unsupervised data derived from prior experiments. This approach enables the integration of data-driven insights into the solution of inverse problems governed by physical models. \emph{Inverse problems}, in general, aim to uncover the \emph{inner mechanisms} of an observed system based on indirect…

SPIRiT Regularization: Parallel MRI with a Combination of Sensitivity Encoding and Linear Predictability
Nicholas Dwork, Alex McManus, Stephen Becker, Gennifer T. Smith
https://arxiv.org/abs/2508.15132

SPIRiT Regularization: Parallel MRI with a Combination of Sensitivity Encoding and Linear Predictability
Accelerated Magnetic Resonance Imaging (MRI) permits high quality images from fewer samples that can be collected with a faster scan. Two established methods for accelerating MRI include parallel imaging and compressed sensing. Two types of parallel imaging include linear predictability, which assumes that the Fourier samples are linearly related, and sensitivity encoding, which incorporates a priori knowledge of the sensitivity maps. In this work, we combine compressed sensing with both types …

Game-Theoretic Gradient Control for Robust Neural Network Training
Maria Zaitseva, Ivan Tomilov, Natalia Gusarova
https://arxiv.org/abs/2507.19143 https://…

Game-Theoretic Gradient Control for Robust Neural Network Training
Feed-forward neural networks (FFNNs) are vulnerable to input noise, reducing prediction performance. Existing regularization methods like dropout often alter network architecture or overlook neuron interactions. This study aims to enhance FFNN noise robustness by modifying backpropagation, interpreted as a multi-agent game, and exploring controlled target variable noising. Our "gradient dropout" selectively nullifies hidden layer neuron gradients with probability 1 - p during backpropagation, w…

An Improved Solution to the Two Normal Means Problem via Regularization
Yang Liu, Jonathan P. Williams
https://arxiv.org/abs/2508.13012 https://arxiv.org/p…

An Improved Solution to the Two Normal Means Problem via Regularization
The many-normal-means problem is a classic example that motivates the development of many important inferential procedures in the history of statistics. In this short note, we consider a further special case of the problem, which involves only two normally distributed data points with a constraint that the pair of means are not too far apart from one another. Starting with a regularized ML estimator, we construct a novel possibilistic IM for marginal inference on one of the two means. Not only …

Hyperspherical Variational Autoencoders Using Efficient Spherical Cauchy Distribution
Lukas Sablica, Kurt Hornik
https://arxiv.org/abs/2506.21278 https://

Hyperspherical Variational Autoencoders Using Efficient Spherical Cauchy Distribution
We propose a novel variational autoencoder (VAE) architecture that employs a spherical Cauchy (spCauchy) latent distribution. Unlike traditional Gaussian latent spaces or the widely used von Mises-Fisher (vMF) distribution, spCauchy provides a more natural hyperspherical representation of latent variables, better capturing directional data while maintaining flexibility. Its heavy-tailed nature prevents over-regularization, ensuring efficient latent space utilization while offering a more expres…

Fast Flexible LSQR with a Hybrid Variant for Efficient Large-Scale Regularization
Eva Miku\v{s}ov\'a, Iveta Hn\v{e}tynkov\'a
https://arxiv.org/abs/2506.19666

Fast Flexible LSQR with a Hybrid Variant for Efficient Large-Scale Regularization
A wide range of applications necessitates solving large-scale ill-posed problems contaminated by noise. Krylov subspace regularization methods are particularly advantageous in this context, as they rely solely on matrix-vector multiplication. Among the most widely used techniques are LSQR and CGLS, both of which can be extended with flexible preconditioning to enforce solution properties such as nonnegativity or sparsity. Flexible LSQR (FLSQR) can also be further combined with direct methods to…

Ill-Posedness in Limited Discrete Fourier Inversion and Regularization for Quasi Distributions in LaMET
Ao-Sheng Xiong, Jun Hua, Ting Wei, Fu-Sheng Yu, Qi-An Zhang, Yong Zheng
https://arxiv.org/abs/2506.16689

Ill-Posedness in Limited Discrete Fourier Inversion and Regularization for Quasi Distributions in LaMET
We systematically investigated the limited inverse discrete Fourier transform of the quasi distributions from the perspective of inverse problem theory. This transformation satisfies two of Hadamard's well-posedness criteria, existence and uniqueness of solutions, but critically violates the stability requirement, exhibiting exponential sensitivity to input perturbations. To address this instability, we implemented Tikhonov regularization with L-curve optimized parameters, demonstrating its val…

Online Algorithms for Recovery of Low-Rank Parameter Matrix in Non-stationary Stochastic Systems
Yanxin Fu, Junbao Zhou, Yu Hu, Wenxiao Zhao
https://arxiv.org/abs/2506.19299

Online Algorithms for Recovery of Low-Rank Parameter Matrix in Non-stationary Stochastic Systems
This paper presents a two-stage online algorithm for recovery of low-rank parameter matrix in non-stationary stochastic systems. The first stage applies the recursive least squares (RLS) estimator combined with its singular value decomposition to estimate the unknown parameter matrix within the system, leveraging RLS for adaptability and SVD to reveal low-rank structure. The second stage introduces a weighted nuclear norm regularization criterion function, where adaptive weights derived from th…

A smoothed proximal trust-region algorithm for nonconvex optimization problems with $L^p$-regularization, $p\in (0,1)$
Harbir Antil, Anna Lentz
https://arxiv.org/abs/2508.15446 …

A smoothed proximal trust-region algorithm for nonconvex optimization problems with $L^p$-regularization, $p\in (0,1)$
We investigate a trust-region algorithm to solve a nonconvex optimization problem with $L^p$-regularization for $p\in(0,1)$. The algorithm relies on descent properties of a so-called generalized Cauchy point that can be obtained efficiently by a line search along a suitable proximal path. To handle the nonconvexity and nonsmoothness of the $L^p$-pseudonorm, we replace it by a smooth approximation and construct a convex upper bound of that approximation. This enables us to use results of a trust…

Towards Reliable WMH Segmentation under Domain Shift: An Application Study using Maximum Entropy Regularization to Improve Uncertainty Estimation
Franco Matzkin, Agostina Larrazabal, Diego H Milone, Jose Dolz, Enzo Ferrante
https://arxiv.org/abs/2506.14497

Towards Reliable WMH Segmentation under Domain Shift: An Application Study using Maximum Entropy Regularization to Improve Uncertainty Estimation
Accurate segmentation of white matter hyperintensities (WMH) is crucial for clinical decision-making, particularly in the context of multiple sclerosis. However, domain shifts, such as variations in MRI machine types or acquisition parameters, pose significant challenges to model calibration and uncertainty estimation. This study investigates the impact of domain shift on WMH segmentation by proposing maximum-entropy regularization techniques to enhance model calibration and uncertainty estimat…

Random feature approximation for general spectral methods
Mike Nguyen, Nicole M\"ucke
https://arxiv.org/abs/2506.16283 https://a…

Random feature approximation for general spectral methods
Random feature approximation is arguably one of the most widely used techniques for kernel methods in large-scale learning algorithms. In this work, we analyze the generalization properties of random feature methods, extending previous results for Tikhonov regularization to a broad class of spectral regularization techniques. This includes not only explicit methods but also implicit schemes such as gradient descent and accelerated algorithms like the Heavy-Ball and Nesterov method. Through this…

Numerical analysis of scattered point measurement-based regularization for backward problems for fractional wave equations
Dakang Cen, Zhiyuan Li, Wenlong Zhang
https://arxiv.org/abs/2506.18948

Numerical analysis of scattered point measurement-based regularization for backward problems for fractional wave equations
In this work, our aim is to reconstruct the unknown initial value from terminal data. We develop a numerical framework on nonuniform time grids for fractional wave equations under the lower regularity assumptions. Then, we introduce a regularization method that effectively handles scattered point measurements contaminated with stochastic noise. The optimal error estimates of stochastic convergence not only balance discretization errors, the noise, and the number of observation points, but also …

Dynamic mode decomposition for detecting transient activity via sparsity and smoothness regularization
Yutaro Tanaka, Hiroya Nakao
https://arxiv.org/abs/2508.10266 https://

Dynamic mode decomposition for detecting transient activity via sparsity and smoothness regularization
Dynamic Mode Decomposition (DMD) is a data-driven modal decomposition technique that extracts coherent spatio-temporal structures from high-dimensional time-series data. By decomposing the dynamics into a set of modes, each associated with a single frequency and a growth rate, DMD enables a natural modal decomposition and dimensionality reduction of complex dynamical systems. However, when DMD is applied to transient dynamics, even if a large number of modes are used, it remains difficult to in…

GRASP: Grouped Regression with Adaptive Shrinkage Priors
Shu Yu Tew, Daniel F. Schmidt, Mario Boley
https://arxiv.org/abs/2506.18092 https://

GRASP: Grouped Regression with Adaptive Shrinkage Priors
We introduce GRASP, a simple Bayesian framework for regression with grouped predictors, built on the normal beta prime (NBP) prior. The NBP prior is an adaptive generalization of the horseshoe prior with tunable hyperparameters that control tail behavior, enabling a flexible range of sparsity, from strong shrinkage to ridge-like regularization. Unlike prior work that introduced the group inverse-gamma gamma (GIGG) prior by decomposing the NBP prior into structured hierarchies, we show that dire…

On the Convergence Rates of Iterative Regularization Algorithms for Composite Bi-Level Optimization
Shimrit Shtern, Adeolu Taiwo
https://arxiv.org/abs/2506.16382

On the Convergence Rates of Iterative Regularization Algorithms for Composite Bi-Level Optimization
This paper investigates iterative methods for solving bi-level optimization problems where both inner and outer functions have a composite structure. We provide novel theoretical results, including the first convergence rate analysis for the Iteratively REgularized Proximal Gradient (IRE-PG) method, a variant of Solodov's algorithm. Our results establish simultaneous convergence rates for the inner and outer functions, highlighting the inherent trade-offs between their respective convergence ra…

Global Convergence of Iteratively Reweighted Least Squares for Robust Subspace Recovery
Gilad Lerman, Kang Li, Tyler Maunu, Teng Zhang
https://arxiv.org/abs/2506.20533

Global Convergence of Iteratively Reweighted Least Squares for Robust Subspace Recovery
Robust subspace estimation is fundamental to many machine learning and data analysis tasks. Iteratively Reweighted Least Squares (IRLS) is an elegant and empirically effective approach to this problem, yet its theoretical properties remain poorly understood. This paper establishes that, under deterministic conditions, a variant of IRLS with dynamic smoothing regularization converges linearly to the underlying subspace from any initialization. We extend these guarantees to affine subspace estima…

An Analysis of the Riemann Problem for a $2 \times 2$ System of Keyfitz-Kranzer Type Conservation Laws Using Shadow Waves and Dafermos Regularization
Josh Culver, Aubrey Ayres, Evan Halloran, Ryan Lin, Emily Peng, Charis Tsikkou
https://arxiv.org/abs/2508.05927

An Analysis of the Riemann Problem for a $2 \times 2$ System of Keyfitz-Kranzer Type Conservation Laws Using Shadow Waves and Dafermos Regularization
We consider a system of two conservation laws and provide a detailed description of both classical and non-classical self-similar Riemann solutions. In particular, we demonstrate the existence of overcompressive delta shocks as singular limits of the Dafermos regularization of the system. The system is chosen for its minimal yet representative structure, which captures the essential features of transport dynamics under density constraints. Our analysis is carried out using blow-up techniques wi…

Embedding $\mathrm{SL}(2,\mathbb{C})/\mathbb{Z}_2$ in Complex Riemannian Geometry
John. W. Moffat, Ethan. J. Thompson
https://arxiv.org/abs/2506.19158 http…

Embedding $\mathrm{SL}(2,\mathbb{C})/\mathbb{Z}_2$ in Complex Riemannian Geometry
We present a unified framework demonstrating how the spinor complex Lorentz group SL(2,C)/Z\_2 is realized as a canonical subgroup within a four-dimensional complex Riemannian manifold. Building on the complex, holomorphic metric extension and contour-integration regularization of classical singularities, we show that promoting the metric to a complex-valued tensor on a complex 4-fold enlarges the frame bundle to SO(4,C). Its spin double cover factorizes as a product of two independent SL(2,C) …

On existence of a variational regularization parameter under Morozov's discrepancy principle
Liang Ding, Long Li, Weimin Han, Wei Wang
https://arxiv.org/abs/2506.11397

On existence of a variational regularization parameter under Morozov's discrepancy principle
Morozov's discrepancy principle is commonly adopted in Tikhonov regularization for choosing the regularization parameter. Nevertheless, for a general non-linear inverse problem, the discrepancy $\|F(x_α^δ)-y^δ\|_Y$ does not depend continuously on $α$ and it is questionable whether there exists a regularization parameter $α$ such that $τ_1δ\leq \|F(x_α^δ)-y^δ\|_Y\leq τ_2 δ$ $(1\le τ_1<τ_2)$. In this paper, we prove the existence of $α$ under Morozov's discrepan…

$\ell_{1}^{2}-\eta\ell_{2}^{2}$ regularization for sparse recovery
Long Li, Liang Ding
https://arxiv.org/abs/2506.11372 https://arxiv…

$\ell_{1}^{2}-η\ell_{2}^{2}$ regularization for sparse recovery
This paper presents a regularization technique incorporating a non-convex and non-smooth term, $\ell_{1}^{2}-η\ell_{2}^{2}$, with parameters $0<η\leq 1$ designed to address ill-posed linear problems that yield sparse solutions. We explore the existence, stability, and convergence of the regularized solution, demonstrating that the $\ell_{1}^{2}-η\ell_{2}^{2}$ regularization is well-posed and results in sparse solutions. Under suitable source conditions, we establish a convergence rate of $\m…

Bayesian Inference for Left-Truncated Log-Logistic Distributions for Time-to-event Data Analysis
Fahad Mostafa, Md Rejuan Haque, Md Mostafijur Rahman, Farzana Nasrin
https://arxiv.org/abs/2506.17852

Bayesian Inference for Left-Truncated Log-Logistic Distributions for Time-to-event Data Analysis
Parameter estimation is a foundational step in statistical modeling, enabling us to extract knowledge from data and apply it effectively. Bayesian estimation of parameters incorporates prior beliefs with observed data to infer distribution parameters probabilistically and robustly. Moreover, it provides full posterior distributions, allowing uncertainty quantification and regularization, especially useful in small or truncated samples. Utilizing the left-truncated log-logistic (LTLL) distributi…

A Cubic Regularization Method for Multiobjective Optimization
Douglas S. Gon\c{c}alves, Max L. N. Gon\c{c}alves, Jefferson G. Melo
https://arxiv.org/abs/2506.08181

A Cubic Regularization Method for Multiobjective Optimization
This work introduces a new cubic regularization method for nonconvex unconstrained multiobjective optimization problems. At each iteration of the method, a model associated with the cubic regularization of each component of the objective function is minimized. This model allows approximations for the first- and second-order derivatives, which must satisfy suitable error conditions. One interesting feature of the proposed algorithm is that the regularization parameter of the model and the accura…

Neural operators for solving nonlinear inverse problems
Otmar Scherzer, Thi Lan Nhi Vu, Jikai Yan
https://arxiv.org/abs/2508.19347 https://arxiv.org/pdf/25…

Neural operators for solving nonlinear inverse problems
We consider solving a probably infinite dimensional operator equation, where the operator is not modeled by physical laws but is specified indirectly via training pairs of the input-output relation of the operator. Neural operators have proven to be efficient to approximate operators with such information. In this paper, we analyze Tikhonov regularization with neural operators as surrogates for solving ill-posed operator equations. The analysis is based on balancing approximation errors of neur…

A Generalized Framework for Approximate Co-Sufficient Sampling
Jie Xie, Dongming Huang
https://arxiv.org/abs/2506.12334 https://arxiv…

A Generalized Framework for Approximate Co-Sufficient Sampling
Approximate co-sufficient sampling (aCSS) offers a principled route to hypothesis testing when null distributions are unknown, yet current implementations are confined to maximum likelihood estimators with smooth or linear regularization and provide little theoretical insight into power. We present a generalized framework that widens the scope of the aCSS method to embrace nonlinear regularization, such as group lasso and nonconvex penalties, as well as robust and nonparametric estimators. More…

Learned Regularization for Microwave Tomography
Bowen Tong, Hao Chen, Shaorui Guo, Dong Liu
https://arxiv.org/abs/2508.08114 https://arxiv.org/pdf/2508.081…

Learned Regularization for Microwave Tomography
Microwave Tomography (MWT) aims to reconstruct the dielectric properties of tissues from measured scattered electromagnetic fields. This inverse problem is highly nonlinear and ill-posed, posing significant challenges for conventional optimization-based methods, which, despite being grounded in physical models, often fail to recover fine structural details. Recent deep learning strategies, including end-to-end and post-processing networks, have improved reconstruction quality but typically requ…

Learning Acceleration Algorithms for Fast Parametric Convex Optimization with Certified Robustness
Rajiv Sambharya, Jinho Bok, Nikolai Matni, George Pappas
https://arxiv.org/abs/2507.16264

Learning Acceleration Algorithms for Fast Parametric Convex Optimization with Certified Robustness
We develop a machine-learning framework to learn hyperparameter sequences for accelerated first-order methods (e.g., the step size and momentum sequences in accelerated gradient descent) to quickly solve parametric convex optimization problems with certified robustness. We obtain a strong form of robustness guarantee -- certification of worst-case performance over all parameters within a set after a given number of iterations -- through regularization-based training. The regularization term is …

Inverse source problem with a posteriori interior measurements for space-time fractional diffusion equations
Kai Yu, Zhiyuan Li, Yikan Liu
https://arxiv.org/abs/2506.21070

Inverse source problem with a posteriori interior measurements for space-time fractional diffusion equations
This paper investigates an inverse source problem for space-time fractional diffusion equations from a posteriori interior measurements. The uniqueness result is established by the memory effect of fractional derivatives and the unique continuation property. For the numerical reconstruction, the inverse problem is reformulated as an optimization problem with the Tikhonov regularization. We use the Levenberg-Marquardt method to identity the unknown source from noisy measurements. Finally, we giv…

One loop in $D=11$ vs $D=10$: a mismatch
Aviral Aggarwal, Subhroneel Chakrabarti, Steven Weilong Hsia, Ahmed Rakin Kamal, Linus Wulff
https://arxiv.org/abs/2506.16391

One loop in $D=11$ vs $D=10$: a mismatch
The one-loop correction to eleven-dimensional supergravity involves a term $t_8t_8R^4$, with four Riemann tensors. With a suitable UV regularization, this term is expected to reduce to a similar one-loop term present in the type IIA effective action. We show that, while this is indeed the case in the NSNS sector, it fails when one includes the RR fields. Specifically, we identify 4-point couplings involving the dilaton, the graviton and two RR one-forms which lead to amplitudes that disagree wi…

Understanding Learning Invariance in Deep Linear Networks
Hao Duan, Guido Mont\'ufar
https://arxiv.org/abs/2506.13714 https://arx…

Understanding Learning Invariance in Deep Linear Networks
Equivariant and invariant machine learning models exploit symmetries and structural patterns in data to improve sample efficiency. While empirical studies suggest that data-driven methods such as regularization and data augmentation can perform comparably to explicitly invariant models, theoretical insights remain scarce. In this paper, we provide a theoretical comparison of three approaches for achieving invariance: data augmentation, regularization, and hard-wiring. We focus on mean squared e…

Regularization for time-dependent inverse problems: Geometry of Lebesgue-Bochner spaces and algorithms
Gesa Sarnighausen, Thorsten Hohage, Martin Burger, Andreas Hauptmann, Anne Wald
https://arxiv.org/abs/2506.11291

Regularization for time-dependent inverse problems: Geometry of Lebesgue-Bochner spaces and algorithms
We consider time-dependent inverse problems in a mathematical setting using Lebesgue-Bochner spaces. Such problems arise when one aims to recover a function from given observations where the function or the data depend on time. Lebesgue-Bochner spaces allow to easily incorporate the different nature of time and space. In this manuscript, we present two different regularization methods in Lebesgue Bochner spaces: 1. classical Tikhonov regularization in Banach spaces 2. variational regulari…

Dictionary Learning Based Regularization in Quantitative MRI: A Nested Alternating Optimization Framework
Guozhi Dong, Michael Hinterm\"uller, Clemens Sirotenko
https://arxiv.org/abs/2506.11977

Dictionary Learning Based Regularization in Quantitative MRI: A Nested Alternating Optimization Framework
In this article, we propose a novel regularization method for a class of nonlinear inverse problems that is inspired by an application in quantitative magnetic resonance imaging (qMRI). The latter is a special instance of a general dynamical image reconstruction technique, wherein a radio-frequency pulse sequence gives rise to a time-discrete physics-based mathematical model which acts as a side constraint in our inverse problem. To enhance reconstruction quality, we employ dictionary learning …

Variational Learning Finds Flatter Solutions at the Edge of Stability
Avrajit Ghosh, Bai Cong, Rio Yokota, Saiprasad Ravishankar, Rongrong Wang, Molei Tao, Mohammad Emtiyaz Khan, Thomas M\"ollenhoff
https://arxiv.org/abs/2506.12903

Variational Learning Finds Flatter Solutions at the Edge of Stability
Variational Learning (VL) has recently gained popularity for training deep neural networks and is competitive to standard learning methods. Part of its empirical success can be explained by theories such as PAC-Bayes bounds, minimum description length and marginal likelihood, but there are few tools to unravel the implicit regularization in play. Here, we analyze the implicit regularization of VL through the Edge of Stability (EoS) framework. EoS has previously been used to show that gradient d…

D-ideal of generic mass banana integrals in dimensional regularization
Wojciech Flieger
https://arxiv.org/abs/2508.04309 https://arxiv.org/pdf/2508.04309…

D-ideal of generic mass banana integrals in dimensional regularization
We present a set of $\ell + 3$ simple differential operators and prove that they annihilate an $\ell$-loop generic mass banana integral in dimensional regularization. We study the singular locus of the ideal generated by these operators and show that it is contained in the set of Landau singularities of the first and second type. Through the Macaulay matrix method, we calculate the corresponding holonomic rank up to $\ell = 8$, obtaining $2^{\ell +1}-1$, which agrees with the number of master i…

SVD method for sparse recovery
Long Li, Liang Ding
https://arxiv.org/abs/2506.11379 https://arxiv.org/pdf/2506.11379

SVD method for sparse recovery
Sparsity regularization has garnered significant interest across multiple disciplines, including statistics, imaging, and signal processing. Standard techniques for addressing sparsity regularization include iterative soft thresholding algorithms and their accelerated variants. However, these algorithms rely on Landweber iteration, which can be computationally intensive. Therefore, there is a pressing need to develop a more efficient algorithm for sparsity regularization. The Singular Value Dec…

A Dual Optimization View to Empirical Risk Minimization with f-Divergence Regularization
Francisco Daunas, I\~naki Esnaola, Samir M. Perlaza
https://arxiv.org/abs/2508.03314 htt…

A Dual Optimization View to Empirical Risk Minimization with f-Divergence Regularization
The dual formulation of empirical risk minimization with f-divergence regularization (ERM-fDR) is introduced. The solution of the dual optimization problem to the ERM-fDR is connected to the notion of normalization function introduced as an implicit function. This dual approach leverages the Legendre-Fenchel transform and the implicit function theorem to provide a nonlinear ODE expression to the normalization function. Furthermore, the nonlinear ODE expression and its properties provide a compu…

Automatic reproducing kernel and regularization for learning convolution kernels
Haibo Li, Fei Lu
https://arxiv.org/abs/2507.11944 https://

Automatic reproducing kernel and regularization for learning convolution kernels
Learning convolution kernels in operators from data arises in numerous applications and represents an ill-posed inverse problem of broad interest. With scant prior information, kernel methods offer a natural nonparametric approach with regularization. However, a major challenge is to select a proper reproducing kernel, especially as operators and data vary. We show that the input data and convolution operator themselves induce an automatic, data-adaptive RKHS (DA-RKHS), obviating manual kernel …

A trust-region method for optimal control of ODEs with continuous-or-off controls and TV regularization
Markus Friedemann, Gerd Wachsmuth
https://arxiv.org/abs/2508.10692 https:…

A trust-region method for optimal control of ODEs with continuous-or-off controls and TV regularization
A solution algorithm for a special class of optimal control problems subject to an ordinary differential equation is proposed. The controls possess a continuous-or-off structure and are priced by a convex function. Additionally a total variation regularization is applied to penalize switches. Our solution method combines a trust-region method and a proximal gradient method. The subproblems are solved via Bellman's optimality principle. Convergence with respect to a criticality measure is proven…

Addendum on data driven regularization by projection
Martin Hanke, Otmar Scherzer
https://arxiv.org/abs/2508.07709 https://arxiv.org/pdf/2508.07709

Addendum on data driven regularization by projection
We study the stability of regularization by projection for solving linear inverse problems if the forward operator is given indirectly but specified via some input-output training pairs. We extend the approach in "Data driven regularization by projection" (Aspri, Korolev, and Scherzer; Inverse Problems; 36 (2020), 125009) to data pairs, which are noisy and, possibly, linearly dependent.

Replaced article(s) found for math.OC. https://arxiv.org/list/math.OC/new
[1/1]:
- Orthogonal Constrained Minimization with Tensor $\ell_{2,p}$ Regularization for HSI Denoising and...
Xiaoxia Liu, Shijie Yu, Jian Lu, Xiaojun Chen

A space-time interface-fitted method for moving-subdomain distributed control problems with energy regularization
Quang Huy Nguyen, Phuong Cuc Hoang, Van Chien Le, Thi Thanh Mai Ta
https://arxiv.org/abs/2506.10924

A space-time interface-fitted method for moving-subdomain distributed control problems with energy regularization
This paper investigates a space-time interface-fitted approximation of a moving-interface optimal control problem with energy regularization. We reformulate the optimality conditions into a variational problem involving both the state and adjoint. This problem is shown to be equivalent to our optimal control problem. Based on fully unstructured, space-time interface-fitted meshes, we propose and analyze a Petrov-Galerkin approximation of the problem. An optimal error estimate with respect to a …

Learning-Enhanced Variational Regularization for Electrical Impedance Tomography via \Calderon's Method
Kai Li, Kwancheol Shin, Zhi Zhou
https://arxiv.org/abs/2507.06114

Learning-Enhanced Variational Regularization for Electrical Impedance Tomography via \Calderon's Method
This paper aims to numerically solve the two-dimensional electrical impedance tomography (EIT) with Cauchy data. This inverse problem is highly challenging due to its severe ill-posed nature and strong nonlinearity, which necessitates appropriate regularization strategies. Choosing a regularization approach that effectively incorporates the \textit{a priori} information of the conductivity distribution (or its contrast) is therefore essential. In this work, we propose a deep learning-based meth…

State-based approach to the numerical solution of Dirichlet boundary optimal control problems for the Laplace equation
Ulrich Langer, Richard L\"oscher, Olaf Steinbach, Huidong Yang
https://arxiv.org/abs/2507.11646

State-based approach to the numerical solution of Dirichlet boundary optimal control problems for the Laplace equation
We investigate the Dirichlet boundary control of the Laplace equation, considering the control in $H^{1/2}(\partial Ω)$, which is the natural space for Dirichlet data when the state belongs to $H^1(Ω)$. The cost of the control is measured in the $H^{1/2}(\partial Ω)$ norm that also plays the role of the regularization term. We discuss regularization and finite element error estimates enabling us to derive an optimal relation between the finite element mesh size $h$ and the regularization par…

A Monotonicity-Based Regularization Approach to Shape Reconstruction for the Helmholtz Equation
Sarah Eberle-Blick, Bastian Harrach, Xianchao Wang
https://arxiv.org/abs/2508.11439

A Monotonicity-Based Regularization Approach to Shape Reconstruction for the Helmholtz Equation
We consider an inverse boundary value problem for determining unknown scatterers, which is governed by the Helmholtz equation in a bounded domain. To address this, we develop a novel convex data-fitting formulation that is capable of reconstructing the shape of the unknown scatterers.Our formulation is based on a monotonicity relation between the scattering index and boundary measurements. We use this relation to obtain a pixel-wise constraint on the unknown scattering index, and then minimize …

A derivative-free regularization algorithm for equality constrained nonlinear least squares problems
Xi Chen, Jinyan Fan
https://arxiv.org/abs/2507.05623 h…

A derivative-free regularization algorithm for equality constrained nonlinear least squares problems
In this paper, we study the equality constrained nonlinear least squares problem, where the Jacobian matrices of the objective function and constraints are unavailable or expensive to compute. We approximate the Jacobian matrices via orthogonal spherical smoothing and propose a derivative-free regularization algorithm for solving the problem. At each iteration, a regularized augmented Lagrangian subproblem is solved to obtain a Newton-like step. If a sufficient decrease in the merit function of…

Geometric flow regularization in latent spaces for smooth dynamics with the efficient variations of curvature
Andrew Gracyk
https://arxiv.org/abs/2506.09679

Geometric flow regularization in latent spaces for smooth dynamics with the efficient variations of curvature
We design strategies in nonlinear geometric analysis to temper the effects of adversarial learning for sufficiently smooth data of numerical method-type dynamics in encoder-decoder methods, variational and deterministic, through the use of geometric flow regularization. We augment latent spaces with geometric flows to control structure. Our techniques rely on adaptations of curvature and Ricci flow. We invent new geometric flows or discover them neurally and non-parametrically. All of our flows…

Low-rankness and Smoothness Meet Subspace: A Unified Tensor Regularization for Hyperspectral Image Super-resolution
Jun Zhang, Chao Yi, Mingxi Ma, Chao Wang
https://arxiv.org/abs/2508.03049

Low-rankness and Smoothness Meet Subspace: A Unified Tensor Regularization for Hyperspectral Image Super-resolution
Hyperspectral image super-resolution (HSI-SR) has emerged as a challenging yet critical problem in remote sensing. Existing approaches primarily focus on regularization techniques that leverage low-rankness and local smoothness priors. Recently, correlated total variation has been introduced for tensor recovery, integrating these priors into a single regularization framework. Direct application to HSI-SR, however, is hindered by the high spectral dimensionality of hyperspectral data. In this pa…

Regularization of non-overshooting quasi-continuous sliding mode control for chattering suppression at equilibrium
Michael Ruderman, Denis Efimov
https://arxiv.org/abs/2506.05283 …

Regularization of non-overshooting quasi-continuous sliding mode control for chattering suppression at equilibrium
Robust finite-time feedback controller introduced for the second-order systems in [1] can be seen as a non-overshooting quasi-continuous sliding mode control. The paper proposes a regularization scheme to suppress inherent chattering due to discontinuity of the control [1] in the origin, in favor of practical applications. A detailed analysis with ISS and iISS proofs are provided along with supporting numerical results.

Rank Inspired Neural Network for solving linear partial differential equations
Wentao Peng, Yunqing Huang, Nianyu Yi
https://arxiv.org/abs/2506.17654 https…

Rank Inspired Neural Network for solving linear partial differential equations
This paper proposes a rank inspired neural network (RINN) to tackle the initialization sensitivity issue of physics informed extreme learning machines (PIELM) when numerically solving partial differential equations (PDEs). Unlike PIELM which randomly initializes the parameters of its hidden layers, RINN incorporates a preconditioning stage. In this stage, covariance-driven regularization is employed to optimize the orthogonality of the basis functions generated by the last hidden layer. The key…

Optimal control of the Poisson equation with transport regularization: Properties of optimal transport plans and transport map
Christian Meyer, Gerd Wachsmuth
https://arxiv.org/abs/2506.02808

Optimal control of the Poisson equation with transport regularization: Properties of optimal transport plans and transport map
An optimal control problem in the space of Borel measures governed by the Poisson equation is investigated. The characteristic feature of the problem under consideration is the Tikhonov regularization term in form of the transportation distance of the control to a given prior. Existence of optimal solutions is shown and first-order necessary optimality conditions are derived. The latter are used to deduce structural a priori information about the optimal control and its support based on propert…

On the convergence of iterative regularization method assisted by the graph Laplacian with early stopping
Harshit Bajpai, Gaurav Mittal, Ankik Kumar Giri
https://arxiv.org/abs/2506.23483

On the convergence of iterative regularization method assisted by the graph Laplacian with early stopping
We present a data-assisted iterative regularization method for solving ill-posed inverse problems in Hilbert space settings. The proposed approach, termed \texttt{IRMGL+\(Ψ\)}, integrates classical iterative techniques with a data-driven regularization term realized through an iteratively updated graph Laplacian. Our method commences by computing a preliminary solution using any suitable reconstruction method, which then serves as the basis for constructing the initial graph Laplacian. The sol…

Diff-ANO: Towards Fast High-Resolution Ultrasound Computed Tomography via Conditional Consistency Models and Adjoint Neural Operators
Xiang Cao, Qiaoqiao Ding, Xinliang Liu, Lei Zhang, Xiaoqun Zhang
https://arxiv.org/abs/2507.16344

Diff-ANO: Towards Fast High-Resolution Ultrasound Computed Tomography via Conditional Consistency Models and Adjoint Neural Operators
Ultrasound Computed Tomography (USCT) constitutes a nonlinear inverse problem with inherent ill-posedness that can benefit from regularization through diffusion generative priors. However, traditional approaches for solving Helmholtz equation-constrained USCT face three fundamental challenges when integrating these priors: PDE-constrained gradient computation, discretization-induced approximation errors, and computational imbalance between neural networks and numerical PDE solvers. In this work…