Tootfinder

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 …

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…

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 cs.LG. https://arxiv.org/list/cs.LG/new/
[1/7]:
Effective Regularization Through Loss-Function Metalearning
https://…

Uncertainty-aware Cross-training for Semi-supervised Medical Image Segmentation
Kaiwen Huang, Tao Zhou, Huazhu Fu, Yizhe Zhang, Yi Zhou, Xiao-Jun Wu
https://arxiv.org/abs/2508.09014

Uncertainty-aware Cross-training for Semi-supervised Medical Image Segmentation
Semi-supervised learning has gained considerable popularity in medical image segmentation tasks due to its capability to reduce reliance on expert-examined annotations. Several mean-teacher (MT) based semi-supervised methods utilize consistency regularization to effectively leverage valuable information from unlabeled data. However, these methods often heavily rely on the student model and overlook the potential impact of cognitive biases within the model. Furthermore, some methods employ co-tr…

Diffusion prior as a direct regularization term for FWI
Yuke Xie, Herv\'e Chauris, Nicolas Desassis
https://arxiv.org/abs/2506.10141 https://

Diffusion prior as a direct regularization term for FWI
Diffusion models have recently shown promise as powerful generative priors for inverse problems. However, conventional applications require solving the full reverse diffusion process and operating on noisy intermediate states, which poses challenges for physics-constrained computational seismic imaging. In particular, such instability is pronounced in non-linear solvers like those used in Full Waveform Inversion (FWI), where wave propagation through noisy velocity fields can lead to numerical a…

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…

Admissibility of Stein Shrinkage for Batch Normalization in the Presence of Adversarial Attacks
Sofia Ivolgina, P. Thomas Fletcher, Baba C. Vemuri
https://arxiv.org/abs/2507.08261

Admissibility of Stein Shrinkage for Batch Normalization in the Presence of Adversarial Attacks
Batch normalization (BN) is a ubiquitous operation in deep neural networks used primarily to achieve stability and regularization during network training. BN involves feature map centering and scaling using sample means and variances, respectively. Since these statistics are being estimated across the feature maps within a batch, this problem is ideally suited for the application of Stein's shrinkage estimation, which leads to a better, in the mean-squared-error sense, estimate of the mean and …

The thermal backreaction of a scalar field in de Sitter spacetime
Nikos Irges, Antonis Kalogirou, Fotis Koutroulis
https://arxiv.org/abs/2507.08774 https:/…

The thermal backreaction of a scalar field in de Sitter spacetime
We argue that a scalar field in de Sitter spacetime should feel explicit thermal effects associated with its curvature. Starting from the Bunch-Davies vacuum and a scalar field with small mass compared to the de Sitter curvature, we use the thermo-field dynamics formalism in order to expose these thermal effects. We compute the thermal Wightman function connecting two spacetime points and from it, via the point-splitting regularization technique, the renormalized thermal energy-momentum tensor.…

A New Method of Deriving Doppler Velocities for Solar Orbiter SPICE
J. E. Plowman, D. M. Hassler, M. E. Molnar, A. K. Shrivastav, T. Varesano, F. Auch\`ere, A. Fludra, T. A. Kucera, T. J. Wang, Y. Zhu
https://arxiv.org/abs/2508.09121

A New Method of Deriving Doppler Velocities for Solar Orbiter SPICE
This paper presents a follow-up to previous work on correcting PSF-induced Doppler artifacts in observations by the SPICE spectrograph on Solar Orbiter. In a previous paper, we demonstrated correction of these artifacts in the $y-λ$ plane with PSF Regularization, treating the forward problem with a method based on large sparse matrix inversion. It has since been found that similar apparent artifacts are also present in the $x-λ$ direction, i.e., across adjacent slit positions. This is difficu…

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…

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…

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…

This https://arxiv.org/abs/2409.17464 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Computation of $\langle Φ^2\rangle$ and quantum fluxes at the polar interior of a spinning black hole
Renormalization of physical quantities for quantum field theories in curved spacetimes can be achieved via the consistent subtraction of counterterms within a regularization scheme such as a point-splitting method. Pragmatic mode-sum regularization (PMR) is a point-splitting method which is particularly suitable for rotating black hole spacetimes. We extend and tailor the t-splitting variant of PMR specifically for the interior of a Kerr black hole on the axis of rotation, focusing on a minimal…

Three-loop QCD Mass Relation between the $\overline{\mathrm{MS}}$ and Symmetric-momentum Subtraction Scheme Away from the Chiral Limit
Long Chen, Marco Niggetiedt
https://arxiv.org/abs/2506.07451

Three-loop QCD Mass Relation between the $\overline{\mathrm{MS}}$ and Symmetric-momentum Subtraction Scheme Away from the Chiral Limit
The perturbative result for the quark-mass conversion factor between the $\overline{\mathrm{MS}}$ and regularization-independent symmetric-momentum subtraction scheme (RI/SMOM) away from the chiral limit, i.e. at non-zero quark masses (RI/mSMOM), is derived up to three loops in QCD, extending the existing result by two additional orders. We further explore an illuminating possibility that in Dimensional Regularization, the original RI/(m)SMOM renormalization conditions may be interpreted merely…

Reservoir computing with large valid prediction time for the Lorenz system
Lauren A Hurley, Sean E Shaheen
https://arxiv.org/abs/2508.06730 https://arxiv.o…

Reservoir computing with large valid prediction time for the Lorenz system
We study the dependence of the Valid Prediction Time (VPT) of Reservoir Computers (RCs) on hyperparameters including the regularization coefficient, reservoir size, and spectral radius. Under carefully chosen conditions, the RC can achieve approximately 70% of a benchmark performance, based on the output of a single prediction step used as initial conditions for the Lorenz equations. We report high VPT values (>30 Lyapunov times), as we are predicting a noiseless system where overfitting can be…

Functional Tensor Regression
Tongyu Li, Fang Yao, Anru R. Zhang
https://arxiv.org/abs/2506.09358 https://arxiv.org/pdf/2506.09358

Functional Tensor Regression
Tensor regression has attracted significant attention in statistical research. This study tackles the challenge of handling covariates with smooth varying structures. We introduce a novel framework, termed functional tensor regression, which incorporates both the tensor and functional aspects of the covariate. To address the high dimensionality and functional continuity of the regression coefficient, we employ a low Tucker rank decomposition along with smooth regularization for the functional m…

Noise Consistency Regularization for Improved Subject-Driven Image Synthesis
Yao Ni, Song Wen, Piotr Koniusz, Anoop Cherian
https://arxiv.org/abs/2506.06483

Noise Consistency Regularization for Improved Subject-Driven Image Synthesis
Fine-tuning Stable Diffusion enables subject-driven image synthesis by adapting the model to generate images containing specific subjects. However, existing fine-tuning methods suffer from two key issues: underfitting, where the model fails to reliably capture subject identity, and overfitting, where it memorizes the subject image and reduces background diversity. To address these challenges, we propose two auxiliary consistency losses for diffusion fine-tuning. First, a prior consistency regul…

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…

Replaced article(s) found for physics.gen-ph. https://arxiv.org/list/physics.gen-ph/new
[1/1]:
- Topological Regularization
Sebasti\'an Al\'i Sacasa-C\'espedes

Asymptotic Consistency and Generalization in Hybrid Models of Regularized Selection and Nonlinear Learning
Luciano Ribeiro Galv\~ao, Rafael de Andrade Mora
https://arxiv.org/abs/2508.07754

Asymptotic Consistency and Generalization in Hybrid Models of Regularized Selection and Nonlinear Learning
This study explores how different types of supervised models perform in the task of predicting and selecting relevant variables in high-dimensional contexts, especially when the data is very noisy. We analyzed three approaches: regularized models (such as Lasso, Ridge, and Elastic Net), black-box models (such as Random Forest, XGBoost, LightGBM, CatBoost, and H2O GBM), and hybrid models that combine both approaches: regularization with nonlinear algorithms. Based on simulations inspired by the …

Computational algorithm for downward continuation of gravity anomalies
D. K. Ivanov, L. N. Temirbekova, P. N. Vabishchevich
https://arxiv.org/abs/2507.08506

Computational algorithm for downward continuation of gravity anomalies
The downward continuation of potential fields from the Earth's surface into the subsurface is a critical task in gravity exploration, as it helps to identify the sources of gravity anomalies. This problem is often addressed by solving a first-kind integral equation using regularization techniques to stabilize an inherently unstable process. A similar approach is used in our work, where the continued field is represented as the potential of a simple layer or its vertical derivative. The constanc…

A physics-informed neural network for modeling fracture without gradient damage: formulation, application, and assessment
Aditya Konale, Vikas Srivastava
https://arxiv.org/abs/2507.07272

A physics-informed neural network for modeling fracture without gradient damage: formulation, application, and assessment
Accurate computational modeling of damage and fracture remains a central challenge in solid mechanics. The finite element method (FEM) is widely used for numerical modeling of fracture problems; however, classical damage models without gradient regularization yield mesh-dependent and usually inaccurate predictions. The use of gradient damage with FEM improves numerical robustness but introduces significant mathematical and numerical implementation complexities. Physics-informed neural networks …

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…

This https://arxiv.org/abs/2412.08674 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nuc…

Thermomagnetic Effects of Quark Matter in the NJL Model: Application of Regularization Schemes
In the SU(3) Nambu-Jona-Lasinio (NJL) model of a thermally magnetized medium, the regularization methods adopted for the thermodynamic potential and the mass gap equation are utilized to calculate the relevant thermodynamic quantities in thermomagnetic quark matter. When dealing with the thermodynamic quantities and the gap equation, three schemes can be chosen, namely magnetic field-independent regularization, soft cut-off regularization, and Pauli-Villars regularization. These three regulariz…

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…

This https://arxiv.org/abs/2505.20111 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Preference Disaggregation Analysis with Criteria Selection in a Regularization Framework
Limited by cognitive abilities, decision-makers (DMs) may struggle to evaluate decision alternatives based on all criteria in multiple criteria decision-making problems. This paper proposes an embedded criteria selection method derived from preference disaggregation technique and regularization theory. The method aims to infer the criteria and value functions used by the DM to evaluate decision alternatives. It measures the quality of criteria subsets by investigating both the empirical error (…

The unitary group of a $\mathrm{II}_1$ factor is SOT-contractible
David Jekel
https://arxiv.org/abs/2508.05834 https://arxiv.org/pdf/2508.05834

The unitary group of a $\mathrm{II}_1$ factor is SOT-contractible
We show that the unitary group of any SOT-separable $\mathrm{II}_1$ factor $M$, with the strong operator topology, is contractible. Combined with several old results, this implies that the same is true for any SOT-separable von Neumann algebra with no type $\mathrm{I}_n$ direct summands ($n < \infty$). The proof for the $\mathrm{II}_1$-factor case uses regularization via free convolution and Popa's theorem on the existence of approximately free Haar unitaries in $\mathrm{II}_1$ factors.

Additivity of quantum relative entropies as a single-copy criterion
Salman Beigi, Roberto Rubboli, Marco Tomamichel
https://arxiv.org/abs/2507.05696 https:…

Additivity of quantum relative entropies as a single-copy criterion
The fundamental goal of information theory is to characterize complex operational tasks using efficiently computable information quantities, Shannon's capacity formula being the prime example of this. However, many tasks in quantum information can only be characterized by regularized entropic measures that are often not known to be computable and for which efficient approximations are scarce. It is thus of fundamental importance to understand when regularization is not needed, opening the door …

Replaced article(s) found for cs.GT. https://arxiv.org/list/cs.GT/new
[1/1]:
- The Power of Regularization in Solving Extensive-Form Games
Mingyang Liu, Asuman Ozdaglar, Tiancheng Yu, Kaiqing Zhang

Semi-discrete moduli of smoothness and their applications in one- and two- sided error estimates
Danilo Costarelli, Donato Lavella
https://arxiv.org/abs/2506.10723

Semi-discrete moduli of smoothness and their applications in one- and two- sided error estimates
In this paper, we introduce a new semi-discrete modulus of smoothness, which generalizes the definition given by Kolomoitsev and Lomako (KL) in 2023 (in the paper published in the J. Approx. Theory), and we establish very general one- and two- sided error estimates under non-restrictive assumptions. The proposed results have been proved exploiting the regularization and approximation properties of certain Steklov integrals introduced by Sendov and Popov in 1983, and differ from the ones given b…

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 …

WhisQ: Cross-Modal Representation Learning for Text-to-Music MOS Prediction
Jakaria Islam Emon, Kazi Tamanna Alam, Md. Abu Salek
https://arxiv.org/abs/2506.05899

WhisQ: Cross-Modal Representation Learning for Text-to-Music MOS Prediction
Mean Opinion Score (MOS) prediction for text to music systems requires evaluating both overall musical quality and text prompt alignment. This paper introduces WhisQ, a multimodal architecture that addresses this dual-assessment challenge through sequence level co-attention and optimal transport regularization. WhisQ employs the Whisper Base pretrained model for temporal audio encoding and Qwen 3, a 0.6B Small Language Model (SLM), for text encoding, with both maintaining sequence structure for…

Replaced article(s) found for cs.LG. https://arxiv.org/list/cs.LG/new
[4/6]:
- Deep learning from strongly mixing observations: Sparse-penalized regularization and minimax opti...
William Kengne, Modou Wade

One-Bit Model Aggregation for Differentially Private and Byzantine-Robust Personalized Federated Learning
Muhang Lan, Song Xiao, Wenyi Zhang
https://arxiv.org/abs/2507.03973

One-Bit Model Aggregation for Differentially Private and Byzantine-Robust Personalized Federated Learning
As the scale of federated learning (FL) systems expands, their inherent performance limitations like communication overhead, Byzantine vulnerability, and privacy leakage have become increasingly critical. This paper considers a personalized FL framework based on model regularization, and proposes a model aggregation algorithm named PRoBit+ to concurrently overcome these limitations. PRoBit+ employs one-bit stochastic quantization and maximum likelihood estimation for parameter aggregation, and …

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…

Supersymmetric M2-Brane Matrix Model with Restricted Volume-Preserving Deformations: Lorentz Covariance and BPS Spectrum
So Katagiri
https://arxiv.org/abs/2508.07259 https://

Supersymmetric M2-Brane Matrix Model with Restricted Volume-Preserving Deformations: Lorentz Covariance and BPS Spectrum
We present a novel supersymmetric Lorentz-covariant matrix model for M2-branes in M-theory, constructed via the framework of Restricted Volume-Preserving Deformations (RVPD) which is a residual symmetry from gauge-fixed volume-preserving diffeomorphisms. The model reformulates the supermembrane action entirely in terms of Nambu brackets, whose decomposition into Poisson brackets allows for a consistent matrix regularization that preserves both the Fundamental Identity and Lorentz covariance. Un…

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…

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…

Regularization Prescription for the Mixing Between Nonlocal Gluon and Quark Operators
Yao Ji, Zhuoyi Pang, Fei Yao, Jian-Hui Zhang
https://arxiv.org/abs/2506.00639

Regularization Prescription for the Mixing Between Nonlocal Gluon and Quark Operators
It is well-known that in the study of mixing between nonlocal gluon and quark bilinear operators there exists an ambiguity when relating coordinate space and momentum space results, which can be conveniently resolved through Mellin moments matching in both spaces. In this work, we show that this ambiguity is due to the lack of a proper regularization prescription of the singularity that arises when the separation between the gluon/quark fields approaches zero. We then demonstrate that dimension…

Fitness and Overfitness: Implicit Regularization in Evolutionary Dynamics
Hagai Rappeport, Mor Nitzan
https://arxiv.org/abs/2508.03187 https://arxiv.org/pd…

Fitness and Overfitness: Implicit Regularization in Evolutionary Dynamics
A common assumption in evolutionary thought is that adaptation drives an increase in biological complexity. However, the rules governing evolution of complexity appear more nuanced. Evolution is deeply connected to learning, where complexity is much better understood, with established results on optimal complexity appropriate for a given learning task. In this work, we suggest a mathematical framework for studying the relationship between evolved organismal complexity and enviroenmntal complexi…

Replaced article(s) found for cs.CV. https://arxiv.org/list/cs.CV/new
[4/10]:
- MORPH-LER: Log-Euclidean Regularization for Population-Aware Image Registration
Mokshagna Sai Teja Karanam, Krithika Iyer, Sarang Joshi, Shireen Elhabian

Projective Transformations for Regularized Central Force Dynamics: Hamiltonian Formulation
Joseph T. A. Peterson, Manoranjan Majji, John L. Junkins
https://arxiv.org/abs/2506.22681

Projective Transformations for Regularized Central Force Dynamics: Hamiltonian Formulation
This work introduces a Hamiltonian approach to regularization and linearization of central force particle dynamics through a new canonical extension of the so-called "projective decomposition". The regularization scheme is formulated within the framework of classic analytical Hamiltonian dynamics as a redundant-dimensional canonical/symplectic coordinate transformation, combined with an evolution parameter transformation, on extended phase space. By considering a generalized version of the stan…

Regularizing Learnable Feature Extraction for Automatic Speech Recognition
Peter Vieting, Maximilian Kannen, Benedikt Hilmes, Ralf Schl\"uter, Hermann Ney
https://arxiv.org/abs/2506.09804

Regularizing Learnable Feature Extraction for Automatic Speech Recognition
Neural front-ends are an appealing alternative to traditional, fixed feature extraction pipelines for automatic speech recognition (ASR) systems since they can be directly trained to fit the acoustic model. However, their performance often falls short compared to classical methods, which we show is largely due to their increased susceptibility to overfitting. This work therefore investigates regularization methods for training ASR models with learnable feature extraction front-ends. First, we e…

This https://arxiv.org/abs/2409.13414 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

An Eulerian-Lagrangian formulation for compressible Euler Equations
In this paper, we present a novel Eulerian-Lagrangian formulation for the compressible isentropic Euler equations with a general pressure law. Using the developed Lagrangian formulation, we show a short-time solution which is unique in the framework of Bessel space $H_{p}^β(\mathbb{T}^{d})$ for $β>\frac{d}{p}+1$. The proof is precise and relatively simple, relying on the application of the Implicit Function Theorem in Banach spaces combined with a carefully designed regularization procedure. …

Neural-Augmented Kelvinlet: Real-Time Soft Tissue Deformation with Multiple Graspers
Ashkan Shahbazi, Kyvia Pereira, Jon S. Heiselman, Elaheh Akbari, Annie C. Benson, Sepehr Seifi, Xinyuan Liu, Garrison L. Johnston, Erwin Terpstra, Anne Draaisma, Jan-Jaap Severes, Jie Ying Wu, Nabil Simaan, Michael L. Miga, Soheil Kolouri
https://

Neural-Augmented Kelvinlet: Real-Time Soft Tissue Deformation with Multiple Graspers
Fast and accurate simulation of soft tissue deformation is a critical factor for surgical robotics and medical training. In this paper, we introduce a novel physics-informed neural simulator that approximates soft tissue deformations in a realistic and real-time manner. Our framework integrates Kelvinlet-based priors into neural simulators, making it the first approach to leverage Kelvinlets for residual learning and regularization in data-driven soft tissue modeling. By incorporating large-sca…

Higher Order Regularization using Harmonic Eigenfunctions for Model-Based Reconstruction in Magnetic Particle Imaging
Thomas M\"arz, Vladyslav Gapyak, Andreas Weinmann
https://arxiv.org/abs/2508.06306

Higher Order Regularization using Harmonic Eigenfunctions for Model-Based Reconstruction in Magnetic Particle Imaging
Magnetic Particle Imaging (MPI) is a recent imaging modality where superparamagnetic nanoparticles are employed as tracers. The reconstruction task is to obtain the spatial particle distribution from a voltage signal induced by the particles. Generally, in computational imaging variational reconstruction techniques are common and rely on a mathematical model to describe the underlying physics. For the MPI reconstruction task we propose a model-based variational reconstruction technique which in…

Power System Voltage Stability Boundary: Computational Results and Applications
Zhenyao Li, Yifan Yao, Deqiang Gan
https://arxiv.org/abs/2508.03119 https://

Power System Voltage Stability Boundary: Computational Results and Applications
The objective of this paper is to report some computational results for the theory of DAE stability boundary, with the aim of advancing applications in power system voltage stability studies. Firstly, a new regularization transformation for standard differential-algebraic equations (DAEs) is proposed. Then the existence of anchor points on voltage stability boundary is examined, and an optimization method for computing the controlling pseudo-saddle is suggested. Subsequently, a local representa…

On fractional differential equations, dimensional analysis, and the double gamma function
J. Vaz, E. Capelas de Oliveira
https://arxiv.org/abs/2506.00026 h…

On fractional differential equations, dimensional analysis, and the double gamma function
In this paper we discuss some issues that arise in the process of writing a fractional differential equation (FDE) by replacing an integer order derivative by a fractional order derivative in a given differential equation. To address these issues, we propose a dimensional regularization of the Caputo fractional derivative, ensuring consistency in physical dimensions. Then we solve some FDEs using this proposed dimensional regularization. We show that the solutions of these FDEs are most conveni…

Replaced article(s) found for stat.ML. https://arxiv.org/list/stat.ML/new
[1/1]:
- Deep learning from strongly mixing observations: Sparse-penalized regularization and minimax opti...
William Kengne, Modou Wade

From Motion to Meaning: Biomechanics-Informed Neural Network for Explainable Cardiovascular Disease Identification
Comte Valentin, Gemma Piella, Mario Ceresa, Miguel A. Gonzalez Ballester
https://arxiv.org/abs/2507.05783

From Motion to Meaning: Biomechanics-Informed Neural Network for Explainable Cardiovascular Disease Identification
Cardiac diseases are among the leading causes of morbidity and mortality worldwide, which requires accurate and timely diagnostic strategies. In this study, we introduce an innovative approach that combines deep learning image registration with physics-informed regularization to predict the biomechanical properties of moving cardiac tissues and extract features for disease classification. We utilize the energy strain formulation of Neo-Hookean material to model cardiac tissue deformations, opti…

Label-Context-Dependent Internal Language Model Estimation for CTC
Zijian Yang, Minh-Nghia Phan, Ralf Schl\"uter, Hermann Ney
https://arxiv.org/abs/2506.06096

Label-Context-Dependent Internal Language Model Estimation for CTC
Although connectionist temporal classification (CTC) has the label context independence assumption, it can still implicitly learn a context-dependent internal language model (ILM) due to modern powerful encoders. In this work, we investigate the implicit context dependency modeled in the ILM of CTC. To this end, we propose novel context-dependent ILM estimation methods for CTC based on knowledge distillation (KD) with theoretical justifications. Furthermore, we introduce two regularization meth…

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.

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…

Predictive posteriors under hidden confounding
Carlos Garc\'ia Meixide, David R\'ios Insua
https://arxiv.org/abs/2507.05170 https://

Predictive posteriors under hidden confounding
Predicting outcomes in external domains is challenging due to hidden confounders that influence both predictors and outcomes, complicating generalization under distribution shifts. Traditional methods often rely on stringent assumptions or overly conservative regularization, compromising estimation and predictive accuracy. Generative Invariance (GI) is a novel framework that facilitates predictions in unseen domains without requiring hyperparameter tuning or knowledge of specific distribution s…

A universal relation among Euclidean integrals for black holes in higher-derivative gravity theories
Yong Xiao, Qiang Wang, Aonan Zhang
https://arxiv.org/abs/2508.05326 https://…

A universal relation among Euclidean integrals for black holes in higher-derivative gravity theories
In this paper, we establish a universal equality governing Euclidean integrals of gravitational actions in higher-derivative theories. This relation is shown to hold universally for asymptotically flat black holes in pure gravity, and is generalized to asymptotically anti-de Sitter (AdS) spacetimes through appropriate regularization. We further examine its validity in systems with matter-gravity coupling, identifying that violations occur only when matter fields exhibit pathological behaviors: …

Topological Regularization
Sebasti\'an Al\'i Sacasa-C\'espedes
https://arxiv.org/abs/2508.00885 https://arxiv.org/pdf/2508.00885

Topological Regularization
This work introduces topological regularization as a framework for handling ultraviolet divergences in quantum field theory, reinterpreting infinities as topological obstructions at spacetime boundaries. Through geometric compactification via stereographic projection, singularities are reframed as boundary artifacts. The framework employs causal embeddings and the causality group to preserve Lorentz invariance and unitarity, while homotopy-equivalent defect structures guarantee regularization i…

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 …

Robust Learning on Noisy Graphs via Latent Space Constraints with External Knowledge
Chunhui Gu, Mohammad Sadegh Nasr, James P. Long, Kim-Anh Do, Ehsan Irajizad
https://arxiv.org/abs/2507.05540

Robust Learning on Noisy Graphs via Latent Space Constraints with External Knowledge
Graph Neural Networks (GNNs) often struggle with noisy edges. We propose Latent Space Constrained Graph Neural Networks (LSC-GNN) to incorporate external "clean" links and guide embeddings of a noisy target graph. We train two encoders--one on the full graph (target plus external edges) and another on a regularization graph excluding the target's potentially noisy links--then penalize discrepancies between their latent representations. This constraint steers the model away from overfitting spur…

Improvement of the Parabolic Regularization Method and Applications to Dispersive Models
Alysson Cunha
https://arxiv.org/abs/2507.23530 https://arxiv.org/p…

Improvement of the Parabolic Regularization Method and Applications to Dispersive Models
We prove that the Benjamin Ono equation is globally well-posed in $H^s(\mathbb{R})$ for $s > 1/2$. Our approach does not rely on the global gauge transformation introduced by Tao (arXiv:math/0307289). Instead, we employ a modified version of the standard parabolic regularization method. In particular, this technique also enables us to establish global well-posedness, in the same Sobolev space, for the dispersion-generalized Benjamin Ono (DGBO) equation.

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…

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…

Contact potentials in presence of a regular finite-range interaction using dimensional regularization and the $N/D$ method
David R. Entem, Juan Nieves, Jose Antonio Oller
https://arxiv.org/abs/2506.01461

Contact potentials in presence of a regular finite-range interaction using dimensional regularization and the $N/D$ method
We solve the Lippman-Schwinger equation (LSE) with a kernel that includes a regular finite-range potential and additional contact terms with derivatives. We employ distorted wave theory and dimensional regularization, as proposed in Physics Letters B 568 (2003) 109. We analyze the spin singlet nucleon-nucleon $S-$wave as case of study, with the regular one-pion exchange (OPE) potential in this partial wave and up to ${\cal O}(Q^6)$ (six derivatives) contact interactions. We discuss in detail th…

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…

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…

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…

D-dimensional black holes in extended Gauss-Bonnet gravity
Jia-Zhou Liu, Si-Jiang Yang, Chun-Chun Zhu, Yu-Xiao Liu
https://arxiv.org/abs/2508.04292 https://

D-dimensional black holes in extended Gauss-Bonnet gravity
In this work, we present charged spherically symmetric anti-de Sitter black hole solutions in $d$ dimensions ($d \geq 5$) within the framework of extended Gauss--Bonnet gravity. Moreover, by employing dimensional regularization of the extended Gauss--Bonnet term, we further obtain charged anti-de Sitter black hole solutions in three- and four-dimensional spacetimes. Furthermore, we also obtain a three-dimensional rotating black hole solution in a special case. These solutions exhibit markedly d…

On surface energies in scaling laws for singular perturbation problems for martensitic phase transitions
Angkana R\"uland, Camillo Tissot, Antonio Tribuzio, Christian Zillinger
https://arxiv.org/abs/2507.06773 https://arxiv.org/pdf/2507.06773 https://arxiv.org/html/2507.06773
arXiv:2507.06773v1 Announce Type: new
Abstract: The objective of this article is to compare different surface energies for multi-well singular perturbation problems associated with martensitic phase transformations involving higher order laminates. We deduce scaling laws in the singular perturbation parameter which are robust in the choice of the surface energy (e.g., diffuse, sharp, an interpolation thereof or discrete). Furthermore, we show that these scaling laws do not require the presence of isotropic surface energies but that generically also highly anisotropic surface energies yield the same scaling results. More precisely, the presence of essentially generic partial directional derivatives in the regularization terms suffices to produce the same scaling behaviour as in the isotropic setting. The only sensitive directional dependences are directly linked to the lamination directions of the well structure -- and even for these only the ``inner-most'' lamination direction is of significance in determining the scaling law. In view of experimental applications, this shows that also for higher-order laminates, the precise structure of the surface energies -- which is often very difficult to determine experimentally -- does not have a crucial impact on the scaling behaviour of the investigated structures but only enters when considering finer properties.
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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…

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…

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…

Three-loop singularity structure for a non-linear sigma model
P. V. Akacevich, A. V. Ivanov, I. V. Korenev
https://arxiv.org/abs/2507.05923 https://…

Three-loop singularity structure for a non-linear sigma model
The paper is devoted to the three-loop renormalization of the effective action for a two-dimensional non-linear sigma model using the background field method and a cutoff regularization in the coordinate representation. The coefficients of the renormalization constant and the necessary auxiliary vertices are found, as well as the asymptotic expansions of all three-loop diagrams, and their dependence on the type of regularizing function. A comparison is also made with the standard case of cutoff…

Sample-Based Consistency in Infinite-Dimensional Conic-Constrained Stochastic Optimization
Caroline Geiersbach, Johannes Milz
https://arxiv.org/abs/2507.06982

Sample-Based Consistency in Infinite-Dimensional Conic-Constrained Stochastic Optimization
This paper is concerned with a class of stochastic optimization problems defined on a Banach space with almost sure conic-type constraints. For this class of problems, we investigate the consistency of optimal values and solutions corresponding to sample average approximation. Consistency is also shown in the case where a Moreau--Yosida-type regularization of the constraint is used. Additionally, the consistency of Karush--Kuhn--Tucker conditions is shown under mild conditions. This work provid…

This https://arxiv.org/abs/2506.03074 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

GL-LowPopArt: A Nearly Instance-Wise Minimax Estimator for Generalized Low-Rank Trace Regression
We present `GL-LowPopArt`, a novel Catoni-style estimator for generalized low-rank trace regression. Building on `LowPopArt` (Jang et al., 2024), it employs a two-stage approach: nuclear norm regularization followed by matrix Catoni estimation. We establish state-of-the-art estimation error bounds, surpassing existing guarantees (Fan et al., 2019; Kang et al., 2022), and reveal a novel experimental design objective, $\mathrm{GL}(π)$. The key technical challenge is controlling bias from the non…

Perimeter on a manifold, with applications to partial differential equations
Satyanad Kichenassamy (DMA)
https://arxiv.org/abs/2507.04740 https://

Perimeter on a manifold, with applications to partial differential equations
The perimeter of a measurable subset of $\mathbb R^N$ is the total variation of its characteristic function. We generalize this notion to a subset $E$ of a closed Riemannian manifold. We show that the perimeter of $E$ is the limit of the hear kernel regularization of its characteristic function. A generalization of the isoperimetric inequality and of the Fleming-Rishel formula follow. These results are applied to a quasilinear elliptic problem in $\mathbb R^N$ for which the usual symmetrization…

Replaced article(s) found for cs.LG. https://arxiv.org/list/cs.LG/new
[1/6]:
- Non-Convex Optimization with Spectral Radius Regularization
Adam Sandler, Diego Klabjan, Yuan Luo

Replaced article(s) found for math.NA. https://arxiv.org/list/math.NA/new
[1/1]:
- New Feedback Control and Adaptive Evolve-Filter-Relax Regularization for the Navier-Stokes Equati...
Maria Strazzullo, Francesco Ballarin, Traian Iliescu, Claudio Canuto

Unrolling Nonconvex Graph Total Variation for Image Denoising
Songlin Wei, Gene Cheung, Fei Chen, Ivan Selesnick
https://arxiv.org/abs/2506.02381 https://

Unrolling Nonconvex Graph Total Variation for Image Denoising
Conventional model-based image denoising optimizations employ convex regularization terms, such as total variation (TV) that convexifies the $\ell_0$-norm to promote sparse signal representation. Instead, we propose a new non-convex total variation term in a graph setting (NC-GTV), such that when combined with an $\ell_2$-norm fidelity term for denoising, leads to a convex objective with no extraneous local minima. We define NC-GTV using a new graph variant of the Huber function, interpretable …

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…

On the regularization property of Levenberg-Marquardt method with Singular Scaling for nonlinear inverse problems
Rafaela Filippozzi, Everton Boos, Douglas S. Gon\c{c}alves, Fermin S. V. Baz\'an
https://arxiv.org/abs/2506.00190

On the regularization property of Levenberg-Marquardt method with Singular Scaling for nonlinear inverse problems
Recently, in Applied Mathematics and Computation 474 (2024) 128688, a Levenberg-Marquardt method (LMM) with Singular Scaling was analyzed and successfully applied in parameter estimation problems in heat conduction where the use of a particular singular scaling matrix (semi-norm regularizer) provided approximate solutions of better quality than those of the classic LMM. Here we propose a regularization framework for the Levenberg-Marquardt method with Singular Scaling (LMMSS) applied to nonline…

Adaptive Iterative Soft-Thresholding Algorithm with the Median Absolute Deviation
Yining Feng, Ivan Selesnick
https://arxiv.org/abs/2507.02084 https://

Adaptive Iterative Soft-Thresholding Algorithm with the Median Absolute Deviation
The adaptive Iterative Soft-Thresholding Algorithm (ISTA) has been a popular algorithm for finding a desirable solution to the LASSO problem without explicitly tuning the regularization parameter $λ$. Despite that the adaptive ISTA is a successful practical algorithm, few theoretical results exist. In this paper, we present the theoretical analysis on the adaptive ISTA with the thresholding strategy of estimating noise level by median absolute deviation. We show properties of the fixed points …

Existence of weak solution of 3D ferrohydrodynamic equations with transport noise: Bloch-Torrey regularisation
Aristide Ndongmo Ngana, Paul Razafimandimby
https://arxiv.org/abs/2507.03388

Existence of weak solution of 3D ferrohydrodynamic equations with transport noise: Bloch-Torrey regularisation
In this article, we consider a stochastic ferrohydrodynamic system which describes the Bloch-Torrey regularization of the motion of an electrically conducting ferrofluids driven by transport noise filling a 3D bounded domain with a smooth boundary. We prove the global existence of a probabilistic weak solution of the stochastic system by making use of the combination of Galerkin method and compactness method. The system under study is basically a coupling of the Navier-Stokes equations with int…

This https://arxiv.org/abs/2505.08740 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations
Parametric differential equations of the form du/dt = f(u, x, t, p) are fundamental in science and engineering. While deep learning frameworks such as the Fourier Neural Operator (FNO) can efficiently approximate solutions, they struggle with inverse problems, sensitivity estimation (du/dp), and concept drift. We address these limitations by introducing a sensitivity-based regularization strategy, called Sensitivity-Constrained Fourier Neural Operators (SC-FNO). SC-FNO achieves high accuracy in…

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…

Localized evaluation and fast summation in the extrapolated regularization method for integrals in Stokes flow
Joseph Siebor, Svetlana Tlupova
https://arxiv.org/abs/2507.00156

Localized evaluation and fast summation in the extrapolated regularization method for integrals in Stokes flow
Boundary integral equation methods are widely used in the solution of many partial differential equations. The kernels that appear in these surface integrals are nearly singular when evaluated near the boundary, and straightforward numerical integration produces inaccurate results. In Beale and Tlupova (Adv. Comput. Math, 2024), an extrapolated regularization method was proposed to accurately evaluate the nearly singular single and double-layer surface integrals for harmonic potentials or Stoke…

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…

Regularization of Inverse Problems by Filtered Diagonal Frame Decomposition under general source
Dang Duc Trong, Nguyen Dang Minh, Luu Xuan Thang, Luu Dang Khoa
https://arxiv.org/abs/2507.23651

Regularization of Inverse Problems by Filtered Diagonal Frame Decomposition under general source
Let $X$ and $Y$ be Hilbert spaces, and $\mathbf{K}: \text{dom} \mathbf{K} \subset X \to Y$ a bounded linear operator. This paper addresses the inverse problem $\mathbf{K}x = y$, where exact data $y$ is replaced by noisy data $y^δ$ satisfying $\|y^δ- y\|_Y \leq δ$. Due to the ill-posedness of such problems, we employ regularization methods to stabilize solutions. While singular value decomposition (SVD) provides a classical approach, its computation can be costly and impractical for…

$\ell_{1}^{2}-\eta\ell_{2}^{2}$ 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…

AdS$_3$ black holes with primary Proca hair from regularized Gauss-Bonnet coupling
Gokhan Alkac, Murat Mesta, Gonul Unal
https://arxiv.org/abs/2508.03386 https://

AdS$_3$ black holes with primary Proca hair from regularized Gauss-Bonnet coupling
We construct a consistent three-dimensional Einstein-Gauss-Bonnet theory as a vector-tensor theory within the generalized Proca class by employing a regularization procedure based on the Weyl geometry, which was introduced recently in arXiv:2504.13084. We then obtain an asymptotically AdS$_3$, static, and circularly symmetric black hole solution with primary Proca hair. Afterwards, we investigate the effect of the scalar-tensor Gauss-Bonnet coupling constructed previously by different regulariz…

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…

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…

This https://arxiv.org/abs/2403.06708 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Tikhonov Regularization for Stochastic Non-Smooth Convex Optimization in Hilbert Spaces
To solve convex optimization problems with a noisy gradient input, we analyze the global behavior of subgradient-like flows under stochastic errors. The objective function is composite, being equal to the sum of two convex functions, one being differentiable and the other potentially non-smooth. We then use stochastic differential inclusions where the drift term is minus the subgradient of the objective function, and the diffusion term is either bounded or square-integrable. In this context, un…

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 …

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 …

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…

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…

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…

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 …

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…

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…