Tootfinder

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

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…

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.

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 …

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…

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…

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…

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…

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…

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…

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…

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…

Replaced article(s) found for nlin.AO. https://arxiv.org/list/nlin.AO/new
[1/1]:
- How more data can hurt: Instability and regularization in next-generation reservoir computing
Yuanzhao Zhang, Edmilson Roque dos Santos, Huixin Zhang, Sean P. Cornelius

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…

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…

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…

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…

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…

This https://arxiv.org/abs/2503.10569 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Low-Rank Matrix Regression via Least-Angle Regression
Low-rank matrix regression is a fundamental problem in data science with various applications in systems and control. Nuclear norm regularization has been widely applied to solve this problem due to its convexity. However, it suffers from high computational complexity and the inability to directly specify the rank. This work introduces a novel framework for low-rank matrix regression that addresses both unstructured and Hankel matrices. By decomposing the low-rank matrix into rank-1 bases, the …

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…

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 …

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…

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…

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 …

EMO-Debias: Benchmarking Gender Debiasing Techniques in Multi-Label Speech Emotion Recognition
Yi-Cheng Lin, Huang-Cheng Chou, Yu-Hsuan Li Liang, Hung-yi Lee
https://arxiv.org/abs/2506.04652

EMO-Debias: Benchmarking Gender Debiasing Techniques in Multi-Label Speech Emotion Recognition
Speech emotion recognition (SER) systems often exhibit gender bias. However, the effectiveness and robustness of existing debiasing methods in such multi-label scenarios remain underexplored. To address this gap, we present EMO-Debias, a large-scale comparison of 13 debiasing methods applied to multi-label SER. Our study encompasses techniques from pre-processing, regularization, adversarial learning, biased learners, and distributionally robust optimization. Experiments conducted on acted and …

Orthogonality-Constrained Deep Instrumental Variable Model for Causal Effect Estimation
Shunxin Yao
https://arxiv.org/abs/2506.02790 https://

Orthogonality-Constrained Deep Instrumental Variable Model for Causal Effect Estimation
OC-DeepIV is a neural network model designed for estimating causal effects. It characterizes heterogeneity by adding interaction features and reduces redundancy through orthogonal constraints. The model includes two feature extractors, one for the instrumental variable Z and the other for the covariate X*. The training process is divided into two stages: the first stage uses the mean squared error (MSE) loss function, and the second stage incorporates orthogonal regularization. Experimental res…

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…

Consecutive collision orbits in the restricted three-body problem above the first critical energy value
Jungsoo Kang, Kevin Ruck
https://arxiv.org/abs/2506.01735

Consecutive collision orbits in the restricted three-body problem above the first critical energy value
In this paper, we study the planar circular restricted three-body problem for energy levels slightly above the first critical value. We first observe that the energy hypersurfaces in the Birkhoff regularization corresponding to these energy levels are of contact type. Then, using a version of Rabinowitz Floer homology and an analytic continuation argument, we establish the existence of a symmetric consecutive collision orbit and, furthermore, prove the existence of infinitely many such orbits f…

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 …

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…

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

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…

This https://arxiv.org/abs/2411.09097 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

On the Selection Stability of Stability Selection and Its Applications
Stability selection is a widely adopted resampling-based framework for high-dimensional variable selection. This paper seeks to broaden the use of an established stability estimator to evaluate the overall stability of the stability selection results, moving beyond single-variable analysis. We suggest that the stability estimator offers two advantages: it can serve as a reference to reflect the robustness of the results obtained, and it can help identify a Pareto optimal regularization value to…

Conformal Operator Flows of the Deconfined Quantum Criticality from $\mathrm{SO}(5)$ to $\mathrm{O}(4)$
Shuai Yang, Liang-dong Hu, Chao Han, W. Zhu, Yan Chen
https://arxiv.org/abs/2507.01322

Conformal Operator Flows of the Deconfined Quantum Criticality from $\mathrm{SO}(5)$ to $\mathrm{O}(4)$
The deconfined quantum critical point (DQCP), which separates two distinct symmetry-broken phases, was conjectured to be an example of (2+1)D criticality beyond the standard Landau-Ginzburg-Wilson paradigm. However, this hypothesis has been met with challenges and remains elusive. Here, we perform a systematic study of a microscopic model realizing the DQCP with a global symmetry tunable from $\mathrm{SO}(5)$ to $\mathrm{O}(4)$. Through the lens of fuzzy sphere regularization, we uncover the ke…

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…

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…

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

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…

Entropy Regularized Belief Reporting
Elchin Suleymanov
https://arxiv.org/abs/2506.22649 https://arxiv.org/pdf/2506.22649

Entropy Regularized Belief Reporting
This paper investigates a model of partition dependence, a widely reported experimental finding where the agent's reported beliefs depend on how the states are grouped. In the model, called Entropy Regularized Belief Reporting (ERBR), the agent is endowed with a latent benchmark prior that is unobserved by the analyst. When presented with a partition, the agent reports a prior that minimizes Kullback-Leibler divergence from the latent benchmark prior subject to entropy regularization. This capt…

A variational approach to fracture incorporating any convex strength criterion
Blaise Bourdin, Jean-Jacques Marigo, Corrado Maurini, Camilla Zolesi
https://arxiv.org/abs/2506.22558

A variational approach to fracture incorporating any convex strength criterion
We propose a variational phase-field model of fracture capable of accounting for arbitrary closed convex strength domains. Unlike traditional models based on Ambrosio and Tortorelli regularization, the phase-field variable does not affect the material stiffness. Instead, our elastic energy exhibits linear growth outside a strength domain, which shrinks to 0 as the phase-field variable goes to 1. We characterize this model through a fundamental problem on a cube subject to boundary loads. …

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…

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…

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…

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…

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…

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…

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…

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…

Conformal scalar field theory from Ising tricriticality on the fuzzy sphere
Joseph Taylor, Cristian Voinea, Zlatko Papi\'c, Ruihua Fan
https://arxiv.org/abs/2506.22539

Conformal scalar field theory from Ising tricriticality on the fuzzy sphere
Free theories are landmarks in the landscape of quantum field theories: their exact solvability serves as a pillar for perturbative constructions of interacting theories. Fuzzy sphere regularization, which combines quantum Hall physics with state-operator correspondence, has recently been proposed as a promising framework for simulating three-dimensional conformal field theories (CFTs), but so far it has not provided access to free theories. We overcome this limitation by designing a bilayer qu…

This https://arxiv.org/abs/2409.08335 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Mixed precision iterative refinement for linear inverse problems
This study investigates the iterative refinement method applied to the solution of linear discrete inverse problems by considering its application to the Tikhonov problem in mixed precision. Previous works on mixed precision iterative refinement methods for the solution of symmetric positive definite linear systems and least-squares problems have shown regularization to be a key requirement when computing low precision factorizations. For problems that are naturally severely ill-posed, we formu…

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…

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) …

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…

$\ell_{1}^{2}-\eta\ell_{2}^{2}$ 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…

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…

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…

Three-dimensional Deep Shape Optimization with a Limited Dataset
Yongmin Kwon, Namwoo Kang
https://arxiv.org/abs/2506.12326 https://a…

Three-dimensional Deep Shape Optimization with a Limited Dataset
Generative models have attracted considerable attention for their ability to produce novel shapes. However, their application in mechanical design remains constrained due to the limited size and variability of available datasets. This study proposes a deep learning-based optimization framework specifically tailored for shape optimization with limited datasets, leveraging positional encoding and a Lipschitz regularization term to robustly learn geometric characteristics and maintain a meaningful…

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…

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…

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 …

The Grothendieck duality and sparse minimizing in spaces of Sobolev solutions to elliptic systems
Alexander Shlapunov, Alexander Polkovnikov, Kseniya Gagelgans
https://arxiv.org/abs/2506.23087

The Grothendieck duality and sparse minimizing in spaces of Sobolev solutions to elliptic systems
We present an instructive example of using Banach spaces of solutions to (linear, generally, non-scalar) elliptic operator $A$ to investigate variational inverse problems related to neural networks and/or to regularization of solutions to boundary value problems. More precisely, inspired by kernel's method for optimization problems in locally convex spaces, we prove the existence of the so-called sparse minimizers for the related variational problem and produce a representer theorem where a sui…

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…

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…

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…

Optimized binning for response function reconstruction via Chebyshev expansions
Immo C. Reis, Joanna E. Sobczyk, Sonia Bacca
https://arxiv.org/abs/2507.00587

Optimized binning for response function reconstruction via Chebyshev expansions
We propose an optimized histogram binning strategy to reconstruct nuclear response functions via the Chebyshev expansion bound-state method. Our approach employs a stochastic regularization of the density of states to define adaptive, equal-area bins. Using the deuteron solved in a harmonic-oscillator basis with a chiral interaction, we benchmark on dipole and longitudinal responses, obtaining excellent agreement with exact theory and experiment. This general framework readily extends to other …

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 …

EKPC: Elastic Knowledge Preservation and Compensation for Class-Incremental Learning
Huaijie Wang, De Cheng, Lingfeng He, Yan Li, Jie Li, Nannan Wang, Xinbo Gao
https://arxiv.org/abs/2506.12351

EKPC: Elastic Knowledge Preservation and Compensation for Class-Incremental Learning
Class-Incremental Learning (CIL) aims to enable AI models to continuously learn from sequentially arriving data of different classes over time while retaining previously acquired knowledge. Recently, Parameter-Efficient Fine-Tuning (PEFT) methods, like prompt pool-based approaches and adapter tuning, have shown great attraction in CIL. However, these methods either introduce additional parameters that increase memory usage, or rely on rigid regularization techniques which reduce forgetting but …

Moments, Time-Inversion and Source Identification for the Heat Equation
Kang Liu, Enrique Zuazua
https://arxiv.org/abs/2507.02677 https://

Moments, Time-Inversion and Source Identification for the Heat Equation
We address the initial source identification problem for the heat equation, a notably ill-posed inverse problem characterized by exponential instability. Departing from classical Tikhonov regularization, we propose a novel approach based on moment analysis of the heat flow, transforming the problem into a more stable inverse moment formulation. By evolving the measured terminal time moments backward through their governing ODE system, we recover the moments of the initial distribution. We then …

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…

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…

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.

Block triangular preconditioning for inverse source problems in time-space fractional diffusion equations
Monoswini Majumdar, Stefano Serra-Capizzano, Rosita L. Sormani
https://arxiv.org/abs/2507.02809

Block triangular preconditioning for inverse source problems in time-space fractional diffusion equations
The current work investigates the effectiveness of block triangular preconditioners in accelerating and stabilizing the numerical solution of inverse source problems governed by time-space fractional diffusion equations (TSFDEs). We focus on the recovery of an unknown spatial source function in a multi-dimensional TSFDE, incorporating Caputo time-fractional derivatives and the fractional Laplacian. The inherent ill-posedness is addressed via a quasi-boundary value regularization, followed by a …

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…

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…

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…

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 …

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…

Exact operator inference with minimal data
Henrik Rosenberger, Benjamin Sanderse, Giovanni Stabile
https://arxiv.org/abs/2506.01244 https://

Exact operator inference with minimal data
This work introduces a novel method to generate snapshot data for operator inference that guarantees the exact reconstruction of intrusive projection-based reduced-order models (ROMs). To ensure exact reconstruction, the operator inference least squares matrix must have full rank, without regularization. Existing works have achieved this full rank using heuristic strategies to generate snapshot data and a-posteriori checks on full rank, but without a guarantee of success. Our novel snapshot dat…

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 …

Replaced article(s) found for cs.LG. https://arxiv.org/list/cs.LG/new/
[1/7]:
Effective Regularization Through Loss-Function Metalearning
https://…

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…

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 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…

A new sparsity promoting residual transform operator for Lasso regression
Yao Xiao, Anne Gelb, Aditya Viswanathan
https://arxiv.org/abs/2506.22689 https://…

A new sparsity promoting residual transform operator for Lasso regression
Lasso regression is a widely employed approach within the $\ell_1$ regularization framework used to promote sparsity and recover piecewise smooth signals $f:[a,b) \rightarrow \mathbb{R}$ when the given observations are obtained from noisy, blurred, and/or incomplete data environments. In choosing the regularizing sparsity-promoting operator, it is assumed that the particular type of variability of the underlying signal, for example, piecewise constant or piecewise linear behavior across the ent…

This https://arxiv.org/abs/2412.11313 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Stable Recovery of Regularized Linear Inverse Problems
Recovering a low-complexity signal from its noisy observations by regularization methods is a cornerstone of inverse problems and compressed sensing. Stable recovery ensures that the original signal can be approximated linearly by optimal solutions of the corresponding Morozov or Tikhonov regularized optimization problems. In this paper, we propose new characterizations for stable recovery in finite-dimensional spaces, uncovering the role of nonsmooth second-order information. These insights en…

Shock formation in 1D conservation laws II: Vanishing viscosity
John Anderson, Sanchit Chaturvedi, Cole Graham
https://arxiv.org/abs/2506.17156 https://

Shock formation in 1D conservation laws II: Vanishing viscosity
We study the effects of weak viscosity on shock formation in 1D hyperbolic conservation laws. Given an inviscid solution that forms a nondegenerate shock, we add a small viscous regularization and study the limit as the viscosity vanishes. Using a matched asymptotic expansion, we determine the sharp rate of convergence in strong norms up to the time of inviscid shock formation, and we identify universal viscous behavior near the first singularity. To treat the complex interactions between multi…

This https://arxiv.org/abs/2412.11313 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Stable Recovery of Regularized Linear Inverse Problems
Recovering a low-complexity signal from its noisy observations by regularization methods is a cornerstone of inverse problems and compressed sensing. Stable recovery ensures that the original signal can be approximated linearly by optimal solutions of the corresponding Morozov or Tikhonov regularized optimization problems. In this paper, we propose new characterizations for stable recovery in finite-dimensional spaces, uncovering the role of nonsmooth second-order information. These insights en…

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…

An \textsf{AT1} phase-field framework for quasi-static anti-plane shear fracture: Unifying $\xi$-based adaptivity and nonlinear strain energy density function
Maria P. Fernando, S. M. Mallikarjunaiah
https://arxiv.org/abs/2506.23249

An \textsf{AT1} phase-field framework for quasi-static anti-plane shear fracture: Unifying $ξ$-based adaptivity and nonlinear strain energy density function
This work introduces a novel \textsf{AT1} phase-field framework for simulating quasi-static anti-plane shear fracture in geometrically linear elastic bodies. A key feature of this framework is the unification of $ξ$-based local mesh adaptivity -- where $ξ$ represents the characteristic length of the damage zone -- and an algebraically nonlinear strain energy density function. A modified Francfort-Marigo energy functional, together with its Ambrosio-Tortorelli-type regularization, is hereby pr…

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 (…

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…

Proximal Operators of Sorted Nonconvex Penalties
Anne Gagneux, Mathurin Massias, Emmanuel Soubies
https://arxiv.org/abs/2506.15315 https://

Proximal Operators of Sorted Nonconvex Penalties
This work studies the problem of sparse signal recovery with automatic grouping of variables. To this end, we investigate sorted nonsmooth penalties as a regularization approach for generalized linear models. We focus on a family of sorted nonconvex penalties which generalizes the Sorted L1 Norm (SLOPE). These penalties are designed to promote clustering of variables due to their sorted nature, while the nonconvexity reduces the shrinkage of coefficients. Our goal is to provide efficient ways t…

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…

Gradient-Normalized Smoothness for Optimization with Approximate Hessians
Andrei Semenov, Martin Jaggi, Nikita Doikov
https://arxiv.org/abs/2506.13710 http…

Gradient-Normalized Smoothness for Optimization with Approximate Hessians
In this work, we develop new optimization algorithms that use approximate second-order information combined with the gradient regularization technique to achieve fast global convergence rates for both convex and non-convex objectives. The key innovation of our analysis is a novel notion called Gradient-Normalized Smoothness, which characterizes the maximum radius of a ball around the current point that yields a good relative approximation of the gradient field. Our theory establishes a natural …

Faster Computation of Entropic Optimal Transport via Stable Low Frequency Modes
Reda Chhaibi, Serge Gratton, Samuel Vaiter
https://arxiv.org/abs/2506.14780

Faster Computation of Entropic Optimal Transport via Stable Low Frequency Modes
In this paper, we propose an accelerated version for the Sinkhorn algorithm, which is the reference method for computing the solution to Entropic Optimal Transport. Its main draw-back is the exponential slow-down of convergence as the regularization weakens $\varepsilon \rightarrow 0$. Thanks to spectral insights on the behavior of the Hessian, we propose to mitigate the problem via an original spectral warm-start strategy. This leads to faster convergence compared to the reference method, …

Heterogeneous and anisotropic elastic parameter estimation using a novel semi-analytical forward solver
Xiaopeng Zhu, Zhongyi Huang
https://arxiv.org/abs/2506.15185

Heterogeneous and anisotropic elastic parameter estimation using a novel semi-analytical forward solver
An efficient procedure using a novel semi-analytical forward solver for identifying heterogeneous and anisotropic elastic parameters from only one full-field measurement is proposed and explored. We formulate the inverse problem as an special energy functional minimization with total variation(TV) regularization. The minimization problem is solved by Adam algorithm, which only requires solving one forward problem and no adjoint problem in each iteration. In order to deal with the irregularity o…

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations
Md Mamun Miah, Ryuhei Wakida, Masato Kimura
https://arxiv.org/abs/2506.14788

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations
Phase field models have emerged as a powerful and flexible framework for simulating complex interface-driven phenomena across a wide range of scientific and engineering applications. In fracture mechanics, the phase field approach--formulated as a gradient flow of the Griffith fracture energy with Ambrosio-Tortorelli regularization--has gained significant attention for its ability to capture complex crack topologies. In this study, we propose a dynamic fracture phase field model (DF-PFM) based …