Tootfinder

Primal-Dual Coordinate Descent for Nonconvex-Nonconcave Saddle Point Problems Under the Weak MVI Assumption
Iyad Walwil, Olivier Fercoq
https://arxiv.org/abs/2506.15597

Primal-Dual Coordinate Descent for Nonconvex-Nonconcave Saddle Point Problems Under the Weak MVI Assumption
We introduce two novel primal-dual algorithms for addressing nonconvex, nonconcave, and nonsmooth saddle point problems characterized by the weak Minty Variational Inequality (MVI). The first algorithm, Nonconvex-Nonconcave Primal-Dual Hybrid Gradient (NC-PDHG), extends the well-known Primal-Dual Hybrid Gradient (PDHG) method to this challenging problem class. The second algorithm, Nonconvex-Nonconcave Stochastic Primal-Dual Hybrid Gradient (NC-SPDHG), incorporates a randomly extrapolated prima…

Almost uniform convergence for noncommutative Vilenkin-Fourier series
Yong Jiao, Sijie Luo, Tiantian Zhao, Dejian Zhou
https://arxiv.org/abs/2506.14431 htt…

Almost uniform convergence for noncommutative Vilenkin-Fourier series
In the present paper, we study almost uniform convergence for noncommutative Vilenkin-Fourier series. Precisely, we establish several noncommutative (asymmetric) maximal inequalities for the Cesàro means of the noncommutative Vilenkin-Fourier series, which in turn give the corresponding almost uniform convergence. The primary strategy in our proof is to explore a noncommutative generalization of Sunouchi square function operator, and the very recent advance of the noncommutative Calderón-Zygm…

Users have uploaded 5,000 AI models, previously banned from Civitai for generating nonconsensual sexual content of real people, to Hugging Face (Emanuel Maiberg/404 Media)
https://www.404media.co/hugging-face-is-hosting-5-000-nonconsensual-ai-mod…

Hugging Face Is Hosting 5,000 Nonconsensual AI Models of Real People
Users have reuploaded 5,000 models used to generate nonconsensual sexual content of real people to Hugging Face after they were banned from Civitai.

A ringed-space-like structure on coalgebras for noncommutative algebraic geometry
So Nakamura
https://arxiv.org/abs/2506.14689 https://

A ringed-space-like structure on coalgebras for noncommutative algebraic geometry
Inspired by the perspective of Reyes' noncomutative spectral theory, we attempt to develop noncommutative algebraic geometry by introducing ringed coalgebras, which can be thought of as a noncommutative generalization of schemes over a field $k$. These objects arise from fully residually finite-dimensional(RFD) algebras introduced by Reyes and from schemes locally of finite type over $k$. The construction uses the Heyneman-Sweedler finite dual coalgebra and the Takeuchi underlying coalgebra. Wh…

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Nina Simone:
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https://open.spotify.com/track/5ywoRjfVIlcJiSAxwPT3Pt

A Nonconforming Finite Element Method for Elliptic Interface Problems on Locally Anisotropic Meshes
Hua Wang, Qichen Zhang
https://arxiv.org/abs/2506.15077

A Nonconforming Finite Element Method for Elliptic Interface Problems on Locally Anisotropic Meshes
We propose a new nonconforming \(P_1\) finite element method for elliptic interface problems. The method is constructed on a locally anisotropic mixed mesh, which is generated by fitting the interface through a simple connection of intersection points on an interface-unfitted background mesh, as introduced in \cite{Hu2021optimal}. We first establish interpolation error estimates on quadrilateral elements satisfying the regular decomposition property (RDP). Building on this, the main contributio…

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…

A noncommutative construction of families of biunitary matrices and application to subfactors
Keshab Chandra Bakshi, Satyajit Guin, Guruprasad
https://arxiv.org/abs/2506.14351

A noncommutative construction of families of biunitary matrices and application to subfactors
We introduce a construction that, given a pair (u,v) of complex Hadamard matrices of the same order, generates infinitely many biunitary matrices of varying (and distinct) orders. As a key application, this framework yields nested sequences of vertex model subfactors that are not a tower of downward basic construction. Notably, the construction is noncommutative: interchanging the matrices (i.e., considering (v,u) instead of (u,v)) can lead to non-isomorphic subfactors. Focusing on the Hadamard…

On second-order weak sharp minima of general nonconvex set-constrained optimization problems
Xiaoxiao Ma, Wei Ouyang, Jane Ye, Binbin Zhang
https://arxiv.org/abs/2507.12682

On second-order weak sharp minima of general nonconvex set-constrained optimization problems
This paper explores local second-order weak sharp minima for a broad class of nonconvex optimization problems. We propose novel second-order optimality conditions formulated through the use of classical and lower generalized support functions. These results are based on asymptotic second-order tangent cones and outer second-order tangent sets. Specifically, our findings eliminate the necessity of assuming convexity in the constraint set and/or the outer second-order tangent set, or the nonempti…

Heavy Ball and Nesterov Accelerations with Hessian-driven Damping for Nonconvex Optimization
N. Hadjisavvas, F. Lara, R. T. Marcavillaca, P. T. Vuong
https://arxiv.org/abs/2506.15632

Heavy Ball and Nesterov Accelerations with Hessian-driven Damping for Nonconvex Optimization
In this work, we investigate a second-order dynamical system with Hessian-driven damping tailored for a class of nonconvex functions called strongly quasiconvex. Buil\-ding upon this continuous-time model, we derive two discrete-time gra\-dient-based algorithms through time discretizations. The first is a Heavy Ball method with Hessian correction, incorporating cur\-va\-tu\-re-dependent terms that arise from discretizing the Hessian damping component. The second is a Nesterov-type accelerated m…