Tootfinder

Sufficiency-principled Transfer Learning via Model Averaging
Xiyuan Zhang, Huihang Liu, Xinyu Zhang
https://arxiv.org/abs/2507.15416 https://

Sufficiency-principled Transfer Learning via Model Averaging
When the transferable set is unknowable, transfering informative knowledge as much as possible\textemdash a principle we refer to as \emph{sufficiency}, becomes crucial for enhancing transfer learning effectiveness. However, existing transfer learning methods not only overlook the sufficiency principle, but also rely on restrictive single-similarity assumptions (\eg individual or combinatorial similarity), leading to suboptimal performance. To address these limitations, we propose a sufficiency…

Stability for multiple Lamb dipoles
Ken Abe, In-Jee Jeong, Yao Yao
https://arxiv.org/abs/2507.16474 https://arxiv.org/pdf/2507.16474

Stability for multiple Lamb dipoles
In the class of nonnegative vorticities on the half-plane, we establish the Lyapunov stability of finite sums of Lamb dipoles under the initial assumptions that the dipoles are sufficiently separated and that the faster dipoles are positioned to the right of the slower ones. Our approach combines sharp energy estimates near the Lamb dipoles with a Lagrangian bootstrapping scheme, enabling us to quantify the exchanges of circulation, enstrophy, impulse, and energy between various parts of the so…

Entropies of Cox-Ingersoll-Ross and Bessel processes as functions of time and of related parameters
Ivan Kucha, Yuliya Mishura, Kostiantyn Ralchenko
https://arxiv.org/abs/2507.14684

Entropies of Cox-Ingersoll-Ross and Bessel processes as functions of time and of related parameters
We investigate the long-time asymptotic behavior of various entropy measures associated with the Cox-Ingersoll-Ross (CIR) and squared Bessel processes. As the one-dimensional distributions of both processes follow noncentral chi-squared laws, we first derive sufficient conditions for the existence of these entropy measures for a noncentral chi-squared random variable. We then analyze their limiting behavior as the noncentrality parameter approaches zero and apply these results to the CIR and sq…

On isomorphisms of semi-free Hamiltonian $S^1$-manifolds and fixed point data
Liat Kessler, Nikolas Wardenski
https://arxiv.org/abs/2505.14000 https://

On isomorphisms of semi-free Hamiltonian $S^1$-manifolds and fixed point data
Following Gonzales, we answer the question of whether the isomorphism type of a semi-free Hamiltonian $S^1$-manifold of dimension six is determined by certain data on the critical levels. We first give counter examples showing that Gonzales' assumptions are not sufficient for a positive answer. Then we prove that it is enough to further assume that the reduced spaces of dimension four are symplectic rational surfaces and the interior fixed surfaces are restricted to at most one level. The addit…

Efficient Parallel Training Methods for Spiking Neural Networks with Constant Time Complexity
Wanjin Feng, Xingyu Gao, Wenqian Du, Hailong Shi, Peilin Zhao, Pengcheng Wu, Chunyan Miao
https://arxiv.org/abs/2506.12087

Efficient Parallel Training Methods for Spiking Neural Networks with Constant Time Complexity
Spiking Neural Networks (SNNs) often suffer from high time complexity $O(T)$ due to the sequential processing of $T$ spikes, making training computationally expensive. In this paper, we propose a novel Fixed-point Parallel Training (FPT) method to accelerate SNN training without modifying the network architecture or introducing additional assumptions. FPT reduces the time complexity to $O(K)$, where $K$ is a small constant (usually $K=3$), by using a fixed-point iteration form of Leaky Inte…

An infinite horizon sufficient stochastic maximum principle for regime switching diffusions and applications
Kai Ding, Xun Li, Siyu Lv, Xin Zhang
https://arxiv.org/abs/2506.11523 …

An infinite horizon sufficient stochastic maximum principle for regime switching diffusions and applications
This paper is concerned with a discounted stochastic optimal control problem for regime switching diffusion in an infinite horizon. First, as a preliminary with particular interests in its own right, the global well-posedness of infinite horizon forward and backward stochastic differential equations with Markov chains and the asymptotic property of their solutions when time goes to infinity are obtained. Then, a sufficient stochastic maximum principle for optimal controls is established via a d…

On pure monomorphisms and pure epimorphisms in accessible categories
Leonid Positselski
https://arxiv.org/abs/2506.13374 https://arxi…

On pure monomorphisms and pure epimorphisms in accessible categories
In all $κ$-accessible additive categories, $κ$-pure monomorphisms and $κ$-pure epimorphisms are well-behaved, as shown in our previous paper arXiv:2311.02418. This is known to be not always true in $κ$-accessible nonadditive categories. Nevertheless, mild assumptions on a $κ$-accessible category are sufficient to prove good properties of $κ$-pure monomorphisms and $κ$-pure epimorphisms. In particular, in a $κ$-accessible category with finite products, all $κ$-pure monomorphisms are $κ…

Parsimonious Compactly Supported Covariance Models in the Gauss Hypergeometric Class: Identifiability, Reparameterizations, and Asymptotic Properties
Moreno Bevilacqua, Christian Caama\~no-Carrillo, Tarik Faouzi, Xavier Emery
https://arxiv.org/abs/2506.13646

Parsimonious Compactly Supported Covariance Models in the Gauss Hypergeometric Class: Identifiability, Reparameterizations, and Asymptotic Properties
We study the covariance model belonging to the Gauss hypergeometric ($GH$) class, a highly flexible and compactly supported correlation model (kernel). This class includes the well-known Generalized Wendland ($GW$) and Matérn ($MT$) kernels as special cases. First, we provide necessary and sufficient conditions for the validity of the $\mathcal{GH}$ model. We then demonstrate that this family of models suffers from identifiability issues under both increasing and fixed-domain asymptotics. To…

Parabolic De Giorgi classes with doubly nonlinear, nonstandard growth: local boundedness under exact integrability assumptions
Simone Ciani, Eurica Henriques, Mariia O. Savchenko, Igor I. Skrypnik
https://arxiv.org/abs/2506.14258

Parabolic De Giorgi classes with doubly nonlinear, nonstandard growth: local boundedness under exact integrability assumptions
We define a suitable class $\mathcal{PDG}$ of functions bearing unbalanced energy estimates, that are embodied by local weak subsolutions to doubly nonlinear, double-phase, Orlicz-type and fully anisotropic operators. Yet we prove that members of $\mathcal{PDG}$ are locally bounded, under critical, sub-critical and limit growth conditions typical of singular parabolic operators, with quantitative a priori estimates that follow the lines of the pioneering work of Ladyzhenskaya, Solonnikov and Ur…

Towards Robust Causal Effect Identification Beyond Markov Equivalence
Kai Z. Teh, Kayvan Sadeghi, Terry Soo
https://arxiv.org/abs/2506.15561 https://

Towards Robust Causal Effect Identification Beyond Markov Equivalence
Causal effect identification typically requires a fully specified causal graph, which can be difficult to obtain in practice. We provide a sufficient criterion for identifying causal effects from a candidate set of Markov equivalence classes with added background knowledge, which represents cases where determining the causal graph up to a single Markov equivalence class is challenging. Such cases can happen, for example, when the untestable assumptions (e.g. faithfulness) that underlie causal d…