Tootfinder

Stochastic gradient descent based variational inference for infinite-dimensional inverse problems
Jiaming Sui, Junxiong Jia, Jinglai Li
https://arxiv.org/abs/2506.08380

Stochastic gradient descent based variational inference for infinite-dimensional inverse problems
This paper introduces two variational inference approaches for infinite-dimensional inverse problems, developed through gradient descent with a constant learning rate. The proposed methods enable efficient approximate sampling from the target posterior distribution using a constant-rate stochastic gradient descent (cSGD) iteration. Specifically, we introduce a randomization strategy that incorporates stochastic gradient noise, allowing the cSGD iteration to be viewed as a discrete-time process.…

This https://arxiv.org/abs/2409.08469 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Improved Finite-Particle Convergence Rates for Stein Variational Gradient Descent
We provide finite-particle convergence rates for the Stein Variational Gradient Descent (SVGD) algorithm in the Kernelized Stein Discrepancy ($\mathsf{KSD}$) and Wasserstein-2 metrics. Our key insight is that the time derivative of the relative entropy between the joint density of $N$ particle locations and the $N$-fold product target measure, starting from a regular initial distribution, splits into a dominant `negative part' proportional to $N$ times the expected $\mathsf{KSD}^2$ and a smalle…

Introduction to Nonlinear Spectral Analysis
Leon Bungert, Yury Korolev
https://arxiv.org/abs/2506.08754 https://arxiv.org/pdf/2506.08…

Introduction to Nonlinear Spectral Analysis
These notes are meant as an introduction to the theory of nonlinear spectral theory. We will discuss the variational form of nonlninear eigenvalue problems and the corresponding non-linear Euler--Lagrange equations, as well as connections with gradient flows. For the latter ones, we will give precise conditions for finite time extinction and discuss convergence rates. We will use this theory to study asymptotic behaviour of nonlinear PDEs and present applications in $L^\infty$ variational probl…

Constrained Stein Variational Gradient Descent for Robot Perception, Planning, and Identification
Griffin Tabor, Tucker Hermans
https://arxiv.org/abs/2506.00589

Constrained Stein Variational Gradient Descent for Robot Perception, Planning, and Identification
Many core problems in robotics can be framed as constrained optimization problems. Often on these problems, the robotic system has uncertainty, or it would be advantageous to identify multiple high quality feasible solutions. To enable this, we present two novel frameworks for applying principles of constrained optimization to the new variational inference algorithm Stein variational gradient descent. Our general framework supports multiple types of constrained optimizers and can handle arbitra…

Markov Blanket Density and Free Energy Minimization
Luca M. Possati
https://arxiv.org/abs/2506.05794 https://arxiv.org/pdf/2506.05794…

Markov Blanket Density and Free Energy Minimization
This paper presents a continuous, information-theoretic extension of the Free Energy Principle through the concept of Markov blanket density, i.e., a scalar field that quantifies the degree of conditional independence between internal and external states at each point in space (ranging from 0 for full coupling to 1 for full separation). It demonstrates that active inference dynamics (including the minimization of variational and expected free energy) naturally emerge from spatial gradients in t…

This https://arxiv.org/abs/2412.04574 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Gradient flows of $(K,N)$-convex functions with negative $N$
We discuss $(K,N)$-convexity and gradient flows for $(K,N)$-convex functionals on metric spaces, in the case of real $K$ and negative $N$. In this generality, it is necessary to consider functionals unbounded from below and/or above, possibly attaining as values both the positive and the negative infinity. We prove several properties of gradient flows of $(K,N)$-convex functionals characterized by Evolution Variational Inequalities, including contractivity, regularity, and uniqueness.

This https://arxiv.org/abs/2502.16492 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Convergence of Clipped SGD on Convex $(L_0,L_1)$-Smooth Functions
We study stochastic gradient descent (SGD) with gradient clipping on convex functions under a generalized smoothness assumption called $(L_0,L_1)$-smoothness. Using gradient clipping, we establish a high probability convergence rate that matches the SGD rate in the $L$ smooth case up to polylogarithmic factors and additive terms. We also propose a variation of adaptive SGD with gradient clipping, which achieves the same guarantee. We perform empirical experiments to examine our theory and algor…

This https://arxiv.org/abs/2505.22398 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Numerical Optimization Strategies for the Variational Hamiltonian Ansatz in Noisy Quantum Environments
We conduct a benchmark of eight optimization algorithms for variational quantum chemistry using the tVHA, evaluating performance on $H_2$, $H_4$, and $LiH$ (in both full and active spaces) under noiseless and sampling noise conditions. Sampling noise fundamentally alters optimizer behavior, with gradient-based methods performing best in ideal conditions, while population-based algorithms, such as CMA-ES, show greater resilience under noise. Hartree-Fock initialization reduces the number of func…

Effective flows across diffusio-phoretic membranes
Kevin Wittkowski, Pier Giuseppe Ledda, Edoardo Carlo Giordano, Fran\c{c}ois Gallaire, Giuseppe Antonio Zampogna
https://arxiv.org/abs/2505.22197

Effective flows across diffusio-phoretic membranes
Flows enabled by phoretic mechanisms are of significant interest in several biological and biomedical processes, such as bacterial motion and targeted drug delivery. Here, we develop a homogenization-based macroscopic boundary condition which describes the effective flow across a diffusiophoretic microstructured membrane, where the interaction between the membrane walls and the solute particles is modeled via a potential-approach. We consider two cases where potential variations occur (i) at th…

This https://arxiv.org/abs/2505.13929 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Numerical analysis for the regularised total variation flow
We perform the numerical analysis of the regularised total variation flow using the gradient discretisation method (GDM). GDM is a unified convergence analysis framework that covers conforming and non-conforming numerical methods, for instance, conforming and non-conforming finite element, two-point flux approximation, etc.. In this paper, a fully discretised implicit scheme of the model is proposed, the existence and uniqueness of the solution to the scheme is proved, the stability and consist…