arXiv:2603. 13546v2 Announce Type: replace Abstract: We introduce Probabilistic Gaussian Homotopy (PGH), a probability-space continuation framework for nonconvex optimization.
arXiv:2511. 13592v2 Announce Type: replace-cross Abstract: The existing method of GS-PowerOpt solves the non-convex optimization problem of the form $\max_{\boldsymbol{x} \in \mathbb{R}^d} f(\boldsymbol{x})$ through maximizing a Gaussian-smoothed surrogate $F_{N,\sigma}(\boldsymbol{\mu}) = \mathbb{E}_{\boldsymbol{x}\sim\mathcal{N}(\boldsymbol{\mu},\sigma^2 I_d)}[e^{N f(\boldsymbol{x})}]$.
arXiv:2604. 17838v2 Announce Type: replace Abstract: Generative modeling within constrained sets is essential for scientific and engineering applications involving physical, geometric, or safety requirements (e.
arXiv:2601. 21026v2 Announce Type: replace-cross Abstract: Sampling configurations at thermodynamic equilibrium is a central challenge in statistical physics.
arXiv:2602. 02241v2 Announce Type: replace Abstract: Entropic optimal transport (EOT) in continuous spaces with quadratic cost is a classical tool for solving the domain translation problem.
arXiv:2608. 02844v1 Announce Type: cross Abstract: We develop a class of diffusion-based stochastic particle optimisation methods for loss functions with intractable gradients.
arXiv:2607. 23008v1 Announce Type: cross Abstract: Optimization over probability measures has become an increasingly important paradigm in modern machine learning, scientific computing, and uncertainty quantification.
arXiv:2606. 07841v1 Announce Type: cross Abstract: Black-box variational inference (BBVI) is a methodology for posterior approximation that relies on stochastic optimization.
arXiv:2602. 10204v2 Announce Type: replace Abstract: We introduce MVN-Grad (Momentum on Variance-Normalized Gradients), an Adam-style optimizer that improves stability and performance by combining two complementary ideas: variance-based normalization and momentum applied after normalization.
arXiv:2606. 30228v1 Announce Type: new Abstract: Modern engineering workflows increasingly rely on massive parallel simulation, driving the need for scalable, large-batch Bayesian Optimization (BO).
arXiv:2605. 24795v2 Announce Type: replace-cross Abstract: We study stochastic density control between Gaussian-mixture endpoint distributions under Brownian prior dynamics.
Energy-Based Models (EBMs) provide an interpretable framework for generative modeling of scientific data, but poor Markov Chain Monte Carlo mixing often limits their reliability. We introduce a training algorithm based on Parallel Trajectory Tempering (PTT), which exploits the continuity of the optimization path to maintain equilibrium sampling throughout learning.
arXiv:2603. 09923v4 Announce Type: replace Abstract: Exponential moving averages (EMAs) are a central component of widely used adaptive optimizers such as Adam.