6 papers
RAISE: LLM-based Automated Heuristic Design with Robust Adversary Instance Search
Fei Liu, Alessio Figalli, Patrick Owen +1
Automated Heuristic Design (AHD) with Large Language Models (LLMs) has shown remarkable progress in discovering high-quality heuristics. However, existing LLM-based AHD methods opt…
Variational inference via radial transport
Luca Ghafourpour, Sinho Chewi, Alessio Figalli +1
In variational inference (VI), the practitioner approximates a high-dimensional distribution with a simple surrogate one, often a (product) Gaussian distribution. However, in…
Sharp comparisons between sliced and standard -Wasserstein distances
Guillaume Carlier, Alessio Figalli, Quentin Mérigot +1
Sliced Wasserstein distances are widely used in practice as a computationally efficient alternative to Wasserstein distances in high dimensions. In this paper, motivated by theoret…
Generic regularity of equilibrium measures for the logarithmic potential with external fields
Giacomo Colombo, Alessio Figalli
It is a well-known conjecture in -models and in their discrete counterpart that, generically, external potentials should be ``off-critical'' (or, equivalently, ``regular''). Exp…
Sharp Quantitative Stability for the Prékopa-Leindler and Borell-Brascamp-Lieb Inequalities
Alessio Figalli, Peter van Hintum, Marius Tiba
The Borell-Brascamp-Lieb inequality is a classical extension of the Prékopa-Leindler inequality, which in turn is a functional counterpart of the Brunn-Minkowski inequality. The s…
Improved stability versions of the Prékopa-Leindler inequality
Alessio Figalli, João P. G. Ramos
We consider the problem of stability for the Prékopa-Leindler inequality. Exploiting properties of the transport map between radially decreasing functions and a suitable functiona…