# Probabilistic Smoothing with Ratio-Monotone Transforms for Global Optimization

arXiv: https://arxiv.org/abs/2605.27316 · HTML: https://mlsanity.com/paper/2605.27316/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 17 references that are in the map.
- First posted on arXiv 26 May 2026.

## Builds on (most cited first, 9 of 9)

- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [Distillation as a Defense to Adversarial Perturbations against Deep Neural Networks](https://mlsanity.com/paper/1511.04508/) (2015)
- [ZO-AdaMM: Zeroth-Order Adaptive Momentum Method for Black-Box Optimization](https://mlsanity.com/paper/1910.06513/) (2019)
- [On Graduated Optimization for Stochastic Non-Convex Problems](https://mlsanity.com/paper/1503.03712/) (2015)
- [Single Loop Gaussian Homotopy Method for Non-convex Optimization](https://mlsanity.com/paper/2203.05717/) (2022)
- [Generalizing Gaussian Smoothing for Random Search](https://mlsanity.com/paper/2211.14721/) (2022)
- [Global Optimization with A Power-Transformed Objective and Gaussian Smoothing](https://mlsanity.com/paper/2412.05204/) (2024)

## Abstract (arXiv)

Probabilistic smoothing is a standard tool for global optimization, but existing methods rely on Gaussian kernels and specific transforms, often resulting in strong hyperparameter sensitivity and limited robustness. We propose a general smoothing framework that combines flexible symmetric unimodal kernels with monotonic ratio-based transformations. Under mild conditions, we show that the smoothed objective preserves the global maximizer and that all stationary points concentrate near the true optimum for sufficiently large amplification, without requiring a decreasing smoothing schedule. We further provide explicit complexity bounds for stochastic gradient ascent and show that a leave-one-out baseline provably reduces variance. Experiments on high-dimensional benchmarks and black-box adversarial attacks demonstrate improved robustness and competitive performance.