# Using Witten Laplacians to locate index-1 saddle points

arXiv: https://arxiv.org/abs/2212.10135 · HTML: https://mlsanity.com/paper/2212.10135/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Dec 2022.

## Built on by (most cited first, 1 of 1)

- [Operator-Level Quantum Acceleration of Non-Logconcave Sampling](https://mlsanity.com/paper/2505.05301/) (2025)

## Abstract (arXiv)

We introduce a new stochastic algorithm to locate the index-1 saddle points of a function V:mathbb Rd → mathbb R, with d possibly large. This algorithm can be seen as an equivalent of the stochastic gradient descent which is a natural stochastic process to locate local minima. It relies on two ingredients: (i) the concentration properties on index-1 saddle points of the first eigenmodes of the Witten Laplacian (associated with V) on 1-forms and (ii) a probabilistic representation of a partial differential equation involving this differential operator. Numerical examples on simple molecular systems illustrate the efficacy of the proposed approach.