# Detecting Metastable Basins in High Dimensions via Marginal Trajectory Distribution Discrimination

arXiv: https://arxiv.org/abs/2605.24136 · HTML: https://mlsanity.com/paper/2605.24136/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 39 references that are in the map.
- First posted on arXiv 22 May 2026.

## Builds on (most cited first, 8 of 8)

- [Exploration by Random Network Distillation](https://mlsanity.com/paper/1810.12894/) (2018)
- [VAMPnets: Deep learning of molecular kinetics](https://mlsanity.com/paper/1710.06012/) (2017)
- [Online stochastic gradient descent on non-convex losses from high-dimensional inference](https://mlsanity.com/paper/2003.10409/) (2020)
- [OpenMM 8: Molecular Dynamics Simulation with Machine Learning Potentials](https://mlsanity.com/paper/2310.03121/) (2023)
- [Online Stochastic Gradient Descent with Arbitrary Initialization Solves Non-smooth, Non-convex Phase Retrieval](https://mlsanity.com/paper/1910.12837/) (2019)
- [Stochasticity helps to navigate rough landscapes: comparing gradient-descent-based algorithms in the phase retrieval problem](https://mlsanity.com/paper/2103.04902/) (2021)
- [Variational Koopman models: slow collective variables and molecular kinetics from short off-equilibrium simulations](https://mlsanity.com/paper/1610.06773/) (2016)
- [Characterizing metastable states with the help of machine learning](https://mlsanity.com/paper/2204.07391/) (2022)

## Abstract (arXiv)

We study the problem of identifying dynamically distinct basins of attraction in high dimensional time-homogeneous Markov processes using only trajectory sampling. This problem is fundamental in the analysis of metastable dynamical systems, where the process rapidly mixes within basins while transitions between basins occur rarely on the timescale of interest, or even when the state space is reducible. Existing approaches typically rely on spatial discretization or spectral analysis of estimated transition operators, which can become unreliable in high dimensional settings or when the underlying basin geometry is highly nonlinear. We propose a discriminative approach to basin identification based on marginal trajectory distribution comparison. We prove a simple risk separation result: if two initial states belong to the same basin, the Bayes-optimal classifier distinguishing their marginal trajectory distributions achieves risk close to 1/2, whereas if they lie in distinct basins, the optimal risk is close to zero. This observation reduces basin detection to a two-sample discrimination problem between marginal trajectory distributions. Motivated by this principle, we develop a neural algorithm that receives a set of candidate basin representatives and iteratively merges them by estimating classification risk with a neural network that approximates the Bayes classifier. We evaluate the method on various metastable systems. These include synthetic systems constructed by embedding low-dimensional dynamics into high dimensional noisy ambient spaces. In these settings, standard spectral and clustering-based methods often fail, while our approach accurately recovers the underlying basin structure. These results display a shortcoming of existing methods and highlight trajectory discrimination as an effective tool for identifying dynamical basins in high dimensional stochastic systems.