# The fast committor machine: Interpretable prediction with kernels

arXiv: https://arxiv.org/abs/2405.10410 · HTML: https://mlsanity.com/paper/2405.10410/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 46 references that are in the map.
- First posted on arXiv 16 May 2024.

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

- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences](https://mlsanity.com/paper/1807.02582/) (2018)
- [Solving for high dimensional committor functions using artificial neural networks](https://mlsanity.com/paper/1802.10275/) (2018)
- [Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations](https://mlsanity.com/paper/2207.06503/) (2022)
- [Computing Committor Functions for the Study of Rare Events Using Deep Learning](https://mlsanity.com/paper/1906.06285/) (2019)
- [Average gradient outer product as a mechanism for deep neural collapse](https://mlsanity.com/paper/2402.13728/) (2024)
- [Calibration and generalizability of probabilistic models on low-data chemical datasets with DIONYSUS](https://mlsanity.com/paper/2212.01574/) (2022)
- [Robust, randomized preconditioning for kernel ridge regression](https://mlsanity.com/paper/2304.12465/) (2023)

## Built on by (most cited first, 5 of 5)

- [Embrace rejection: Kernel matrix approximation by accelerated randomly pivoted Cholesky](https://mlsanity.com/paper/2410.03969/) (2024)
- [Feature maps for the Laplacian kernel and its generalizations](https://mlsanity.com/paper/2502.15575/) (2025)
- [An exact multiple-time-step variational formulation for the committor and the transition rate](https://mlsanity.com/paper/2509.03539/) (2025)
- [Nonparametric Reaction Coordinate Optimization with Histories: A Framework for Rare Event Dynamics](https://mlsanity.com/paper/2508.07326/) (2025)
- [Machine learning kinetics from molecular dynamics data](https://mlsanity.com/paper/2609.17736/) (2026)

## Abstract (arXiv)

In the study of stochastic systems, the committor function describes the probability that a system starting from an initial configuration x will reach a set B before a set A. This paper introduces an efficient and interpretable algorithm for approximating the committor, called the "fast committor machine" (FCM). The FCM uses simulated trajectory data to build a kernel-based model of the committor. The kernel function is constructed to emphasize low-dimensional subspaces that optimally describe the A to B transitions. The coefficients in the kernel model are determined using randomized linear algebra, leading to a runtime that scales linearly in the number of data points. In numerical experiments involving a triple-well potential and alanine dipeptide, the FCM yields higher accuracy and trains more quickly than a neural network with the same number of parameters. The FCM is also more interpretable than the neural net.