# Configuration Interaction Guided Sampling with Interpretable Restricted Boltzmann Machine

arXiv: https://arxiv.org/abs/2409.06146 · HTML: https://mlsanity.com/paper/2409.06146/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 62 references that are in the map.
- First posted on arXiv 10 Sep 2024.

## Builds on (most cited first, 4 of 4)

- [Emergence of Compositional Representations in Restricted Boltzmann Machines](https://mlsanity.com/paper/1611.06759/) (2016)
- [Revisiting the Gelman-Rubin Diagnostic](https://mlsanity.com/paper/1812.09384/) (2018)
- [Learning a Restricted Boltzmann Machine using biased Monte Carlo sampling](https://mlsanity.com/paper/2206.01310/) (2022)
- [Hierarchical Models as Marginals of Hierarchical Models](https://mlsanity.com/paper/1508.03606/) (2015)

## Abstract (arXiv)

We propose a data-driven approach using a Restricted Boltzmann Machine (RBM) to solve the Schr"odinger equation in configuration space. Traditional Configuration Interaction (CI) methods construct the wavefunction as a linear combination of Slater determinants, but this becomes computationally expensive due to the factorial growth in the number of configurations. Our approach extends the use of a generative model such as the RBM by incorporating a taboo list strategy to enhance efficiency and convergence. The RBM is used to efficiently identify and sample the most significant determinants, thus accelerating convergence and substantially reducing computational cost. This method achieves up to 99.99% of the correlation energy while using up to four orders of magnitude fewer determinants compared to full CI calculations and up to two orders of magnitude fewer than previous state of the art methods. Beyond efficiency, our analysis reveals that the RBM learns electron distributions over molecular orbitals by capturing quantum patterns that resemble Radial Distribution Functions (RDFs) linked to molecular bonding. This suggests that the learned pattern is interpretable, highlighting the potential of machine learning for explainable quantum chemistry