# Deformations of Boltzmann Distributions

arXiv: https://arxiv.org/abs/2210.13772 · HTML: https://mlsanity.com/paper/2210.13772/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 26 references that are in the map.
- First posted on arXiv 25 Oct 2022.

## Builds on (most cited first, 13 of 13)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities](https://mlsanity.com/paper/2006.02425/) (2020)
- [Sampling using SU(N) gauge equivariant flows](https://mlsanity.com/paper/2008.05456/) (2020)
- [Learning Lattice Quantum Field Theories with Equivariant Continuous Flows](https://mlsanity.com/paper/2207.00283/) (2022)
- [Introduction to Normalizing Flows for Lattice Field Theory](https://mlsanity.com/paper/2101.08176/) (2021)
- [Gauge-equivariant flow models for sampling in lattice field theories with pseudofermions](https://mlsanity.com/paper/2207.08945/) (2022)
- [Flow-based sampling for fermionic lattice field theories](https://mlsanity.com/paper/2106.05934/) (2021)
- [Scaling Up Machine Learning For Quantum Field Theory with Equivariant Continuous Flows](https://mlsanity.com/paper/2110.02673/) (2021)
- [Flow-based sampling in the lattice Schwinger model at criticality](https://mlsanity.com/paper/2202.11712/) (2022)
- [Integrable Nonparametric Flows](https://mlsanity.com/paper/2012.02035/) (2020)

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

- [Learning Interpolations between Boltzmann Densities](https://mlsanity.com/paper/2301.07388/) (2023)

## Abstract (arXiv)

Consider a one-parameter family of Boltzmann distributions pt(x) = tfrac1Zte-St(x). This work studies the problem of sampling from pt0 by first sampling from pt1 and then applying a transformation Psit1t0 so that the transformed samples follow pt0. We derive an equation relating Psi and the corresponding family of unnormalized log-likelihoods St. The utility of this idea is demonstrated on the φ4 lattice field theory by extending its defining action S0 to a family of actions St and finding a τ such that normalizing flows perform better at learning the Boltzmann distribution pτ than at learning p0.