Normalizing flows

Normalizing flows ($f$ below) are a type of invertible deep learning framework capable of generating samples from a target distribution. It maps configuration $\text{x}$ drawn from a prior distribution $q(\text{x})$ to a target distribution $q^{\prime }(\text{x})$.

Details

Since $f$ is invertible, the output probability distribution can be mapped as:

$$q^{\prime }({\text{x}}^{\prime })=q(\text{x})|\det J_f(\text{x}){|}^{-1}$$

where $\det J_f$ is the determinant of the Jacobian of $f$ and $|\det J_f(\text{x}){|}^{-1}=|\det J_{f^{-1}}(\text{x’})|$

The entirety of this note liberally cites from (1).

Applications

• They have been used in conjunction with Replica-exchange molecular dynamics (1)
• They have been used for conformational sampling via fine-tuned AlphaFold2 and ESMFold (2)

1.

Invernizzi M, Krämer A, Clementi C, Noé F. Skipping the Replica Exchange Ladder with Normalizing Flows. The Journal of Physical Chemistry Letters. 2022;13(50):11643–9. Available from: https://doi.org/10.1021/acs.jpclett.2c03327

2.

Jing H, Gao Z, Xu S, Shen T, Peng Z, He S, et al. Accurate prediction of antibody function and structure using bio-inspired antibody language model. Briefings in Bioinformatics. 2024;25(4). Available from: https://doi.org/10.1093/bib/bbae245