CARD: Coarse-to-fine Autoregressive Modeling with Radix-based Decomposition for Transferable Free Energy Estimation

2026-05-04

AI Summary

This work addresses the limitations of existing free energy estimation methods, which either rely on computationally expensive molecular dynamics simulations or employ deep learning models with insufficient expressivity and generalization. The authors propose a hybrid discrete-continuous autoregressive generative model based on cardinality decomposition. By employing bijective coordinate encoding to transform 3D molecular structures into learnable sequences and integrating zero-free-energy distribution modeling, the method enables absolute free energy estimation for arbitrary systems without requiring alchemical pathways. Evaluated on diverse unseen molecular systems, the approach achieves accuracy comparable to classical methods while accelerating inference by approximately 40-fold, substantially improving both transferability and computational efficiency.

Abstract

Estimating free energy differences quantifies thermodynamic preferences in molecular interactions, which is central to chemistry and drug discovery. Despite fruitful progress, existing methods still face key limitations: classical computational approaches remain prohibitively expensive due to their reliance on extensive molecular dynamics simulations, while deep learning-based methods are constrained by either less-expressive generative models or input dimensions tied to a specific system, resulting in negligible generalization. To address these challenges, we propose CARD, a generative framework that employs a novel radix-based decomposition to bijectively convert 3D coordinates into mixed discrete-continuous sequences, enabling coarse-to-fine autoregressive modeling with enhanced expressiveness. Notably, the model corresponds to a distribution with zero free energy, serving as a proposal for absolute free energy computation of arbitrary systems without relying on alchemical pathways. Experiments across diverse tasks demonstrate that CARD matches the accuracy of classical computational methods on unseen systems with diverse topologies, while achieving an approximately 40-fold speedup in inference.

Problem

• free energy estimation
• molecular dynamics
• deep learning
• generalization
• thermodynamic preferences

Innovation

• radix-based decomposition
• coarse-to-fine autoregressive modeling
• free energy estimation
• transferable generative model
• zero free energy proposal