Implicit Neural Representations of Molecular Vector-Valued Functions

TL;DR

This paper introduces molecular neural fields, a novel vector-valued function representation for molecules that captures complex features, enabling resolution-independent interpolation and generation of molecular structures, with promising applications in protein modeling.

Contribution

The paper proposes molecular neural fields as a new representation for molecules, demonstrating their ability to capture external features and enable superresolution reconstruction and embedding.

Findings

Molecular neural fields are compact and resolution independent.

They enable interpolation between molecular conformations.

Proof-of-concept applications include protein-ligand reconstruction and molecular embedding.

Abstract

Molecules have various computational representations, including numerical descriptors, strings, graphs, point clouds, and surfaces. Each representation method enables the application of various machine learning methodologies from linear regression to graph neural networks paired with large language models. To complement existing representations, we introduce the representation of molecules through vector-valued functions, or $n$-dimensional vector fields, that are parameterized by neural networks, which we denote molecular neural fields. Unlike surface representations, molecular neural fields capture external features and the hydrophobic core of macromolecules such as proteins. Compared to discrete graph or point representations, molecular neural fields are compact, resolution independent and inherently suited for interpolation in spatial and temporal dimensions. These properties inherited by molecular neural fields lend themselves to tasks including the generation of molecules based on their desired shape, structure, and composition, and the resolution-independent interpolation between molecular conformations in space and time. Here, we provide a framework and proofs-of-concept for molecular neural fields, namely, the parametrization and superresolution reconstruction of a protein-ligand complex using an auto-decoder architecture and the embedding of molecular volumes in latent space using an auto-encoder architecture.