Mass spectrometry, especially so-called tandem mass spectrometry, is commonly used to assess the chemical diversity of samples. The resulting mass fragmentation spectra are representations of molecules of which the structure may have not been determined. This poses the challenge of experimentally determining or computationally predicting molecular structures from mass spectra. An alternative option is to predict molecular properties or molecular similarity directly from spectra. Various methodologies have been proposed to embed mass spectra for further use in machine learning tasks. However, these methodologies require preprocessing of the spectra, which often includes binning or sub-sampling peaks with the main reasoning of creating uniform vector sizes and removing noise. Here, we investigate two alternatives to the binning of mass spectra before down-stream machine learning tasks, namely, set-based and graph-based representations. Comparing the two proposed representations to train a set transformer and a graph neural network on a regression task, respectively, we show that they both perform substantially better than a multilayer perceptron trained on binned data.

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.