Molecular Representations in Implicit Functional Space via Hyper-Networks
🤖 AI Summary
This work proposes a novel molecular representation by modeling molecules as continuous functions—termed molecular fields—over 3D space, in contrast to conventional approaches that treat molecules as discrete objects and thereby overlook their intrinsic continuous field characteristics. To ensure SE(3) invariance, the molecular fields are defined in a canonical coordinate frame, and a sequential hypernetwork is employed to learn the distribution over these fields. The method introduces structured weight tokenization to encode shared priors, enabling a paradigm shift from discrete embeddings to a continuous function space. Experimental results demonstrate that this representation significantly enhances generalization performance in both molecular dynamics simulations and property prediction tasks, while exhibiting strong robustness to variations in molecular discretization and query mechanisms.
Application Category
📝 Abstract
Molecular representations fundamentally shape how machine learning systems reason about molecular structure and physical properties. Most existing approaches adopt a discrete pipeline: molecules are encoded as sequences, graphs, or point clouds, mapped to fixed-dimensional embeddings, and then used for task-specific prediction. This paradigm treats molecules as discrete objects, despite their intrinsically continuous and field-like physical nature. We argue that molecular learning can instead be formulated as learning in function space. Specifically, we model each molecule as a continuous function over three-dimensional (3D) space and treat this molecular field as the primary object of representation. From this perspective, conventional molecular representations arise as particular sampling schemes of an underlying continuous object. We instantiate this formulation with MolField, a hyper-network-based framework that learns distributions over molecular fields. To ensure physical consistency, these functions are defined over canonicalized coordinates, yielding invariance to global SE(3) transformations. To enable learning directly over functions, we introduce a structured weight tokenization and train a sequence-based hyper-network to model a shared prior over molecular fields. We evaluate MolField on molecular dynamics and property prediction. Our results show that treating molecules as continuous functions fundamentally changes how molecular representations generalize across tasks and yields downstream behavior that is stable to how molecules are discretized or queried.
Problem
Research questions and friction points this paper is trying to address.
molecular representations
continuous functions
function space
molecular fields
discretization
Innovation
Methods, ideas, or system contributions that make the work stand out.
molecular field
function space
hyper-network
SE(3) invariance
continuous representation
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