将分子视为三维空间中的连续函数,提升模型泛化能力。
Molecular Representations in Implicit Functional Space via Hyper-Networks
- 用超网络学习分子在3D空间的连续函数表示,替代离散编码。
- 在分子动力学和性质预测任务上,对离散化方式不敏感,性能更稳定。
- 适合需要高物理一致性的分子建模场景,如药物设计。
分子表征从根本上决定了机器学习系统对分子结构与物理性质的推理方式。现有方法多采用离散流程:将分子编码为序列、图或点云,映射到固定维度嵌入,再用于特定任务预测。这一范式将分子视为离散对象,忽视了其内在的连续场特性。本文提出将分子学习定义为函数空间中的学习:将每个分子建模为三维空间上的连续函数,以分子场作为核心表征对象。传统表征可视为该连续对象的特定采样方案。我们提出MolField框架,基于超网络学习分子场分布。为保证物理一致性,函数定义在规范坐标系下,实现对全局SE(3)变换的不变性。通过结构化权重标记化,训练序列型超网络以建模共享的分子场先验。在分子动力学与性质预测任务上验证,将分子视为连续函数能显著改变表征的跨任务泛化能力,且下游表现对分子离散化或查询方式具有稳定性。
原文摘要 · Abstract (English)
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.
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