Higher-Order Molecular Grammars for Generative and Foundation Models in Chemistry

2026-10-01

AI Summary

This study addresses the bottleneck wherein molecular models struggle to efficiently encode higher-order topological structures and decode valid molecules. To this end, we propose the HGR framework, which introduces the first context-free higher-order grammar representation. By elevating molecules into simplicial complexes and parsing them into rule sequences, HGR achieves compatibility with standard sequence models while fully preserving topological expressiveness. Furthermore, we establish the RingDiv benchmark alongside the RDI evaluation metric. Experimental results demonstrate that HGR ranks first in FCD across five generative benchmarks, with generation validity guaranteed by construction and superior distribution alignment. Additionally, it attains the highest average AUC over seven MoleculeNet tasks, significantly outperforming existing baselines.

Abstract

Molecular learning models are strongly shaped by their underlying representations. Yet standard sequential and graph formalisms struggle to explicitly encode higher-order topology, such as ring systems and recurring motifs. Existing higher-order representations can capture these structures directly, but they are often computationally demanding and difficult to decode into valid molecules. Here, we introduce Higher-order Grammar Representation (HGR), a principled, topology-aware framework that lifts molecules to combinatorial complexes and parses each complex into a compact sequence of production rules under a context-free higher-order grammar. By serialising higher-order topology into rule sequences, HGR makes these structures directly compatible with standard sequence models, avoiding the computational overhead of explicit higher-order encodings while preserving topological expressiveness. To reduce benchmark bias towards simple ring systems, we construct RingDiv, a ring-enriched benchmark containing 1.18 million molecules, including the curated RingDiv300k subset, and introduce the ring diversity index (RDI) to quantify ring-system coverage. In molecular generation, HGR-based models uniquely combine 100% validity by construction with leading distributional alignment, ranking first in FCD on all five generation benchmarks. In representation learning, HGR-FM achieves the highest mean AUC across seven MoleculeNet benchmarks under both transfer protocols, improving on the strongest baseline by 8.3 and 3.3 AUC points under probing and full fine-tuning, respectively. Collectively, these results establish HGR as an efficient higher-order representation for molecular generation and transferable representation learning.

Problem

• molecular representation
• higher-order topology
• molecular generation
• representation learning
• ring systems

Innovation

• Higher-order Grammar Representation
• Combinatorial Complexes
• Molecular Generation
• Representation Learning
• Ring Diversity Index