Spectral Analysis of Molecular Kernels: When Richer Features Do Not Guarantee Better Generalization

Understanding the spectral properties of kernels offers a principled perspective on generalization and representation quality. While deep models achieve state-of-the-art accuracy in molecular property prediction, kernel methods remain widely used for their robustness in low-data regimes and transparent theoretical grounding. Despite extensive studies of kernel spectra in machine learning, systematic spectral analyses of molecular kernels are scarce. In this work, we provide the first comprehensive spectral analysis of kernel ridge regression on the QM9 dataset, molecular fingerprint, pretrained transformer-based, global and local 3D representations across seven molecular properties. Surprisingly, richer spectral features, measured by four different spectral metrics, do not consistently improve accuracy. Pearson correlation tests further reveal that for transformer-based and local 3D representations, spectral richness can even have a negative correlation with performance. We also implement truncated kernels to probe the relationship between spectrum and predictive performance: in many kernels, retaining only the top 2% of eigenvalues recovers nearly all performance, indicating that the leading eigenvalues capture the most informative features. Our results challenge the common heuristic that "richer spectra yield better generalization" and highlight nuanced relationships between representation, kernel features, and predictive performance. Beyond molecular property prediction, these findings inform how kernel and self-supervised learning methods are evaluated in data-limited scientific and real-world tasks.

Unified Molecule Pre-training with Flexible 2D and 3D Modalities: Single and Paired Modality Integration

Molecular representation learning plays a crucial role in advancing applications such as drug discovery and material design. Existing work leverages 2D and 3D modalities of molecular information for pre-training, aiming to capture comprehensive structural and geometric insights. However, these methods require paired 2D and 3D molecular data to train the model effectively and prevent it from collapsing into a single modality, posing limitations in scenarios where a certain modality is unavailable or computationally expensive to generate. To overcome this limitation, we propose FlexMol, a flexible molecule pre-training framework that learns unified molecular representations while supporting single-modality input. Specifically, inspired by the unified structure in vision-language models, our approach employs separate models for 2D and 3D molecular data, leverages parameter sharing to improve computational efficiency, and utilizes a decoder to generate features for the missing modality. This enables a multistage continuous learning process where both modalities contribute collaboratively during training, while ensuring robustness when only one modality is available during inference. Extensive experiments demonstrate that FlexMol achieves superior performance across a wide range of molecular property prediction tasks, and we also empirically demonstrate its effectiveness with incomplete data. Our code and data are available at https://github.com/tewiSong/FlexMol.

MMM: Quantum-Chemical Molecular Representation Learning for Combinatorial Drug Recommendation

Drug recommendation is an essential task in machine learning-based clinical decision support systems. However, the risk of drug-drug interactions (DDI) between co-prescribed medications remains a significant challenge. Previous studies have used graph neural networks (GNNs) to represent drug structures. Regardless, their simplified discrete forms cannot fully capture the molecular binding affinity and reactivity. Therefore, we propose Multimodal DDI Prediction with Molecular Electron Localization Function (ELF) Maps (MMM), a novel framework that integrates three-dimensional (3D) quantum-chemical information into drug representation learning. It generates 3D electron density maps using the ELF. To capture both therapeutic relevance and interaction risks, MMM combines ELF-derived features that encode global electronic properties with a bipartite graph encoder that models local substructure interactions. This design enables learning complementary characteristics of drug molecules. We evaluate MMM in the MIMIC-III dataset (250 drugs, 442 substructures), comparing it with several baseline models. In particular, a comparison with the GNN-based SafeDrug model demonstrates statistically significant improvements in the F1-score (p = 0.0387), Jaccard (p = 0.0112), and the DDI rate (p = 0.0386). These results demonstrate the potential of ELF-based 3D representations to enhance prediction accuracy and support safer combinatorial drug prescribing in clinical practice.

Transformers Discover Molecular Structure Without Graph Priors

Graph Neural Networks (GNNs) are the dominant architecture for molecular machine learning, particularly for molecular property prediction and machine learning interatomic potentials (MLIPs). GNNs perform message passing on predefined graphs often induced by a fixed radius cutoff or k-nearest neighbor scheme. While this design aligns with the locality present in many molecular tasks, a hard-coded graph can limit expressivity due to the fixed receptive field and slows down inference with sparse graph operations. In this work, we investigate whether pure, unmodified Transformers trained directly on Cartesian coordinates$\unicode{x2013}$without predefined graphs or physical priors$\unicode{x2013}$can approximate molecular energies and forces. As a starting point for our analysis, we demonstrate how to train a Transformer to competitive energy and force mean absolute errors under a matched training compute budget, relative to a state-of-the-art equivariant GNN on the OMol25 dataset. We discover that the Transformer learns physically consistent patterns$\unicode{x2013}$such as attention weights that decay inversely with interatomic distance$\unicode{x2013}$and flexibly adapts them across different molecular environments due to the absence of hard-coded biases. The use of a standard Transformer also unlocks predictable improvements with respect to scaling training resources, consistent with empirical scaling laws observed in other domains. Our results demonstrate that many favorable properties of GNNs can emerge adaptively in Transformers, challenging the necessity of hard-coded graph inductive biases and pointing toward standardized, scalable architectures for molecular modeling.

Learning the Neighborhood: Contrast-Free Multimodal Self-Supervised Molecular Graph Pretraining

High-quality molecular representations are essential for property prediction and molecular design, yet large labeled datasets remain scarce. While self-supervised pretraining on molecular graphs has shown promise, many existing approaches either depend on hand-crafted augmentations or complex generative objectives, and often rely solely on 2D topology, leaving valuable 3D structural information underutilized. To address this gap, we introduce C-FREE (Contrast-Free Representation learning on Ego-nets), a simple framework that integrates 2D graphs with ensembles of 3D conformers. C-FREE learns molecular representations by predicting subgraph embeddings from their complementary neighborhoods in the latent space, using fixed-radius ego-nets as modeling units across different conformers. This design allows us to integrate both geometric and topological information within a hybrid Graph Neural Network (GNN)-Transformer backbone, without negatives, positional encodings, or expensive pre-processing. Pretraining on the GEOM dataset, which provides rich 3D conformational diversity, C-FREE achieves state-of-the-art results on MoleculeNet, surpassing contrastive, generative, and other multimodal self-supervised methods. Fine-tuning across datasets with diverse sizes and molecule types further demonstrates that pretraining transfers effectively to new chemical domains, highlighting the importance of 3D-informed molecular representations.

GeoGraph: Geometric and Graph-based Ensemble Descriptors for Intrinsically Disordered Proteins

While deep learning has revolutionized the prediction of rigid protein structures, modelling the conformational ensembles of Intrinsically Disordered Proteins (IDPs) remains a key frontier. Current AI paradigms present a trade-off: Protein Language Models (PLMs) capture evolutionary statistics but lack explicit physical grounding, while generative models trained to model full ensembles are computationally expensive. In this work we critically assess these limits and propose a path forward. We introduce GeoGraph, a simulation-informed surrogate trained to predict ensemble-averaged statistics of residue-residue contact-map topology directly from sequence. By featurizing coarse-grained molecular dynamics simulations into residue- and sequence-level graph descriptors, we create a robust and information-rich learning target. Our evaluation demonstrates that this approach yields representations that are more predictive of key biophysical properties than existing methods.

Functional Groups are All you Need for Chemically Interpretable Molecular Property Prediction

Molecular property prediction using deep learning (DL) models has accelerated drug and materials discovery, but the resulting DL models often lack interpretability, hindering their adoption by chemists. This work proposes developing molecule representations using the concept of Functional Groups (FG) in chemistry. We introduce the Functional Group Representation (FGR) framework, a novel approach to encoding molecules based on their fundamental chemical substructures. Our method integrates two types of functional groups: those curated from established chemical knowledge (FG), and those mined from a large molecular corpus using sequential pattern mining (MFG). The resulting FGR framework encodes molecules into a lower-dimensional latent space by leveraging pre-training on a large dataset of unlabeled molecules. Furthermore, the proposed framework allows the inclusion of 2D structure-based descriptors of molecules. We demonstrate that the FGR framework achieves state-of-the-art performance on a diverse range of 33 benchmark datasets spanning physical chemistry, biophysics, quantum mechanics, biological activity, and pharmacokinetics while enabling chemical interpretability. Crucially, the model's representations are intrinsically aligned with established chemical principles, allowing chemists to directly link predicted properties to specific functional groups and facilitating novel insights into structure-property relationships. Our work presents a significant step toward developing high-performing, chemically interpretable DL models for molecular discovery.

A Survey of Graph Neural Networks for Drug Discovery: Recent Developments and Challenges

Graph Neural Networks (GNNs) have gained traction in the complex domain of drug discovery because of their ability to process graph-structured data such as drug molecule models. This approach has resulted in a myriad of methods and models in published literature across several categories of drug discovery research. This paper covers the research categories comprehensively with recent papers, namely molecular property prediction, including drug-target binding affinity prediction, drug-drug interaction study, microbiome interaction prediction, drug repositioning, retrosynthesis, and new drug design, and provides guidance for future work on GNNs for drug discovery.

An Equivariant Graph Network for Interpretable Nanoporous Materials Design

Nanoporous materials hold promise for diverse sustainable applications, yet their vast chemical space poses challenges for efficient design. Machine learning offers a compelling pathway to accelerate the exploration, but existing models lack either interpretability or fidelity for elucidating the correlation between crystal geometry and property. Here, we report a three-dimensional periodic space sampling method that decomposes large nanoporous structures into local geometrical sites for combined property prediction and site-wise contribution quantification. Trained with a constructed database and retrieved datasets, our model achieves state-of-the-art accuracy and data efficiency for property prediction on gas storage, separation, and electrical conduction. Meanwhile, this approach enables the interpretation of the prediction and allows for accurate identification of significant local sites for targeted properties. Through identifying transferable high-performance sites across diverse nanoporous frameworks, our model paves the way for interpretable, symmetry-aware nanoporous materials design, which is extensible to other materials, like molecular crystals and beyond.

Monte Carlo Tree Diffusion with Multiple Experts for Protein Design

The goal of protein design is to generate amino acid sequences that fold into functional structures with desired properties. Prior methods combining autoregressive language models with Monte Carlo Tree Search (MCTS) struggle with long-range dependencies and suffer from an impractically large search space. We propose MCTD-ME, Monte Carlo Tree Diffusion with Multiple Experts, which integrates masked diffusion models with tree search to enable multi-token planning and efficient exploration. Unlike autoregressive planners, MCTD-ME uses biophysical-fidelity-enhanced diffusion denoising as the rollout engine, jointly revising multiple positions and scaling to large sequence spaces. It further leverages experts of varying capacities to enrich exploration, guided by a pLDDT-based masking schedule that targets low-confidence regions while preserving reliable residues. We propose a novel multi-expert selection rule (PH-UCT-ME) extends predictive-entropy UCT to expert ensembles. On the inverse folding task (CAMEO and PDB benchmarks), MCTD-ME outperforms single-expert and unguided baselines in both sequence recovery (AAR) and structural similarity (scTM), with gains increasing for longer proteins and benefiting from multi-expert guidance. More generally, the framework is model-agnostic and applicable beyond inverse folding, including de novo protein engineering and multi-objective molecular generation.