Pre-training Molecular Graph Representation with 3D Geometry

Shengchao Liu; Hanchen Wang; Weiyang Liu; Joan Lasenby; Hongyu Guo; Jian Tang

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Pre-training Molecular Graph Representation with 3D Geometry

Shengchao Liu, Hanchen Wang, Weiyang Liu, Joan Lasenby, Hongyu Guo, Jian Tang

arXiv:2110.07728v2Oct 7, 2021cs.LGcs.CVeess.IVq-bio.QM

TL;DR

Molecular graph learning often lacks accessible 3D geometry, despite its relevance to molecular properties. GraphMVP pre-trains a 2D encoder by self-supervised learning across complementary 2D and 3D views, and consistently outperforms existing graph self-supervised methods.

Problem
Molecular representation learning needs self-supervised objectives that exploit 3D geometry even though stereochemical structures are scarce in downstream settings.
Method
GraphMVP performs contrastive and generative self-supervised learning between each molecule’s 2D topology and stochastic 3D conformers.
Results
GraphMVP consistently outperforms existing graph self-supervised methods, with combined contrastive and generative objectives improving performance across settings.
Takeaways & Limitations
GraphMVP supports using 3D geometry as privileged training information to enhance 2D molecular representations when 3D data are unavailable at testing.
Takeaways & Limitations
The framework’s demonstrated application scope is small molecules, with extension to larger molecules such as proteins left for future exploration.

Abstract

from arXiv · show

Molecular graph representation learning is a fundamental problem in modern drug and material discovery. Molecular graphs are typically modeled by their 2D topological structures, but it has been recently discovered that 3D geometric information plays a more vital role in predicting molecular functionalities. However, the lack of 3D information in real-world scenarios has significantly impeded the learning of geometric graph representation. To cope with this challenge, we propose the Graph Multi-View Pre-training (GraphMVP) framework where self-supervised learning (SSL) is performed by leveraging the correspondence and consistency between 2D topological structures and 3D geometric views. GraphMVP effectively learns a 2D molecular graph encoder that is enhanced by richer and more discriminative 3D geometry. We further provide theoretical insights to justify the effectiveness of GraphMVP. Finally, comprehensive experiments show that GraphMVP can consistently outperform existing graph SSL methods.

1 INTRODUCTION

GraphMVP addresses molecular representation learning by pre-training a 2D graph encoder through complementary self-supervised tasks that exploit correspondence with 3D geometry. The framework is supported by theoretical insights explaining mutual-information maximization and 3D geometry as privileged information, alongside strong empirical results.

Molecular representation learning remains challenging because it requires both a suitable graph encoder and an effective training objective.
GraphMVP uses contrastive and generative pretext tasks across paired 2D and 3D molecular graphs to create complementary self-supervised signals.Contrastive learning treats views from the same molecule as positive pairs and views from different molecules as negatives; generative learning uses variation representation reconstruction.
The framework integrates these complementary tasks to learn a more discriminative 2D molecular graph representation, with consistent and significant empirical improvements.
GraphMVP maximizes mutual information between 2D and 3D views, enabling representations to capture high-level factors in molecular data.
The authors identify 3D molecular geometry as privileged information whose use during training can accelerate learning.
The work claims the first incorporation of 3D geometric information into graph SSL and reports state-of-the-art performance among SSL methods.

2 PRELIMINARIES

This section defines molecular SSL through complementary 2D topological and 3D geometric views, then formalizes their graph representations and latent notation. The 3D view includes atom positions and conformers, while the 2D view encodes atoms, bonds, and connectivity.

Molecular views: SSL uses views that capture specific aspects and modalities of data, with molecules offering natural 2D topological and 3D geometric views.The 2D view emphasizes topological information, whereas the 3D view reflects geometry and spatial relations.
2D molecular graph: A 2D molecular graph g2D = (X, E) represents atoms as nodes and bonds as edges, with E containing bond attributes and connectivity.A transformation T2D and a 2D GNN produce the representation h2D.
3D molecular graph: A 3D molecular graph additionally includes atom positions, and its local-minimum structures on a potential energy surface are called conformers.GraphMVP uses 3D conformers for representation learning because molecular properties are conformer-ensembled.
Notation: For notation, x and y denote the 2D and 3D graphs, respectively, while hx and hy denote their latent representations.The 3D graph is written g3D = (X, R), where R is the 3D-coordinate matrix and T3D is the 3D transformation.

3 GRAPHMVP: GRAPH MULTI-VIEW PRE-TRAINING

GraphMVP pre-trains molecular graph representations by aligning complementary 2D topology and 3D geometry through contrastive and generative self-supervised tasks. It produces a 2D representation enhanced with 3D conformational information for downstream tasks using only 2D molecular graphs.

Overview: GraphMVP treats each molecule’s 2D topology and 3D geometry as complementary views, using their correspondence to enrich 2D representations with energy and spatial information.3D conformers encode molecular energy and spatial structure complementary to 2D topology.
Overview: The framework pre-trains with both 2D and 3D structures, then fine-tunes the resulting 2D GNN on downstream tasks where only 2D graphs are available.Pre-training uses auxiliary SSL tasks on paired 2D/3D molecular data.
Pretext Tasks: GraphMVP combines contrastive SSL, which aligns same-molecule 2D–3D pairs and contrasts different-molecule pairs, with generative SSL, which reconstructs one molecular view from the other.The contrastive task uses inter-data positive and negative pairs, while the generative task targets robust 2D/3D representations that recover counterpart views.
Generative SSL: The generative task uses a VAE-like design because multiple 3D conformers can correspond to one 2D topology and downstream tasks require an explicit 2D graph representation.GraphMVP further introduces Variational Representation Reconstruction, switching reconstruction from data space to continuous representation space with an L2 loss.
Effectiveness: Both contrastive and generative SSL individually improve 2D representation learning from 3D conformers, while combining them yields further improvements and an augmented 2D representation.Empirical results also support GraphMVP-G and GraphMVP-C and indicate that existing 2D SSL is complementary to GraphMVP.

4 EXPERIMENTS AND RESULTS

GraphMVP is evaluated through broad low-data molecular prediction benchmarks, ablations, and geometry-focused case studies. It consistently benefits 2D graph representation learning by leveraging complementary 3D conformer information.

Experimental setup: Models are pre-trained on 50k GEOM molecules with 2D and 3D structures, then fine-tuned on 8 binary and 6 regression downstream tasks.The binary tasks follow prior molecular graph SSL settings, while the regression tasks span varied low-data domains.
Main results: GraphMVP significantly outperforms random initialization and existing SSL methods on 8 molecular property prediction tasks, while GraphMVP-G and GraphMVP-C consistently improve performance.The results support that 3D geometry is complementary to 2D topology and that GraphMVP transfers information between both views.
Ablation studies: Masking improves performance more from M = 0 to M = 0.15 than from M = 0.15 to M = 0.3, making larger masking ratios more challenging without extra computational cost.The study explores M ∈{0, 0.15, 0.3} and C ∈{1, 5, 10, 20}.
Ablation studies: Adding conformers generally improves performance but reaches a plateau above certain thresholds, while computation cost grows linearly with dataset size.The authors therefore recommend tuning masking ratios before increasing the number of conformers for efficiency and effectiveness.
Objective ablations: Each individual objective improves performance, and combining contrastive and generative SSL consistently yields further gains.The ablation evaluates InfoNCE, EBM-NCE, VRR, RR, and pairwise combinations, supporting both inter-data and intra-data SSL.
Additional evaluations: GraphMVP delivers consistent gains on four molecular regression tasks and two drug-target affinity tasks, and is also tested for predicting 3D diameter and detecting long-range donor-acceptor structures from 2D graphs.The DTA setting pre-trains the molecular 2D GNN with GraphMVP while modeling target proteins as amino-acid sequences with a CNN.

5 THEORETICAL INSIGHTS

GraphMVP’s contrastive and generative objectives can be understood as maximizing mutual information between 2D and 3D molecular views. Its 3D geometry also acts as privileged information that improves 2D representation learning by making molecules more separable and learning more efficient.

Mutual Information: GraphMVP interprets robust 2D/3D representation learning as maximizing mutual information between the two molecular views.Higher mutual information indicates stronger dependence and greater shared information between corresponding views.
Mutual Information: The mutual-information lower-bound objective LMI contains the conditional log-likelihood terms log p(y|x) + log p(x|y).The lower bound is derived in Appendix C.
Contrastive Self-Supervised Learning: EBM-NCE realizes contrastive self-supervised learning by estimating conditional likelihood with an energy-based model and noise-contrastive estimation, thereby maximizing 2D/3D mutual information.InfoNCE was originally proposed to maximize mutual information directly.
Generative Self-Supervised Learning: VRR provides the generative self-supervised surrogate objective by approximating conditional log-likelihood terms with a variational lower bound.This follows the same pipeline as GraphMVP’s generative method in Section 3.3.
Privileged Information: 1/n is the separable-case convergence rate, versus 1/√n for non-separable training data.Privileged information can make training data separable; GraphMVP treats 3D molecular geometry as privileged information because it can improve separability for some properties.

6 CONCLUSION AND FUTURE WORK … A.2 GENERATIVE GRAPH SSL

GraphMVP is presented as a general, model-agnostic framework that augments 2D molecular graph learning with stochastic 3D conformers through two SSL tasks. The appendix distinguishes contrastive and generative graph SSL and summarizes representative generative reconstruction methods.

6 CONCLUSION AND FUTURE WORK: GraphMVP is the first framework described as incorporating 3D information to augment 2D graph representation learning.It uses 3D conformers while considering their stochasticity in modeling.
6 CONCLUSION AND FUTURE WORK: GraphMVP introduces EBM-NCE and VRR when formulating its two self-supervised learning tasks.The supplied passage identifies these as technical novelties following Equation (9), though the excerpt truncates their full description.
6 CONCLUSION AND FUTURE WORK: GraphMVP is model-agnostic and may extend to other low-data applications.The authors propose exploring stronger 2D and 3D molecular representations and domains beyond small molecules, including proteins.
A SELF-SUPERVISED LEARNING ON MOLECULAR GRAPH: Self-supervised learning methods are broadly used in vision, language, and graph domains and comprise contrastive and generative categories.The categories differ in their supervised signals: contrastive methods operate at the inter-data level, whereas generative methods focus on reconstruction.
A.1 CONTRASTIVE GRAPH SSL: Contrastive graph SSL transforms each graph into multiple views, aligns views from the same data, and contrasts views from different data.Views can encode node-, subgraph-, or graph-level information, producing a uniformly distributed latent space.
A.2 GENERATIVE GRAPH SSL: Generative graph SSL reconstructs important graph structures to learn representations encoding key data ingredients.EdgePred predicts the adjacency matrix, AttrMask predicts masked nodes and edges, and GPT-GNN reconstructs the whole graph autoregressively.

A.3 PREDICTIVE GRAPH SSL · B MOLECULAR GRAPH REPRESENTATION · B.1 2D MOLECULAR GRAPH NEURAL NETWORK

The paper positions GraphMVP as a molecular graph SSL framework that augments topology-focused learning with complementary 3D geometry. It uses 2D and 3D GNN representations, adopting GIN for 2D graphs and SchNet for 3D geometry, while defining molecular representations through atom-bond graphs and message passing.

A.3 PREDICTIVE GRAPH SSL: GraphMVP addresses the limitation that prior molecular graph SSL methods focus only on 2D topology, despite 3D geometry providing complementary information for molecular property prediction.The framework is introduced for science-centric molecular tasks where spatial geometry is important.
A.3 PREDICTIVE GRAPH SSL: GraphMVP leverages 3D geometry through unsupervised graph pre-training to mitigate the gap between topology-focused SSL and geometry-aware molecular representation.The framework is designed to incorporate 3D information without requiring supervised labels for pre-training.
B MOLECULAR GRAPH REPRESENTATION: Molecular graph representation learning includes molecular fingerprints and GNNs, but fingerprint-based models do not benefit from pre-training strategies.Random forest and XGBoost are described as strong learners on fingerprints, while failing to exploit pre-training.
B MOLECULAR GRAPH REPRESENTATION: GNN-based molecular representations divide into 2D GNNs that model graph topology and 3D GNNs that model molecular energy using atoms’ spatial positions.The distinction depends on whether the representation considers topological structure or spatial information.
B MOLECULAR GRAPH REPRESENTATION: GraphMVP is model-agnostic and can use any 2D and 3D GNN representation function, but the paper adopts GIN and SchNet as its current representations.The choice reflects existing graph SSL and graph representation literature rather than a focus on developing specific 2D or 3D encoders.
B.1 2D MOLECULAR GRAPH NEURAL NETWORK: The 2D molecular representation models each molecule as a graph g2D = (X, E), with atoms as nodes, bonds as edges, and feature matrices encoding atom and bond attributes.E also includes graph connectivity; X and E represent atom and bond features, respectively.
B.1 2D MOLECULAR GRAPH NEURAL NETWORK: GIN is selected as the base 2D representation model because it is widely used as a backbone in recent graph self-supervised learning work.The paper situates GIN within a broader research line on 2D graph representation learning.
B.1 2D MOLECULAR GRAPH NEURAL NETWORK: The 2D encoder repeatedly applies atom- and bond-level message passing for K layers, capturing K-hop neighborhoods before mean-pooling final node representations into a graph-level molecular representation.The last layer is used for each node or atom representation, and the graph representation is their mean.

B.2 3D MOLECULAR GRAPH NEURAL NETWORK … D.2.2 EBM FOR MI

GraphMVP uses 3D molecular geometry to strengthen 2D graph representations, addressing conformer-dependent properties through mutual-information-based self-supervised learning. It implements this framework with SchNet, InfoNCE, and an EBM-NCE alternative for maximizing mutual information between 2D and 3D views.

B.2 3D MOLECULAR GRAPH NEURAL NETWORK; B.3 SUMMARY: Conformer ensembles matter because atoms continually move on a potential energy surface, so single 2D or 3D graphs cannot fully account for molecular properties.GraphMVP is described as alleviating this limitation.
B.2 3D MOLECULAR GRAPH NEURAL NETWORK: 3D molecular graphs augment topology with atom spatial positions, represented for each conformer as g3D = (X, R), where R ∈ R^n×3 is the coordinate matrix.Positions also determine plane and torsion angles.
B.2 3D MOLECULAR GRAPH NEURAL NETWORK: SchNet models continuous atom positions with continuous-filter convolution and is adopted because benchmarking shows comparable performance with substantially better efficiency.QM9 contains approximately 12 thermodynamic properties calculated using DFT; the comparison uses fair data splitting and implementation conditions.
B.3 SUMMARY: GraphMVP’s central aim is to extract useful 3D geometry information that augments 2D representations during downstream fine-tuning, while remaining model-agnostic.More advanced 3D and 2D GNNs are left for future exploration.
C MAXIMIZE MUTUAL INFORMATION; C.1 FORMULATION: Mutual information measures nonlinear dependence, and maximizing MI between 2D and 3D views encourages representations to capture higher-level factors and reduce uncertainty in 2D representations given geometry.The method uses X and Y for the 2D and 3D data spaces, with latent representations h_x and h_y.
C.2 A LOWER BOUND TO MI: GraphMVP converts MI maximization into minimizing a lower-bound objective involving conditional entropies H(Y|X) and H(X|Y), yielding general self-supervised methods.The methods are applied primarily to make 3D geometry useful for 2D molecular representation learning.
D CONTRASTIVE SELF-SUPERVISED LEARNING: Contrastive self-supervised learning aligns positive view pairs and contrasts negative pairs; GraphMVP considers InfoNCE and EBM-NCE as widely used graph-SSL approaches.The contrastive pipeline includes subgraph masking.
D.1 INFONCE: InfoNCE approximates MI by constructing objectives from randomly sampled 2D and 3D views, with flexible scoring functions instantiated as exp(⟨h_x, h_y⟩).The formulation combines objectives anchored on either the 2D or 3D view.

D.2.3 DERIVATION OF CONDITIONAL EBM WITH NCE

The derivation uses noise-contrastive estimation to make conditional energy-based modeling tractable through binary classification. It indirectly matches model and data conditionals via posterior fitting, then applies three approximations to obtain the final contrastive SSL objective.

NCE formulation: NCE converts conditional EBM estimation into binary classification by treating the partition function as a parameter and mixing data with a noise distribution.The mixture labels z = 0 for noise samples and z = 1 for data samples.
Posterior matching: The method fits the EBM-induced posterior to the data-induced posterior by minimizing their KL-divergence, indirectly matching pθ(x|y) to pdata(x|y).The same procedure is applied to pθ(y|x).
Objective approximations: Three strategies approximate the objective: self-normalization sets A = 1, exponential tilting uses a reference distribution, and sampling uses ν = 1.The sampling strategy corresponds to one negative point for each data point.
Final objective: Following these strategies, the conditional EBM objective is transformed into the final EBM-NCE contrastive self-supervised learning objective.The intermediate objective first approximates the conditional model before reaching the final contrastive form.

D.3 EBM-NCE V.S. JSE AND INFONCE … E.2 VARIATIONAL REPRESENTATION RECONSTRUCTION

The paper distinguishes EBM-NCE from JSE and InfoNCE through its derivation, flexibility, and noise-distribution choices, while reporting advantages over InfoNCE. GraphMVP then develops VAE-like generative learning and VRR to transfer reconstruction into representation space for stochastic 2D–3D molecular views.

D.3 EBM-NCE V.S. JSE AND INFONCE: EBM-NCE models the conditional distribution in the MI lower bound with an energy-based model and solves it using NCE, unlike JSE’s f-divergence variational derivation.JSE starts from f-divergence, variational estimation, and Fenchel duality, whereas EBM-NCE directly models the conditional distribution.
D.3 EBM-NCE V.S. JSE AND INFONCE: EBM provides a broader SSL family because NCE is one solution, while score matching and contrastive divergence offer additional directions.The paper presents EBM as a potential unified framework for structuring self-supervised learning.
D.3 EBM-NCE V.S. JSE AND INFONCE: EBM-NCE uses a different noise-distribution discipline from graph SSL methods that adopt empirical noise, supporting fixed, adaptively learnable, and potentially adversarial sampling.Classic EBM-NCE uses a fixed distribution, later work introduces adaptively learnable noise, and adversarial negative sampling is cited as an example.
D.3 EBM-NCE V.S. JSE AND INFONCE: EBM-NCE outperforms InfoNCE on graph-level self-supervised learning because binary cross-entropy can classify many positive and negative pairs, unlike softmax cross-entropy.The paper attributes this to constructing many positives and negatives per anchor point.
E GENERATIVE SELF-SUPERVISED LEARNING: GraphMVP starts with a VAE-like generative model because multiple 3D conformers can correspond to one 2D topology, requiring stochastic modeling and an explicit representation function.Complicated graph decoders, including autoregressive generation, are considered suboptimal, motivating a lightweight surrogate loss.
E.1 VARIATIONAL MOLECULE RECONSTRUCTION: The variational reconstruction objectives combine conditional log-likelihood with KL divergence, interpreting the likelihood term as reconstructing 3D conformers from sampled 2D representations.Because molecules are discrete, reconstruction directly in data space is difficult to model and measure.
E.2 VARIATIONAL REPRESENTATION RECONSTRUCTION: VRR transfers reconstruction from discrete molecule space to continuous representation space using MSE, approximating the two-step decoding process with a direct projection from zx to the 3D representation.The objective additionally uses β-VAE disentanglement control and stop-gradient regularization; it is exact when the encoding functions satisfy the stated bijection condition, while GIN and SchNet work robustly empirically without doing so.

E.3 VARIATIONAL REPRESENTATION RECONSTRUCTION AND NON-CONTRASTIVE SSL · F DATASET OVERVIEW

The section presents VRR as a perspective for understanding generative and non-contrastive SSL, and unifies intra-data generative SSL around reconstruction in data or representation space. It further shows that RR, BYOL, and SimSiam arise as special cases of VRR under progressively stronger simplifications.

E.3 VARIATIONAL REPRESENTATION RECONSTRUCTION AND NON-CONTRASTIVE SSL: VRR provides another perspective for understanding generative SSL, including recently proposed non-contrastive SSL methods.
E.3 VARIATIONAL REPRESENTATION RECONSTRUCTION AND NON-CONTRASTIVE SSL: The framework gives a unified structure for intra-data generative SSL.
E.3 VARIATIONAL REPRESENTATION RECONSTRUCTION AND NON-CONTRASTIVE SSL: Generative SSL can reconstruct representations in the data space, as illustrated by Equations (5), (31), and (32).
E.3 VARIATIONAL REPRESENTATION RECONSTRUCTION AND NON-CONTRASTIVE SSL: VRR reconstructs representations in representation space through Equation (35).
E.3 VARIATIONAL REPRESENTATION RECONSTRUCTION AND NON-CONTRASTIVE SSL: Removing stochasticity from VRR yields representation reconstruction (RR), which was tested in the Section 4.4 ablation study.
E.3 VARIATIONAL REPRESENTATION RECONSTRUCTION AND NON-CONTRASTIVE SSL: Removing stochasticity and sharing one representation function across two views reduces VRR to BYOL and SimSiam, making them special cases.

F.1 PRE-TRAINING DATASET OVERVIEW … G.1 SELF-SUPERVISED LEARNING BASELINES

The paper characterizes GEOM’s conformer distribution and explains how its molecular datasets support diverse downstream evaluations. It also specifies baseline differences and evaluation choices for fair comparison with GraphMVP.

F.1 PRE-TRAINING DATASET OVERVIEW: Over 80% of GEOM molecules have fewer than 100 conformers, while some molecules have over 1000 possible 3D conformer structures.
F.1 PRE-TRAINING DATASET OVERVIEW: The top 5 or 10 conformers capture nearly all natural observations because conformer occurrence weights follow a long-tailed distribution.The authors report that using the top five conformers in GraphMVP reaches an ideal setting.
F.2 DOWNSTREAM DATASET OVERVIEW: The downstream datasets span pharmacology, physical chemistry, biophysics, and drug-target affinity tasks.They include BBBP, toxicity and side-effect datasets, solubility, lipophilicity, photovoltaic efficiency, HIV, BACE, malaria, Davis, and KIBA measurements.
F.2 DOWNSTREAM DATASET OVERVIEW: Pharmacology datasets evaluate blood-brain barrier penetration, compound toxicity, and adverse drug reactions.BBBP measures central nervous system penetration; Tox21, ToxCast, and ClinTox concern toxicity; SIDER stores marketed-drug adverse reactions.
F.2 DOWNSTREAM DATASET OVERVIEW: Physical chemistry, biophysics, and affinity datasets measure properties including aqueous solubility, octanol/water distribution, photovoltaic efficiency, HIV inhibition, malaria efficacy, and kinase binding.Davis uses Kd, while KIBA combines Ki, Kd, and IC50 values for consistency.
G.1 SELF-SUPERVISED LEARNING BASELINES: Most SSL baselines use larger pre-training datasets such as ZINC-2m, and G-{Contextual, Motif} also uses a different backbone GNN.The authors generally match original-paper settings while noting these differences from GraphMVP.
G.1 SELF-SUPERVISED LEARNING BASELINES: The study runs both original JOAO versions and reports the optimal one.
G.1 SELF-SUPERVISED LEARNING BASELINES: GraphLoG is rerun using the same downstream evaluation strategy because its reported 73.2 uses last-epoch performance, unlike baselines selecting optimal validation error.The authors identify the last-epoch result as potentially over-optimized through overfitting and use rerunning for a fair comparison.

G.2 ABLATION STUDY: THE EFFECT OF MASKING RATIO AND NUMBER OF CONFORMERS … G.6 CASE STUDIES

The supplementary analyses vary GraphMVP’s masking ratio and conformer count, isolate loss components, evaluate broader prediction tasks, and examine 2D-to-3D reasoning in case studies. The case studies cover 3D diameter prediction, long-range donor-acceptor recognition, and chirality, with negligible improvement reported for chirality.

G.2 ABLATION STUDY: THE EFFECT OF MASKING RATIO AND NUMBER OF CONFORMERS: Table 9 reports a GraphMVP ablation over masking ratio M with C = 0.15.MVP is short for GraphMVP.
G.2 ABLATION STUDY: THE EFFECT OF MASKING RATIO AND NUMBER OF CONFORMERS: Table 10 reports a GraphMVP ablation over the number of conformers C with M = 0.5.MVP is short for GraphMVP.
G.4 BROADER RANGE OF DOWNSTREAM TASKS: MOLECULAR PROPERTY PREDICTION PREDICTION: Table 12 reports four molecular property prediction regression tasks using mean and standard variance RMSE across 3 seeds with scaffold splitting.GraphMVP uses M = 0.15 and C = 5, and the best performance for each task is marked in bold.
G.5 BROADER RANGE OF DOWNSTREAM TASKS: DRUG-TARGET AFFINITY PREDICTION: Table 13 reports two drug-target affinity regression tasks using mean and standard variance MSE across 3 seeds with random splitting.GraphMVP uses M = 0.15 and C = 5, and the best performance for each task is marked in bold.
G.6 CASE STUDIES: The case studies use 2D graphs to predict 3D molecular diameter when 2D and 3D landscapes differ substantially, including molecules with large differences between topological and geometric structure.The study notes that longer 2D diameters usually imply larger 3D diameters, but this relationship is not always true; numerical results are provided in Table 14.
G.6 CASE STUDIES: The donor-acceptor case study classifies structures that are close in 3D Euclidean distance but far apart in 2D adjacency, with numerical results provided in Table 15.Donor-acceptor structures affect molecular geometry and physical properties, and examples include close O...H atom pairs.
G.6 CASE STUDIES: GraphMVP yields negligible improvements for molecular chirality prediction because of SchNet’s model capacity, which the paper leaves for ongoing work.The paper describes chirality prediction as challenging when only 2D molecular graphs are provided.