Journal Title Here, 2022, pp. 1–11 doi: DOI HERE Advance Access Publication Date: Day Month Year Paper
PAPER
arXiv:2605.16088v1 [cs.LG] 15 May 2026
Multi-level Self-supervised Pretraining on Compositional Hierarchical Graph for Molecular Property Prediction Xiayu Liu
,1 Zhengyi Lu
2
and Hou-biao Li 1,∗
1
School of Mathematical Sciences, University of Electronic Science and Technology of China, No.2006, Xiyuan Avenue, West Hi-tech Zone, 611731, Chengdu, China and 2 Department of Computer Science and Engineering, Oakland University, 201 Meadow Brook RD, Rochester Hills, 48309, MI, USA ∗ Corresponding author: Hou-biao Li, [email protected] FOR PUBLISHER ONLY Received on Date Month Year; revised on Date Month Year; accepted on Date Month Year
Abstract Self-supervised pretraining on molecular graphs has emerged as a promising approach for molecular property prediction, yet most existing methods operate at a single structural granularity and treat bond information as auxiliary edge attributes rather than as an independent semantic layer. In this work, we propose MolCHG, a multi-level self-supervised pretraining framework built upon a novel Compositional Hierarchical Graph that organizes molecular structure into four types of nodes across three semantic levels. By introducing a bond graph that operates in parallel with the atom graph, our architecture elevates bond-level information to independently evolving node representations, enabling fragment nodes to aggregate atom-level and bond-level semantics on an equal footing. We design three level-specific pretraining objectives: an atom–bond cross-view contrastive task that aligns the atom-view and bond-view representations within each fragment, a fragment-level functional group prediction task to inject domain-relevant chemical knowledge, and graph-level structure prediction tasks to encode global molecular topology. Experiments on nine MoleculeNet benchmarks demonstrate that MolCHG achieves the best performance on seven datasets across both classification and regression tasks, remaining competitive with the strongest baselines on the rest. Ablation studies further confirm that the multi-level supervision signals are complementary and that each component contributes to the overall performance. Key words: Molecular Property Prediction, Representation Learning, Self-supervised Learning
Introduction Molecular property prediction aims to infer physicochemical properties from molecular structures and plays a central role in drug discovery [1], computational biology [2], and toxicity assessment [3]. Because obtaining reliable property labels typically requires expensive and time-consuming wetlab experiments, large-scale annotated datasets remain scarce, which significantly limits the generalization of purely supervised models. Self-supervised pretraining offers a promising alternative: by learning transferable representations from large volumes of unlabeled molecular data, pretrained models can be adapted to downstream property prediction tasks with considerably less labeled supervision [4, 5, 6]. Existing molecular pretraining methods mainly fall into two categories: contrastive learning and predictive learning [7]. Contrastive methods improve representation quality by maximizing agreement between augmented views of the same molecule, whereas predictive methods design self-supervised objectives such as recovering masked node attributes or predicting local structural contexts [8, 9]. Despite their
effectiveness, most existing methods in both families tend to operate at a single structural granularity. For instance, MolCLR [10] defines its contrastive objective at the graph level, while Attribute Masking and Context Prediction [11] focus on node-level objectives that encode local structural and attribute information. Because these objectives are defined at a single level, the learned representations may not fully reflect the hierarchical nature of molecular structures, which spans from individual atoms and bonds through functional substructures to the overall molecular topology. To move beyond single-granularity pretraining, recent studies have begun to explore multi-level molecular representation learning [12, 13, 14]. In particular, fragment-aware methods such as MGSSL [15] and GraphFP [16] have shown that chemically meaningful substructures can serve as effective intermediate semantic units, bridging local atom-level patterns and global molecular properties. However, these methods still derive fragment-level semantics primarily from atom-centered message passing, treating bond information as auxiliary edge attributes rather than as an independent semantic layer. In these methods, node representations are iteratively updated
© The Author 2022. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: [email protected] 1
2
Author Name et al.
through neighborhood aggregation, whereas edge features only serve to modulate the messages passed between nodes without maintaining independently evolving representations. As a result, even when bond descriptors are provided as edge features, the bond-level semantics encoded in fragment representations remain inherently less prominent than atomlevel semantics—even though, from a chemical standpoint, a fragment is jointly constituted by its atoms and their connecting bonds, both of which are important compositional elements that deserve explicit representation. Prior supervised studies, including DMPNN [17], CMPNN [18], and DeMol [19], have confirmed that explicitly modeling atom–bond interactions yields more expressive molecular representations, yet their bond-level modeling relies on downstream property labels and has not been extended to the label-free pretraining setting. These considerations motivate us to decouple bond information from edge attributes and organize it as an independent structural layer within a hierarchical pretraining framework. Among existing hierarchical approaches, HiMol [20] is the most closely related to our work: it constructs a node– motif–graph hierarchy and designs self-supervised pretraining tasks over this structure. HimNet [21], while not a pretraining method, further demonstrates that hierarchical graph construction incorporating multi-level interactions can improve molecular representation quality. However, in both frameworks, bond information is encoded only as edge attributes and does not constitute a separate structural layer. We address this limitation by introducing a bond graph that operates in parallel with the atom graph, yielding what we term the Compositional Hierarchical Graph. In this architecture, fragments are explicitly modeled as compositions of atom nodes and bond nodes from two parallel graphs, rather than being derived solely from atom-centered aggregation with bond information as auxiliary edge attributes. On top of this hierarchy, we develop MolCHG, a multi-level self-supervised pretraining framework that assigns a dedicated objective to each structural level: an atom–bond cross-view contrastive objective that aligns atom-view and bond-view representations within each fragment, a fragment-level functional group prediction task to inject domain-relevant semantics, and graphlevel structure prediction tasks to encode global molecular topology. The main contributions of this work are summarized as follows: •
•
We propose the Compositional Hierarchical Graph, a heterogeneous molecular graph that organizes atoms, bonds, fragments, and the whole molecule as four coexisting node types across three semantic levels. In this architecture, fragment nodes are explicitly connected to atom nodes and bond nodes from two parallel structural layers, serving as compositional hubs rather than derived summaries of atom-centered pooling. This design elevates bond-level information from auxiliary edge attributes to independently evolving node representations and, more importantly, enables atom-level and bond-level semantics to be aggregated at the fragment level on an equal footing—an interaction that is architecturally absent in prior atomcentric hierarchies. We design three level-specific self-supervised pretraining tasks—atom-bond cross-view contrastive learning, fragmentlevel functional group prediction, and graph-level structure
•
prediction—each targeting a distinct structural granularity of the Compositional Hierarchical Graph. We conduct extensive experiments on nine MoleculeNet benchmarks spanning both classification and regression tasks. MolCHG achieves the best performance on seven datasets while remaining competitive with the strongest baselines on the rest. Ablation studies and representation visualizations further verify the contribution of each proposed component.
Methods Overview of MolCHG MolCHG is a multi-level self-supervised pretraining framework built upon a novel graph structure that we term the Compositional Hierarchical Graph. The overall architecture consists of two main components: (i) the construction of the Compositional Hierarchical Graph, which organizes molecular structure into multiple semantic levels, and (ii) a set of levelspecific pretraining objectives that operate over this hierarchy. An illustration of the overall framework is provided in Figure 1. Given a molecular input, we first construct the Compositional Hierarchical Graph, which comprises four types of nodes arranged across three structural levels. At the bottom level, an atom graph and a bond graph operate in parallel: atom nodes represent individual atoms and bond nodes represent individual bonds, with edges in both graphs encoding only topological connectivity without carrying additional feature information. At the intermediate level, fragment nodes are introduced by decomposing the molecule into chemically meaningful substructures. Each fragment node is connected to its constituent atom nodes and bond nodes, serving as a compositional hub that aggregates both atomic and bondlevel semantics. In addition, fragment nodes are interconnected according to the connectivity relationships among their corresponding substructures, forming a fragment-level graph that captures the higher-order topology of the molecule. At the top level, a virtual graph node, whose representation is iteratively refined through message passing, is connected to all fragment nodes. On top of this hierarchical structure, we design three selfsupervised pretraining objectives, each targeting a specific level of the hierarchy. At the atom-bond level, we employ a cross-view contrastive objective that maximizes the agreement between atom-view and bond-view representations within each fragment, encouraging atom-level and bond-level semantics that jointly constitute the same fragment to align in a shared representation space. At the fragment level, we formulate a functional group prediction task that injects chemically meaningful supervision into the intermediate layer. At the graph level, we introduce structure prediction tasks based on molecular scaffolds and topological fingerprints to capture the global structural organization. The three objectives are jointly optimized to provide complementary supervision signals ranging from local compositional patterns to global molecular properties.
Compositional Hierarchical Graph Construction Conventional molecular graph representations encode bond information as edge attributes that modulate the messages passed between atom nodes during neighborhood aggregation. While this design retains bond descriptors within the
Short Article Title
3
Atom-level Representation
Atom-level
. .. 2
L GIN GIN
Add Edges
RDKit
Graph Encoder
Bond-level
Bond-level Representation
1 GIN
Cc1cccc(C)c1NC(=O)CN(CC)CC
Fragment-level Representation
Fragment-level
Graph-level Representation
Compositional Hierarchical Graph
Graph-level
Multi-level Self-supervised Pretraining Atom-bond-level Pretraining
Fragment 1
Fragment 2
Fragment 3
Fragment-level Pretraining
Graph-level Pretraining
MLP
MLP
Topological Fingerprint Prediction
NT-Xent Contrastive Learning
Scaffold Property Prediction
Functional Group Existence Prediction
Fig. 1. Overview of the MolCHG framework.
computation, it does not grant bonds independently evolving representations, leaving the resulting representations inherently atom-centric. To address this limitation, the Compositional Hierarchical Graph organizes bonds as an independent node layer that operates in parallel with the atom graph, and introduces fragment nodes as compositional intermediaries that aggregate semantics from both layers. The remainder of this section details its construction. Given a SMILES string, we first use RDKit to construct the atom graph Ga = (Va , Ea ), where each node v ∈ Va represents an atom and each edge (vi , vj ) ∈ Ea indicates the existence of a chemical bond between atom vi and vj . We simultaneously construct a bond graph Gb = (Vb , Eb ), in which each node u ∈ Vb corresponds to a bond in the original molecule and two bond nodes are connected by an edge if their corresponding bonds share a common atom. For example, consider three atoms connected as A–B–C with bonds e1 (A, B) and e2 (B, C). In the bond graph, e1 and e2 become two nodes connected by an edge because they share atom B. To introduce the intermediate structural level, we decompose each molecule into chemically meaningful substructures using the Principal Subgraph Mining algorithm [22]. Unlike rule-based fragmentation methods, such as BRICS [23], which tend to produce a large and diverse set of fragment types, Principal Subgraph Mining identifies a compact vocabulary of recurring substructures from the pretraining corpus. A smaller vocabulary concentrates the training signal on the frequently occurring structural patterns, allowing the model to learn more robust fragment-level representations during pretraining. Each fragment is represented by a fragment node
f ∈ Vf . We deliberately avoid initializing fragment nodes via pooling over their constituent atom nodes, as is done in several prior methods [24]. This design choice preserves the role of fragment nodes as intermediary hubs: on the one hand, their initial features provide connected atom and bond nodes with contextual information about the local substructure they belong to; on the other hand, their representations are further informed by atom-level and bond-level information through message passing, allowing atom and bond semantics to interact through them. Each fragment node is connected to all of its constituent atom nodes in Ga and to all of its constituent bond nodes in Gb . Two fragment nodes are connected by an edge if their corresponding substructures are adjacent in the original molecule, forming a fragment-level graph Gf = (Vf , Ef ) that captures the higher-order topology. Finally, a virtual graph node g is introduced and connected to all fragment nodes, serving as the graph-level representation hub. The initial features for all four node types are designed to capture relevant chemical or structural descriptors while deliberately excluding any information targeted by the pretraining objectives, thereby preventing leakage. The initial features for each node type are listed in Table 1. The resulting Compositional Hierarchical Graph is defined as G = (V, E), where V = Va ∪ Vb ∪ Vf ∪ {g} denotes the union of all node sets and E = Ea ∪ Eb ∪ Ef ∪ Eaf ∪ Ebf ∪ Ef g denotes the union of intra-level edges and interlevel edges that connect atom nodes to fragment nodes Eaf , bond nodes to fragment nodes Ebf , and fragment nodes to virtual graph node Ef g . Throughout the entire graph, all edges
4
Author Name et al.
Table 1. Initial node features for each node type in the Compositional Hierarchical Graph. Features are designed to exclude information targeted by the pretraining objectives.
Node Type
Description
Dim
Atom Node
Atomic number, degree, formal charge, radical electrons, hybridization (one-hot), scaled atomic mass, total hydrogens, chirality center indicator, chirality type Bond existence indicator, bond type (single, double, triple), whether connecting different elements, bond direction, formal charge difference between endpoints, conjugation indicator, stereo chemistry (one-hot) Number of atoms, bonds, heteroatoms, C/N/O atoms, halogens, single/double/triple bonds, average atomic mass, average degree, sum of formal charges, total hydrogens, total valence Number of atoms, bonds, fragments, average/max/min fragment atom count, average/max/min fragment bond count, small/medium/large/single-atom fragment counts, atom and bond count variance
15
Bond Node Fragment Node Graph Node
serve solely as topological connectors and carry no additional feature information. Because fragment nodes are explicitly connected to both atom nodes and bond nodes, they serve as compositional intermediaries through which atom-level and bond-level semantics can interact during message passing—an interaction that is architecturally absent in conventional atomcentric hierarchies where bond information resides only in edge attributes.
Multi-level Pretraining Objectives The Compositional Hierarchical Graph organizes molecular structure into three semantic levels, each capturing a distinct aspect of molecular composition. We design a dedicated selfsupervised objective for each level, so that the resulting supervision signals span from local compositional patterns to global structural properties. At the atom-bond level, we leverage the dual connectivity between fragment nodes and their constituent atom and bond nodes to define a cross-view contrastive objective that aligns the atom-view and bond-view representations of each fragment in a shared semantic space. For a given fragment fk , we apply mean pooling over its constituent atom node representations and bond node representations separately, yielding two summary vectors. Each summary vector is then passed through a (k) (k) learnable projection head, producing z̃a and z̃b for the atom view and bond view, respectively. Within a minibatch containing N valid fragments (excluding single-atom fragments), the atom summary and bond summary of the same fragment form a positive pair, while all cross-fragment pairings serve as negatives. The contrastive loss follows the symmetric NT-Xent formulation: (k) (k) exp sim z̃a , z̃b /τ (k) (j) /τ j=1 exp sim z̃a , z̃b
(k) ℓa→b = − log P N
(1)
15 15 15
same substructure may serve different functional roles across distinct molecular contexts, and the information propagated to fragment nodes through message passing varies with the surrounding molecular environment. At the fragment level, we inject chemically meaningful supervision into the intermediate layer of the hierarchy by formulating a multi-label classification task. Each fragment node is trained to predict which functional groups are present within the corresponding substructure. We select the C most frequently occurring functional groups from the pretraining corpus as the target label set, and use RDKit substructure (k) matching to produce a binary label vector yf ∈ {0, 1}C for each fragment fk . The fragment node representation after message passing is fed into a prediction head to produce logits (k) ỹf ∈ RC , and the loss is computed via binary cross-entropy: Lf rag = −
C 1 X X (k) (k) (k) (k) [y log σ(ỹf,c )+(1−yf,c ) log(1−σ(ỹf,c ))] |F | f ∈F c=1 f,c k
(3) where σ(·) is the sigmoid function and F denotes the set of valid fragments. By training fragment nodes to recognize chemically meaningful substructure types, this objective encourages the intermediate representations to encode domain-relevant semantic knowledge that complements the compositional information captured at the atom-bond level. At the graph level, the virtual graph node participates in the message passing process to form a unified molecular representation. We design two complementary prediction tasks at this level. The first targets topological fingerprints: for each molecule, we compute a D-bit topological fingerprint using RDKit, which captures the global topological connectivity of the molecule. The graph node representation is passed through a prediction head, and the loss is computed via binary cross-entropy: D
where sim(·, ·) denotes cosine similarity and τ is a temperature (k) hyperparameter. The reverse direction ℓb→a is defined analogously. The overall atom-bond cross-view contrastive loss is: N 1 X (k) (k) (ℓ + ℓb→a ) (2) Lab = 2N k=1 a→b
Ltopo = −
1 X [yd log σ(ỹd ) + (1 − yd ) log(1 − σ(ỹd ))] D d=1
(4)
The second task focuses on the molecular scaffolds, which characterize the core ring systems of a molecule. We predict five scaffold-related properties: the total number of rings, the number of aromatic rings, and three binary indicators denoting the presence of fused rings, heterocyclic rings, and bridged This objective aligns the atom-view and bond-view representations rings. These properties collectively characterize the global of each fragment in a shared semantic space, reinforcing topological organization of the molecular scaffold. The scaffold the semantic agreement between atom-level and bond-level loss is defined as: information that jointly constitutes the same fragment. Simultaneously, the negative-sample mechanism pushes representations Lscaf = Lring + Laro + Lbin (5) of different fragments apart, enhancing their discriminability. Notably, fragments of the same substructure type appearing in where Lring and Laro are cross-entropy losses for the total ring different molecules are also treated as negative pairs, since the count and aromatic ring count classification, respectively, and
Short Article Title
5
Table 2. Performance comparison on molecular property prediction benchmarks. Classification tasks are evaluated by ROC-AUC (%, ↑) and regression tasks by RMSE (↓). The best results are highlighted in bold. Classification (ROC-AUC ↑) Methods
BACE
BBBP
ClinTox
ContextPred
78.39±0.58
69.10±0.29
55.63±1.35
AttrMasking
75.95±0.50
67.12±0.45
60.11±1.19
EdgePred
74.29±1.37
64.73±1.10
61.62±1.25
Infomax
77.80±0.46
68.39±0.64
JOAO
74.94±1.35
JOAOv2
SIDER
Regression (RMSE ↓) Tox21
HIV
ESOL
FreeSolv
Lipophilicity
61.83±0.60
73.26±0.59
72.04±0.48
2.190±0.026
3.195±0.058
1.053±0.048
61.21±0.65
73.37±0.55
72.71±0.70
2.954±0.087
4.023±0.039
0.982±0.052
60.18±0.76
70.32±1.62
70.55±1.68
2.368±0.070
3.192±0.023
1.085±0.061
58.62±0.83
59.02±0.56
72.66±0.16
73.55±0.47
2.953±0.049
3.033±0.026
0.970±0.023
71.63±1.11
77.02±1.64
63.55±0.81
73.67±1.06
77.55±1.94
1.978±0.029
3.282±0.002
1.093±0.097
74.38±1.71
71.98±0.18
65.22±0.75
59.88±1.72
73.95±1.88
77.13±1.51
2.144±0.009
3.842±0.012
1.116±0.024
GraphCL
77.80±0.46
68.39±0.64
61.62±1.25
61.83±0.60
73.26±0.59
73.55±0.47
1.390±0.363
3.166±0.027
1.014±0.018
GraphLoG
76.60±1.04
66.75±0.32
53.76±0.95
59.09±0.53
71.64±0.49
73.76±0.29
1.542±0.026
2.335±0.052
0.932±0.052
GraphFP
80.28±3.06
72.05±1.17
76.80±1.83
65.93±3.09
77.35±1.40
75.71±1.39
2.136±0.096
2.528±0.016
1.371±0.058
MICRO-Graph
63.57±1.55
67.21±1.85
77.56±1.56
60.34±0.96
71.79±1.70
76.73±1.07
0.842±0.055
1.865±0.061
0.851±0.073
MGSSL
82.03±3.79
79.52±1.98
75.84±1.82
57.46±1.45
74.82±1.60
77.45±2.94
2.936±0.071
2.940±0.051
1.106±0.077
GROVER
81.13±0.14
87.15±0.06
72.53±0.14
57.53±0.23
68.59±0.24
75.04±0.13
1.237±0.403
2.712±0.327
0.823±0.027
SimSGT
79.75±1.28
71.51±1.75
74.11±1.05
59.74±1.32
76.23±1.27
78.13±1.07
0.932±0.026
1.953±0.038
0.771±0.041
MoAMa
81.32±1.06
85.89±0.61
77.11±1.67
62.69±0.37
78.29±0.55
78.11±0.64
1.125±0.029
2.072±0.053
1.085±0.024
HiMol
86.14±1.59
82.24±1.77
77.47±1.71
61.82±2.02
80.16±1.04
76.95±1.20
0.971±0.047
1.653±0.085
0.826±0.04
S-CGIB
86.46±0.81
88.75±0.49
78.58±2.01
64.03±1.04
80.94±0.17
78.33±1.34
0.816±0.019
1.648±0.074
0.762±0.042
MolCHG (Ours) 87.20±0.86 89.46±0.54 80.83±1.69
63.89±1.20
82.51±1.20
77.83±0.67
0.797±0.027 1.523±0.062 0.745±0.036
Lbin is a binary cross-entropy loss over the three structural indicators. The four loss terms across three structural levels are jointly optimized during pretraining: L = λab Lab + λf rag Lf rag + λtopo Ltopo + λscaf Lscaf
(6)
where λab , λf rag , λtopo , and λscaf are hyperparameters controlling the relative contribution of each task.
mean pooling over atom nodes, bond nodes, and fragment nodes within each molecule separately, and concatenate the three pooled vectors with the graph node representation to form the final molecular representation. A single linear layer is then appended as the prediction head, mapping the concatenated representation to the target property. The model is finetuned for 100 epochs using the Adam optimizer with a learning rate of 1e−3 and a batch size of 32.
Baseline
Experiments Experimental Setup We evaluate MolCHG on molecular property prediction tasks using benchmarks from MoleculeNet [25]. The downstream datasets include six classification tasks (BACE, BBBP, ClinTox, SIDER, Tox21, and HIV) evaluated by ROCAUC (%), and three regression tasks (ESOL, FreeSolv, and Lipophilicity) evaluated by RMSE. Following S-CGIB [26], all downstream datasets are randomly split into training, validation, and test sets with a ratio of 6:2:2. We report the mean and standard deviation over 10 independent runs. For pretraining, we use the same subset of 250K unlabeled molecules from the ZINC15 dataset [27] as used by HiMol to ensure a fair comparison. The GNN encoder is a 5layer GIN [28] with a hidden dimension of 300, dropout rate of 0.5, and sum-based jumping knowledge aggregation. The fragment vocabulary is constructed using the Principal Subgraph Mining algorithm with a vocabulary size of 800. The model is pretrained for 100 epochs using the Adam optimizer with a learning rate of 1e−3 and weight decay of 1e−5. The batch size is set to 256 to provide sufficient negative samples for the atom-bond cross-view contrastive objective, with the temperature τ set to 0.1. The loss weights are set to λab = 0.2, λf rag = 0.4, λtopo = 0.4 and λscaf = 0.4, where a smaller weight is assigned to the contrastive loss since its magnitude is typically larger than that of the predictive losses. For finetuning, the pretrained GNN encoder weights are transferred to the downstream model. To fully exploit the multi-level representations learned during pretraining, we apply
We compare MolCHG against a comprehensive set of selfsupervised pretraining baselines, which can be grouped into three categories. The first category is node-level pretraining methods, including ContextPred [11], AttrMasking [11], and EdgePred [29], which design pretraining objectives at the node level such as context prediction, attribute recovery, and edge prediction. The second category is contrastive learning methods, including Infomax [30], JOAO [31], JOAOv2 [31], GraphCL [32], and GraphLoG [33], which learn molecular representations by contrasting augmented or multi-view graph representations. The third category is subgraph/fragmentlevel pretraining methods, including GraphFP [16], MICROGraph [14], MGSSL [15], GROVER [34], SimSGT [35], MoAMa [36], and HiMol [20], which leverage substructure or fragment information to capture higher-order structural patterns during pretraining. We also compare with S-CGIB [26], which compresses molecular graphs into core subgraphs through a graph information bottleneck principle. The results of all baseline methods except HiMol are taken from S-CGIB under the random splitting protocol. The results of HiMol are reproduced using the authors’ publicly available code with the same 250K pretraining corpus and downstream splitting protocol to ensure a fair comparison.
Results Table 2 summarizes the performance comparison between MolCHG and 16 self-supervised pretraining baselines across nine molecular property prediction benchmarks. MolCHG achieves the best performance on 7 out of 9 datasets,
6
Author Name et al.
Table 3. Ablation study on graph structures. Classification tasks are evaluated by ROC-AUC (↑) and the regression task by RMSE (↓).
Graph Structure Atom Graph Hierarchical Graph Compositional Hierarchical Graph
BACE↑ 71.61 ± 1.41 74.34 ± 0.68 76.33 ± 0.80
BBBP↑ 74.96 ± 1.43 76.59 ± 0.72 77.97 ± 0.95
covering both classification and regression tasks, and remains competitive on the remaining two. Among the classification tasks, MolCHG consistently outperforms all baselines on BACE, BBBP, ClinTox, and Tox21. Compared with the strongest baseline S-CGIB, MolCHG improves ROC-AUC by 0.74 percentage points on BACE (86.46 → 87.20), 0.71 on BBBP (88.75 → 89.46), 2.25 on ClinTox (78.58 → 80.83), and 1.57 on Tox21 (80.94 → 82.51). Notably, the improvement on ClinTox is particularly substantial, where MolCHG surpasses all prior methods by a clear margin. On SIDER and HIV, MolCHG achieves results comparable to the best-performing baselines (GraphFP and S-CGIB, respectively), with differences within one standard deviation. On all three regression tasks, MolCHG achieves the lowest RMSE. Compared with the previous best results, MolCHG reduces RMSE from 0.816 to 0.797 on ESOL, from 1.648 to 1.523 on FreeSolv, and from 0.762 to 0.745 on Lipophilicity. The improvement on FreeSolv is especially notable (a 7.6% relative reduction), suggesting that the multi-level representations learned by MolCHG are particularly effective for tasks where both local functional group characteristics and global molecular topology contribute to the target property. Compared with node-level pretraining methods (ContextPred, AttrMasking, EdgePred), MolCHG achieves substantial improvements across all datasets, confirming the advantage of learning representations at multiple structural granularities rather than focusing solely on atom-level objectives. Compared with contrastive learning methods (Infomax, JOAO, JOAOv2, GraphCL, GraphLoG), MolCHG also demonstrates consistent superiority, indicating that the proposed level-specific predictive objectives provide more targeted supervision signals than general-purpose contrastive augmentation strategies. Among fragment-level pretraining methods, HiMol is the most closely related to our approach as it also constructs a hierarchical molecular graph. MolCHG outperforms HiMol on all 9 datasets, with notable improvements on BBBP (89.46% vs 82.24%) and Tox21 (82.51% vs 80.16%). These gains can be attributed to two key differences: the incorporation of bond-level information as an independent structural layer, and the design of level-specific pretraining objectives that provide complementary supervision across the hierarchy.
Ablation Study Ablation on Graph Structures To validate the contribution of the proposed Compositional Hierarchical Graph, we compare three graph structures under identical training conditions: (1) the standard atom graph, (2) the hierarchical graph that organizes atoms, fragments, and a virtual graph node into a multi-level structure but without an independent bond graph, and (3) our Compositional Hierarchical Graph that incorporates the bond graph as an independent structural layer. All three variants are trained from random initialization on a 5-layer GIN without pretraining, so that the observed differences can be attributed solely to
ClinTox↑ 67.33 ± 0.83 68.52 ± 0.94 69.97 ± 1.45
Tox21↑ 69.54 ± 0.56 70.81 ± 0.71 72.10 ± 0.67
HIV↑ 68.29 ± 0.79 70.16 ± 0.59 71.42 ± 0.80
Lipophilicity↓ 1.137 ± 0.027 1.073 ± 0.013 1.057 ± 0.016
the graph structure. We evaluate on six downstream datasets: BACE, BBBP, ClinTox, HIV, Tox21 and Lipophilicity. As shown in Table 3, introducing the hierarchical structure with fragment and graph nodes consistently improves performance over the atom graph alone, confirming the benefit of multi-level organization. More importantly, further incorporating the bond graph into the hierarchy yields additional gains across all six datasets. For instance, the Compositional Hierarchical Graph improves ROC-AUC over the hierarchical graph by 2.0 percentage points on BACE (74.34 → 76.33), 1.4 on BBBP (76.59 → 77.97), and 1.5 on ClinTox (68.52 → 69.97), while reducing RMSE on Lipophilicity from 1.073 to 1.057. Similar improvements are observed on Tox21 (70.81 → 72.10) and HIV (70.16 → 71.42). These results demonstrate that elevating bond-level information from auxiliary edge attributes to independent node representations provides the model with richer structural semantics, validating the core design principle of our proposed graph structure.
Ablation on Pretraining Objectives To assess the contribution of each pretraining objective, we systematically remove individual loss terms and groups of losses from the full framework. As shown in Table 5, all pretraining variants substantially outperform the No Pretraining baseline, confirming the overall effectiveness of self-supervised pretraining on the Compositional Hierarchical Graph. Among the single-loss ablations, removing any individual objective leads to a consistent performance degradation across all six datasets. Notably, removing Lf rag causes the largest average drop among classification tasks (e.g., BACE decreases from 87.20% to 84.14%, Tox21 from 82.51% to 78.55%), highlighting the importance of injecting domainrelevant functional group knowledge into the intermediate layer. Removing Ltopo results in a pronounced decline on HIV (from 77.83% to 75.34%), suggesting that topological fingerprint prediction is particularly beneficial for tasks involving largescale molecular screening where global connectivity patterns are informative. More importantly, removing an entire level of objectives produces substantially larger performance drops than removing any single loss. The w/o Graph-level variant, which retains only atom-bond and fragment-level supervision, shows notable degradation on BBBP (89.46% → 84.30%) and HIV (77.83% → 74.38%). Similarly, the w/o Atom-bond & Fragment-level variant, which retains only graph-level supervision, yields the lowest performance among all pretraining variants on most datasets (e.g., ClinTox drops to 76.03%, Lipophilicity increases to 0.814). The fact that both level-removal variants perform substantially worse than any single-loss variant demonstrates that the supervision signals from different levels are complementary rather than redundant: graph-level objectives alone cannot compensate for the absence of the local compositional and fragment-level semantics, and vice versa. These results validate the core design principle of MolCHG— that multi-level pretraining objectives operating across the full
Short Article Title
7
Table 4. Sensitivity analysis of pretraining loss weights. Classification tasks are evaluated by ROC-AUC (%) (↑) and the regression task by RMSE (↓). The default setting is λab = 0.2, λf rag = 0.4, λtopo = 0.4, λscaf = 0.4.
λab
λf rag
λtopo
λscaf
BACE ↑
BBBP ↑
ClinTox ↑
Tox21 ↑
HIV ↑
Lipophilicity ↓
0.2
0.4
0.4
0.4
87.20 ± 0.86
89.46 ± 0.54
80.83 ± 1.69
82.51 ± 1.20
77.83 ± 0.67
0.745 ± 0.036
0.1 0.4
0.4 0.4
0.4 0.4
0.4 0.4
86.41 ± 1.04 86.29 ± 1.07
88.63 ± 1.28 88.39 ± 1.21
80.18 ± 1.31 79.71 ± 1.48
81.28 ± 1.12 81.79 ± 0.77
76.54 ± 1.02 76.97 ± 1.01
0.761 ± 0.030 0.770 ± 0.029
0.2 0.2
0.2 0.6
0.4 0.4
0.4 0.4
86.66 ± 0.77 86.25 ± 0.60
87.09 ± 1.39 88.16 ± 1.56
80.46 ± 1.57 80.26 ± 1.59
82.18 ± 1.01 81.60 ± 0.92
77.22 ± 0.57 77.12 ± 0.75
0.756 ± 0.026 0.759 ± 0.026
0.2 0.2
0.4 0.4
0.2 0.6
0.2 0.6
86.96 ± 0.94 86.47 ± 0.81
88.43 ± 1.19 87.56 ± 0.71
80.54 ± 1.60 80.48 ± 1.62
81.41 ± 0.89 81.45 ± 1.42
77.06 ± 0.90 76.50 ± 0.76
0.758 ± 0.015 0.767 ± 0.029
Table 5. Ablation study on pretraining objectives. Classification tasks are evaluated by ROC-AUC (%) (↑) and the regression task by RMSE (↓).
BACE ↑
BBBP ↑
ClinTox ↑
Tox21 ↑
HIV ↑
Lipophilicity ↓
No Pretraining
76.33 ± 0.80
77.97 ± 0.95
69.97 ± 1.45
72.10 ± 0.67
71.42 ± 0.80
1.057 ± 0.016
w/o Lab w/o Lf rag w/o Ltopo w/o Lscaf
85.53 ± 1.08 84.14 ± 1.53 85.93 ± 0.99 84.60 ± 1.64
86.23 ± 1.47 87.08 ± 2.29 87.94 ± 1.32 87.62 ± 0.80
77.60 ± 1.26 77.20 ± 2.44 78.65 ± 1.71 77.68 ± 1.36
79.62 ± 1.02 78.55 ± 0.68 78.37 ± 0.92 78.99 ± 0.99
76.93 ± 1.00 76.20 ± 1.70 75.34 ± 0.58 76.62 ± 0.78
0.789 ± 0.034 0.797 ± 0.035 0.788 ± 0.024 0.767 ± 0.025
w/o Graph-level w/o Atom-bond & Fragment-level
83.69 ± 1.44 82.83 ± 1.17
84.30 ± 1.56 85.51 ± 0.92
76.87 ± 1.88 76.03 ± 2.60
77.54 ± 0.91 76.70 ± 1.06
74.38 ± 1.78 74.09 ± 1.80
0.809 ± 0.025 0.814 ± 0.026
MolCHG (Full)
87.20 ± 0.86
89.46 ± 0.54
80.83 ± 1.69
82.51 ± 1.20
77.83 ± 0.67
0.745 ± 0.036
Variant
hierarchy are essential for learning comprehensive molecular representations.
Sensitivity Analysis of Loss Weights We examine the robustness of MolCHG with respect to the pretraining loss weights by varying each weight while keeping others at their default values (λab = 0.2, λf rag = 0.4, λtopo = 0.4, λscaf = 0.4). As shown in Table 4, MolCHG maintains stable performance across all weight configurations, with no variant causing drastic performance degradation. This indicates that the framework is robust to the specific choice of loss weights within a reasonable range. Among the individual weights, λab is the most sensitive to changes: increasing it to 0.4 leads to a consistent drop across most datasets (e.g., BBBP from 89.46% to 88.39%, Lipophilicity from 0.745 to 0.770), confirming our design choice of assigning a smaller weight to the contrastive loss due to its inherently larger magnitude. For λf rag , reducing it to 0.2 causes a notable decline on BBBP (89.46% → 87.09%), suggesting that sufficient weight on the functional group prediction task is important for injecting domain-relevant semantics into the fragment-level representations. For the graph-level weights varied jointly, over-emphasizing them to 0.6 results in more pronounced degradation than reducing them to 0.2 (e.g., HIV drops from 77.83% to 76.50%), indicating that excessively strong graph-level supervision may overshadow the fine-grained local patterns captured by the lower-level objectives. Overall, the default configuration achieves the best balance among the multi-level objectives.
Visualization To examine whether each level of the proposed multi-level pretraining framework fulfills its intended role, we conduct t-SNE [37] visualizations of the learned representations at the graph, fragment, and bond levels. The clustering
quality is quantified by DBI [38] and Silhouette Score [39] computed on the original 300-dimensional representation space rather than on the t-SNE projections, since t-SNE is a nonlinear dimensionality reduction technique that can distort inter-cluster distances. We expect pretraining to improve clustering metrics across all levels, indicating that the learned representations capture semantically meaningful structure. However, perfect clustering by any single categorical label is neither expected nor desirable: a representation that separates one label perfectly would have collapsed its information content to that label alone, sacrificing the multi-faceted chemical semantics needed for diverse downstream tasks. The moderate inter-cluster overlap observed at each level therefore reflects this intended property rather than a deficiency.
Graph-level representation analysis To verify whether the graph-level pretraining objectives enable the graph node to capture the global topological organization of molecules, we visualize the graph node representations using t-SNE [37]. We select the 10 most frequent Murcko scaffolds [40] from the pretraining corpus and sample 500 molecules per scaffold. As shown in Figure 2, the randomly initialized model produces interleaved representations with no meaningful clustering structure (DBI = 7.95, Silhouette = −0.050). After pretraining, molecules sharing the same scaffold are organized into more distinguishable regions (DBI = 6.06, Silhouette = 0.074), and structurally similar scaffolds such as benzene and pyridine form neighboring clusters, indicating that the learned representations preserve underlying structural relationships. The moderate inter-cluster overlap is consistent with our expectation, as molecules sharing the same scaffold can differ substantially in side chains and substituents, and the graph-level representation encodes the full molecular topology beyond the scaffold alone.
8
Author Name et al.
Fig. 2. t-SNE visualization of graph-level representations colored by Murcko scaffolds. Left: Randomly initialized model. Right: pre-trained model.
Fig. 3. t-SNE visualization of fragment-level representations colored by functional group types. Left: randomly initialized model. Right: pre-trained model.
Fragment-level representation analysis The fragment-level pretraining objective is designed to inject domain-relevant semantic knowledge into the intermediate layer of the hierarchy by predicting the presence of functional groups within each fragment. We select 8 common functional groups and sample 500 fragments per group for t-SNE visualization. Figure 3 reveals that pretraining substantially improves the separability of fragment representations across functional group categories (DBI: 7.54 → 4.36, Silhouette: −0.169 → −0.050), with groups such as aldehyde, ether, and primary amine forming more distinguishable regions. The residual overlap reflects the context-dependent nature of fragment representations, as the same functional group can exhibit different chemical behavior depending on its molecular environment.
(single, double, triple, and aromatic), with 1,500 bonds per type sampled from 2,000 molecules. As shown in Figure 4, the randomly initialized model already exhibits partial separation because the initial bond node features encode bond-type descriptors (DBI = 3.49, Silhouette = −0.093). After pretraining, separation becomes substantially clearer (DBI = 2.97, Silhouette = 0.053). The improvement over the random baseline thus reflects how pretraining refines and contextualizes the initial type descriptors through message passing, rather than discovering bond-type information from scratch. Aromatic and triple bonds form more coherent clusters, while the remaining overlap among single and double bonds reflects that bond type is a coarse label that does not fully determine chemical behavior, and the atom-bond crossview contrastive objective encourages bond nodes to capture contextual semantics beyond their initial type descriptors.
Bond-level representation analysis In conventional molecular graphs, bond information is encoded as edge attributes that are consumed during message construction but never updated as independent entities. Our Compositional Hierarchical Graph addresses this limitation by organizing bonds as an independent node layer. We visualize bond node representations using t-SNE, colored by bond type
Conclusion In this work, we proposed MolCHG, a multi-level selfsupervised pretraining framework built upon the Compositional Hierarchical Graph, which introduces a bond graph as an independent structural layer and enables fragment nodes
Short Article Title
9
Fig. 4. t-SNE visualization of bond-level representations colored by bond types. Left: randomly initialized model. Right: pretrained model.
to aggregate atom-level and bond-level semantics on an equal footing. Three level-specific pretraining objectives—– atom–bond cross-view contrastive learning, fragment-level functional group prediction, and graph-level structure prediction—–provide complementary supervision signals spanning from local compositional patterns to global molecular topology. Extensive experiments on nine MoleculeNet benchmarks demonstrated that MolCHG achieved the best performance on seven datasets and remained competitive on the remaining two. Ablation studies confirmed that each component contributed meaningfully to the overall performance and that multi-level supervision was essential for learning comprehensive molecular representations.
Competing interests
Key points
Data availability
•
The dataset and code are available at https://github.com/ lhb0189/MolCHG
•
•
We propose the Compositional Hierarchical Graph, a heterogeneous molecular graph with four co-existing node types across three semantic levels, in which fragment nodes are explicitly connected to both atom nodes and bond nodes from two parallel structural layers. This design elevates bond information from auxiliary edge attributes to independently evolving node representations and enables atom-level and bond-level semantics to be aggregated at the fragment level on an equal footing. We design three level-specific self-supervised pretraining objectives that jointly operate over the Compositional Hierarchical Graph: an atom–bond cross-view contrastive task aligning the atom-view and bond-view representations of each fragment, a fragment-level functional group prediction task injecting domain-relevant chemical knowledge, and graph-level structure prediction tasks encoding global molecular topology. MolCHG achieves the best performance on seven out of nine MoleculeNet benchmarks across both classification and regression tasks, and remains competitive on the rest. Ablation studies and representation visualizations confirm that the supervision signals from different levels are complementary and that each component contributes meaningfully to the overall performance.
No competing interest is declared.
Author contributions statement X.L. conceived the study, designed the methodology, implemented the framework, conducted the experiments, and wrote the original manuscript. Z.L. contributed to the data preprocessing and assisted with the experimental evaluation. H.L. provided supervision and contributed to the revision of the manuscript. All authors reviewed and approved the final manuscript.
Acknowledgments This work was supported by National Natural Science Foundation of China (Grant: 11101071). The authors also acknowledge the Center for High Performance Computing, University of Electronic Science and Technology of China, for computational support.”
References 1. Zhaoping Xiong, Dingyan Wang, Xiaohong Liu, Feisheng Zhong, Xiaozhe Wan, Xutong Li, Zhaojun Li, Xiaomin Luo, Kaixian Chen, Hualiang Jiang, et al. Pushing the boundaries of molecular representation for drug discovery with the graph attention mechanism. Journal of medicinal chemistry, 63(16):8749–8760, 2019. 2. Yingxu Wang, Victor Liang, Nan Yin, Siwei Liu, and Eran Segal. Sgac: a graph neural network framework for imbalanced and structure-aware amp classification. Briefings in Bioinformatics, 27(1):bbag038, 2026. 3. Zhichao Tan, Youcai Zhao, Tao Zhou, and Kunsen Lin. Hi-mgt: a hybrid molecule graph transformer for
10
Author Name et al.
toxicity identification. Journal of Hazardous Materials, 457:131808, 2023. 4. Haohui Zhang, Juntong Wu, Shichao Liu, and Shen Han. A pre-trained multi-representation fusion network for molecular property prediction. Information Fusion, 103:102092, 2024. 5. Ruizhe Chen, Chunyan Li, Longyue Wang, Mingquan Liu, Shugao Chen, Jiahao Yang, and Xiangxiang Zeng. Pretraining graph transformer for molecular representation with fusion of multimodal information. Information Fusion, 115:102784, 2025. 6. Xiuyu Jiang, Liqin Tan, and Qingsong Zou. Dgcl: dualgraph neural networks contrastive learning for molecular property prediction. Briefings in Bioinformatics, 25(6):bbae474, 2024. 7. Wenbo Zhang, Yihui Wang, Jin Liu, Bowen Ke, Jiancheng Lv, and Xianggen Liu. Task-specific pretraining for molecular property prediction. Briefings in Bioinformatics, 27(1):bbag010, 2026. 8. Yuankai Luo, Lei Shi, and Veronika Thost. Improving self-supervised molecular representation learning using persistent homology. Advances in Neural Information Processing Systems, 36:34043–34073, 2023. 9. Pengyong Li, Jun Wang, Yixuan Qiao, Hao Chen, Yihuan Yu, Xiaojun Yao, Peng Gao, Guotong Xie, and Sen Song. An effective self-supervised framework for learning expressive molecular global representations to drug discovery. Briefings in Bioinformatics, 22(6):bbab109, 2021. 10. Yuyang Wang, Jianren Wang, Zhonglin Cao, and Amir Barati Farimani. Molecular contrastive learning of representations via graph neural networks. Nature Machine Intelligence, 4(3):279–287, 2022. 11. Weihua Hu, Bowen Liu, Joseph Gomes, Marinka Zitnik, Percy Liang, Vijay Pande, and Jure Leskovec. Strategies for pre-training graph neural networks. arXiv preprint arXiv:1905.12265, 2019. 12. Jiele Wu, Haozhe Ma, Zhihan Guo, Thanh Vinh Vo, and Tze Yun Leong. Hierarchical molecular representation learning via fragment-based self-supervised embedding prediction. arXiv preprint arXiv:2602.20344, 2026. 13. Jiahe Li, Wenjie Du, and Yang Wang. Molclw: Molecular contrastive learning with learnable weighted substructures. In 2024 IEEE International Conference on Bioinformatics and Biomedicine (BIBM), pages 828–831. IEEE, 2024. 14. Shichang Zhang, Ziniu Hu, Arjun Subramonian, and Yizhou Sun. Motif-driven contrastive learning of graph representations. arXiv preprint arXiv:2012.12533, 2020. 15. Zaixi Zhang, Qi Liu, Hao Wang, Chengqiang Lu, and Chee-Kong Lee. Motif-based graph self-supervised learning for molecular property prediction. Advances in Neural Information Processing Systems, 34:15870–15882, 2021. 16. Kha-Dinh Luong and Ambuj K Singh. Fragment-based pretraining and finetuning on molecular graphs. Advances in Neural Information Processing Systems, 36:17584– 17601, 2023. 17. Kevin Yang, Kyle Swanson, Wengong Jin, Connor Coley, Philipp Eiden, Hua Gao, Angel Guzman-Perez, Timothy Hopper, Brian Kelley, Miriam Mathea, et al. Analyzing learned molecular representations for property prediction. Journal of chemical information and modeling, 59(8):3370–3388, 2019.
18. Ying Song, Shuangjia Zheng, Zhangming Niu, Zhang-Hua Fu, Yutong Lu, and Yuedong Yang. Communicative representation learning on attributed molecular graphs. In 29th International Joint Conference on Artificial Intelligence and the 17th Pacific Rim International Conference on Artificial Intelligence (IJCAI-PRICAI2020). International Joint Conferences on Artificial Intelligence Organization, 2020. 19. Yunqing Liu, Yi Zhou, and Wenqi Fan. Enhancing molecular property predictions by learning from bond modelling and interactions. arXiv preprint arXiv:2603.00568, 2026. 20. Xuan Zang, Xianbing Zhao, and Buzhou Tang. Hierarchical molecular graph self-supervised learning for property prediction. Communications Chemistry, 6(1):34, 2023. 21. Huiyang Hong, Xinkai Wu, Hongyu Sun, Chaoyang Xie, Qi Wang, and Yuquan Li. A hierarchical interaction message net for accurate molecular property prediction. Communications Chemistry, 2026. 22. Xiangzhe Kong, Wenbing Huang, Zhixing Tan, and Yang Liu. Molecule generation by principal subgraph mining and assembling. Advances in Neural Information Processing Systems, 35:2550–2563, 2022. 23. Jorg Degen, Christof Wegscheid-Gerlach, Andrea Zaliani, and Matthias Rarey. On the art of compiling and using’drug-like’chemical fragment spaces. ChemMedChem, 3(10):1503, 2008. 24. Gihan Panapitiya, Peiyuan Gao, C Mark Maupin, and Emily G Saldanha. Fragnet: a graph neural network for molecular property prediction with four levels of interpretability. Journal of the American Chemical Society, 148(9):9930–9950, 2026. 25. Zhenqin Wu, Bharath Ramsundar, Evan N Feinberg, Joseph Gomes, Caleb Geniesse, Aneesh S Pappu, Karl Leswing, and Vijay Pande. Moleculenet: a benchmark for molecular machine learning. Chemical science, 9(2):513– 530, 2018. 26. O-Joun Lee et al. Pre-training graph neural networks on molecules by using subgraph-conditioned graph information bottleneck. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 39, pages 17204–17213, 2025. 27. Teague Sterling and John J Irwin. Zinc 15–ligand discovery for everyone. Journal of chemical information and modeling, 55(11):2324–2337, 2015. 28. Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka. How powerful are graph neural networks? arXiv preprint arXiv:1810.00826, 2018. 29. Will Hamilton, Zhitao Ying, and Jure Leskovec. Inductive representation learning on large graphs. Advances in neural information processing systems, 30, 2017. 30. Petar Veličković, William Fedus, William L Hamilton, Pietro Liò, Yoshua Bengio, and R Devon Hjelm. Deep graph infomax. arXiv preprint arXiv:1809.10341, 2018. 31. Yuning You, Tianlong Chen, Yang Shen, and Zhangyang Wang. Graph contrastive learning automated. In International conference on machine learning, pages 12121–12132. PMLR, 2021. 32. Yuning You, Tianlong Chen, Yongduo Sui, Ting Chen, Zhangyang Wang, and Yang Shen. Graph contrastive learning with augmentations. Advances in neural information processing systems, 33:5812–5823, 2020. 33. Minghao Xu, Hang Wang, Bingbing Ni, Hongyu Guo, and Jian Tang. Self-supervised graph-level representation
Short Article Title
learning with local and global structure. In International conference on machine learning, pages 11548–11558. PMLR, 2021. 34. Yu Rong, Yatao Bian, Tingyang Xu, Weiyang Xie, Ying Wei, Wenbing Huang, and Junzhou Huang. Self-supervised graph transformer on large-scale molecular data. Advances in neural information processing systems, 33:12559–12571, 2020. 35. Zhiyuan Liu, Yaorui Shi, An Zhang, Enzhi Zhang, Kenji Kawaguchi, Xiang Wang, and Tat-Seng Chua. Rethinking tokenizer and decoder in masked graph modeling for molecules. Advances in Neural Information Processing Systems, 36:25854–25875, 2023. 36. Eric Inae, Gang Liu, and Meng Jiang. Motif-aware attribute masking for molecular graph pre-training. arXiv preprint arXiv:2309.04589, 2023. 37. Laurens Van der Maaten and Geoffrey Hinton. Visualizing data using t-sne. Journal of machine learning research, 9(11), 2008. 38. David L Davies and Donald W Bouldin. A cluster separation measure. IEEE transactions on pattern analysis and machine intelligence, (2):224–227, 1979. 39. Peter J Rousseeuw. Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. Journal of computational and applied mathematics, 20:53–65, 1987. 40. Guy W Bemis and Mark A Murcko. The properties of known drugs. 1. molecular frameworks. Journal of medicinal chemistry, 39(15):2887–2893, 1996.
11