SubDyve: Subgraph-Driven Dynamic Propagation for Virtual Screening Enhancement Controlling False Positive
Authors: Jungseob Yi
Seoyoung Choi
Sun Kim
Sangseon Lee
Venue: ICLR 2026 Poster (2026)
Keywords: Virtual screening
Data mining
Subgraph pattern fingerprint
Chemical similarity-based network
LFDR-based seed refinement
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)

Abstract: Virtual screening (VS) aims to identify bioactive compounds from vast chemical libraries, but remains difficult in low-label regimes where only a few actives are known. Existing methods largely rely on general-purpose molecular fingerprints and overlook class-discriminative substructures critical to bioactivity. Moreover, they consider molecules independently, limiting effectiveness in low-label regimes. We introduce SubDyve, a network-based VS framework that constructs a subgraph-aware similarity network and propagates activity signals from a small known actives. When few active compounds are available, SubDyve performs iterative seed refinement, incrementally promoting new candidates based on local false discovery rate. This strategy expands the seed set with promising candidates while controlling false positives from topological bias and overexpansion. We evaluate SubDyve on ten DUD-E targets under zero-shot conditions and on the CDK7 target with a 10-million-compound ZINC dataset. SubDyve consistently outperforms existing fingerprint or embedding-based approaches, achieving margins of up to +34.0 on the BEDROC and +24.6 on the $EF_{1\\%}$ metric.

Published as a conference paper at ICLR 2026
SUBDYVE: SUBGRAPH-DRIVEN DYNAMIC PROPA- GATION FOR VIRTUAL SCREENING ENHANCEMENT CONTROLLING FALSE POSITIVE
Jungseob Yi!
Seoyoung Choi² Sun Kim 1,2,3,4
Sangseon Lee
'Interdiscipliaary Program in Artificial Intelligence, Seoul National University
2 *Department of Computer Science and Engineering, Seoul National University "Interdisciplinary Program in Bioinformatics, Scoul National University "AIGENDRUG Co., Ltd., Scoul "Department of Artificial Intelligence, Inha University
ABSTRACT
Virtual screening (VS) aims to identify bioactive compounds from vast chemical libraries, but remains difficult low-label regimes where only a few actives are known. Existing methods largely rely general-purpose molecular fingerprints and overlook ciiasddisrrmmnative substructures criti- cal to bioactivily. Moreover, they consider molecules independently, limiting effectiveness in low-label regimes. We introduce SubDyve, a network-based VS framework that constructs a subgraph-awan similarity network and propagates activity signals from a small known actives. When few active compounds are available, SubDyve performs iterative seed refinement, incre- mentally promoting new candidates basod on local false discovery rate. This strategy expands the seed set with promising candidates while controlling false positives from topological bias and overexpansion. We evaluate Sub- Dyve on ten DUD-E largels under zero-shot conditions and on the CDK7 target with 10-million 10-millooncomppuun ZINC dataset. SubDyve consistently outperforms existing fingerprint or embedding based approaches, achieving margins of up to +34.0 the BEDROC and +24.6 on the F metric.
INTRODUCTION
The chemical space in drug discovery is vast, comprising more than 10eh synthetically accessible drug-like molecules (Virshup et al.] 2013 Exhaustive exploration infeasible, making virtual screening (VS) key tool for identifying promising compounds small enough for experimental validation. However, in early stage discovery, most protein targets lack substantial ligand data; researchers often start with only few known active molecules (Deng et al. 2024 Jiang et al. 2024 Chen et al.) 22244 Scott et al.) (2016). The central challenge in such low-data settings is retrieve additional actives from billions of candidates, given only target protein and sparse activity labels.
Deep learning approaches virtual screening fall into two main categories: supervised models and foundation models. The first trains on large, balanced datasets using graph neural networks or 3D molecular representations, but requires extensive labeled data and often overfits in low-data settings. The second leverages foundation models (FMs) pre-trained on large-scale unlabeled molecular corpora to support inference with minimal supervision. Representative FMs include ChemBERTa (Ahmad et al. 2022) MolBERT (Fabian et al. 2020). MoLFormer (Ross et al. 2022. GROVER (Rong et al. 2020 and AMOLE (Lee et al. 2024), which support zero-shot VS. Protein-language-monn
pipelines (Lam et al. 2024] show similar promise in structure-fres contexts. However, FM-based methods screen compounds independently, failing to capture molecular dependencies.

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An orthogonal line of approach addresses these limitations with network- based label-efficient learning YYiet al.) 2023 Saha et al. 2024 Ma et al. 2024). Among these, network propagation (NP) has emerged nodes in a molecular graph, diffusing influence across net worksrks to prioritize candidates based on global connectivity to the seed set. This framework captures higher-order molecular associations and naturally supports generalization from few labeled molecules.
promising and effective strategy. NP treats known actives as seed
Despite its promise, two critical limitations of NP remain to be resolved. First, VS tasks often hinge on substructural variations bet ween closely related molecules (Ottaná et al. 2021 Stumpfe et al.) 2019). Yet standard NP relies on similarity graphs uses general general-purpose fingerprints (e.g., ECFP), which fail to encode greingrinnd subgraph features that distinguish actives from inactive molecules (Yi et al.; 2023) often blurring critical activity-releva distinctions. Second, NP inherits the topological bias of the underlying graph: nodes in dense clusters may be ranked highly due to connectivity alone, inflating false positives (FP), particularly when the seed set is small (Picart-
et al. 2021
To address these limitations, we propose SubDyve, a graph-based virtual screening framework for label-efficient compound prioritization. Rather than relying generic molecular finger- prints, SubDyve builds a subgraph fingerprint graph using disssiiiiiiiiitivee substructures mined via supervised subgraph selection (Lim et al., 2023). It then performs iterative seed refinement guided by local false discovery rate (LFDR, estimates (Efron 2005), expanding high-confidence compounds new seeds while controlling false positives. This process is integrated into joint learning framework that trains graph neural network with objectives for classification, ranking, and contrastive embedding. By combining subgraph-aware graph construction with incertainty-caaibrrteed propagation, SubDyve improves precision and gen- eralization under sparse supervision. We evaluate SubDyve on the DUD-E benchmark and a 10M- coM-oompund ZINC/PubChin dataset for CDK7 target, where it achieves strong early enrichment using substantially fewer labels than deep learning and mining-based based baselines. Our contributions are follows:
We demonstrate that SubDyve achieves state-of state-of-the-art performance on public and large-scale datasets under severe label constraints.
We propose a subgraph fingerprint graph ronstouction method that identifies class- discriminative subgraphs, preserving subtle activity- features that are over- looked by conventional fingerprints.
We introduce an LFDR-based seed refinement mechanism that overcomes graph- induced bias and enhances screening specificity while controlling false positive rates.
RELATED WORK
Representation-Centii Virtual Screening Traditional VS methods use fixed fin- gerprints (e.g,, ECFP, MACCS) or 3D aligmments with shallow classifiers, but often miss substructural patterns critical to bioactivity. Recent deep learning approaches embed molec- ular structures into task-optimized latent spaces. PharmacoMatch (Rose et al. 2025) frames pharmacophore screening as neural subgraph matching over 3D features. PSICHIC (Koh ct al. 2024 and BIND [Lam et al.] 2024) integrate protein sequence embeddings with ligand graphs. Large-scale pretrained encoders like ChemBERTa (Ahmad al., 2022). MoLFormer (Ross et al.) 2022). and AMOLE (Lee et al. 2024) reduce label demands via foundation model generalization. However, these methods treat compounds independently, ignoring higher-order molecular dependencies.
Label-Efficient Network Propagation Network propagation (NP) enables label-officient VS by diffusing activity signals over molecular similarity graphs. Yi et al. (Yi et al. 2023 build target-aware graphs from multiple similarity measures to rank candidates from known actives. GRAB (Yoo et al. 2021) applies positive uulabeled (PU) learning to infer soft labels from few positives, demonstrating robustness in low-supervision settings. While ND-based methods capture higher-order dependencies, they often rely on generic fingerprints (e.g., ECFP) that overlook discriminative substructures and suffer from topological bias, inflating false positives under sparse uneven labeling (Picart-Armada et al. 2021: Hill et al. 2019
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Figure 1: Architecture of SubDyve Framework. (A) Overall process SubDyve. Consists of subgrapb-similarry network construction, dynamic seed refinement with LFDR, and prioritization. (B) Dynamic seed refinement with LFDR: seed weights are iteratively updated within each stratified split and aggregated for final prioritization.
uwassrrectureAAwree Similarity Graphs Recent work enhances molecular graphs with substruucuue-awwaee representations to capture subtle activity-relevant patterns. Supervised Subgraph Mining (SSM) (Lim et al. 2023) identifies class-specific motifs that improve prediction and reveal mechanistic effects like toxicity. ACANet (Shen et al.) 2024) applics attention over local fragments to detect activity cliffs. While effective in property prediction, such met hods remain underexplored virtual screening, where subgraph-aware graphs could better resolve activily-specifie features.
3 METHODOLOGY
In this section, we present the architecture of SubDyve, a virtual screening framework for settings with few known actives. SubDyve first const a subgraph fingerprint network using class-discriminative subgraph patterns (Figure TA). Based on this network, it performs dynamic seed refinement guided by LFDR to iteratively update seed weights (Figure B). To ensure robustness, refinement is repeated across N settings, and the ensembled seed weights are used for a final network propagation prioritize unlabeled compounds.
3.1 PROBLEM FORMULATION
We define virtual screening as the problem of ranking large set of unlabeled candidate compounds, especially under low-label regime. Let Q be the of candidate molecules, and C C Q the subset of known actives against target protein p. The goal is to assign a relevance score r(g) cach q E Q such that compounds in are ranked higher than inactives. In low-label scttings, a small subset Strain: Stest C of seed actives is available (Strain Steest = 0). We assumne access to a compound similarity graph = (V,E) over Q, where each node E V is compound and each edge (i,j) E & encodes structural similarity. The task is to propagate activity signals from Strain over and assign relevance scores r(q) to all Q, prioritizing Steat-
3.2 SUBGRAPH FINGERPRINT NETWORK CONSTRUCTION
We first mine dinsrmiiscrmminative subgraph patterns SP from the labeled seed set Strain using the SSM algorithm (Lim et al. 2023) with curated negative molecules. Each molecule is then encoded as a d-dimensional subgraph pattern fingerprint, where each dimension reflects the frequency of discriminative subgraph combination (DiSC) (see Appendix B.2.1 B.2.2
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We filter the candidate set Q to retain only compounds that match at least subgraph in SP, forming a reduced set Q'. A subgraph fingerprint graph g is then constructed over Q' using pairwise cosine similarity between subgraph pattern fingerprints (Appendix (B2.3).. This graph serves as the foundation for network propagation and compound ranking.
3.3 DYNAMIC SEED REFINEMENT WITH LFDR ESTIMATION
Using Strain as seed nodes, we perform initial network propagation over G to assign soft rele- vance scores to all compounds. While this provides a baseline prioritization, its effectiveness is limited by the small size of Strain Signals tend to diffuse broadly or become biased toward topologically dense regions, resulting in reduced specificity and inflated false positives.
To address this, SubDyve introduces dynamic seed refinement procedure that iteratively improves the sced set using GNN-basod inference and local false discovery rate (LFDR) estimation. To enable robust screening, we stratify Strain into disjoint subsets S and S2, where S₁ initiates the initial network propagation, and S2 guides seed refinement via iterative loss updates in both the GNN and propagation modules. This mechanism enables confident expansion of the supervision signal while suppressing propagation-induee errors.
3.3.1 FEATURE ENCODING FOR GNN
Before refinement, we compute feature vectors for all compounds using SMILES 1988) and graph-derived descriptors. Fach compound E Q' is encoded as:
x; = = ni NP F.P :s. ..PCA ,e, , e
(1)
where wi denotes a weight of seed S₁ for network propagation. na is a network propagation score using wy. sPCA is RBF similarity to seed S in PCA latent space, and h is hybrid ranking computed as the average of the PCA and NP ranks, (rank(sPCA) + rank(n ef PT-CB and F!P encode semantic and substructural properties, respectively. Details of the feature encoding are described in Appendix B.3
3.3.2 ITERATIVE SEED REFINEMENT WITH LFDR ESTIMATION
Building on the initial propagation with SJ, SubDyve performs iterative seed refinement over hyperparameter M iterations. each iteration, the model trained to recover held-out actives in Sn through three steps: (1) GNN training with a composite loss, (2) LFDR-guided seed refinement, and (3) network propagation and evaluation.
(1) GNN Training. A graph neural network processes the subgraph fingerprint graph G to produce logits l and embeddings 2; for compound i. The model is trained using a composite loss that combines three objectives:
Liotal = -r-Akank)=
LBCE + Arank LRankNet
+ Accntrrat LContrast.
Here, LBCE is a binary cross-entrope loss that adjusts for class imbalance by weighting active compounds more heavily according to their low prevalence. LRaukNet is a pairwise ranking loss that encourages known actives in the held-out, set S2 to be ranked above unlabeled candidates. LContrast is a contrastive loss on the held-out set S2, where each compound pairs with its most similar member, treating the rest negatives. The coefficients Arank and Acontrast are hyperparameters controlling the contribution of each loss term. Full loss definitions and model optimization are described in Appendix B.4
(2) AFDR-Guided Seed Refinement. Given logits i, compute standardized score:
gi = LLFDR
(3)
with a estimated from all logits in Q'. Details of LFDR algorithm is described in Algorithu 3 at Appendix B The seed set S and its weights are then updated as
S (i E Q' qs < TEDR): w (1+1) w." + B(a(z)) Ro); E S4t1,
(4)
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that only compounds satisfying 9: FEDR remain seeds while others removed, where a(-) is the sigmoid function, my the prior null probability, and B controls the update rate. This procedure ensures provable upper bound on the false discovery rate (Efron 2005), as detailed in Proposition [
Proposition Lel Z.,..., , Zm Follow the two group misture f(z) = mo]((2) + (1()) and define the selection rule
Ra = {i: lfdr( (.) S sa
a<a<l.
Denole R. = |Ral and Va Eisl Hi R. Then
mFDR(Ra) V I a.
(1)
RaRal
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FDR(Ra) = R. V1
S a.
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Proof is provided in Appendia A.
(3) Network Propagation and Evaluation. We apply network propagation with the updated seed weights and evaluate performance S2 using enrichment factor at early ranking thresholds. While Sn contributes to Lrotal: early stopping relies solely on intermediate enrichment scores, preventing bias from direct training objectives. If enrichment improves, the iteration continues; otherwise, early stopping is triggered. Among all iterations, we retain the seed weights that yield the highest performance on S2 for final ensemble aggregation.
3.4 FINAL AGGREGATION AND PRIORITIZATION
To improve robustness under limited supervision, we perform N stratified splits of the initial seed set Strain into disjoint subsets S₁ and S2. From each split, we retain the best-performing seed weights S2 and aggregate them across all N splits using element-win max pooling to construct the final ensemble seed vector. Using this ensembled vector, we perform final round of network propagation over to score all compounds in Q', producing the final compound ranking used for virtual screening evaluation.
EXPERIMENTS
In this section, we evaluate the SubDyve framework on set of virtual screening tasks, including 10 benchmark targets from the DUD-E datasct and real-world case study curated using ZINC20 (Irwin et al.] 2020) compounds and PubChem (Kim et al. 2023) active com- pounds. This evaluation highlights the applicability of the framework in both standardized benchmarks and real-world drug discovery environments. Detailed experimental setup and hyperparameter configurations are provided in Appendix C We present comprehensive parisons with state-of-the-art methods, alongside extensive ablation studies, interpretation analyzes, and case studies to highlight the effectiveness and robustness of each component.
4.1 VIRTUAL SCREENING PERFORMANCE
4.1.1
ZERO-SHOT SCREENING ON DUD-E TARGETS
Task. The goal of this evaluation is to assess whether SubDyve can effectively generalize in zero-shot virtual screening by prioritizing active compounds without target-specific training.
Datasot & Evaluation. We follow the evaluation protocol of PharmacoMatch (Rose et al. 2025), using the same 10 protein targets from the DUD-E benchmark (Mysinger et al. 2012] Since SubDyve requires small number of active molecules to construct subgraph newtork and initiate network propagation, directly using actives from the test targets would violate the zero-shot assumption and compromise fairness. To ensure fair comparison, curated related proteins from PubChem using MMseqs2 (Steinegger & Söding, 2017) tool with similarity thresholds of 0.9 to filter out proteins in PubChem. In addition, additionally
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Table 1: Performance comparison of SubDyve (threshold=0.9) and baselines on the ten DUD-E targets. The top results are shown in bold, and the second-best are underlined.
respectively. Confidence intervals are reported with 100 bootstrap resamples (DiCiccio & The complete results, including all baselines and metrics are Appendix F.L.1
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considered stricter configuration with threshold of 0.5, which forces seeds to be drawn from more distant homologous proteins. Bioactive compounds associated with these PubChem proteins were then used as sced molccules. Detailed filtering criteria and dataset statistics are provided in Appendix D.1 All baseline modcls were evaluated using the best hyperparameter settings reported in their respective papers to ensure fair comparison. For evaluation, we measure early recognition metrics: BEDROC (a = 20), EFN%, as well as AUROC for completeness. Full metric panels are in Appendix
Performance. Table reports BEDROC (a = 20) and EF 1% scores, highlighting Sub- Dyve's early recognition performance on threshold 0.9 setting. Full results, including AUROC and per-target metrics, are provided Appendix F.I.1 SubDyve achieves the highest aver- age rank across all metrics; 1.6 for BEDROC and 1.6 for FF For example, EGFR and PLK1, two pharmacologically important targets known for their conformational flexibility and multiple ligand binding modes (Zhao et al. 2018 Murugan et al.) 2011), SubDyve achieved BEDROC scores of 86 and 85, substantially hy higher than those of MoLFormer (75 and 69). Even for structurally challenging targets such ACES, which features a deep, narrow binding gorge that imposes strict shape complementarity and limits ligand accessibility (Mishra & Basu 2013), SubDyve yields meaningful enrichment 1 57.0), substantially higher than Drug (32.4) and AutoDock Vina (13.87). These results highlight SubDyve's robust across diverse targets and its strength in early active identificatinn.
To examine whether SubDyve relies on close homologs when constructing seed sets, we repeated the experiment using a stricter MMseqs2 identity threshold of 0.5. Due to the increased number of homolog candidates when lowering the MMscqs2 identity threshold from 0.9 to 0.5, we conducted this stricter analysis on a subset of three targets (EGFR, PLKI, SRC). Despile receiving less informative and more diverse seed molecules, SubDyve maintained strong early-recognition performance and remained better or compelitive with all baselines on both BEDROC and FF (Appendix F.1.2). These findings indicate that SubDyve does not depend on highly similar homologs and remains effective even when only distant pootein-ligand annotations are available.
Multi-Targer Screening Analysis. To evaluate SubDyve beyond the single-target. setting, we conducted a multi-target analysis on three tyrosine kinases (EGFR, KIT, SRC), which share related molecular functions and signaling roles. Rather than constructing separate subgraph networks, we identified homologous PubChem proteins common to the three targets and performed a single subgraph-mining step using their associated bioactive compounds. The resulting unified subgraph fingerprint network was reused across all evaluations without additional target-specific preprocessing. Details are summarized in Appendix[F... F.1.3..
We assessed SubDyve under four multi-target activity definitions (shared actives across all three targets or each target pair). SubDyve maintained strong early-rocognition performance. For example, on the EGFR-SEE pair, SubDyve achieved a BEDROC of 84.11 and EF 1% of 41.21, outperforming CLuP (BEDROC 14, EF1% 7.26). Even in the target setting (EGFR KIT SRC), SubDyve reached a BEDROC of 69.52 compared to DrugCLIP's 4.55. Full results are provided in Appendix Table 16 These results suggest that for biologically related targets with shared ligand annotations, SubDyve's extracted structural patterns transfer effectively, enabling the preprocessing cost of subgraph mining to be amortized over multiple screening tasks.
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Table Performance comparison of SubDyve and baselines on the PU dataset. The top results are shown in bold, and the second-best are underlined, respectively. The complete results, including all basclines are at Appendix F.2
Meshod
BEDROC (%)
EF
0.3%
156
3%
55
10%
Deep bhueing-bused
BIND
2024
AutoDoni Enremadd
DrugCLIP Goo 2
2024
2.7 #: 1,26
1/63 #: 1:99
1.63
0.81
2.45 #: 1:02
2.53 = 1.35
2.00
0.62
PSICHIC KWa 0 m
2721
9.37
3.08
1.07 1 2.58
6.92
3,30
7.06 1 2.47
7.02
1.80
5.35
1: 0..1
GRAB (Yo
10.68
10.60
11.22 8.35
45.21
5.03
29.78 1 1.58
18.09
0.47
10.00
0.00
Data mining-haased
avalon NP
31.55
ewtate
62.44
94.4
13.68
57.87
7.15
22.71
2.7
15.92
0.85
8.24 0.39
fp4 4-N-
NP
V
70.
2112
00.62
3.69
122.76
13.02
76.01 + 4.21
28.96
1.34
18:36 + 1.0
9.50
0.29
graph NE
Yree 51 20:4
75.86
3.90
126.72
10.05
84.73 + 3.74
31.88
0.92
19.1 0.47
9.75 (1.24
NP
75.44 + 4.85
136.72
12.7
79.82 +: 4.76
31.0
1.41
18.05 0.66
9.67 0.21
pulcheem
10.17
+:
148.00
89.24
2.08
31.68
0.92
19.02
9:55
standard NT
11:00 2tm 2023
72.42
3.51
121.07
15.51
81.34
5.56
31.27
0.96
19.01
0.33
9.71 0.24
SebDyve (Ours)
83.41
1.44
155.31
6.38
97.59
:: 1.44
33.01 1: 0.60
19.90
0.18
10.00 1: 0.00
Statistical Significance (p-valac)
4.1.2 PU-STYLE SCREENING ON CDK7 TARGET
Task. This task simulates a realistic virtual screening scenario with few known actives for given target. We mask portion of actives to evaluate the model's ability to rank them highly among many unlabeled candidates.
Dataset & Evaluation. We construct PU (positive-unlabell)) dataset consisting of 1,468 CDK7-active compounds from PubChem and 10 million unlabeled molecules from ZINC. To ensure efficiency, apply subgraph-basee based reduction strategy that retains only compounds containing relevatte substructures, yielding a filtered subset of approximately 30,000 ZINC compounds. We randomly select 30% of the actíves for Strain, from which only 10% are used as a held-out set S2. These S2 compounds are excluded from subgraph generation prevent leakage. Each experiment is repeated five times with different random seeds. We report BEDROC (a = 85) and EF scores at various thresholds to assess early recognition. Detailed statistics and explanation of the evaluation settings are provided in Appendix D.2
Baselines. We compare SubDyve with multiple baselines: (i) data mining- mining-based methods using 12 standard molecular fingerprints (Yi et al. 2023), (ii) BIND (Lam et al. 2024), a foundation model trained on 2.4 million BindingDB interactions, (iii) PSICHTC (Koh al. 20241, which learns protein-ligand interaction fingerprints, and (iv) GRAB Yoo et al.] 2021 PC learning algorithm. For the data mining baselines, we construct chemical similarity network and apply one round of propagation.
Performance. Table 2 presents the screening results. SubDyve achieves the highest BEDROC score (83.44) and consistently Icads across cnrichment thresholds, including FFa.5% (155.31), EFix (97.59), and FF3x (33.01). Compared to GRAB Yoo et al. 2021 a PU learning baseline, SubDyve improves EF%% by more than 2x (98.0 vs. 45.2) and BEDROC by over 80%. Against PSICHIC (Koh al.) 2024). which leverages interpretable interaction fingerprints, SubDyve improves ET by over 38x and achieves a BEDROC nearly 9x higher. The foundation model BIND (Lam al. 2024). despite being trained on millions of interactions, performs poorly in this setting (EF 10% = 0.04), likely due to distri- bution mismatch. Notably, SubDyve not only achieves superior accuracy but also requires substantially less runtime than most basclines (e.g., AutoDock Vina: 13,343s; DrugCI.IP: 2,985s; GRAB: 1,040s; RDKit: 957s; SubDyve: 1,088s), with full details summarized in Appendix D.3. Notably, SubDyve not only achieves superior accuracy but also runs approxi- mately 12.3x faster than AutoDock Vina and requires 15.06x less memory than DrugCLIP, with complete runtime and memory comparisons provided in Appendix F.9 These results highlight SubDyve's s strength in prioritizing true actives under minimal supervision and its robustness across compound representations and model classes.
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Table 4: Ablation study on the number of seed compounds in the PU dataset. For each seed size (50, 150, 250), the first and second rows show the average and best-performing of general fingerprint basclines. Best values are bold, socond-best are underlined. Full results are in Appondix F.4
No. of Seeds
Method
BEDROC (%)
0.30%
0.50%
1%
3%5
B36
pubchhe 4. XP
41.13 + 4.46
44.69 + 14.09
45.51
7.91
41.97
6.91
26.7
1.90
17.34 + 1.00
NP
47.02
56.77 15.24
60.92
3.15
21.74
2.04
17.00
1.20
Suhgraph NP
46.33 1.26
37.79
31.81
12.08
27.61
17:27 0.51
SubDyre
51.78 3.38
69.5 d: 11.81
62.53 1: 14.84
32.00 3.91
29.48 d: 2.37
18:15
0.90
edlant + NP
50.52 #: 3.79
52.69 d: 6.75
54.02 :: 10:48
54.02
7.24
29.5 1.39
17.79
0.55
NP
55.22 4.39
79.99
15.80
71.05
13.30
80.09
6.59
30.6
1.29
0:48 18.85
Subgraph
30.07
SubDyre
59.07
2:25
71.67 1: 7.48
73.55 + 10.51
86.72 3.29
32.26 :: 1.04
19.73 0.36
fp2 NP
50.88 1: 5.26
67. 65 16.53
75.57 1: 15.28
65.15 8.30
30. 1.26
18.52
0.61
amioon NP
61.29 2.44
97.18 13:25
86.96
9.16
68.05 4.42
31.14 +: 0.52
10.51 0.48
Subgraph Subllyee
0.65
66.73 2.71
97.60 16.55
85.44 12.82
78. 3.38
32.85 + 0.60
19.72 0.38
4.2 ABLATION STUDY
To demonstrate the effectiveness of SubDyve components, we conduct ablation studies: (1) impact of subgraph-basen similarity network and LFDR seed refinement, (2) initial seed size, (3) behavior of LFDR refinement, (4) false positive (FP)-pressure via LFDR threshold, (5) subgraph pattern size, (6) impact GNN features. Due the limited space, experimental result of (4), (5), (6) is reported in Appendix F.6
F.7 and F.8 respectively.
4.2.1 EFFECTS OF SUBGRAPHI NETWORK AND LFDR SEED REFINEMENT
We conduct an ablation study on the PU datasct to assess the impact of SubDyve's two main components: (i) the subgraph-based similarity network and (ii) LFDR-guided seed refinement. The experiments on the 10 DUDE targets are provided in Appendix F.3
Table 3 shows that combining both compo- nents achieves the best performance (BEDRÓC 83.44, EFi% 97.59), with improvements over all partial variants being statistically significant (p < 0.01, paired t-test). Using LFDR with- out subgraph features Icads to substantial drop in both BEDROC and EF, indicating that accurate refinement depends the quality of the underlying network. Applying subgraph features without LFDR yields only modest im- provements, suggesting most gains come from their interaction. These results highlight that chemically meaningful network construction and uncertainty-aware refinement are complementary and essential for robust virtual screening in low-label settings.
Table 3: Ablation results for the effect of subgraph fingerprints and LFDR-guided re- finement with significance testing on the PU dataset. Top and second-best results are bold and underline, respectively.
Subgraph LFDR
BEDROC
EF 15
79.01 # 1.96
89.21 1: 2.08
63.78 11:43
16.61 89.68 4 3.53
78.68 : 2.87
83.44 = 1.14"
97.59 = 1.44"
4.2.2 PERFORMANCE UNDER VARYING SEED SET SIZES
We conduct an ablation study evaluate the effect of seed set size on the PU dataset. For each setting (50, 150, 250 seeds), compare SubDyve against baselines using general- purpose molecular fingerprints and subgraph fingerprint network (Subgraph+NP). Detailed experimental settings are described in Appendix D.3
Table 4 shows that SubDyve outperform across all seed sizes, demonstrating strong early enrichment even under limited supervision. While the best-performing general fingerprints vary by seed size (c.g., MACCS at 50, Avalon at 250), SubDyve achieves best performance without fingerrint-speeiffe tuning. Notably, +NP using network constructed from class discrimiiiii patterns, performs comparably to the best baselines, highlighting the effectiveness of substructure-aware graph construction. These results suggest that
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Subgraph fingerprints
RDKit fingerprints
COCNCCNNm..-ee
C.c.CCYY.CNO
Seeds
Sends
Seade) Seade:
Seedell
Seacez
FC2 (16.229
Compouddes
Compareri
Sabgoghh
RDKE
PiLL (58.55%)
(17.288))
Figure 2: Case study of seed- hit patterns from SubDyve RDKit. (A) PCA
visualization of top 1% ranked compounds and seeds under each method, illustrating that SubDyve produces more coherent clustering in subgraph fingerprint space than RDKit. (B) Examples of structurally similar seed- hit pairs prioritized only by SubDyve, highlighting its ability to recover compounds with shared functional substructures. (C) Heatmaps of
pairwise fingerprint similarity between seeds and retrieved hits, showing stronger sced-hit consistency with SubDyve fingerprints.
SubDyve combines robustness and adaptability across diverse label regimes without requiring task-specific fingerprint optimization.
4.2.3 STABILITY AND CALIBRATION BEHAVIOR OF LFDR REFINEMENT
We investigated the stability of SubDyve's LFDR-guided refinement by varying the cal- ibration threshold while fixing the number of refinement iterations to six. Thresholds (r 0.05, 0.10, 0.30, 0.50) cover settings that em- phasize either high-confidence updates or mid- confidence regions where many candidates fall between ambiguous structural cues. As summa- rized in Table 5 performance remained highly consistent:
Table 5: Sensitivity analysis of SubDyve
under varying LFDR thresholds (r e (0.05, 0.10, 0.30, 0.50)). Each entry reports the relative performance difference (%)
from the baseline configuration (r 0.10).
A BEDROC
AEFi% AEFs
0.05
+0.04
+0.40
-0.48
0.10 (base)
+0.00
+0.00
+0.00
0.30
-0.07
-0.33
-0.04
deviations in BEDROC, FF and EFaz 6% were all within approximately 0.4% of
0.50
+0.44
+-0.27
+00.5
the default configuration (r 0.10). These results indicate that LFDR refinement is not overly sensitive to the choice of threshold and maintains stable ranking behavior even when the calibration boundary is shifted toward more uncertain regions. A full two-dimensional
sweep over thresholds and iteration counts provided in Appendix F.5
4.3
CASE STUDY
To further demonstrate the interpretability and structural behavior of SubDyve, we conduct four case studies: (1) a comparison with RDKit fingerprints on CDK7 to assess local substructure similarity; (2) ranking gap for structurally similar molecules DUD-E targets; (3) an analysis of eetive/decoy recovery patterns on DUD-E targets with varying seed sizes; (4) characterization of subgraph patterns from augmented seeds on CDK7; and
(5) pharmacophoric relevance assessment of the mined subgraphs on CDK7. Due to the limited space, experimental results of (3), (4), (5) are reported in Appendix G.1 respectively.
4.3.1 SUBSTRUCTURE SIMILARITY CDK7-TARGET COMPOUND RETRIEVAL
To evaluate the representational advantage of SubDyve over general-purpose molecular fingerprints, compare its retrieval behavior with RDKit on pair of structurally similar seed compounds on PU dataset. Specifically, we visualize the compounds prioritized in the top 1% by each method, alongside their seed compounds, using PCA projections of their respective fingerprint spaces (Figure A SubDyve's retrieved compounds form a tight cluster around the seeds in the subgraph fingerprint space, indicating high local consistency and
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shared substructural motifs. In contrast, HDKKit-priorttin compounds are scattered, despite being selected from the same ranking percentile, highlighting the method's weaker capacity to preserve functional substructure similarity.
closer inspection of two representative seed hit pairs (Figure 23) reveals that SubDyve successfully prioritizes compounds containing key substructures, such as penta-1,3-diene(ce cce) or butadienc groups (cc-cc), that align well with the sceds. These hits were not retrieved by RDKit, likely due to its reliance on predefined global fingerprints that overlook localized structural aligmment.
To further quantify this effect, Figure 2C presents similarity heatmaps between seeds and retrieved compounds. Subgraph fingerprint similarities remain consistently high across pairs, while RDKit similarities are notably lower, even for structurally related hits.
These results suggest that SubDyve offers superior sensitivity to activity-relevant substruc- tures, making it especially well-suited for discovering functionally analogous compounds in early-stage virtual screening.
4.3.2 RANKING GAP ANALYSIS FOR STRUCTURALIY SIMILAR PAIRS
To evaluate the ranking efficiency of Sub- Dyve, we perform ranking gap comparison analysis with general-purpose molecular fin- gerprints on structurally similar molecule pairs with activity differences. For the FA10 target in the DUD-E benchmark, we ex- tract active-decee decoy pairs with high structural similarity (Tanimoto similarity 2 0.85) and find that SubDyve significantly ranks actives higher and decoys lower than the RDKit + NP model, as shown in the Figure 3 Sim- ilar trends are observed for other DUD-E targets, as shown in Appendix G.2
PA10| Similarity- based pairs comparison Pair 1- Decoy: D C44019989 +4647 1 3.55e-12
Pair 1 Active: CHEMBLA02761
Similarity (SubDyve RDKI
Suböyve:
Sub0yve:
18890
Figure 3: Ranking gap and visualization of highly similar active decoy pairs for FA10 on DUD-E targets shown with model relevance ranks. Statistical significance is reported as Wilcoxon signed-rank p-value.
CONCLUSION
We present SubDyve, a label-efficient virtual screening framework that constructs a lask- adaptive subgraph fingerprint network by mining duss-diicrimmnntivee substructures from bioactivity-labeled compounds. Built upon these chemically meaningful patterns, SubDyve performs iterative seed refinement using L.DR-guided calibration to prioritize candidate molecules with minimal supervision. Our method achieves more than a twofold improvement in average EFi% on the zero-shot DUD-E benchmark and delivers strong BEDROC and EF performance in large-scale screening on the PU dataset. These results demonstrate that integrating aubsstrccuur--smmilartyy network construction with uncertainty-aware propagation offers a scalable and effective solution for virtual screening in low-label regimes, advancing the feasibility of early-phase hit discovery.
Although SubDyve is formulated as a target-specific screening framework, its design suggests potential for broader applicability. The subgraph-based similarity network can incorporate protein-informed or structure-derived descriptors (Koh et al., 2024 Desaphy et al. 2013). while the LFDR refinement remains compatible with such extensions because it operates only on propagated scores. Our study focuses ligand-only benchmarks, and applying SubDyve to settings that integrate protein information or involve multiple related targets remains a limitation; however, the observed correspondence between mined substructures and pocket- relevant chemotypes indicates that extending the framework toward richer protein-ligant contexts represents meaningful direction for future work.
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6 ACKNOWLEDGEMENT
This research was supported by the Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korean government (MSIT) for the Arti- ficial Intelligence Graduate School Program at Scoul National University (RS-2021-I12118)) and the Artificial Intelligence Convergence Innovation Human Resources Development Pro- gram al Inha University (RS-2022-00155915)) as well as by the National Research Foundation of Korea. (NRF) grants funded by the Korean government (MSIT) (RS-2023-00) 2023-00257479), the Bio & Medical Technology Development Program (IS-2022-NR067933) and the Basic Science Research Program funded by the Ministry of Education (RS-2023 0023-00246686).
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APPENDIX
A PROOF FOR PROPOSITION
Proof. of proposition
[local FDR < a implies FDR < a]
Let Zi...., Zm be test statistics following the two group mixture
f(z) = mofo(2) + fi),,,, To + =
क. > 0.
Define the local
rate (Efron, 2005)
Efron 2005
1fdr(=) Pr(H 0 2 2) fof((22)
f(z)
Choose hypotheses by
R₂ (f:l saf.
0<a<l.
Let Ra = RRal and Va = Em= lii E R. H.
Then
E[Va] Sa,
V. FDR E
mFDR
aa
Ra
Ra V
Write [8[a]
Σ (i) R.
Because Ifdr(Z,) S a whenever i E Ras
E[V.] S a B(R...
Dividing both sides gives mFDR S a. Since V, S Ro, Jenson's incquality yiclds FDR < mFDR S a.
mFDR (Marginal FDR)
E[V
mFDR
E
Marginal FDR takes expectations the numerator and denominator separately, providing a mean proportion of false discoveries. It is always defined (no 0/0 issue when R 0) and satisfies FDR < mFDR.
B MODEL ARCHITECTURE AND Loss DETAILS
B.1 PSEUDOCODE OF SUBDYVE
Algorithm I outlines the full SubDyve framework for virtual screening. The procedure consists of three main stages: (1) Subgraph fingerprint network construction, (2) Dynamic seed refinement. with LFDR calibration, and (3) Final compound prioritization via network propagation. In Step 1, we mine clas-ddisriminative substructures and use them to construct a molecular similarity graph (details in Appendix B.2). Step performs N-fold stratified refinement using GNN model with composite loss and iteratively expands the seed set based on LFDR calibration. For each split, the seed weights from the best-performing iteration are retained. Step 3 aggregates the N seed weight vectors via max pooling and performs final propagation to produce the ranked list candidate compounds. The LFDR refinement step described in detail in Algorithm 2
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Algorithm 1 SUBDYVE FRAMEWORK FOR VIRTUAL SCREENING
Require:
Initial labeled set Strains unlabeled pool Q' Number of stratified splits N, number of iterations M Hlyee-parameeee (Arank; Acou: Tap: T,3,0)
1: // Step 1: Subgraph fingerprint Network Construction (see Appendix B.2)
2: Mine disrmmiicrim subgraph patterns from Strain using supervised subgraph mining algorithm
3: Construct subgraph pattern fingerprints for all O'
4: Compute pairwise cosine similarity between fingerprints to construct the subgraph fingerprint graph 9 (V,E, we)
5: // Step 2: Dynamic Seed Refinement with LFDR
6: for = to N do
> Stratified bootstraps of Strain
7:
(S). < Split(Serain: ratio)
8:
Compute node features x(v) for all v E E
b Appendix B.3
9:
Initialize augmented seeds Saug + Ø, seed weight map s
10:
for
to M do
b Iteration loop
11:
x x(v)]oev
12:
(L,z) t M,(X,E,w: we)
Logits l and embeddings from GNN
13:
LBCE t WeightedBCE(4, S2, Yap)
14:
LRank PairviseRankNet S2)
15:
Loon < InfoNCE(2,, Sg)
16:
Lrotal (1 Arank) LBCE Arank LRank + Acon LCon
P Appendix B.4
17:
Update model parameters via V Lrotal
(Saug s) ALGORITHM S1. Saug. S, 3) LFDDRggided Seed Refinement
19:
end for
20: Save 8, from best-performing iteration on S2
21: end for
22:
// Step 3: Final Prioritization
23: Aggregate {sn J via element-wise max pooling to obtain ensembled seed vector s*
24: Perform final network propagation over g using s" to score O'
25: return Final ranked list of compounds based on propagation scores
B.2 DETAILS OF SUBGRAPH FINGERPRINT NETWORK CONSTRUCTION
This section describes the full pipeline for constructing a subgraph fingerprint notwork. The objective is to extract class-discrmminative substructures, enabling more effective propagation and compound ranking. The process consists of three main stages: (1) mining class- discriminative subgraph patterns, (2) generating continuous subgraph pattern fingerprints, and (3) constructing the subgraph fingerprint network.
B.2.1 MINING CLASS- DISSSRMIIIIINTVTEE SUBGRAPH PATTERNS
We adopt the Supervised Subgraph Mining (SSM) algorithm (Lim et al. 2023 to identify substructures that dilferentiate active and inactive compounds. We curate activity-labeled data from the PubChem dataset by extracting compounds annotated as bioactive against the target of interest. Candidate subgraphs are generated using supervised random walk strategy: for each node E VG),, a fixed-length walk is repeated multiple times to sample a diverse set of subgraphs. Each subgraph is decomposod into atom-pait pair doublets to estimate class-spccific transition preferences. These preferences itcratively refinc the walk policy, guiding subsequent sampling toward inas-inforrmtive regions.
The mined subgraphs are evaluated using a classifier, and the subgraph set that yields the highest predictive performance (e.g., in AUC) is selected as the final set Subopt In parallel,
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Algorithm 2 LFDR-guided Seed Refinement
Require: Ranking logits for all i V, initial train seeds S1, current augmented seeds Saugs
seed weight wi E seed weight map s, LFDR thresholds TFDR, update rate B baseline b
1: Compute z-scores: 2 < z8core(4)
2: Estimate local FDR: LFDR; local fdr(z)
Algorithm
3: for cach node i E V do
4: if i E Sang and LFDR, < TDDR then Saug f Sang {i}
5:
> Add high-confidence node
6:
wi 1.0 else if i E Saug \ Si and LFDR, TFDR then
7:
8:
Saug f Saug {i}
Remove low-confidence node
9:
Wi 0
10: else if i E Saug then
Wi wi B (o(4)
> Update existing seed weight
12:
end if
13:
end for
14: return Updated Saug:
Algorithm 3 LFDR Estimation
Require: Observed Z-scores Z {Ze)-- null density fo(z), bin count B, polynomial degree d, regularization parameter a 2 0, null proportion mo
Ensure: Local FDR estimates Ifdr(Z:) for all = i.,...,
1: Partition the range [min Z, max Z] into B equal-width bins (by-1, with centers 2, =
I (bj-1 bb)
2: Count samples in each bin: Nj + #1Z, E (bj-1, bb]l for j = I,...,
3: Construct design matrix X E Bx (d+1) with X5* = 2 k-1 1 for 1: = -.....d d+1
4: Fit Poisson distribution:
+ arg min
Σ j=1
N (x] - exx((x]x
B
+ 113113
5: for each i = 1,...,, , do
6:
Construct polynomial features x(2i) (Z 07 ...,... Z;)
7:
Estimate marginal density: f(Z,) exp (2,))² 3
8: Compute null density: fo(2.) mull pdf (2:)
9: Compute LFDR:
fo()s)
lfdr Z2)
f(Zz)
10: Clip to [0, 1]: Ifdr(Z.) + min(1, max(0, Ifdr (Z;)))
end for
12:
return [[fd((Z))22
we identify single-subgraph structural alerts (SAs) by computing feature importance scores using a random forest model. Subgraphs with importance above 0.0001 and entropy below 0.5 are retained as interpretable indicators of activity.
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B.2.2 GENERATING SUBGRAPH PATTERN FINGERPRINTS
To capture higher-order structure, construct Discriminative Subgraph Combinations (DiSCs) co-occurring subgraph sets that frequently appear in actives. Starting with 1- mer subgraphs, we iteratively build k-mer combinations using branch-and-bound search with SMARTS-based pattern grouping. Candidates are scored using an entropy-based metric Entropy(Supp,or pos SupPneg), and only those with sufficiett support (2 2%) and discriminative power are retained. Entropy filtering is not applied to 1-mers to preserve informative small motifs.
The top-d DiSCs are selected based on entropy rank and used to construct d-dimensional fingerprint vector, where each entry encodes the frequency specific subgraph combination within the molecule. These fingerprint vectors serve as task-aware molecular represenlations for graph construction.
B.2.3 CONSTRUCTING MOLECULAR SIMILARITY NETWORKS
We construct similarity graph G (V,&, w.) by computing pairwise cosine similarity wetween subgraph pattern fingerprints. Each compound in Q' is represented as a node, and weighted edges reflect structural proximity in the DiSC space.
B.3 DETAILS OF FEATURE ENCODING FOR GNN
In the dynamic seed refinement step, we use a two-layer GNN to predict activity scores over the subgraph fingerprint network. Each compound E Q' is encoded as:
[wi, NP P. PCA, hyb PT-CB
.sPCA ,e,
The components of the feature vector described below:
wy: Weight of seed to use for network propagation. Initially set wies, to 1, otherwise set to O.
N Network propagation score drive from w.
prr: Class-disriminative substructure features extracted from subgraph pattern fingerprints.
s SPCA REF Similarity to seed compounds in PCA-projected latent space based subgraph pattern fingerprints F.P..
h,by; Hybrid ranking score computed weighted average of the rankings of s POA and n! NNP.
e eTT-BB Semantic features derived from a pretrained ChemBERTa model, repre- senting molecular sequence semantics.
Each GNN layer followed by a residual connection and LayerNorm, with the second layer reducing the hidden dimension by half. The model outputs scalar logit computed via lincar layer for ranking, along with 32-dimensional embedding vector for represcntation regularization.
B.4 DETAILS COMPOSITE LOss FOR GNN
Following LLin et al. 2024 SubDyve jointly optimizes classification, ranking, and representa- tion learning objectives within the GNN during scod refinement. The final loss weighted sum of three components: binary cross-entropy LBCE, pairwise ranking loss LRankNet. and contrastive loss LContrast. Each component is designed enhance model performance under sparse supervision.
BINARY ENTROPY Loss (BCE)
We employ a class balanced BCE loss to accommodate severe class imbalance. Additionally, compound-level weights modulated by network propagation scores enhance robustness to
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noisy supervision:
CBCB
lo.logor or (4:)
Q'
+ +PW (1 yi) log( 1 -(((i)
(6)
o(4) 1+e wi + 7op n2
NP
where 4 is the predicted logit for compound i, and yi E {0, 1 is the ground truth label indicating whether E S2 (active) or not (inactive). n the NP score from initial propagation. Top is set to 5. The term PW balances class skew by weighting the active class more heavily: pos weight
1119==011 [[
2. PAIRWISE RANKNET Loss
To improve early recognition, we adopt a pairwise margin- based loss that encourages higher scores for known actives in S2 relative likely inactives:
LRanNNet = Σ (63)
(0,--(1-44))
max
i 12,2i E \2)
Here, m is a margin hyperparameter and denotes the number of valid (i.j) pairs.
3. CONTRASTIVE Loss (INFONCE)
This loss promotes intra-class consistency in the learned embeddings. For each compound i Q', we select its most similar positive compound 2,1 from S2 based on subgraph pattern fingerprint similarity, and treat the remaining compounds in S2 2,-
Coontrast
S2]
(8)
exp
log
TT
FES2
exp
2,+
+
Σx
exp
where is temperature parameter.
4. TOTAL COMPOSITE Loss
The total loss a weighted combination:
Liotal (1 Arank) LBCE+
Arank LRankNer +
(9)
Acontrast LContrast-
where Arank = 0.3 and Acontrast = 0.6 fixed across all experiments. The GNN is trained using Adam optimizer (Kingina & Ba, 2014) with a fixed learning rate 8 x 10-4 and weight decay of 1.57 x 10 Hyperparameter selection is discussed in Appendix C.2. The entire code and reproduced experiments is available at /ttpp::/giii gitbbb.tttuut/..///gg com J- Sar-SubbSSubDye
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C IMPLEMENTATION & EVALUATION DETAILS
C.1 NETWORK PROPAGATION ALGORITHM
Network propagation (NP) is used to prioritize candidate compounds by diffusing signals from a small number of known actives across chemical similarity network. This approach has been shown to effectively integrate relational structure for large-scale inference (Cowen ett al. 2017). NP itcratively balances the initial bioactivity signal carried by $ with the topological context supplicd by the graph, allowing evidence to flow along indirect paths and uncovering nodes that are not immediate neighbors of the seeds:
(1 - a) WN p(t) + a p(O),
=
(10)
where p(0) is one-hot vector encoding compounds S, Wy the column-normaliizd adjacency matrix, and a E [0, 1] controls the restart probability. Over iterations, the score vector p(t) converges to a stationary distribution that captures both local and global connectivity, thereby ranking compounds Q by their network proximity to S. By integrating signals along multiple paths rather than relying solely direct neighbors, NP effectively highlights previously unconnected yet pharnacologically relevant candidates, making it well suited for large-scale virtual screening task.
Network propagation (NP) prioritizes candidate compounds by diffusing activity signals from small set of known actives across chemical similarity network. This method effectively incorporates both local and global graph structure, enabling inference over indirect molecular relationships (Cowen et al.) 2017)
The propagation is formulated as an ilerative update:
(11) where W is the column-normallo adjacency matrix of the molecular graph, and a E [0,
p(t+1) = (1 w)W,P(t + aP(())
is the restart probability. The initial vector p(0) encodes seed activity, typically assigning 1 to known actives and elsewhere.
As iterations proceed, p(t) converges to a stationary distribution that reflects both direct and indirect connectivity the seed set. This enables the identificaton of structurally distant yet functionally related candidates, making NP suitable backbone for large-scale virtual screening under sparse supervision.
C.2 HYPERPARAMETER SEARCH SPACE
We perform hyperparameter optimization in two phases depending on the parameter type. GNN model architecture and loss-related parameters are tuned using Bayesian Optimization (100 iterations) (Appendix Table Hyperparameters related to iteration process on dynamic seed refinement are searched via random search (Appendix Table G
C.3 EVALUATION METRICS
To evaluate the performance of early retrieval in virtual screening, we adopt the BEDROC and Enrichment Factor (EF) metrics.
The Boltzmann- Enhanced Discrimination of ROC (BEDROC) is designed to emphasize early recognition by assigning exponentially decrcasing weights to lower-ranked active compounss. It is defined as:
BEDROC.
( 6
11----0 )
1 Σ
BEDROC,
e on
x
i=1
(12)
sinh(a/2)
+ 1 ca(1-Rm)
cosh(a:/) - ccoh) (a/2 a.,))
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Table 5: Hyperparameters related to GNN model
Parameter
Search Space
Selected Value
Hidden dimension
(16, 32, 64, 128)
64
Embedding dimension
{8, 16, 32, 64)
32
Arank
0.00 1.0]
0.3
Acontrast
0.0, 1.0)
0.6
Margin for RankNet loss
0.., ... 1.0)
0.5
Weight decay
10-6,10-4]
1.57 x 10-5
(seed weight update rate)
0.1. 1.0)
0.7
Learning rate
10 100+,10-2]
0.0008
NN (NP score weight)
(0.0, .... 5.0)
5.0
GNN layer type
(GCN, GIN, GAT)
GCN
Table 6: Hyperparameters related to iteration of seed refinement
Parameter
Search Space
Selected Value
Training epochs
{10, 20, 30, 40, 50}
50
Max iterations (M)
{3, 4, 5, 6, 7}
Early stopping patience of iterations
{1, 2, 3}
Stratified split (N)
{10, 5, 3, 2}
LFDR threshold TDDR
(0.03, 0.05, 0.1, 0.3, 0.5}
0.1
is the number of active compounds, .N is the total number of molecules, r; is the rank of the i-th active compound, and R. = n/N. Following prior work (Truchon & Bayly 2007). we set a = 85 to prioritize carly retrieval.
Enrichment Factor (EF). The EF quantifies the proportion of actives retrieved within the top-ranked subset relative to a random distribution. It computed as:
Na/N2%
EF 2%
(13)
n/N
is the number of active compounds, N is the total number of molecules, N2% is the number of molecules in the top x% of the ranking, and n, is the number of actives within that portion. Higher EF values indicate better prioritization of active compounds in the early ranks.
D EXPERIMENT DETAILS
D.1 ZERO-SHOT VIRTUAL SCREENING SETUP ON TEN DUD-E TARGETS
For each DUD-E larget, we curate high-quality dataset of bioactive compounds from PubChem while preserving the zero-shot setling. To avoid data leakage, we filter protein homologs using MMseqs2 (Steinegger & Söding (017). excluding any proteins with sequence identity greater than 90% relative to the target. From the remaining homologs (identity < 0..9), we retrieve associated compounds and their bioactivity annotations, retaining only those labeled as active inactive with valid potency measurements. Duplicate entries and records with missing values are removed to ensure data reliability. We additionally compare the FM-based baseline model with ChemBERTa (Ahmad et al. 2022) and MoLFormer (Ross ct al. )022) models for further comparison. Using the pre- models, we calculate performance by averaging the embeddings of bioactive compounds using the pre-trained models and taking the active and inactive compounds from DUD-E and ranking them according to their cosine similarity to each compound. For the ADA target, where PubChem
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Table 7: Summary of mubChem-auggentee data for DUD-E targets, including similarity
ranges, and number of seed molecules used in propagation.
Target
PDB code
Active Ligands
Decoy Ligands
PubChem Total (Act/Inact)
Similarity Range
Count
ACES
lef66
451
26198
1001 (1502/102)
0.6477-099
1277
ADA
2e1W
5448
444 (386) (58)
0.908 0.953
335
ANDR
Band
14333
918 (822/966
0.56 0.3
700
EGER
2rgp
511
35001
576 (127/119)
0.478-0099
S74
FAJO
3kl6
537
28149
261 [297 24
0.845 0.9
195
3gli:
10439
3299 (3164/135)
0.537
771
PLKI
Bowb
107
6791
353 (16))
0.61-0.9
174
SRC
3d16
523
31107
1232 (827/ 405)
0188 1.88-0.9
624
THRB
lype
3126 (3071 (
0.833
UROK
latt
162
9837
825 (760/ 76)
0.489-0.9
615
annotations are sparse, slightly higher identity threshold (up to 0.953) is used to enable sufficient subgraph extraction.
Appendix Table summarizes the number of actives/inactives and the protein similarity thresholds used per target. For downstream propagation, we construct a target-specific subgraph fingerprint network comprising PubChem actives and DUD-E molecules (including actives and decoys). PubChem actives with IC50 S 500 nM are selected as seed molecules, while the remaining actives are incorporated as unlabeled nodes. Subgraph patterns are extracted via a Murcko-scaffold split and encoded into 2000 -ineeiinniio subgraph fingerprints, which serves as the molecular representation for each node the graph.
Baseline Models Training Summary We evaluate SubDyve against two structure-base virtual screening baselines: CDPKit (Alignment) (Seidel 2024) and PharmacoMatch (Rose) el al. 2025) (Table S). CDPKit is geometric alignment algorithm that performs unsu- pervised pharmacophore matching without model training, relying solely on spatial fit. In contrast, PharmacoMateh is self-supervised learning framework trained on 1.2 million drug-like compounds from ChEMBL( (Davies et al.) 2015 Zdrazil et al.) 2024)). ). It learns joint embedding space for pharmacophore graphs using contrastive loss and an order embedding objective, enabling similarity based retrieval of actives without direct supervision.
Table 8: Key characteristics for baseline methods.
Model
Training Data Description
MinemacoMateh
1.2M small molecules from CLEMBL after Lipinski filtering and duplication removal; trained in self supervised fushion on 3D pharmacophore graphs using contrastive loss and order embeedingss.
CDPK& (Aligument)
Unsupervised aligument of 3D pharmacophores using geouettic (no training)-
ChemBERTh
ChemBERTa-2 2 is model based ChemBERTa that optimises pre-training performance through large-seale pre-training and multi-task-eelf-uperrvis learning comparisons using up to 77 million molecular data.
Former
MoLFormer is transformer- based molecular langusge model trained using effecient linear atteutions and rolational positional cubeedlings on 1.1 billion molecales (SMILES) data, outperforming traditional graph and language- models in many of the benchmarks.
DrugCLIP
DrugCLIP is a deuse retrieval based contrastive learning model that solves the virtual screening problem by learning the similarity between protein pocket and molecule. The model leverages exiensive data, including tures from PDBbind, Biol and ChEMBl datasots, and utilizes the HomoAng data angmentation method to maximize the diversity of the training set.
120,000 protein-molreatl molecale pairs and more than 17,000 complex strue-
Robustness to distant homologs Setup To examine whether SubDyve depends on closely related homologs when operating in the wero-shot setting, the sequence--identity threshold in MMseqs2 used for seed generation was lowered from 0.9 to 0.5. This adjustment ensures that seeds originate from substantially more distant PubChem proteins, thereby creating a more challenging and realistic zero-shot condition in which homologs often exhibit considerable variation in binding-site geometry and domain composition (McNutt et al.
2024 Lam et al.] 2024 Pourmirzaci et al. 2025).
In this setting, experiments were constructed using three DUD-E targets for which suffi- ciently low-similarity homologs were available. Appendix Table 3 summarizes the number of compounds utilized per target as function of protein similarity. To enhance enrich-
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Table 9: Summary of PubChem data for DUD-E targets with similarity below 0.5, including similarity ranges.
Target
PDB code
Active Ligands
Decoy Ligands
PubChem Total (Act/Inact)
Similarity Range
EGER
2tgp
35001
428 (413/15)
0.272 0.294
PLK1
2owb
107
6794
391 (225/166)
0.292-0.306 0.394-0.453
SRC
3e18
523
34407
974 (612/ (62)
ment performance, all available active compounds were incorporated into the downstream
propagation process.
D.2 PU-STYLE SCREENING SETUP PU DATASET
To evaluate the screening effectiveness of SubDyve in realistic compound discovery scenario, we construct a dataset using molecules from the ZINC20 and PubChem databases. Specifically, we retrieve 10,082,034 compounds from ZINC20 (https: /tttps:/zzinc0. docking, home/) and select CDK7 as the target protein. From PubChem, we obtain 1,744 unique compounds annotated for CDK7 after deduplication, of which 1,468 labeled active based on curated assay data.
To simulate sparse supervision, randomly select 30% of the active compounds for Stain From this subset, we designate 10% as a held-out set S₂ and use the remainder as initial seed nodes St. The other 70% of actives included in the screening graph unlabeled nodes, emulating the presence of under-characterized actives in large-scale librarics. This setup ensures that the test set remains completely unseen and that the majority of actives do not contribute label information during propagation.
For fair comparison across network propagation (NP)-based baselines, we the same seed sets across all runs, providing identical supervision to all models. We extract subgraph patterns using the SSM algorithm (Appendix B.2.1), excluding all test compounds to prevent leakage. A total of 100 discriminative patterns are used to construct subgraph- based fingerprints. To assess whether the difference in performance between methods was statistically significant, applied the paired I-test over results from five independent runs. The hyperparameter settings follow Appendix Table i except the stratified split N set to 5.
D.3 DETAILS OF EXPERIMENTAL SETUP FOR VARYING SEED SET SIZE
To demonstrate that SubDyve can effectively rank the 10% held-out set S2 specified in the PU-style screening setup created with the PÚ dataset with much fewer seeds, we conduct ablation study with much fewer S₁. Each seed count was randomly selected, and performance reported over five runs. This setup creates much harsher situation where the test set is completely unseen and a much larger amount of active is prevented from contributing label information during propagation.
For fairness, we use the same number of seeds in the network propagation-basee bascling and perform five runs on randomly selected S2 as same Appendix D.2] When extracting subgraph patterns with the SSM algorithun, we exclude all test compounds to prevent leakage.
E COMPUTE RESOURCES AND TIME PROFILING
Training Environments. Appendix Table 10 presents the system and software environ- ment used for all experiments. The setup includes a high-memory server equipped with single NVIDIA RTX A6000 GPU, dual Intel Xeon processors, and 512GB of RAM, running Ubuntu 22.04.4 with CUDA 11.1. All experiments are conducted on single server.
Time Profiling of Components in SubDyve. Appendix Table summarizes the per-module runtime of SubDyve across ten DUD-E targets. Subgraph mining is the dominant cost,, requiring approximately 108 seconds per iteration, whereas similarity computation,
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network construction, and propagation remain lightweight (sub-millisecond per pair edge, and tens of seconds per graph). LFDR refinement, which includes a small GNN training loop, adds about 1.27 seconds per epoch on average. Notably, computing chemical similarity for one million compound pairs takes approximately 5 hours. Note that profiling time of I.DDRguidded seed refinement. integrates the GNN training time.
To contextualize the preprocessing overhead, Appendix Table 12 provides the end-to-end comparison against standard RDKit+NNP pipeline. While RDKit preprocessing averages 9.27 minutes per target, SubDyve's full network-building pipeline, comprised of SubDyve's subgraph mining, similarity computation, and graph construction, averages 17.88 minutes. The additional cost arises primarily from SubDyve's discriminative subgraph mining step, which extracts target-adaptive substructures that conventional fingerprint methods do not generate. In practice, this one-time mining overhead is comparable to the cumulative cost of evaluating multiple fingerprints in standard workflows, while enabling a more expressive and task-specific representation. Overall, SubDyve maintains practical preprocessing time while offering richer structural abstraction than traditional finerprint-basee pipelines.
Table 10: System and software environment.
Component
Specification
GPU
NVIDIA RTX A6000 (49GB)
CPU
Intel Xeon Gold 6248R @ 3.00GHZ (48 cores)
RAM
512 GB
OS
Ubuntu 22.04.4 LTS
CUDA
11.1
Python
3.9.16
PyTorch
1.10.1 + culll 2.0.4
PyTorch Geometric
scikit-learn
1.6.1
scipy
1.10.1
Table 11: Profiling time of each module.
Module
Profiling Time
Subgraph Mining (SSM)
108.55 = 15 sec / /tterttinn
Subgraph Pattern Similarity Computation
0.4 0.2 ms / compound pair
Subgraph fingerprint Network Construction
0.1 1 0.1 ms edge
Network Propagation
16 1 23 see graph
Dynamic Seed Refinement with LFDR (inel. GNN training)
1.27 = 0.56 see epocc
Table 12: End-to-end timing comparison of subgraph network building (SubDyve) versus baseline preprocessing (RDKit+NP) on DUD-E targets. Times are reported in minutes. SubDyve's network building includes subgraph mining and network construction (including similarity computation). RDKit preprocessing includes network construction (fingerprint generation and similarity computation).
SubDyve Network Building
RDKit
Target
Subgraph Mining Network Construction
Total
Preprocessing
Average
10.68
7.20
17.88
9.27
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F ADDITIONAL EXPERIMENTAL RESULTS
F.1 ZERO-SHOT VIRTUAL SCREENING RESULTS ON TEN DUD-E TARGETS
F.1.1 COMPREHENSIVE EVALUATION
Appendix Table 13 shows a comprehensive evaluation of SubDyve and baseline methods across ten DUD-E largets. Metrics include AUROC, BEDROC, EF 1%, EF 5% and EF 10%. with confidence intervals estimated via 100 resampling trials. SubDyve achieves the best average performance across all five metrics, consistently outperforming other methods in early recognition and enrichment, while maintaining high AUROC. These results support the effectiveness of combining subgraph fingerprint network construction with LFDR-based refinement for zero-shot virtual screening.
Table 13: Comprehensive evaluation of SubDyve and baseline methods on ten DUD-E targets. Confidence intervals were estimated via bootstrapping (DiCiccio & Efron 1996), using 100 resampled datasets to compute the standard deviations. AUROC and BEDROC are reported as percentages. The best and second-best. scores per metric are in bold and underline, respectively.
BADmm (Dan)
17:
FFom
F7
1Pu
Flax
FFrs
Fim
17-
B113
1345
-31-
3040
12
10963
13483
$451
12
-2483
X06
22012 813054
[13
013911
125
-061
193
1341
11961
19-83
1145
2045
13366
13-83
526-2 23611
11.0
F41
15882
1161
$140
45366
1
147881
$18-2
1aad m98
37
19
16
17
24
Astoback Viua
ChamBtrts
MolFormer
XUBICC
12
AUROU
BEDROU
10
XUROC
10
EFye
71401
450-0
1:2005
Tex1
ADA
523110
7:2.7
10221.
0-228.77
212332
7043
1523
12414
1.32133
M623
1241
1131161
7.23112
ARDDR
04111
31211
15.11:35
08018.1
1432012
668212
LE:03
1.3113
2.7
FA3H
RE3RC
11217
13.77284
72868-1
3152232
7583
2523
12521.
54305
10.00
GESNLE
1.51213
180.0.11
1323
431114
2.5313
1.2213
SBC
6150L
13012
13ke5.3
1.000
0182
1981
3.34677
S1503
59:01
UBOK
SI2RLE
25:133
1.
3.00m3
9285
1m1
E8860
0.300
18500
10
3662
00.00 5
6,26044
Finst rank
5
6
0
3
3
In addition, recent advances in protein ligand prediction increasingly leverage explicit 3D structural information. To complement the main results and to investigate SubDyve against such structuro-aware approaches, we further evaluated two representative 3D methods, DifDDock-NMDN (Xia et al. 2025) and DynamicBind (Lu et al. 2024). under the same DUD-E evaluation protocol.
As shown in Appendix Table 14 across ten DUD-E targets SubDyve consistently achieved substantially higher BEDROC and FF1 scores than both 3D generative approaches and the physics-based based AutoDock- Vina scoring function. While AutoDock- Vina provides moderate enrichment, both DiffDock-NMDD and DynamicBind exhibit notably low rarly-recognition performance under this evaluation setting.
A likely explanation is the mismatch between the objectives used to train modern 3D generative models and the requirements of ligand ranking. Most structure-awart deep models are optimized for accurate pose ceneration-rewardeee of ligand and protein aloms rather than for discriminating true binders from decoys. As a result, these models often assign high confidence to plausible poses even for non-binding decoys, yielding weak enrichment. This gap between gose-generation accuracy and screening effectiveness has also been observed in recent analyses of 3D docking and diffusion--aasee
geometrically plausible arrangements
models LL ct al. 2025 Buttenschoen et al. 2024).
Moreover, DUD-E decoys are intentionally constructed to mimic drug-like physicochemical properties, and the docked complexes provided in DUD-E contain non-negligible geometric noise. Structure-aware generative models, which are trained on curated datasets such as PDBbind, tend to be more sensitive to such noise, whereas physics-based scoring functions
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Table 14: Performance comparison including 3D structure-aware model on the DUD-E targets. The top results are shown in bold, and the second-best best are underlined, respectively. Confidence intervals are reported with 100 bootstrap resamples (DiCiccio Efron 1996)
Protein Tugee
SubDyve [Ours]
DUNDocG-NMDN Xin 2020
Dynami:Buud Lu et 2024
AutoDock Vina (Eberburdi es a.. 2021
ACRS 66:22
57.011-244
41.1
1/5:0:4
11:11
S8100
1511
15ai0.
ADA
K32-4
50.611-.33
201.2
3.9:1.2
9112
11M.1:1
71.2
ANDR
73:2
87.1+33.1
721
0.850.3
0461
B1 18760.3
11th1
15.650
46.8:21.7
00000
KIT
64233
13.822.
521
1.231
1822
PLKI
8523
81-72:4.0
621
1.11
15331
30.0211.
62.1
UROK
25.0-12.4
Avg. rank
10
1.0
36
32
310
3.6
2.
22
Table 15: Performance comparison across EGFR, PLK1, and SRC with similarity below 0.5. AUROC and BEDROC are reported as percentages. Confidence intervals are estimated via bopiig (DiCiccio & Efron 1996), using 100 resampled datasets to compute the standard deviations.
EGFR
PLK1
SRC
Model
BEDROC
EF
BEDROC
EF
BEDROC
EF EF
SubDyvea.9
86 + 2
60.0
2.3
85
51.7
4.0
61
35.0
1.8
SubDyveo.s
60.0
2.2
60.6
3.6
+
16.2
1.6
PharmacoMatch
3.1
9
1.5
+ 1
6.0
CDPKIT
26
12.2 1.6
3
5.7
2.3
28 1111
11.1
1.2
DrugCLIP
40 +
28.7 + 2.1
66 4
45.0 + 4.0
16 2
8.1 + 1.3
MoLFormer
75 =
48,1 + 2.8
69 0
35.2 - 4.0
48
21.5
- 1.5
AutoDock Vina
14
3.68
1 0.7
13
1.83
+ 0.3
13
4.00
+ 0.5
like AutoDock-V Vina exhibit greater robustness compared to learned 3D models.
explaining its relatively better performance
Taken together, these observations suggest that current 3D generative pipelines may require additional calibration or hybrid scoring strategies to achieve reliable ligand ranking under this experiment setting. A deeper examination of structure-aware models remains important direction for future work.
F.1.2 ROBUSTNESS DISTANT HOMOLOGS
Based on the experiment sctting in Appendix D.1 "Robustness to distant homologs Sctup", Appendix Table 15 summarizes the performance of SubDyve and bascline models under the restricted similarity condition. Even under this more challenging setting with less informative seeds, SubDyve maintained strong early-recognition performance and remained better or competitive with all baselines on both BEDROC and EF1%.
Notably, for EGER, the BEDROC score decreases by less than seven points relative to the 0.9 sequence-idente identity setting, while still maintaining a large performance gap over pharmacophore- based, FM-based and deep lcarning-base based basclines. For PLK1, performance remains stable undor the restricted similarity threshold and exceeds the results obscrved at 0.9 similarity. These observations reinforce that SubDyve remains effective even when only distant homologs with sparse annotations are available.
F.1.3 MULTI-TARGET SCALABILITY EVALUATION ON THREE DUD-E KINASES
To investigate whether SubDyve can amortize preprocessing costs across biologically related targets, we conducted multi-targe evaluation using three tyrosine kinases from DUD-E: EGER, KIT, and SRC. These targets share regulatory roles in signaling pathways and possess overlapping ligand-proton annotation profiles (Tomuleasa. et al. 2024 Tatton al. 2003
Rao et al. 2015). Leveraging this structure, we identified homologous protcins common to the three targets using PubChem annotations and collected the corresponding compounds.
From this joint compound set, we performed a single supervised sabgraph-mining step, extracted clas-ddisciminnatiee patterns, and constructed unified subgraph-based fingerprint
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network that reused for all analyses. SubDyve's network propagation with LFDR refinement was then applied under four activity definitions: (i) ligands active across all three targets, and (ii-iv) ligands active across each target pair (EGFR-KIT, EGFR-SEER KIT-SRC). We limited the number of seeds for multi-target to 189 to account for multi- target scalability and low-label regimes. The number of known active compounds targeting the tyrosine kinases is limited: EGFR SRC and KIT SRC share 27 and 15 compounds, respectively, while only three compounds active across all three targets and EGFR KIT. All other hyperparameter scttings are configured identically to the single-target DUD-E experiments.
Across all configurations, SubDyve consistently demonstrated strong carly-recognition perfor- mance and substantially outperformed DrugCIIP on BEDROC and EF metrics (Appendix Table 16 These results indicate that subgraph patterns mined once from shared homol- ogous annotations can transfer across related kinase targets, suggesting that SubDyve's preprocessing cost can be partially amortized when targets exhibit biological or ligand-based similarity.
While this experiment does not constitule full multi-target joint training nor address scala- bility for highly heterogeneous target sets, it provides evidence that subgraph-leve represen- tations extracted by SubDyve remain informative across related protein families. Extending the approach toward broader transfer-learnig or multi-target VS frameworks is a promising direction for future work.
Table 16: Comparison of SubDyve (Ours) and DrugCLIP across multi larget combinations.
SubDyve (Ours)
DrugCLIP
Combination
BEDROC
EF 1%
EF 5%%
EF 10%
BEDROC
EF
EFss
EF 10%
EGER-KIT-SRC
69.52
35.93
19.38
9.69
1.55
0.00
0.00
2.22
EGFR-KIT
79.37
57.27
18.18
9.09
5.19
0.00
0.00
1.66
EGER-SRC
84.11
41.21
19.20
9.99
13.14
7.26
2.95
1.66
KIT-SRC
55.76
20.25
14.40
8.81
1.66
0.00
0.00
0.33
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Table 17: Complete performance comparison of SubDyve and baselines on the PU dataset. The top results are shown in bold, and the second-best are underlined, respectively.
Methad
BEDROC (8)
0.%
15
5%
10%
Deap harning-hoed
1,0
DrigULIP (NemiPS)
1.99
163 0.0
1,00
2.53
0.62
PSICHIC (Nu: Mi Notre
9:57 5.05
4.7 2. 2.55
6.02 2 5.90
7.48
2.47
7.02 4: 1.80
5.36 0.94
GRAU (IC05) Y00 3701
00.05
10.50
44.32 4 5.35
45.31
29.75 8: 1:38
15:00
0.47
10.00 :: 0.00
Date miningpbasd
N01
185.70
6.64
0.4
NP
Yest
02.44
22.71
extended
3.5
0.53
83.54
15.85
0.50
1163 0.3
32 4 XP
STevbii PiH
08
3.77
120
11.89
85.40
3.80
50.56
0.08
18.69 0.6
9.21 0.36
ipl NP
Tyseea 20103
00
3.00
132
13.02
75.01 4
28-96
1.34
18:36
9.30
6:79
groph
10.00
3.00
126-72
10.05
84.73 4: 5.74
31.63
0.92
19.1 4: 0.47
9.70 0.24
syleiilaatio
A0:51
5.18
15
17.18
80.25
135.72
12.7
79.92
1.41
0.00
4.25
88.04
0.55
standard
84.31
3,50
0.30
0.24
Sablyyw
63.01 1 1.44
155.51 6.58
97.59 1: 1.44
33.01 0.80
19,90 0.18
10.00 :: 0.00
Statletion) Seuifranco (p-salue)
Table 18: Description of various molecular fingerprints used in virtual screening.
Fingerpeiat
Description
Standard
Bused persence
modecuk.. efflciout but lack specifictty. of specific functional groupe bond sterochemistty. counts, and brazching patteras.
Estended
Sinilar
fingeprinia but inclade addiition topological loys predefined peededied substructuze Developed by NilL. deetrollaii propertiss modeenle.
MACCS
MACCS project indicsting presene abermce spectfe eobetroctures. mokeeu..
Encndio topological
Hybondrttion
Encodes the hybridization states stoms in molecnle.
Copturee the preeince or aheence of spectfic chemical subtrrucurres.
RDKit
Eingerptints geserated using RDDIi tooladi, use similarity soarches and cheminformatics applications. Pall-baeed fingeppints repromnting fnstures derived from at atmmic path within molscaos.
Asdlan
PP2
Developed by Openly:: uses topoloiical and pharmacaphori: information for similaitt sourch and screening. Also from OpenEye: inceporates topologioll pharmacophoric, and electroetatic features for mokentar comparison.
PP4
F.2 PU-STYLE SCREENING RESULTS ON PU DATASET
To supplement the results in Section 4.1.2, report additional baseline results for the PU-style virtual screening experiment on the PU dataset. Table 17 extends Table 2 by including all evaluated general-purposs molecular fingerprints. These are combined with the same network propagation pipeline as in SubDyve, allowing a controlled comparison of representation effectiveness. Descriptions of the fingerprints used are provided in Table I8
As shown in Table 17 SubDyve achieves the best performance across all BEDROC and EF metrics, outperforming deep learning models and general fingerprint-bast baselines. While some fingerprints (e.g., rdkit, Graph) perform competitively under certain thresholds, they fall short in consistency across metrics. These results support the advantage of task-specific subgraph representations combined with uncertainty-awart refinement for robust screening under sparse supervision.
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F.3 ABLATION STUDY: IMPACT OF SUBGRAPH PATTERN FINGERPRINT NETWORK AND LFDR-GUIDED SEED REFINEMENT ON TEN DUD-E TARGETS
We conduct ablation study 10 DUD-E largets evaluate the individual and joint contributions of two core components of SubDyve: (1) the subgraph-based similarity network and (2) the LFDR-based seed refinement. Tn Table 19 combining both components yields the best results, with the highest E'Fi% on all 10 targets and top BEDROC scores on 9. This highlights SubDyve's robustness beyond the PU dataset and its screening performance on DUD-E targets.
We also observed that applying LFDR refinement alone without the subgraph- based similar- ity network often degrades or remains unchanged, while using both components together consistently improves performance. This finding highlights the complementarity of chemically meaningful network construction and uncerlainty-awarenee both essential for robust and generalizable virtual screening under low supervision.
Table 19: Ablation study results for the effect of subgraph fingerprint network and LFDR- guided seed refinement the 10 DUD-E dataset. The top results are shown in bold, and the second-best are underlined, respectively.
Target
Subgraph
LFDR BEDROC
EF 18
ACES
61
38 24
38
76
35.7 1.7
244
ADA
87
41.1 = 4.1
76
36.3 4.9
83
50.6 5.3
ANDR
27 =
18.9 2.1
184 2.1
45 3
21.1 2.7
72 2
37.1 2.1
EGFR
40
30.9 1.7
18.2 1.6
79 22
53.2 1
86 2
60.0 2.3
PAIO
17 222
11.8 1.3
6
1.0 0.4
56 22
48.8 2.0
58
47.0 1.7
KIT
11
3.7 1.5
11
2.9 1.3
37 =
3.8 1.9
11 =
13.8 2.6
PLK1
43.2
32.2
78
19.5
85
51.7 4.0
SRC
56 56
28.5
39
12.6 = 1.4
9.4 = 1.3
G1 2
35.0 1.8
THRB
21.3 1.9
21=2
10.7
32
21.2
61
36.6
2.0
UROK
35
22.2
30
13.0 2.6
37 1
25.6 1: 2.4
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F.4 ABLATION STUDY: VARYING SEED SET SIZES
To provide a more comprchensive ovaluation of PU-style virtual screcning on the PU dataset. we present additional baseline results for the number of seeds (50, 150. 250) in Table 20 which expands upon the findings reported in Section 4.2.2 and Table 4 This extended table includes wider range of general-purpose molecular fingerprints, each integrated into the same network propagation framework used by SubDyve, ensuring fair and controlled comparison of representational capabilities. Additionally, we introduce Subgraph NP as control variant, applying standard propagation over subgraph-derived networks without LFDR-based refinement.
Across all seed sizes, SubDyve consistently achieves superior performance, particularly in BEDROC, 3F and EF Subgraph + NP advantage also exlends EF 1%, highlighting the strength of subgraph-based representations in capturing bioactive chemical features beyond those accessible to general fingerprints.
Although certain baselines such MACCS and Avalon exhibit strong results at specific enrichment thresholds, their performance lacks consistency across evaluation metrics, demon- strating the robustness of SubDyve's approach. These results suggest that subgraph patterns and BFDR-based refinement have screening power over other pre-defined fingerprints, even in harsh environments with much sparser seed.
Beyond the settings considered in the main text, we further examined the extreme case in which only very small seed sets available (5, 10, 15 compounds). As summarized in Table 21 SubDyve maintains competitive carly-recognition quality even at these minimal seed sizes, consistently outperforning all generic fingerprints integrated with the same propagation framework. Notably, while overall performance naturally decreases as the seed set becomes extremely sparse, subgraph-driven representations continue to provide meaningful enrichment, and SubDyve remains the rop-performing method across most metrics and seed sizes. These results indicate that the structural patterns extracted by subgraph mining retain useful discriminative power even under highly limited supervision, and that LFDR-guided refinement. further stabilizes ranking performance such challenging regimes.
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Table 20: Ablation study on the number of seed compounds on the PU dataset. For cach seed size (50, 150, 250), the bascline of all generic fingerprint performance is shown. For each number, the best value is highlighted in bold, and the second-best is underlined.
Seods
BEDBOC
0.3055
0.50%%
375
5%
weslon + NP clll-olbiizcttoo
YE ol 315
05.16
3.55
54.00
15-47
50.83 12.07
18.1
7:43
28 91 0.05
18:28
0.87
20220
00.61
50.68 2
63.72
7.0
42.30
2 8.22
22.85 1.4
14.55
0.95
esaae NP
Yiat
34.87
0.38
37.8
15.37
30.52
11.07
37.51
4.77
20.33
2.29
13.57
0.63
27.23
0.79
NP
7.21
22.56
63.04
6.62
51.23
19.33
50.25
9.06
40.34
0.87
20201
43.76
6.14
11.59
22.79
51.10
14.22
18.10
26.11
1.03
18.50
0.76
NP
47.02
8.65
56.77
15.24
02.81
9.24
50.92 6 8.16
27.74
2.04
17.05 :
Nar
11
01:13
8.46
13.00
10.00
45:31
7.04
11.97 9 0.11
05.7
1.00
17.14
1.0
Sdki
Yi
L RMW
43.85 2: 3.37
10.21
19.76
47:92
50.35 2 3.00
25.7 4: 1.89
15.50
1.05
stnndan
+
15.78
54.74
70:85 9.55
60.72
31:01
19.20
0:37
cllesulaizutt
20125
45.25
8.74
75.75 4: 0.68
66.81 4: 10.79
58.70 4: 7.20
25.7 +: 1.09
16.48
0,91
marce NP Yi
00.03
5.07
$1.37
17.13
15.75
7.003
17.40
10.35
21
3.35
14:28
2.07
extended
51.87
68.4
6.54
56.57
12.75
60.28 2: 5.23
30.18
1.52
18:58
0.76
Nirair Pac43
7.793
1.14
0.71
ipl
55.36
groph
solidiiation
Yi
05.22 8:30
79.00
15.50
00.00 0.50
30.
subehum
46.74 6.88
62.37
19.0
58.68
11.775
48.0
7.76
28.01
1.63
18.44 0.7
alkes
56.82
3.79
52.09
0.75
54.02
$3.62 0 7.51
19.5
1.59
17.79
0.05
standand +
$1.59
4.95
60.85
11.29
63.12
13.46
55.39 + 5:00
79.78
1.85
18.61
0.75
Subgraph
NP
1.39
$3.30
22.99
10.07
67.17
7.24
30.03
1.70
18:22
ollseahttruct
7.06
0.61
0101
estate + NP
2000
44.54 4: 6.85
64.77
19.25
66.51
12.27
50.14 8
22.16
2.07
15.18
1.82
estended aeddddd.....
07.43 8.71
64.79
10.11
70.67
10.2
64.30
30.59
1.26
18.80
0.64
go ND
minu
56.80 5.76
67.45
1635
75.57
05.15
30.19
1.30
18.50
0.01
54 KP
05.01 9.27
91.76
18.15
51.27
62.75 4:
27.33
0.05
18:00
0.79
graph 11m0210
1.75
sylotdlationn
56.52
1.51
7.00 07.05
70.19
70655
08.80
30.20
1.14
18.50
standaad
Yrot
2125
71.4
16.31
70.12
18.16
61.00 1
31.0
19.02
0.42
Salammph
NP
61.06 9.24
11.04
19.80
36.31 11:98
$0.51 :: 4.60
50.20
1.64
18.10 0.85
Subiyyee
66.73 2: 2.71
07.60
16.55
35.43 3: 19.52
78.19 2: 3.28
92.85
0.60
10.72
0.36
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Table 21: Ablation study on the small number of seed compounds (5, 10, 15) on the PU dataset. For each seed size, the baseline all generic fingerprint performance is shown. For each number, the best value is highlighted in bold, and the second-best is underlined.
33%
avalon + NP Ni
2021
20.22
8.32
13.04
7.41
26.20
11.02
26.46
8.16
21.11 1.00
0.94 10.04
14.77
LABE
96.07
2.42
15.73
7.55
35:37
0.00
29:35
4.55
11:00
2.13
1.51
extace NP
Yaet
Poce
23.78
0.8
36.14
12:36
28.52
6.31
26.51
5,00
14:14
2.87
9.3
1.56
extended
25.07
0.57
10.57
11.86
16:27
5.74
13.70
7.0
20.12
1.51
14.55
1.17
2.13
sybdddattion
11.04
17.10
20.36
140
2:366
1.01
NP Y1
05.64
05.7
31.91
9.50
75
12.3
1.91
pubehccn
25.06
8.25
5.08
7.55
10.58
4.14
26.45
5.52
10.58
2:40
18.00
1.21
nlkes
1m.
11063
18.13
3.79
12.2
6.81
11.39 +
13.55 + 1.15
11.50
1.57
10.54
1.38
standed
Y1:00
2145
20.77 4: 2.50
10.44 2: 6.91
11:19
5.90
19.98 2: 4.18
20.12
1.88
16.34
0.76
Wi
30.92
24.56
24.47
10035
300 0.6
IT.35
76.70
42.32
16.4
13.50
15:37
1.07
estae i. NP Yiul Pares
25.79 4: 6.72
40.27
19.59
84.23
28.50
7.35
15.5 4: 4.05
10,04
3.45
ectended
32.81
3.97
17.55
15.0
$4.15 + 11.60
18.35
0.51
21.18
0.06
17.3
1.17
52 NP ereeri PAPe3
34.52 21 0.36
63.87
2: 7.05
47.13 6.00
30.16 4: 5.92
24.34
1.29
17.00
1.25
ipl
(1sma 23211
9:51
gnaph 11. mim
6.06
sybithbatton
NP
gubchen
36.84 8.36
10.0 10.08
3M00
20.74
20.94
3.77
XP
Y:
81.63
3.96
40.06
7.01
30.14
4.70
18.22
4.02
12,60
2.09
standand +
33.1 0.10--.0 3.18
15:00
10:16
$1.91
10.46
78.44 +1 7.30
23.11
2.80
17.38
0.8
Sabgraph
NP
5,08
53664
17.18
30.74
9.77
15.39
25.3
2:09
Subiyyoe
50.76
11.99
58.27
12.51
06.87
otleanbsteutt
7.50
NP Virt Bares
19.35
10.1
3.046
20.04
10.47
2.51
6.43
1.86
estended
Prres
22.31 3.68
1223 2 11.7
0.25
7.07
17.99
10.44
1.5
11.46
0.73
32 NP Di mie
20.87 0.92
12.16 10.53
13.82
19.4
12.56
6.75
18.36
2.82
13.67
1.03
ipt NP 1Tuezi BaCA1
21.78
25,75
11.02
17.08
5.55
21.59
2.77
11:18
1.20
12.57
0.17
groph NP 11.00 P3141
24.00
5.4 5,05
0.51
30.15-
16.32
1.55
10,56
aphidizatiun m
2.41
standand
21
6.01
65
15.91
19.35
2.00
1.94
Sahgroph NP
01:01 8.10
1U11 7.75
20 6.5.1
17.06
12.1 1.74
15.11 1.41
SubDyve
44.34 2: 7.4
$5.92 2: 31.5
67.50 2: 15.94
45.3 2: 4.97
23.72 2: 3.26
15.4 4: 1.51
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Table 22: Sensitivity analysis of SubDyve under varying LFDR thresholds (r 0.05, 0.10,
0,30, 0.50) and iteration counts (3 10). Each entry reports the relative performance difference (%) from the baseline configuration (r = 0.10, iterations = 6) across three metrics: BEDROC, EF 1% and F The best and second-best values are highlighted.
Ieraatios
=
0.05
+ 0.10
0.30
= 0.50
DEDROC
EFia
EFax
DEDROC
EFis
EFss
BEDROC
EFis
E
BEDROC
EFys
EF
+0.15
-1.67
-0:26
-0.00
-0.30
-0.11
-0.73
+0.67
-0.61
-0.53
-0.41
-0.45
+00221
-0.50
-0:12
+0.02
-0.59
-0.17
-0:28
-0.44
-0.13
+0.04
+1.20
-0.50
+0.01
+0.40
-0:48
+0.00
+0.00
-0.07
-0.33
-0.04
+0.44
-0.27
+0.05
+0.46
40.35
-0.36
+0.82
-0.45
+0.20
4-3.1
-0.16
-0.30
-0.49
-0.45
+0.18
-0.91
40.12
Max [A] (%)
BEDROC: 0.13%, EFig 3.51%, EF 0.81%
Table 23: Overall statistics summarizing the stability of SubDyve across 20 hyperparameter configurations (four LFDR thresholds x five iteration counts). The table reports the mean, standard deviation, coefficient of variation (CV), and performance range for each retrieval metric.
Metric
Mean
Std Dev
CV (%)
Range (%)
BEDROC
86,2093
0.2709
0.31
0.81
EFi
56.69
0.50
0.88
2.27
E Ess
17.04
0.04
0.23
0.60
E110%
8.74
0.03
0.29
0.76
F.5 ABLATION STUDY: COMPUTATIONAL OVERHEAD
SYSTEMATIC ANALYSIS OF LFDR REFINEMENT STABILITY AND
To examine the behavior of LFDR-guided refinement in systematic manner, we first evaluated its sensitivity to calibration parameters. We conducted two-dimensional sweep over both the LFDR threshold 5 and the number of refinement iterations, considering T (0.05, 0.10, 0.30, 0.50} and iteration counts in {1, 3,,3,5,7 5, These settings span regimes that prioritize conservative updates, aggressive seed expansion, and intermediato-coofiddnnee regions in which many compounds lic between clear positive and negative structural evidence. Appendix Table 22 across all tested configurations, SubDyve's early-recoguition metrics (BEDROC, EF 1%, EFs%) varied only slightly relative to the default configuration (r 0.10, 6 iterations), typically within a 1% deviation band. Appendix Table 23 shows consistently low CV values (<1%) and narrow score ranges, indicating that SubDyve maintains stable behavior under variations in both the LFDR threshold and the number of refinement iterations. This demonstrates the robustness of the L.FRR procedure to these hyperparameter choices.
We next examined the computational overhead of LFDR refinement. Although the procodure involves multiple propagation-update cycles, the practical cost remains modest because the subgraph-mining stage extracts highly discriminative structural patterns that govern connectivity within the constructed network. Compounds that do not share meaningful substructures with the seed molecules naturally receive near-zero similarity during network construction, limiting their participation in propagation. Consequently, LFDR primarily operates over compact and behaviorally relevant neighborhood around the seeds rather than over the full candidate library. This selective propagation behavior aligns with the ablation trends in Table 3 where subgraph fingerprints and LFDR refinement reinforce one another enhancing carly-eecognition performance while avoiding unnecessary computation.
F.6 ABLATION STUDY: FALSE POSITIVE PRESSURE VIA LFDR-CUIDED REFINEMENT
g further analyze the effect of the seed-selection rule (TFDR) on calibration and retrieval performance, which is considered controlled false positive (FP))pressure experiment: A low TFDR imposes stricter FDR control (low FP-pressure), whereas a high TFDR relaxes control (high PP-pressure, thereby including more false positives in the refined seed set. In brief, we evaluate the impact of the LFDR threshold TFdr on calibration and screening performance shown in Figure 4
Figure
As baseline, compare against
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probability-based refinement strategy (denoted PROB), which directly thresholds GNN logits without LFDR. estimation.
ACES Seed Calibration
ACES: BEDROC a=20.0
0.40
0425
204
Nomiral thenshard
Nethos
Figure 4: Effect of LFDR Threshold TFDR- (A) Seed-calibration curves for LFDR (blue) and PROB thresholding (orange). Calibration quality improves the curve approaches the diagonal: ECE values are shown for both methods. (B) Boxplot BEDROC (a = 20) scores for LFDR and PROB across threshold values.
Figure shows the seed-calibration curves across thresholds for each method. LFDR achieves substantially better calibration, with an expected calibration error (ECE) of 0.204 compared to 0.511 for PROB. This indicates that LFDR maintains robust performance even under increasing FP-pressure, validating its practical FDR control capability. Figure B shows BEDROC scores across five LFDR thresholds (TFDR) and five probability thresholds (TPROB). LFDR consistently yields higher performance across the threshold range, suggesting robustness against. increasing PP-noise. Similar trends for EF and AUPRC shown in Figure and Figure
Figure 5 Seed- celedcaaibrttoon curves comparing LFDR- and probability- based (PROB) refinement strategies. LFDR yields lower expected calibration error (ECE) across most targets, demonstrating better control of false discovery rates.
Figure 6 BEDROC (a = 20) scores evaluated across thresholds. LFDR generally shows higher BEDRÓC values with reduced variance, reflecting improved early enrichment.
Figure 7 FF plotted as a function of threshold. LFDR consistently outperforms PROB across thresholds for most targets, confirming its robustness under different calibration conditions.
Figure Precision recall (PR) curves at the best-performing threshold per method. LFDR achieves higher PR-AUC for the majority of targets, especially those with imbalanced label distributions.
Together, these results highlight that the L.DR-guided refinement. process controls the false discovery rate and mitigates false positive noise under varying FP-pressures. SubDyve demonstrates strong and stable performance across variety of target proteins, offering reliable solution for virtual screening under sparse supervision.
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Calibratio Comperisun Acrrox
LTDO DOE- 363
LITO 12C3-E120
LITO JOCE-R DIRT
200
LIS3 1P-E-6-301
PR06-E0E-0007
PLKE
THIR
LIBCK
19288 (ICE+8ATI
19228 D020 2013
PacE INCEICCNEERI
Figure 5: Effect of seed-selection rule on FDR control and early recognition for 10 DUD-E targets. Seed-calibration curves for LFDR (blue) and probability thresholding (orange). The closer the curve lies to the diagonal, the better the calibration. Expected calibration error (FCE) annotated for both methods.
BEDROC Comparison (0-20.0)
A750
8.00
657
100000
08.0
8.00
A792
oas
0008
6798
Medbed
Matrod
LPC8
Meried
Hettod
LXGE
Metbed
Veiled
Vaital
Figure 6: Effect of seed-selection rule on FDR control and early recognition for 10 DUD-E targets. BEDROC (a = 20) scores evaluated across the threshold grid; boxes show the interquartile range, whiskers the 5 95 percentiles. Box plot for LFDR (blue) and probability (orange).
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27315 Theesodd
4936
1
11a0
1904
Figure 7: Effect of seed-selection rule FDR control and early recognition for 10 DUD-E targets. Enrichment factor at the top 1% of the ranking (EF 1%) as a function of the threshold. Line plot for LFDR (blue) and probability (orange).
Caree Chet Mithed)
JSS
180
Figure 8: Effect of seed-selection rule FDR control and early recognition for 10 DUD-E targets. Precision recall curves at the best threshold for each rule. Legends indicate the chosen and the corresponding PR-AUC.
F.7 ABLATION STUDY: VARYING d-DIMENSIONAL SUBGRAPH PATTERN FINGERPRINT
To evaluate the impact of subgraph pattern size virtual screening performance, present the results of SubDyve under varying fingerprint sizes in Figures 9 The number of subgraph patterns mined using the SSM algorithm and selected according to their entropy importance was varied as d E (100, 200, 300, 500, 1000, 2000]. The figure shows the average performance for 10 DUD-E targets evaluated using the AUROC, BEDROC, EF E.5%, and FoF10% metrics. As the number of patterns increases, SubDyve shows consistently improved performance across all metrics, indicating that incorporating a broader range of chemically informative substructures improves model representation. For the finalized setting of d 2000, we additionally report target-specific AUROC scores highlight the consistency of performance across targets.
All results are calculated with 100 bootstrap resamples obtain confidence intervals and report both the mean and standard deviation. These results highlight the benefits of capturing different subgraph-level features, which contribute substantially to improving screening accuracy in low-label environments.
F.8 ABLATION STUDY: GNN MODEL FEATURE COMPONENTS
To more thoroughly assess the contribution of each component in GNN model to SubDyve's ranking performance, performed extended set of ablation experiments. These ex- periments isolate the effect of pretrained ChemBERTa embeddings, the hybrid PCA-NP ranking module, and individual scoring elements such the seed-weight term, the network-
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AUROC (%) subgraph
BEDROC (%) subgraph
EF 1% subgraph
40
00
BEDROC (%)
23
40
40
10-
100
200
300
300
1000
2000
100
200
300
500
1000
2000
100
200
300
500
1000
2000
sabgrraph 6/)
subbraph (1)
subgraph (4)
D
subgraph
subgraph
Target-wise (d=2000)
16-
62%
89
10
4
2
100
200
48 sabbgraph
300
500
1000
7000
100
700
subbraph (4)
500
1000
2000
come
ArEs
AD
ANOH
RTT
PR
Tano
UROX
Target
Performance comparison for varying numbers of d in the subgraph pattern removal study. (A-E) Average performance metrics (AUROC, BEDROC, EF E EFiog) for 10 DUD-E targets function of d. Error bars represent the standard deviation of 100 bootstrap resamples. (F) AUROC performance per target at d = 2000, ranked by performance per target.
Figure 9:
Table 24: Ablation study of GNN features on the PU dataset. The full model (with both ChemBERTa features and hybrid ranking) achieves the best performance. Top and second- best results are in bold and underline, respectively.
Setting
BEDROC
EF 1%
Full
83.44 + 1.44
97.59 1.44
-Hybrid
81.73 + 3.10
91.64 + 3.65
-Hybrid (PCA only)
82.25 2.92
96.08 + 2.61
-Hybrid (NP only)
80.16 3.88
91.14 4.06
-FP
81.87 + 2.94
94.35 + 1.93
PCA
80.28 2.84
93.93 2.13
Seed Weight
79.40 + 3.64
89.90 + 3.48
NN Score
79.84 3.51
90.63 4.04
ChemBBERTa
79.82 + 4.40
88.92 + 5.02
propagation (NP) score, and the PCA-derived feature projection. Removing each component allows us quantify marginal influence on carly-rocognition motrics.
Across all settings, we observed consistent decreases in BEDROC and EF 1% relative to the full model (Appendix Table 24h. Disabling the hybrid ranking module replacing with single scoring scheme led to performance degradation, highlighting the benefit of combining complementary signals. Similarly, eliminating ChemBERTa features resulted in one of the largest drops, indicating the role of pretrained molecular representations in enhancing discriminative power.
Taken together, these results demonstrate that SubDyve's performance gains arise from the coordinated effect of multiple interacting modules. The hybrid ranking mechanism, in particular, provides synergistic integration of PCA-derived structure features, propagation- based signals, and pretrained embeddings, each of which contributes meaningfully to the overall retrieval quality.
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Table 25: Comparison of BEDROC, running time (preprocessing, inference), and memory
usage across different models on the PU dataset. Time and memory usage reports average values.
Model
BEDROC
Preprocessing (sec)
Inference (sec)
Memory Used (MiB)
AucoDock Vina
1.0
13343.37
215.7
DrugCLIP
2.7 1.26
2955.93
29.53
9605.1
GRAB
40.68
1038.97
0.03
661.1
rdkit + NP
+: 1.96
956.70
771.7
SubDyve
83.44 1.44"
1088.0
637.9
F.9
TIME AND MEMORY COST
Sattiee
80
80
KINEIT
70
60
60
BEDROC
50
CIBAR
40-
CORAR
40
20
20
DrugCLEP
3.6
3.8
4.0
2:25
2.50
2.78
00
3.25
3,50
3.75
4.00
Log/Memoor/[[Mii)
Figure 10: Comparison of BEDROC, computational runtime, and memory consumption across models.
We conducted comprehensive comparison of the running time and memory consumption across different bascline models on the PU dataset to ensure a fair evaluation. As shown in Table 25 AutoDock Vina required the lowest memory resources but incurred the longest runtime, with the runtime increasing further when advanced functionalities such as multi- ligand docking or force field expansions required for data preparation and model training, whereas inference denotes the time taken for model prediction. The memory requirement was computed from the features each model uses and the cost of loading the data. In Figure 10 RDKIT refers to the model rdkit+NNP, and Vina refers Autodock Vina.
used. Here, preprocessing refers to the time
When the total time, defined as the sum of preprocessing and inference times, is considered, DrugCLIP, in contrast, suffered from substantial preprocessing overhead, requiring 2.74x longer runtime and 15.06x more memory than SubDyve.
SubDyve achieved these computational savings while maintaining moderate resource require- ments compared to rd and GRAB, which consumed similar memory but benefited from slightly lower runtimes as shown in Figure [0] However, this efficiency in RDKit-NP and GRAB came at the expense of predictive accuracy, SubDyve delivered significantly higher BEDROC scores (+4.4% vs. RDK +42.76% vs. GRAB). These findings highlight clear trade-off between computational efficiency and predictive performance, underscoring that while SubDyve does not minimize runtime or memory usage, provides state-of-the-art accuracy acceptable computational cost.
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PLKI (174)
Active NC=Occnmme:OCC Active CCC-OCCON.cooM
Active CNCE
Active CCcoeenCNNOOO
Active ccC=O.cenneN
Active ccNi-OcttO
Docay CEN.NCC.CCo
SRC (624)
Active co0.00-co.0000C. Active ce-ccc.oceco..cc Active co-ccc.cccco..oo Active hooks--n
Active cerOC
Acsive eecence diooecnee
Active sileee
Active cecence dioocenene
Active cesonce dicoounnne
ACES(1277)
Active CoCN Coloko
Active CecC.NccCCoc
Active - coxccCC=Oxedt Active auc:C=00cc0C Active CCaxC=Dexx:CC
Active COCEECC-OCCCCNC Active coccEO cOOC DOCDDC
DOCCCCOOCCCCCC
COSEEC-D
Figure 11: Top-10 matched Active/ Active/Decoy Decco on the DUD-E Dataset over the number of seeds utilized.
G ADDITIONAL CASE STUDY RESULTS
G.1 ToP-10 MATCHED ACTIVE/DECOY ON THE DUD-E DATASET OVER THE NUMBER SEEDS UTILIZED
To check the distribution of active and decoy sets with subgraphs according to the number of seeds used, we investigated the targets with the lowest, average, and highest number of seeds for the DUD-E dataset. in Figure 11 PLK1 (174 seeds utilized), the target with the lowest number of seeds, captured one decoy molecule with a subgraph, while the rest remained active. Even though decoy ranked in the top-10, the distribution of utilized subgraphs varied, with 10 different subgraphs captured. For the average number of SRC (624) and ACES (1277) targets, all molecules were active, and the distribution of subgraphs captured varied. For SRC, subgraph patterns were captured, and for ACES, 9 were captured.
Therefore, this result suggests that higher number of seeds provides more structural diversity to reflect the subgraphs of active and allows for more reliable structure- based analyses. Nevertheless, the low number of seeds also reveals much structural information
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about the molecule as the number of subgraph patterns, suggesting that the results comparable to those with a higher number of seeds.
G.2 ACTIVE-DECOY RANKING GAP FOR DUD-E DATASETS
CHEMBLAA22G
Decoy: C15451008
Decoy:
Similarity: 0.800 Rank DifE: <21475 poal: 0.002
Similarity: 0,866 Rank INfE: +1132| pval: 0.002 (Subllyee NP)
(Syla NP)
114
4598
ROKST NP:
291
ROKST NP:
3326
ROKLE MP
ROKST + HP:
3496
Patr Activer C25501925509
Patr Decoy: D. CAU360060
Pair 1 Activer CHEMBLS6241
Palr 1 Becoy: D. (4337666663
Similarity: 0.868 Hank DIEE: 3370| pval: 2.66e-11 (SubDyve RDKIt + NP)
similarity; 0.914 Bank Dutt: +572 pval: 1.43-004 (SubDyye RDKIt + NP)
SubDyve: ROKit
Sublyve:
SubDyve:
SubDyve:
ROKiE 18103
ROKEE MP:
ROKEE
2521
Figure 12: Ranking gap for Active Active/Decoy the DUD-E Dataset of 4 targets
To demonstrate the effectiveness of SubDyve's ranking capability, we compare its performance to the best-performing RDKit+NP bascline, which based on general-purpose molccular fingerprints. We focus structurally similar active-decoy pairs and calculate the ranking gap ween them. As shown in Figure 12 SubDyve consistently ranks the active compounds higher and the decoy compounds lower Than the baseline, resulting in much larger ranking gap. This indicates that even under conditions high structural similarity, SubDyve able to distinguish the true active compounds.
To facilitate visual interpretation, we annotated each active compound with an up arrow (one, two, three arrows for the top 50, top 250, and top 500, respectively) based on its rank in the output of each model. For decoys, we annotated with onc, two, or three down arrows when SubDyve rank improved by < 10%, 50%, to the rank difference between SubDyve and RDKiL+NP on a percentile basis. The rank difference is calculated the difference in this gap by model. Higher values indicate that SubDyve separates the active from the decoys more than the baseline. Statistical signíficance evaluated using the Wilcoxon signed rank test for all matched pairs.
50%, respectively, compared
the gap between the active and decoy rankings, and we report
G.3 SUDGRAPI-LEVEL CHARACTERIZATION OF AUGMENTED SEEDS ON THE PU DATASET
To reveal the structural properties of compounds added during SubDyve's refinement, we analyze the differences between the initial and augmented seed sets across three perspec- lives: subgraph motif enrichment, compound-level pattern visualization, and graph-level connectivity.
First, we identify subgraph motifs that are significantly enriched in the augmented seed set. As shown in Figure [3A, multiple motifs exhibit increased presence after refinement, with Fisher's exact test ranking the top 40 patterns by significance. Figure 13B further quantifies these enrichments by measuring the difference in average motif counts, with statistical significance determined using unpaired t-tests and Benjamini-Hochberg correction. These results indicate that SubDyve preferentially amplifies discriminative patterns rather than merely expanding chemical diversity.
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A
B
ZINC ID: 145394039
ZINC ID: 72452583
3ertat 20h legins ad.
Subgraph-level analysis augmented seeds on PU datasct. (A) Top 40 subgraph motifs enriched in the augmented seed set, ranked by p-values from Fisher's exact test. (B) Subgraphs with the largest mean frequency increase relative to the initial seeds, with q-values from unpaired I-lests (Benjamini Hoohhbrrggoogggg correction). (C) Examples of ZINC compounds containing enriched subgraphs that pass Lipinski's rule five; matched motifs are highlighted. (D) Distribution of shortest path lengths from initial seeds to retrieved actives in the SubDyve graph versus a Tanimoto k-NN baseline.
Figure 13:
Second, we examine how enriched substructures manifest in real molecules. Figure 13 presents ZINC compounds from the augmented that satisfy Lipinski's rule of five and contain representative enriched subgraphs. Highlighted regions confirm that these patterns correspond to chemically meaningful and interpretable substructures rather than artifacts of global structural similarity.
Lastly, we assess whether SubDyve can prioritize structurally distant yet bioactive compounds. We compute the shortest path distances from each retrieved compound to the closest known active in the subgraph-similarity network and compare this distribution to a Tanimoto k-NN bascline (similarity 2 0.9). As shown in Figure 13D, SubDyve retrieves candidates with siguificantly longer path distances (p = 2.32 x 10 108 Mann Whitney U-test), supporting its ability generalize beyond immediate struetural neighbors while maintaining high enrichment performance.
These results suggest that SubDyve refines the seed set in substructure-aware and chemically meaningful manner, enabling robust prioritization of active compounds even when they lie outside the reach of traditional fingerprint- based similarity metrics.
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G.4 CHEMICAL AND PHARMACOPHORIC RELEVANCE OF MINED SUBGRAPH PATTERNS
To investigate the chemical interpretability and pharmacophoric relovance of the subgraph patterns mined by SubDyve, we conducted analysis focused on the well-characterized binding-site features of CDK7. Structural and biochemical studies have shown that the ATP-binding pocket of CDK7 contains a predominantly hydrophobie cavity formed by residues such as Phe91 and Leul44, which support я stacking, hydrophobic packing, and van der Waals contacts in addition canonical hinge- binding hydrogen- bond interactions
Düsterr et al. 2024 Kumar et al., 2021 Peissert et al. 2020). Potent CDK7 inhibitors frequently exploit these interaction motils, combining aromatic scaffolds with heteroaromatic hinge-binding fragments and aliphatic substituents that occupy adjacent shallow pockets.
The subgraphs extracted by SubDyve show strong alignment with these experimentally established binding requirements. Among the highest-ranked subgraph patterns, observe frequent occureences of aromatic ring systems (e.g., cec, ce-cce, cc-c(cjc) and nitrogen- containing heterocycles (e.g., necen, ccncNC, [n&:H]]), which correspond to hinge- aigg-binding fragments commonly found across CDK family inhibitors. Additionally, the model identifies aliphatic aminc-linked chains (c.g., CCCNC, CNCCC, CCC(C)N) that resemble substituents known to occupy hydrophobic subpockets adjacent to the hinge region in CDK7. These pat- terns collectively recapitulate the pharmacophoric elements aromaticity, gydrogen-bondingg capability, and hydrophobic chain extension known to drive CDK7 ligand recognition.
Figure 14 shows (i) docking simulation of known active compound from PubChem against the CDK7 target and (ii) the docking pose of high-ranked compound retrieved from the ZINC library. The green molecule represents the high-ranked candidate identified by SubDyve, while the blue molecule corresponds to ATP bound in the CDK7 pocket. The highlighted subgraph contains two hydrophobic pharmacophore features along with an additional non-pharnacophorie fragment. As illustrated in the figure, the hydrophobic regions of the retrieved compound orient loward the ATP-binding pocket in a manner consistent with known binding preferences. These observations support that SubDyve identifies pharmacophorically meaningful subgraphs and that these patterns contribute to its strong early-recognition performance.
Furthermore, we evaluated the mined subgraphs using RDKit's pharmacophore annota- tions (donor, acceptor, aromatic, hydrophobe). Across the top ten subgraphs ranked by discriminative score, 60% contained at least one pharmacophore feature, indicating that the extracted structural motifs correspond to chemically meaningful functional groups rather than arbitrary graph fragments.
Taken together, these observations demonstrate that SubDyve retrieves subgraphs that are not only clasi-iiserininatiie but also chemically interpretable and pharnacophorically coherent, consistently reflecting established principles of CDK7 binding-site engagement as well as broader functional group patterns relevant to small-molecule protein interactions.
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-9.076 kcal/mol
nccen.coneC.CCCCNC
B
PubChem 162641734
-9.082 keal/mol
Cen.CCC(C)N.cc-e(enn
ZINC 113089827
Docking poses of a known CDK7 active compound from PubChem and high-ranked candidate retrieved from the ZINC library (green), shown in comparison to the bound ATP molecule (blue). The highlighted subgraph motifs exhibit hydrophobic and heteroaromatic features that orient toward the ATP-binding pocket, reflecting known CDK7 hinge-binn binding and hydrophobic interaction patterns.
Figure 14:
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H LIMITATIONS
SubDyve requires constructing a target-specific chemical similarity network for each protein target, which introduces preprocessing overhead duc to repeated subgraph mining and graph construction. While this design enables tailored modcling of bioactivity-relovant structures, it may limit scalability when screening across large number of targets. Additionally, although LFDR-based seed calibration consistently outperforms probability-based heuristics in terms of expected calibration error (ECE), performance in the mid-range threshold region remains suboptimal.
Despite these limitations, SubDyve offers a promising foundation for scalable virtual screening. Its modular architecture and uncertainty-aware design make it well suited for future extensions to multi-target or multi-omics settings, where integration with transcriptomic profiles or cell line information could further improve prioritization in complex biological contexts.
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Reviews:
[{"review_id": "soyOnpwiRI", "reviewer": "Reviewer_by4N", "summary": "SubDyve is a virtual screening framework that is label efficient and builds a similarity graph from substructures that are able to discriminate classes. It applies local and dynamic seed refinement based on FDR and performs network propagation to rank candidates. A joint GNN is used to calibrate the propagation. The method tackles two major gaps in NP-based screening by replacing generic fingerprints with mined subgraph patterns. These patterns capture activity relevant signals, while limiting graph topological bias through the usage of LFDR. The proposal also employs ensembles for sake of stabilizing results.", "questions": "It’s not clear how the setting qualifies as zero shot given that seeds are curated from homologous proteins with high sequence identity. Please clarify.\n\nI believe that adding additional ablation studies would strengthen the work. Evaluating the method with and without the pretrained ChemBERTa features and comparing single versus hybrid ranking would clarify the contribution of each component and better support the\nclaimed synergy. Please comment.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "A major contribution of SubDyve is the integration of two complementary ideas: a target-aware sub-graph fingerprint (built from class-discriminating patterns mined from scarce labels) and an LFDR-guided refinement loop that calibrates uncertainty, so that the model is able  to control mFDR and to counteract graph-induced topological bias. Such a design comes from low-label virtual screening and achieves empirical gains considering baselines. The proposal emphasizes that recognizing early, when screening value are more valuable. Further,  the ablations indicate that no component alone achieves the combined performance, demonstrating the benefit of the proposal.", "weaknesses": "A key limitation of SubDyve is regarding its scalability, since each target requires building a separate subgraph fingerprint network. In this case, supervised subgraph mining and graph construction becomes increasingly expensive as the number of targets or compounds grows. The iterative LFDR refinement adds further computational cost at large scale. The method also depends on the availability of homologous protein sequences to obtain annotated compounds for seed generation, which constrains its use to well-characterized targets. These factors limit scalability in large or multi-target screening, and LFDR calibration remains less reliable in intermediate decision regions. The paper should consider these limitations and discuss how they may be effectively addressed.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "EkUR05Ey4I", "reviewer": "Reviewer_1i7n", "summary": "Virtual screening (VS) is a key step in drug discovery that aims to identify potentially active compounds from large molecular libraries. In real-world scenarios, only a few active compounds are known, making it a typical low-label setting. Traditional methods often rely on generic molecular fingerprints or deep embeddings, ignoring substructure features critical for activity. Moreover, they usually treat molecules as independent samples, failing to leverage structural relationships among molecules. This paper proposes SubDyve, a subgraph-driven network propagation framework for robust virtual screening under low-label conditions, with effective control of false positives.", "questions": "Refer to weaknesses", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1. Introduce supervised subgraph mining into VS graph construction, capturing activity-relevant structural patterns and outperforming generic fingerprints.\n2. Proposes an LFDR-based iterative seed updating strategy that expands the seed set while theoretically controlling the FDR upper bound, effectively reducing false positives.\n3. With a few dozen seed molecules, SubDyve achieves nice early enrichment performance on both DUD-E and PU datasets, outperforming existing deep learning and fingerprint-based methods.", "weaknesses": "1. Subgraph mining and graph construction must be repeated per target, making cross-target scalability a potential bottleneck for large-scale multi-target screening.\n2. The subgraph mining stage relies heavily on the representativeness of the initial seed set. If the seed structures are biased, the graph construction may lack generalizability.\n3. All experiments are single-target independent models, with no evaluation on multi-target joint training or transfer learning scenarios.\n4. Current baselines are mostly sequence or graph embedding models, with no direct comparison to recent 3D structure-aware models.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "hG00R8oaXK", "reviewer": "Reviewer_iVxC", "summary": "This paper addresses the problem of virtual screening (VS) in drug discovery under low-label regimes, where very few active ligands are known. The authors argue that existing network propagation (NP) methods suffer from reliance on generic molecular fingerprints and topological bias, leading to high false positive (FP) rates. The paper proposes SubDyve, a framework featuring two main components: 1) Constructing a task-specific similarity network by mining \"class-discriminative subgraphs\"; 2) Introducing a \"dynamic seed refinement\" mechanism that uses the local false discovery rate (LFDR) to iteratively add high-confidence (low FP probability) unlabeled molecules as new seeds, aiming to control FPs. Experiments on the DUD-E benchmark (zero-shot) and a large-scale ZINC dataset for CDK7 (PU learning) show that SubDyve outperforms baselines on early enrichment metrics.", "questions": "1. Can the authors provide an end-to-end average time (e.g., on the DUD-E targets) required to build the subgraph network (including subgraph mining and similarity computation)? How does this compare to the preprocessing time of baselines (like RDKit+NP)?\n2. How sensitive is the method to the size of  $S_{train} $? If $S_{train} $ contained only 10 or 5 molecules, would the SSM step still be effective?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper focuses on the low-label/few-shot VS problem, which is highly relevant and challenging in real-world drug discovery.\n2. The primary highlight is the introduction of LFDR for a principled control of the dynamic seed set expansion to combat topological bias. This is more sophisticated than using fixed similarity or GNN score thresholds.\n3. Evaluating the method on two challenging scenarios (zero-shot and large-scale PU) is a clear strength.\n4. The results demonstrate a clear improvement in early enrichment metrics compared to the baseline methods.", "weaknesses": "1. The most significant concern is the method's scalability and preprocessing overhead. As acknowledged in the limitations (Section H), the method requires re-running the computationally intensive subgraph mining (SSM) and graph construction process for *every single* protein target. This could be a major practical barrier in a real-world drug discovery pipeline that needs to screen hundreds or thousands of targets.\n2. The success of the entire pipeline (especially the SSM step) is highly dependent on the quality and quantity of the initial seed set $\\mathcal{S}_{train}$. If the initial set is extremely small (e.g., < 10-20 molecules) or not representative, the subgraph mining step will likely fail or produce misleading patterns, causing the entire downstream pipeline (GNN training and LFDR refinement) to perform poorly. The 50 seeds used as the minimum in the experiment (Sec 4.2.2) is still a somewhat optimistic setting for a \"low-label\" scenario.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "RVGhAW7Bkr", "reviewer": "Reviewer_yH49", "summary": "The paper introduces SubDyve, a subgraph-aware network propagation framework for label-efficient virtual screening in drug discovery. It combines subgraph fingerprint network construction, dynamic seed refinement using local false discovery rate (LFDR) estimation and a GNN-based model for stratified refinement. They evaluate on on DUD-E (10 targets) and a CDK7 target with a 10M-compound ZINC dataset, showing large performance gains over fingerprint-based and deep learning baselines.", "questions": "1. How sensitive is SubDyve to the LFDR threshold and the number of iterations in seed refinement?\n\n2. How are the mined subgraph patterns evaluated or visualized in terms of chemical or pharmacophoric relevance?\n\n3. Could you check if the provided URL for the code is working? I can't access it.", "limitations": "", "rating": 8, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Paper is well-written and structured. Also, URL containing code and experiments is provided for reproducibility.\n\n2. The presented framework seems novel and efficient. For instance, the introduction of class-discriminative subgraph fingerprints captures fine-grained structural patterns that general-purpose fingerprints miss.\n\n3. Comprehensive benchmarks demonstrate significant improvements across several evaluation metrics, such as outperforming large foundation models while using less data and compute.\n\n4. They also provide beyond-performance analysis through case studies (Figure 2 and 3), where they show that subgraph-level information correlates with biologically meaningful substructures.", "weaknesses": "1. While substructure interpretability is discussed, there is little experimental validation linking retrieved subgraphs to real binding mechanisms.\n\n2. The complexity of the presented pipeline (subgraph mining, LFDR estimation and GNN optimization) could make results to be very sensitive to changes in seeds, thresholds and hyperparameters. For instance, the effect of LFDR thresholds could be explored more systematically to assess stability and sensitivity. This can be specifically important for interpretability. \n\n3. Results are primarily shown on small-molecule benchmarks; applicability to structure-based or protein–ligand joint settings is unclear.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)