S-MolSearch: 3D Semi-supervised Contrastive Learning for Bioactive Molecule Search
Authors: Gengmo Zhou
Zhen Wang
Feng Yu
Guolin Ke
Zhewei Wei
Zhifeng Gao
Venue: NeurIPS 2024 poster (2024)
Keywords: semi-supervised learning;  3D molecule search; contrastive learning
Primary area: machine_learning_for_healthcare
TL;DR: S-MolSearch, a semi-supervised framework for ligand-based virtual screening that leverages molecular 3D information. S-MolSearch efficiently processes labeled and unlabeled data with inverse optimal transport, achieving SOTA on LIT-PCBA and DUD-E

Abstract: Virtual Screening is an essential technique in the early phases of drug discovery, aimed at identifying promising drug candidates from vast molecular libraries. 
Recently, ligand-based virtual screening has garnered significant attention due to its efficacy in conducting extensive database screenings without relying on specific protein-binding site information.
Obtaining binding affinity data for complexes is highly expensive, resulting in a limited amount of available data that covers a relatively small chemical space. Moreover, these datasets contain a significant amount of inconsistent noise. It is challenging to identify an inductive bias that consistently maintains the integrity of molecular activity during data augmentation. To tackle these challenges, we propose S-MolSearch, the first framework to our knowledge, that leverages molecular 3D information and affinity information in semi-supervised contrastive learning for ligand-based virtual screening. 
% S-MolSearch processes both labeled and unlabeled data, trains molecular structural encoders, and generates soft labels for unlabeled data, drawing on the principles of inverse optimal transport.
Drawing on the principles of inverse optimal transport, S-MolSearch efficiently processes both labeled and unlabeled data, training molecular structural encoders while generating soft labels for the unlabeled data.
This design allows S-MolSearch to adaptively utilize unlabeled data within the learning process.
Empirically, S-MolSearch demonstrates superior performance on widely-used benchmarks LIT-PCBA and DUD-E. It surpasses both structure-based and ligand-based virtual screening methods for AUROC, BEDROC and EF.

S-MolSearch: 3D Semi-supervised Contrastive Learning for Bioactive Molecule Search
Gengmo Zhou 1,2 Zhen Wang?; Feng Yu², Guolin Ke² Zhewei Wei Zhifeng Gao
Renmin University of China DD Technology
(zgm2015, zhewei]@ruc. edu. cn, {wangz, yufeng, kegl, @dozf) tech
Abstract
Virtual Sereening is an essential technique in the early phases of drug discovery, aimed at identifying promising drug candidates from vast molecular libraries. Recently, ligand-based virtual screening has garnered significant attention due its efficacy in conducting extensive database screenings without relying on specific protein-binding site information. Obtaining binding affinity data for complexes is highly expensive, resulting in limited amount of available data that covers a relatively small chemical space. Moreover, these datasets contain significant amount of inconsistent noise. It is challenging to identify an inductive bias that consistently maintains the integrity molecular activity during data augmentation. To tackle these challenges, we propose S-MolSearch, the first framework to our knowledge, that leverages molecular 3D information and affinity information semi-supervised contrastive learning for ligand- virtual screening. Drawing on the principles of inverse optimal transport, S-MolSearch efficiently processes both labeled and unlabeled data, training molecular structural encoders while generating soft labels for the unlabeled data. This design allows S-MolSearch adaptively utilize unlabeled data within the learning process. Empirically, S-MolSearch demonstrates superior performance on widely-used benchmarks LIT- PCBA and DUD-E. It surpasses both structure-based and ligand-based virtual screening methods for AUROC, BEDROC and EF.
Introduction
Virtual Screening 2 plays a crucial role in the early stages of drug discovery by identifying po- tential drug candidates from large molecular libraries. Structure- Based Virtual Screening (SBVS) [5]
7, [) widely used virtual screening method, attempts to predict the best interaction between
ligands against protein target form protein-ligand complex. Recently, deep learning methods conduct virtual screening by modeling binding affinities and ranking based prediction. Additionally, method [12] uses similarities between embedding of pockets and molecules to search for active molecules. However, these SBVS methods cannot escape the dependency on the structure of protein targets, which is unavailable for challenging or novel targets, such as disordered proteins like c-Myc, limiting the applicability of SBVS. Besides, plenty of assays used in Virtual Screening [13] are cell-based rather than target-specific, introducing noise into the active molecules since their activity is not entirely dependent on interaction with the protein target.
have also been explored. Methods trained on affinity labels (9) 10 T1)
To remedy this, Ligand-Bas Based Virtual Screening (LBVS) [14 15 16 17 18
searches similar molecules via known bioactive molecules and does not depend the structure of protein targets, which has attracted increasing attention. Computational LBVS methods
[9
20
18 rigidly employ
"quual contribution.
Corresponding authors.
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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structural similarity to search for molecules, often using atom- centeeed,,ed, smooth Gaussian overlays to assess molecular similarity. Searching for bioactive molecules needs to consider both structure and electronic similarity. Some methods [14) also require charge comparison, which is expensive and time-consuming. These methods struggle with inefficiency when handling large databases. Moreover, since only structural or charge information is considered while affinity is ignored, even if molecules with similar structures or charges are identified, they may still exhibit poor affinity in practical applications due to activity cliffs 21
natural question arises: how can we enhance LBVS by collecting molecule similarity data from surge-scale unlabeled molecules? To search both similar and bioactive molecules, we can choose those bioactive molecules that bind the same protein. Meanwhile, labeled molecule-protees perctenn binding data is limited due to the expensive affinity acquisition. Also various standards (22) [3] across different datasets, introducing substantial noise. It is difficult to cover the searching chemical space with affinity data alone. A feasible solution is to leverage similarity from finite affinity data to broader chemical space.
26]. which can extract informative representations from large-scale data, we explore its feasi bility for molecule data. However, those data augmentation techniques in vision or language cannot be directly applied to molecules due to their inherent 3D structure. This limitation stems from a lack of inductive bias to guarantee augmentation maintains the integrity of molecular activity.
Inspired by the success of contrastive learning 23
24
25
To address the challenges, propose S-MolSearch, a novel semi-supervised contrastive learning framework based on inverse optimal transport (IOT) (27). S-MolSearch directly uses 3D molecular structures capture structure similarity. It consists of two main components: one encoder fo for labeled dataset and another encoder Dv for the full dataset, which includes both labeled and unlabeled data. Both encoders are trained simultaneously to effectively leverage the two types of data. We organize a dataset of labeled molecule-protein binding data from ChEMBL (28). Molecules are assigned to different targets based binding affinity, with the active molecules corresponding to each target forming clusters. We sample from these clusters, treating molecules from the same cluster as positive samples and those from different clusters as negative samples to train encoder fe. This approach incorporates affinity information into training and avoids the limitation caused by relying solely on structural similarity. For the update of encoder Jú. we assume that the similarity measurements obtained by encoder fo can be generalized to unlabeled data. We input the same data from the full dataset into these two encoders separately and use optimal transport to obtain soft labels from fe. The encoder dy is then trained using these soft labels. This integration enables S-MolSearch to effectively utilize unlabeled data, ensuring that the model learns from both affinity-labeles samples and broader structural similarities across the molecular dataset.
Empirically. S-MolSearch demonstrates superior performance on widely-used benchmarks LIT- PCBA [13] and DUD-E (22). It consistently achieves state-of-the-art results, surpassing both SBVS methods and LBVS methods on AUROC, BEDROC and EF. Notably, S-MolSearch trained with a 0.9 similarity threshold significantly outperforms existing methods, achieving more than a 49% improvement on BEDROC and over 30% improvement on EF compared the best baseline on DUD-E. These results provide strong empirical support for the effectiveness of S-MolSearch, confirming its advanced capability for virtual screening.
Our main contributions are summarized as follows:
We introduce S-MolSearch, which is the first time integrates both molecular 3D structures and affinity information into molecule search.
Built upon inverse optimal transport, we develop a semi-supervised contrastive learning framework, which induces S-MolSearch. By combining limited labeled data with extensive unlabeled data, S- S-MolSearch can learn more informative representations and explore the chemical space more effectively.
S-Molhearch evaluated on widely-used benchmarks LIT-PCBA and DUD-E, surpassing both SBVS and LBVS methods to achieve sate-of-the-are results.

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2 Related work
2.1 Virtual Screening
Virtual screening can be broadly divided into two main categories: Structure Beaettrre-BBeed Virtual Screening (SBVS) and Ligand-Based Virtual Screening (LBVS). SBVS (5 6. 8] heavily relies on the
structure of protein targets and typically employs molecular docking. Recently, many deep learning methods [29] [0 TT 12] have also emerged. In contrast, LBVS [14
15 T6 17 [8] uses known active ligands as seeds to identify potential ligands. Molecule search is major LBVS approach, typically divided into two categories: 2D similarity search and 3D similarity search. 2D molecule search methods [30, 31] use molecular fingerprints to search for similar molecules, while 3D molecular
search methods 15 16 18] depend on shape overlap.
2.2 Optimal Transport and inverse optimal transport
Optimal Transport (OT) is a mathematical problem that aims to determine the most efficient way to redistribute one initial distribution (known the source distribution) into another distribution (known as the target distribution) while minimizing a defined transportation cost. To handle computational complexities, OT often incorporates regularization (32), leading softened optimization problem. The regularized OT objective is convex function, thereby ensuring a unique solution that can be
efficiently solved using iterative methods [33 34].
Inverse Optimal Transport (IOT) seeks to determine the cost matrix that explains an observed optimal transport. [27] introduces method to infer unknown costs. (35] explores the mathematical theory
behind 1OT. In many IOT studies [36|37], optimization is directly performed over the cost matrix, typically focusing on learnable distances between samples rather than on the sample features.
2.3 Semi-supervised learning
41 is typically used in scenarios where labeled data is limited but unlabeled data abundant. Pseudo-labeling [42] classic technique of semi-supervised learning. (33 introduce self-ensembling method that generates pseudo-labels by forming con- sensus prediction using the outputs of the network under different regularization and augmentation conditions. UPS [44] proposes an uncertainty-aware pseudo-label selection framework that im- proves pscudo-labeling accuracy by reducing the amount of noise in the training process. UST (45) employs teacher-student training paradigm. The teacher model is responsible for selecting and generating pseudo-labels, while the student model learns from the labeled set augmented with these pseudo-labels Recent work (46) utilizes additional unpaired images to construct caption-level and keyword-lewe pseudo-labels, enhancing training.
Semi- Semi-supervised learning 38
39
40
3
Method
3.1 Overview
Molecular similarity search is type of ligand-based virtual screening whose purpose is to perform rapid search and filtering similar molecules in a molecular database based on query molecule provided by the user. We model the task dense retrieval problem, using well-trained encoder to extract embedding representations of molecules and rank them by their cosine similarity to query molecule, thereby identifying the top A most similar candidates.
Building upon the principles of inverse optimal transport (IOT), we have developed the S-Molsearch method. As shown in Figure I S-Molsearch uses a molecular structure encoder fo for labeled dataset Doup and another encoder gy for the full dataset D full, encompassing both labeled and unlabeled dataset. fe utilizes contrastive learning to learn from labeled dataset. Ir optimizes its parameters using the soft labels produced by fa, which have been processed through smooth optimal transport. The two encoders are initialized with a molecular pretraining backbone Uni-Mol [47 Both encoders are trained simultaneously under the guidance of a unified loss function Liotal The encoder ge- trained on full dataset, is used for inference.
3

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Liuup
esbedding
Rusee &.ff Linited Labeled Molecutes
Encoder fa
sinilarity ratrix
Meights
Optinal Transport
Encoder fa
Grad
Maup similarity natrix
exbedding
soft label
Encoder
0+
Lsaft
Molecules
Figure 1: Overview of S-MolSearch Framework
In the following sections, we will provide more details about the core components and training strategies that underpin S-Molsearch. In section 3.2, we explain the pretraining backbone of the molecular structural encoder, Uni-Mol. In sections 3.3 and 3.4, we will sequentially examine the training strategies for both fe and Pv- In section 3.5, we will discuss the regularization techniques employed to enhance model generalizability and stability. In section 3.6, we will provide an analysis of S-Molsearch from the perspective of IOT, offering insights into its methodological strengths.
3.2 Pretraining Backbone of Molecular Encoder
To effectively encode the structural information of molecules, we choose Uni-Mol as the backbone of molecular encoder for S-Molsearch. Uni-Mol is a molecular pretraining model specifically designed adeptly process molccular 3D conformation data. has achieved state-of-the-ar performance across range of downstream tasks. The UniMol model utilizes self-attention mechanism that incorporates distance bias to integrate information about atoms and their spatial relationships. thereby generating structural representation of molecules. The molecular embedding is created by using the embedding of the CLS token, and the embedding vector normalized using the Euclidean norm.
3.3 Training Strategy of Encoder Labeled Dataset
In this part, we employ molecular- ionecular-protein binding data sourced from the ChEMBL. Molecules are assigned to different targets based on binding affinity. The active molecules corresponding each target form clusters. We sample from these clusters to obtain data for contrastive learning. Molecules from the same cluster are considered positive pairs, while molecules from different clusters considered negative pairs. We employ InfoNCE loss for encoder fa on labeled dataset, as shown in Equation]
exp(sim(#;) (2i, TT)
Czup Σ log
Σ/=1 exp(sim(s;, U5)/T)
where x; and yi are the embeddings of positive molecule pairs, while x; and yj form negative molecule embedding pairs within the batch when * i. sim(x.y) denotes the similarity score between embeddings, typically computed as the inner product the normalized vectors xy² is the temperature parameter that scales the similarity scores. By utilizing the InfoNCE loss, fe pulls the embeddings of positive samples close while enforcing them away from the negative samples in the embedding space.
3.4 Training Strategy of Encoder Full Dataset
To harness large-scale unsupervised data effectively, S-MolSearch utilizes the fo to guide the learning of another encoder on full data gø- Specifically, employ fo to preprocess the data for the ge-

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ensuring that fo remains detached from the backpropagation process at this stage. The embeddings obtained from fo are subsequently utilized for computing a similarity matrix Maup E RNNN,, where Msup(1, (i: ssup, jup.j The task of generating soft labels for Ie based this similarity matrix is presented as smooth and sparse optimal transport (OT) problem:
A |||l (I.C)
min (EU().4)
subject to Up, (T E RNNN [IN = Pp
Where I' denotes the transportation plan matrix between the embeddings, C' R RN is the cost matrix derived from the cosine similarities between embeddings: = "C--xxup.ie Exup. sup.j (T,C) denotes Frobenius inner product of I and C, and p and are the source and sink distributions, respectively. this context, ones. By introducing the OT formulation, we guarantee that signals from the supervised model fo are more effectively transferred the unsupervised model Iv, while handling high label uncertainty in the supervised model fe with appropriate regularization. The OT could be effectively addressed by the P4T(48). We define i as pseudo-labels for the similarity matrix y go. where y is created by embedding of gø Mfn((i,) j) = & full.j'
1,
In and 9 IN. 1x is an N N-dimensional vector of all
The cross-entropy loss H is employed to optimize 9v, using the pseudo-labels provided:
Lsoft HT,, Mfw)
3.5 Regularization techniques
In order to promote uniformity of embedding space, apply KoLeo regularizer 49 embeddings of the semi-supervised encoder. KoLeo regularizer is defined as:
50 to the
Greg 1 Σ log(pn,s)
(4)
Here, Pr.. represents the minimum distance between the i-th sample and all other samples, which serves as proxy for local density. This loss function has geometric interpretation that effectively pushes closer points apart, ensuring diminishing returns distances increase, thereby encouraging uniformly dispersed embedding space.
3.6 Framework for S-Molsearch Induced by Inverse Optimal Transport
By integrating the losses and regularization terms from sections 3.3, 3.4, and 3.5, we have derived the overall loss function Liotal for the S-MolSearch model:
Liotal
Suu + Lwoft + phreg
(5)
where f 0.1 in our setting. Building on the relationship between contrastive learning and IOT established in (51). we extend this relationship to semi-supervised contrastive learning in proposition
Proposition 1 Given encoder fo for labeled dataset Xoup and 96 for full dataset X Tsup represents the embeddings of labeled data from Jo while & full represents the embeddings of the full datasel from gv- Semi-supervised contrastive learning is then formulated using 1OT as follows:
min (KL(T9I19) + KL("") puRgg (T ) (e 0.6 I arg
subject to
min (eU(
- -
(6)
r arg
min TEU(
((C*, -TH(())
fired fized Xtabel, X full)
g
5

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vis Fıj + Vuj represents the Kullback-Leibler divergence, and where KL(X = Σ Exsslog tii
H(T)= -To=-oTooloot
by represents entropic regularization. Te, NNN M N
2.j
represents the ground truth based on labeled data, dij denotes the Kronecker delta finctiion , E Rt are cost matrix of fe. 96 and C (i, = c Toup, sup.j' (i, = с - 2 f at ff full.3" T generally refers to a technique for transferring supervised information to unsupervised data. Reg, Regz denotes regularization term
The proof is provided in the Appendix C.1 In proposition 1 model the contrastive learning problem on the labeled dataset and full dataset as two optimal transport problems. Additionally, we use T to transfer knowledge from the labeled dataset to the unlabeled data, with the method of transfer depending on prior assumptions about the dataset and certain bias structures, For instance, If we initially optimize fo on a large-scale labeled dataset to obtain fg. then generate f as (i, = ffull.e jull.j. where f = fō (zi), 24 E Xfuli. we can develop model that leverages knowledge distillation for contrastive learning. In the context of molecular search tasks, we employ smooth optimal transport for the modeling of İ leading to the development of S-MolSearch as follows:
Proposition 2 Assuming the conditions outlined in Proposition 2 are satisfied, the optimal parame- ters 0 and ii* of S-MolSearch can be regarded as the solution to the following 1OT problem:
(KI(T<)TTO) + KI( + (TV)
min 0.0
subject to
1 arg
min (eU(a),
(IC), 11 - (I))
(7)
m = arg
min TEU(e).a=
((C - -T()))
A (Cote r) + + 1
1 arg
min (oU(o, 11. bx
where Cfrixed RNNN and Offixed (i,5)
x fived (1r fizedyr. The xffaed represents the embeddings of the same data in X full obtained from the supervised encoder So, where fo is detached.
The proof is located in the Appendix C.2 We compute the KL divergence guide the optimization of fe and ge. where the regularization term simplification only affects the full data. Moreover, we set the marginal values of U (a, b) to an all-ones vector. In this way, find that the knowledge in fo transfers effectively to go. thereby achieving excellent performance on molecule search task.
4 Experiments
4.1 Training Data
The labeled data comes from ChEMBL 28 an open-access database containing extensive informa- tion on bioactive compounds with drug-like properties. We prepare nearly 600,000 protein-molecule pairs, encompassing about 4,200 protein targets and 300,000 molecules. The details of data curation can be found in appendix [ To prevent information leakage, the data is filtered based on protein sequence similarity. Specifically, the amino acid sequences of all protein targets in the benchmarks DUD-E and LIT-PCBA
extracted. Then, we use MMseqs (52) tool with similarity thresholds of 0.4 and 0.9 to filter out proteins in ChEMBL. Using a 0.9 threshold helps filter out identical and highly similar targets, while the stricter 0.4 threshold filters out nearly all similar targets. After filtering, 3,369 proteins and 327,917 pootein-ligand pairs remain for the 0.4 threshold, while 4, 102 proteins and 529,856 pairs remain for the 0.9 threshold. We sample 1 million pairs from the filtered data as labeled data respectively.
The unlabeled data, consistent with what is used by Uni-Mol, comes from series of public databases, totaling about 19 million entries. Additionally, we incorporate the small molecule data from ChEMBL into this collection, thereby obtaining the full dataset.

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4.2 Benchmarks
We choose widely used virtual screening benchmarks DUD-E [22 and LIT-PCBA [3 to evaluate the performance of S-MolSearch. DUD-E is designed to help benchmark virtual screening programs by providing challenging decoys. includes 102 protein targets along with 22, 22,886 active ligands, each accompanied by 50 decoys with similar physico-chemical properties. LIT-PCBA is designed for virtual screening and machine learning. aiming to address the chemical biases present in other benchmarks such as DUD-E. It consists of 15 targets, with 7,844 confirmed active compounds and 407,381 inactive compounds.
4.3 Baselines
We choose range LBVS and SBVS methods as comparative baselines for a thorough evaluation.
ROCS [14), Phase Shape [15]. LIGSIFT (18), and SHAFTS [19] (0) are LBVS methods that evaluate
similarity by calculating the overlap of molecular 3D shapes. Other methods are SBVS methods.
Among them, DeepDTA (9). OnionNet (TO), Pafnucy (11). BigBind [53], and Planet (54) are trained
on binding affinity labels. Glide 77. Vina (8), and Surflex [55] are molecular docking software.
Gnina [56] is deep learning based molecular docking method. DrugClip [12] utilizes the similarity
between targets and molecules to find active compounds.
4.4 Results
4.4.1 Main Results
Table 1: Performance DUD-E in zero-shot setting. The best results are bolded and the second-best
results are underlined.
Method
AUROC (%)
BEDROC (%)
EF 0.5%
EF 1%
EF 5%
ROCS
75.20
23.79
6.89
Phase Shape
76.70
30.33
9.01
LIGSIFT
78.40
25.89
8.01
SHAFTS
78.20
32.49
9.67
Glide-SP
76.70
40.70
19.39
16.18
7.23
Vina
71.60
9.13
7.32
4.44
Pafnucy
63.11
16.50
4.24
3.86
3.76
OnionNet
59.71
8.62
2.84
8.83
5.40
Planct
71.60
10.23
8.83
5.40
DrugCLIP
80.93
50.52
38.07
31.89
10.66
S-MolScarchuu
84.61
54.22
40.85
34.60
11.44
S S-Molcaarcha
92.56
75.37
51.50
47.94
15.82
Table 2: Performance on LIT-PCBA in zero-shot setting.
Method
AUROC (%)
BEDROC (%)
EF 0.5%
EF 1%
5%
ROCS
52.41
2.48
Phase Shape
52.24
2.98
LIGSIFT
54.94
2,39
SHAFTS
54.53
2.79
Surflex
51.47
2.50
Glide-SP
53.15
4.00
3.17
3.41
2.01
Planet
57.31
4.64
3.87
2.43
Gnina
60.93
5,40
DeepDTA
56.27
2.53
1.47
BigBind
60.80
3.82
DrugCLIP
57.17
6.23
8.56
5.51
2.27
S-MolSearcho.
57.34
7.58
10.93
6.28
2.47
S-MolSearchog
61.78
8.48
11.97
7.36
3.21

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Tables D and respectively present the performance of S-MolSearch on DUD-E and LIT-PCBA compared with other competitive baselines, where the best results are highlighted in bold and the second-best results are underlined. The methods in the upper part of the two tables are ligand-based virtual screening methods, and their results come from [57]. The methods in the middle part of the two tables are structure-baser virtual screening methods, and their results come from DrugClip. We also present the results S-MolSearch trained on data filtered with 0.4 and 0.9 similarity thresholds. Following previous work, we choose AUROC, BEDROC, Enrichment factor (EF) performance metrics to evaluate both general accuracy and screening capacity, with higher values indicating better performance. Their definitions in appendix B The zero-shot setting means inferring directly without using any data from the benchmarks for training, which more close to real virtual screening scenarios.
Table shows that S-MolSearch achieves the best on all metrics. S-MolSearch trained with a strict 0.4 similarity threshold avoid overfitting similar targets and surpasses all ligand-based based and structure- virtual screening baselines. S-MolSearch trained with 0.9 similarity threshold shows substantial improvements over existing methods, with over a 49% increase in BEDROC and more than a 30% boost in EF compared to the best baseline. We find that S-MolSearch, as a ligand-based virtual screening method, demonstrates strong performance without requiring specific protein structures.
S-MolSearch also achieves SOTA on LIT-PCBA shown in Table While its AUROC performance is not the best at the 0.4 similarity threshold, S S-MolSearch perform better in BEDROC and EF, indicating its strength in screening scenarios. We notice that the metries for all methods decline on LIT-PCBA compared to DUD-E. Unlike DUD-E, which uses putative decoys, LITT-PBBA is based on experimental results. Since many of its assays are cell- cell-based rather than target-specifie, there noise in the active molecules, which we consider may lead to the decline. Meanwhile, S-MolSearch demonstrates its advantage over structure- virtual screening by not requiring specific target information, but instead performing searches based on active molecules.
4.4.2 Ablation Study
Table 3: Ablation studies performance on DUD-E and LIT-PCBA.
DUD-E
LIT-PCBA EF 1%
Soft label
Regularizer
Pretrain
EF 0.5%
EF 1 1%
EF 5%
EF 0.5%
EF 5%
/
37.35
30.73
10.43
10.59
6.19
2.72
x
/
39.64
33.32
11.47
9.01
5.24
2.38
V
38.09
31.86
10.88
8.26
5.24
2.30
/
40.85
34.60
11.44
10.93
6.28
2.47
We conduct extensive ablation studies to explore how S-MolSearch works. These results are derived from S-MolSearch trained with a 0.4 similarity threshold. First, we performed ablation studies on several key techniques of S-MolSearch. The results are summarized in Table where the best results are bolded and the second-best results are underlined. 'Soft label' refers to training the encoder J using soft labels obtained from inverse optimal transport. Without this, we directly use the similarity matrix as the hard label for training. 'Regularizer' indicates the use of KoLeo regularizer. 'Pretrain' refers to starting the training of S-MolSearch from pretrained checkpoint of Uni-Mol. Otherwise, it starts from random initialization. The results show that each component contributes to the final results. Although S-MolScarch may not be the best in some individual metrics, the absence of these components leads to poor performance at least one benchmark. For example, not using Soft label significantly degrades performance on DUD-E. S-MolSearch performs consistently on both DUD-E and LIT-PCBA: with nearly all metries being the best.
To visually illustrate the difference between the embeddings learned by S-MolSearch and those from Uni-Mol, we visualize their embeddings, as shown in Figure The molecules are from ChEMBL, with different colors indicating different protein targets. Comparing the two, the classification boundaries in Figure 2b from S-MolSearch are clearer, and the intra-class molecular distances are more appropriate. Some clusters split into several subclusters, possibly reflecting the hierarchical structure within the molecules.
8

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Table 4: Performance under different learning paradigms on DUD-E and LIT-PCBA.
DUD-E
LIT-PCBA
EF 0.5%
EF 1%
EF 5%
EF 0.5%
EF 1%
EF 5%
Self-supervised
27.33
20.13
6.81
4.78
3.26
1.97
Supervised
34.61
28.51
9.83
7.55
4.73
1.98
Finetuning 35.11
29.20
9.96
7.01
5.71
S-MolSearch
40.85
34.60
11.44
10.93
6.28
2.47
In addition, we conduct ablation studies on the semi-supervised learning paradigm of S-MolSearch. The results are summarized Table 4 For "Self-supervised,, we train the model using a self- supervised learning paradigm. Specifically, we cluster the unlabeled molecule data based on their scaffolds. Molecules from the same cluster are considered as positive pairs, while those from different clusters are considered negative pairs, and contrastive learning is performed using the InfoNCE loss. For 'Supervised', we use only the ChEMBL data for supervised contrastive learning, where molecules binding the same target treated positive pairs and those binding different targets as negative pairs. For Finetuning', we first train the model under the self-supervised paradigm described above, then, starting from the self-supervised checkpoint, perform the supervised learning described above on the ChEMBL data. The results show that S-MolSearch consistently performs well both benchmarks, achieving the best results in almost all metrics. Notably, compared to finetuning, S-MolSearch demonstrates superior ability to integrate information from both unlabeled and labeled data in ligand-basee virtual screening scenarios.
15
Representations from pretrained checkpoint
(b) Representations learned by S-MolSearch
Figure 2: t-SNE visualization of molecular representations learned by S-MolSearch versus pretrained checkpoint. Different colors represent different protein targets' active molecules.
4.4.3 Impact of Labeled Data Scale
In the molecular field, obtaining or creating labeled data can be expensive. We also analyze how the scale of labeled data affects the results. These results are derived from S-MolSearch trained with 0.4 similarity threshold. As shown in Figure experiments are conducted with varying amounts of labeled data, while keeping the unlabeled data fixed million. The performance encoder Ie improves as the amount of labeled data increases, especially when the absolute number of labeled data limited. Additionally, the results encoder do are consistently higher than encoder fo trained using only labeled data. The best results are achieved with 50k and 100k labeled data, corresponding data ratios of 1:20 and 1:10, respectively. Beyond these amounts, increasing labeled data results in stable slightly declining performance, suggesting that further improvements

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23.1
20.6 250
56.
234
EF 1% DUD-E
EF 1% LIT-PCBA
Figure 3: Performance on DUD-E and LIT-PCBA with varying numbers of labeled data, while keeping unlabeled data fixed Im. The blue bars represent the results of encoder Js. while the green bars represent the results of encoder fa.
may necessitate an increase in unlabeled data or a reevaluation of hyperparameters. This trend helps to find optimal balance between labeled and unlabeled data maximize efficiency and performance in S-MolSearch.
5 Conclusion
This study introduces S-MolSearch, novel semi-supervised contrastive learning framework that significantly enhances the generalizability machine learning models virtual screening. Built on inverse optimal transport, S-MolSearch skillfully integrates limited labeled data with vast reservoir of unlabeled data and excels at identifying potential drug candidates from extensive molccular libraries, substantially improving the accuracy and efficiency of molecule searches. This advancement addresses current challenges in virtual screening by facilitating efficient filtering of large datasets, highlighting the framework's capability in scenarios where data annotation is costly.
Currently, S-MolSearch predominantly focuses on the molecular affinity data, omitting broader biochemical interactions, which suggests potential area for improvement. Future work could integrate more extensive unsupervised datasets to further refine the framework's effectiveness and explore additional applications in various bioinformatics fields.
Acknowledgments and Disclosure of Funding
This research was supported in part by National Natural Science Foundation of China (No. U2241212. No. 61932001), ), by National Science and Technology Major Project (20227D01 14802), by Beijing Natural Science Foundation (No. 4222028), by Beijing Outstanding Young Scientist Program No. No.BIJWZYJHO 201 2019100000099 This research also outcome of "AI-Aided Drug Design Based on Universal Representation of Multi-Modal Graph Structures" (RUC24QSDLO14), funded by the "Qiushi Academic Dongliang" Talent Cultivation Project Renmin University of China in 2024. We also wish to acknowledge the support provided by the fund for building world-class universities (disciplines) of Renmin University of China, by Engineering Research Center of Next-Generation Intelligent Search and Recommendation, Ministry of Education, Intelligent Social Governance Interdisciplinary Platform, Major Innovation Planning Interdisciplinary Platform for the "Double- First Class" Initiative. Public Policy and Decision Docision-making Research Lab, and Public Computing Cloud, Renmin University China. The work was partially done Gaoling School of Artificial Intelligence, Beijing Key Laboratory of Big Data Management and Analysis Methods, MOE Key Lab of Data Engineering and Knowledge Engineering, and Pazhou Laboratory (Huangpu), Guangzhou, Guangdong 510555, China.
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A Data Curation Details
The data we used are manually extracted from regularly published primary literature, and then further curated and standardized. The whole ChEMBL database of version 33 is downloaded and cleaned via the following steps. The data selected with assay type 'B', target type of 'SIGLE PROTEIN", molecule type of 'Small molecule', standard type of Ki, Kd, IC50, EC50 in nM, and standard relation of =" and '<'. Moreover, data with abnormal concentration value further deleted, such as negative and unreasonable large ones.
B Metrics
The BEDROC metric is designed to assess early retrieval performance, giving higher weights to active compounds that are ranked closer to the top. It is defined as:
En arr/N
Ra sinh(a/2) cosh(ax/2) (o//h(a22220 a aRa)) + ca(1-Ra)
BEDROC,
Ra
1-e-0
en/N-1
where n is the total number of active compounds, .N is the total number of molecules, r; is the rank of the i-th active compound. Following previous work, we set a 85 prioritize early retrieval.
We also use the Enrichment Factor (EF) to evaluate the effectiveness of virtual screening methods. The calculation formula for EF is follows:
Nay Pa/N5% n/N
where n represents the total number of active compounds in the database, N represents the total number of molecules, N,% represents the top x%of all molecules, and n, represents the number of active compounds within the top 2% of molecules.
C Proof for S-Molsearch Induced by Inverse Optimal Transport
First, we introduce a lemma establish the relationship between IOT and contrastive learning from 51]
Lemma The optimization problem and are equivalent:
min KL(PIpP)
(8)
subject to pa = arg min PEU(a)
P)
where C E RxN CRMxN,CC(i.p (i, = c- sty (0) and P(i.j)
8s, denotes the Kronecker delta function.
expl (0p(8)(0)/77
min
log
(9)
0
Ejet expl 8iz (0)/T)
In addition, 8d has the form as follows:
exp(s:(0)/T)
p
(10)
E Neap(s:y00/77
C.1 Proof for Proposition i
In the optimization problem since the setting of T does not involve parameter optimization 0 or sh it is evident that the parameter optimization processes for 0 and are independent. According to
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lemma 3
we can transform the original optimization problem into the following problem:
min 0,10
[KL(T>|L") + (L 1 + (Regi (I*) + RRegz (1
ezp(sn(0)/T)
subject
1 1
Σ jti
(11)
cxp(su(()//T)
Nerp(es))
F -(J
fized Xeup X ((wi) I8
Due to
KL(pllq) H() H(p)
(12)
where (p) represents the entropy of p. and H q) represents the cross-entropy between and g. Given the selection of specific T derive f making (p) constant, Furthermore, we can obtain
thus determine (i,,) fixed quantity,
exp(sx(0)/T)
min 0,0
Σ log
Ejjt (815 (xpp(8i((00/5
(1,
Engi (xp(sxx
(13)
+ + (T + Reg)
where (i.j)) TT
axod _u Xa.))
C.2 Proof for Proposition 2
Since Of fieed does not involve parameter optimization of 0, we can still calculate the value of 1 (i.j).
According to the proof in C.1
we know that
exp(s: (0)/T)
min 8.
Σ log
Σ Ejtt (xp((si((0)/1))))
(xp(sn((t/T))
1a (i,
(14)
+ 11 Reg, (T¹))
A a= b=yy (Creiiss r) + 2
where (i. arg
min
(4.5)
When we choose Reg, as the regularization term S-MolSearch.
we obtain the optimization formulation of
D Reproduce details
For the training of S-MolSearch, we use Adam optimizer at a learning rate of 0.001. The batch size 128, and the training is conducted on 4 NVIDIA V100 32G GPUs. For backbone model, we use the same parameters Uni-Mol. To enhance the training, noise addition for atoms within molecules, as implemented Uni-Mol. The parameters are identical to those in Uni-Mol, with masking ratio of 0.15 and noise following uniform distribution between -1 and Å. We randomly sample data from the labeled and unlabeled datasets to form the validation set, and select checkpoints based on the loss. More detailed configurations can be found the code repository.
retain the masking and coordinate
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E Extending to the Few-Shot Setting
Extending S-MolSearch from zero-shot to a few-shot setting is feasible. Due to the lack of universal few-shot setup standard in this scenario, we explore two few-shot settings. For data splitting in both settings, we randomly selected 70% of the active molecules from each target DUD-E as the training set for few-shot learning, while the remaining 30% and all inactive molecules serve as test data. The initial training set includes approximately 16,000 molecules, while the test dataset contains around I, 1,418,000 molecules. From these 16,000 active molecules, we randomly selected 50,000 pairs as the contrastive learning training data. the first setting, we simply add the query molecule the active molecule set corresponding to the target and randomly sample pairs, denoted as R in Ta Pairs involving molecules bound to the same target are treated as positive, while those involving molecules bound to different targets we fix one side of each contrastive learning pair as the query molecule, denoted as Table. the other molecule in the pair is active molecule bound the pair; bound to a different target, it is considered a negative pair. From Table 5 it can be seen that S MolSearch performs better in the few-shot setting than in the zero-shot setting, indicating its potential in few-shot scenarios.
treated negative. In the second setting,
target, it is considered positive
Table 5: Performance on DUD-E in two few-shot settings.
Method
AUROC (%)
EF 0.5%
EF 5%
Recroshot
85.38
79.08
47.12
11.82
Reew-shot
97.21
154.90
86.00
18.48
Facro shot
84.87
79.07
46.45
11.70
Flew
98.32
165.09
89.98
19.07
F
Qualitative Examples of Similarities
We provide qualitative examples to enhance understanding of S-MolSearch's capabilities. Specifically, select two targets, hdac2 and esflr, from DUD-E. In Figure we present the query molecules along with the top-ranked molecules retrieved by S-MolSearch, all of which are active molecules. We provide the embedding similarity and the Tanimoto similarity of molecular fingerprints between these molecules and the query molecule. The results indicate that molecules with high Tanimoto similarity also tend to have high embedding similarity.
G Limitations
S-MolSearch falls short in terms of interpretability. Traditional 3D molecule search methods can capture shape and functional features required for biological interactions, providing scientists with mechanistic insights. S- S-MolSearch is currently unable to provide such intuitive insights for molecule search. Additionly, its use of two encoders also leads higher memory consumption than single- encoder methods.
H Potential societal impacts
S-MolSearch performs well on LBVS and can help screen bioactive molecules from large molecule databases. This eases the workload of medicinal chemists and may accelerate the discovery of new drug. On the downside, S-MolSearch also runs the risk of being used inappropriately. such as when is used to search for similar molecules to drugs that are addictive.
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Target: hdac2
Query malocale
Embedding similarity: Tanimoto similladyy0.77 0.73
Embedding similarity: Tanimoto simillrity 0.81
Embedding similarit:: Tanimoto sumilartt: 0.75
Target: esflr
Query molecule
Embeddling similarity: Tanimoto similartty 0.82
Embeddingg similacity 0.98 Tenimoto similarity 0.66
Embedilng simil similarty:: Tanimoto lanty
Figure Qualitative examples of similarities for targets hdae2 and esflr in DUD-E.
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Reviews:
[{"review_id": "vzJXp6c6hd", "reviewer": "Reviewer_ZRdZ", "summary": "The paper introduces a new method for ligand-based virtual screening based on contrastive learning and inverse optimal transport. Two molecule encoders are trained. The first encoder is trained using a contrastive loss function on the ChEMBL data by pairing compounds that are active toward the same protein, and compounds active toward different targets are treated as negative pairs. Next, the second encoder is trained by using the pseudo-labels produced by the first model. The proposed model is tested on two benchmark datasets, DUD-E and LIT-PCBA. Additionally, an ablation study is conducted, and the impact of the labeled data scale is visualized.", "questions": "1. How do you solve the cases in contrastive learning where one molecule binds to multiple targets? In this example, you need to be careful not to create a negative pair, where one molecule is the one binding to both targets and the other molecule binds to only one of them.\n2. How do you avoid treating two molecules as a negative pair if both can bind to the same target? For example, they are inhibitors of two similar proteins, which increases the chance of them binding to both at the same time.", "limitations": "The limitations have been described.", "rating": 6, "confidence": 3, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "Originality:\n- The approach seems to be novel. I have not found any similar papers that use optimal transport for the ligand-based virtual screening task.\n\nQuality:\n- The theory described in the paper is formally proven in the Appendix.\n- The proposed method obtains excellent results in both tested benchmarks.\n- The quality of the learned representation is demonstrated in Figure 2.\n\nClarity:\n- The paper is written clearly and is easy to follow.\n- Figure 1 shows the idea of the model very clearly.\n\nSignificance:\n- The presented method is an interesting and effective way to utilize all the available public data to build a strong model for ligand-based virtual screening.", "weaknesses": "Quality:\n- It would be interesting to see some qualitative examples of molecules that were found to be similar to the active compounds in the virtual screening process. Do the trained similarities correlate with the Tanimoto similarity?\n\nClarity:\n- Does the “sup” subscript in Section 3.4 correspond to the “label” subscript in Proposition 1? What is the difference between these two sets?\n\nMinor comments:\n- A typo in line 151, “we employs InfoNCE.”\n- In line 183, something is missing before “1”.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you very much for supporting our work and careful review! We appreciate the detailed review and constructive feedback. We have addressed each of your comments and questions below, aiming to clarify and enhance the understanding of our work.\n\n**Qualitative Examples and Similarities**\n\nWe agree that providing qualitative examples would enhance the understanding of our model's capabilities. We have added two examples of molecules identified as similar to query molecules in DUD-E. These molecules are all active molecules.  The results indicate that molecules with high Tanimoto similarity tend to have high embedding similarity. These qualitative examples can be found in Figure 1 in the attached PDF. \n\n**Clarification on Subscripts in Section 3.4**\n\nThe “sup” subscript in Section 3.4 indeed corresponds to the “label” subscript in Proposition 1. The two subscripts have the same meaning, representing supervised learning on labeled data. For clarity, we have standardized the subscript to \"sup\" throughout the manuscript.\n\n**Minor Comments**\n\nThank you for pointing out the typographical errors. We have corrected the typo in line 151 and added the missing context in line 183 (now it's in line 186). These corrections are reflected in the revised manuscript.\n\n**About Negative Pairs**\n\nIn our view, both of your questions pertain to the potential occurrence of false negative pairs. False negatives may arise in scenarios where a single ligand binds to multiple targets or multiple ligands bind to the same target.\n\nThe way we construct the training data, as described in lines 60-64 of the manuscript, considers molecules binding to the same target as positive pairs, while molecules binding to different targets are considered negative pairs. This approach can mitigate the occurrence of false negatives to some extent.\n\nIn the raw ChEMBL data, approximately 21% of the ligands can bind to two or more targets. To further analyze the situation of false negatives during training, we count the false negative pairs that appear in each batch of the sampled training data over one epoch and find that false negative pairs account for an average of 0.76% of all negative pairs. This is a relatively small number, and considering the robustness of contrastive learning during training, we believe these false negative pairs will not significantly impact the current results [1].\n\nNonetheless, the presence of false negatives remains a concern. In the future, we plan to address this issue by designing more robust contrastive learning objectives and constructing more refined datasets to minimize the occurrence of false negatives. \n\nWe believe our response effectively addresses your concerns. If you have additional questions or need further clarification, we are open to further discussion.\n\n*Reference:*\n\n[1] Wu J, Chen J, Wu J, et al. Understanding contrastive learning via distributionally robust optimization.", "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": "bXoOsM5K8N", "reviewer": "Reviewer_KtU6", "summary": "This paper proposed a Ligand-based Virtual Screening method S-MolSearch. which can  leverages molecular 3D information and affinity information in semi-supervised contrastive learning.", "questions": "Refer to weakness.", "limitations": "S-MolSearch predominantly focuses on the molecular affinity data, omitting broader biochemical interactions, which suggests a potential area for improvement.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1. The method is able to leverage both labeled and unlabeled data simultaneously and achieves excellent performance on DUDE and Lit-PCBA benchmarks.\n2. The approach of using the principles of inverse optimal transport for semi-supervised learning is quite innovative and worth adopting.\n3. The ablation experiments are sufficient, and the experimental section is quite robust.", "weaknesses": "1. In the method section, it is unclear to me whether during inference only encoder$g_{\\psi}$ is used, or both $\\psi$ and $f_{\\theta}$ are used  simultaneously?\n2.  If the application scenario involves a newly provided protein without reference molecules, how should ligand-based virtual screening methods handle this situation?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you very much for supporting our work and careful review! We have considered each of your questions, and we provide detailed responses below.\n\n**Inference Process with Encoders**\n\nDuring inference, only the encoder gψg_{\\psi}gψ is used to generate the molecular embeddings. The encoder fθf_{\\theta}fθ is primarily used during the training phase for generating pseudo-labels. We have clarified this in the revised manuscript in Section 3.1, line131. \n\n**Handling New Proteins Without Reference Molecules**\n\nOur current work is based on known query molecules. If the query molecules are unknown, some existing techniques might be helpful for this situation. One possible approach is to construct a pseudo-ligand based on the shape of the protein pocket, as demonstrated in [1]. Another feasible approach is to combine S-MolSearch with structure-based methods, such as [2]. We believe this can serve as an excellent direction for further enhancing our future work.\n\nThank you for their helpful suggestions. We hope that our responses adequately address your concerns.\n\n\n*Reference:*\n\n[1] Gao B, Jia Y, Mo Y, et al. Self-supervised pocket pretraining via protein fragment-surroundings alignment.\n\n[2] Zhang X, Gao H, Wang H, et al. Planet: A multi-objective graph neural network model for protein-ligand binding affinity prediction.", "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": "szukWBUdqq", "reviewer": "Reviewer_9wcM", "summary": "The paper introduces \"S-MolSearch,\" a semi-supervised contrastive learning framework designed for ligand-based virtual screening in drug discovery. This framework uniquely leverages labeled binding affinity information to produce soft labels for unlabeled molecules, integrating 3D molecular structures and binding affinity data. The paper also proposes a novel semi-supervised learning paradigm that combines contrastive learning with Inverse Optimal Transport (IOT).", "questions": "The same as weakness.", "limitations": "The focus of the paper is predominantly on molecule binding affinity, heavily relying on a pretrained encoder. This reliance could limit the model's applicability across a broader spectrum of bioinformatics data. A more detailed discussion on the dependency on pretrained models and potential strategies to mitigate this limitation would enhance the paper's breadth and applicability.", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1. The supervision idea is novel and useful, and the target application is very impactful with broad implications.\n2. The paper is well-written and the experiments are comprehensive.", "weaknesses": "1.\tMemory Consumption Concerns: The model employs a parallel architecture with two f_\\theta encoders and one g_\\phi encoder, based on the Uni-Mol framework. Although utilizing pretrained models has shown significant performance benefits, the paper should address potential memory management strategies, especially for future applications involving molecules with a greater number of atoms.\n2.\tUtilization of 3D Structures: The paper promotes a novel semi-supervised contrastive learning paradigm, yet the core contribution does not seem to revolve around the innovative use of 3D structures, as this capability primarily stems from the Uni-Mol architecture. It would be beneficial if the authors could clarify any specific enhancements made to ensure the effective preservation and utilization of geometric information within the model. Absent such enhancements, clearer distinctions should be made regarding the role of 3D structures to prevent misconceptions about the paper presenting a new geometric deep learning technique.\n3.\tClarity in Section 3.4: The explanation of how $\\Gamma$, which approximates the distribution of $C$ under constraints from $U(p,q)$, relates to the continuous optimal transport problem is not clear. Moreover, the motivation and necessity of soft labels, beyond experimental justifications, needs further elaboration. The section would benefit from additional visual aids or high-level descriptions, akin to the clarifications provided in sections 3.3 and 3.5, to aid in comprehension.\n4.\tComponent Efficacy in Table 3: There appears to be a discrepancy in the impact of model components across different benchmarks—soft labels are pivotal for DUD-E, whereas pretraining is more crucial for LIT-PCBA, with soft labels showing minimal importance. Insights into this inconsistency would be valuable. Furthermore, an evaluation of how the Uni-Mol encoder alone performs on these tasks would provide additional context on the effectiveness of the proposed enhancements\n\nMinor points and typos:\nL153-154 is not clear.\nL162: It would be beneficial to include illustrations of $M_{sup}$ in the figures for clarity.\nFormula 2 and L 168: It is better to give intuitive explanations of $1_N$.\nL184: Inconsistent notation. $g(\\psi)$ or $g_\\psi$?\nL281: Misplaced comma.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate your thorough review and constructive feedback. Below, we address each of your comments and questions, aiming to clarify and enhance the understanding of our work.\n\n**Memory Consumption Concerns:**\n\nWe measure memory consumption under different scenarios, as shown in the table below. Here, supervised learning corresponds to using one encoder, and S-MolSearch corresponds to using two encoders. The table shows that increasing the number of encoders leads to a linear increase in memory consumption. Since Uni-Mol is relatively lightweight, this does not significantly impact regular use.\n\nConsidering the potential applications involving large-scale data or large molecules in the future, memory consumption poses a challenge. In future work, we plan to explore update strategies, for example, similar to [1], to decrease memory consumption.\n\n| Model                | Memory used |\n|----------------------|-------------|\n| Supervised (Single Encoder) | 9.5 G   |\n| S-MolSearch (Two encoder)   | 22.4 G  |\n\n**Utilization of 3D Structures:**\n\nWe believe that utilizing the 3D information of molecules is advantageous in ligand-based virtual screening scenarios. While we do not introduce a new geometric deep learning technique, we ensure the preservation of geometric information by leveraging Uni-Mol. \nWe want to point out that one of the primary contributions of this work is the combined use of both 3D molecular information and binding affinity information for virtual screening, as described in lines 77-79, rather than providing a new backbone for molecule pretraining.\n\n**Clarity in Section 3.4:**\n\nWe realize that our current phrasing may lead to some misunderstandings. In fact, the optimal transport form we introduce is derived from [2], which presents a smooth and sparse form of optimal transport. This form not only effectively manages the computational cost but also maintains consistency with traditional optimal transport problems.\n\nIn S-MolSearch,  $\\Gamma$ can be interpreted as a joint probability distribution under given marginal probabilities. Through the design of the cost matrix $  C $, we ensure that $ \\Gamma_{i,j} $ is positively correlated with $ x_{i}x_{j}$. The additional $ L2$ norm regularization ensures the sparsity of $\\Gamma $. This implies that for labels with low confidence from the supervised model, the pseudo-labels are heavily punished. Overall, the introduced smooth optimal transport form guarantees that signals from the supervised model are more effectively transferred to the unsupervised model, while handling high uncertainty with appropriate regularization. We have revised the wording in the manuscript and added relevant citations accordingly. \n\n**Component Efficacy in Table 3:**\n\nWe conduct an intuitively analysis to provide insights into why soft labels are pivotal for DUD-E, while pretraining is more crucial for LIT-PCBA. We believe this is related to the inherent biases of each dataset.\n\nRegarding the pivotal role of soft labels for DUD-E [3], the molecular distribution in DUD-E has more analogues and decoy biases, making it crucial for the model to use soft labels to effectively distinguish between closely related molecules. The LIT-PCBA dataset ensures diversity in data representation, offers a broad distribution across chemical space, and effectively minimizes inherent biases, so the impact of soft labels is less pronounced. The importance of pretraining for LIT-PCBA [4] arises because the broader molecular distribution seen during pretraining allows the model to capture a wider variety of molecular features, thereby enhancing performance on this dataset.\n\nAs for the performance of original Uni-Mol, results in the tables demonstrate that the addition of our proposed components significantly enhances performance. The improvements underscore the value of integrating soft labels and pretraining into our framework, particularly in achieving better results across different benchmarks.\n\n| DUDE       | EF 0.5% | EF 1% | EF 5% |\n|--------------|---------|-------|-------|\n| Uni-Mol      | 9.82    | 7.97  | 4.22  |\n| S-MolSearch 0.4 | 40.85   | 34.60 | 11.44 |\n\n| LIT-PCBA       | EF 0.5% | EF 1% | EF 5% |\n|--------------|---------|-------|-------|\n| Uni-Mol      |  3.22 | 1.94  |1.40  |\n| S-MolSearch 0.4 | 10.93   | 6.28  | 2.47 |\n\n\n**Minor Points and Typos:**\n\nThank you for pointing these out. L162: We emphasize $M_{sup}$ in Figure 2 to help readers understand our work more clearly. Formula 2 and L168: 1N is an N-dimensional vector of all ones. We add this in line 170. And we correct other points and typos in the manuscript\n\n**Limitations:**\n\nPre-trained models are versatile and can be utilized for a variety of tasks and Uni-Mol demonstrates strong performance across several applications. In virtual screening tasks, the model benefits from exposure to a broader molecular space, which we believe makes the use of pre-trained models reasonable and advantageous. \n\nWe also conducted ablation studies on pre-training, as shown in Table 3, which demonstrate that pre-training provides improvements.\n\nThank you very much for reading. We hope that our responses address your concerns and demonstrate the enhancements made to our work.\n\n*Reference:*\n\n[1] He K, Fan H, Wu Y, et al. Momentum contrast for unsupervised visual representation learning.\n\n[2] Blondel M, Seguy V, Rolet A. Smooth and sparse optimal transport[C]//International conference on artificial intelligence and statistics. PMLR, 2018: 880-889.\n\n[2] Mysinger M M, Carchia M, Irwin J J, et al. Directory of useful decoys, enhanced (DUD-E): better ligands and decoys for better benchmarking.\n\n[3] Tran-Nguyen V K, Jacquemard C, Rognan D. LIT-PCBA: an unbiased data set for machine learning and virtual screening.", "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": "QuCyzNay1D", "reviewer": "Reviewer_YuaV", "summary": "The paper introduces S-MolSearch, a framework for ligand-based virtual screening in drug discovery that addresses the challenges of limited and noisy binding affinity data. By utilizing molecular 3D information and semi-supervised contrastive learning, S-MolSearch processes both labeled and unlabeled data to train molecular structural encoders and generate soft labels for the unlabeled data, drawing on inverse optimal transport principles. The framework outperforms existing structure-based and ligand-based virtual screening methods, as evidenced by its superior performance on the LIT-PCBA and DUD-E benchmark datasets.", "questions": "- Both S-MolSearch and existing methods experience a decline in performance as the % of EF increases. Additional discussion on the reasons for this phenomenon is needed.\n- Why do soft labels based on inverse optimal transport seem to have a significant impact on the DUD-E dataset but a lesser impact on the LIT-PCBA dataset?\n- What aspects of the semi-supervised approach in Table 4 do the authors think primarily contributed to the performance improvement compared to fine-tuning?\n- Is it possible to extend this method from a zero-shot setting to a few-shot setting? If so, how do the authors think its performance would compare to existing methods in that case?\n- In virtual screening, not only performance but also processing time is important. How does the screening time compare to that in existing studies?\n- How does the performance compare to existing models when using measurements like AUROC or BEDROC instead of EF #%?", "limitations": "The paper addressed limitations and potential social impacts in Appendix.", "rating": 7, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- Well-written\n- Well-organized experimental settings and comparison methods", "weaknesses": "- There is a lack of discussion on the reasons behind the performance differences and improvements, with only numerical comparisons of the experimental results.\n- There is insufficient experimentation and consideration regarding the time required for virtual screening.\n- There are no results for experimental metrics such as AUROC or BEDROC, which were used in previous studies.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate the thoughtful questions and feedback provided by you. We have carefully considered your queries and provide detailed responses below.\n\n**Consideration of Screening Time**\n\nWe have conducted additional experiments to measure the screening time of S-MolSearch compared to traditional methods. The results, as shown in the table below, indicate that S-MolSearch has a significant advantage in search time consumption compared to traditional molecular search methods even if the molecular embeddings are not precomputed. \n\nNotably, if the molecule database is fixed and all molecules are pre-encoded and stored in vector database such as FAISS, S-MolSearch is expected to achieve a search speed of tens of millions of molecules per second.\n\n| Method     | Molecules/sec on DUD-E |\n|------------|-----------------------|\n| Shape-it [1]  | 70                    |\n| ROSHAMBO [2] | 440                   |\n| S-MolSearch| 1316                  |\n\n**Lack of Results for Experimental Metrics Such as AUROC or BEDROC:**\n\nWe have expanded our experimental evaluation to include AUROC and BEDROC metrics. These additional results, found in table 1 and 2 in the addtional PDF, provide a more comprehensive comparison of S-MolSearch with existing models and highlight its robust performance across different evaluation criteria. The results show that S-MolSearch demonstrates superior performance on AUROC and BEDROC. \n\nOn DUD-E, S-MolSearch trained on data with a 0.4 similarity achieves AUROC and BEDROC results of 84.61% and 54.22%, respectively, surpassing all baselines. S-MolSearch trained on data with a 0.9 similarity achieves AUROC and BEDROC results of 92.56% and 75.37%, respectively, exceeding the best baseline by 50% in BEDROC.\n\nOn Lit-PCBA, S-MolSearc$h_{0.4}$ achieves AUROC and BEDROC results of 57.34% and 7.58%, respectively, surpassing all baselines in BEDROC and being comparable to the best baseline in AUROC. S-MolSearch$_{0.9}$ achieves AUROC and BEDROC results of 61.78% and 8.48%, respectively, achieving the best results in both AUROC and BEDROC.\n\n**Decline in Performance as the % of EF Increases:**\n\nWe provide the specific calculation formula for EF in appendix section B. The upper limit of EF decreases with the increasing top x%. The theoretical maximum value of EF is calculated as 100 divided by x. For example, the maximum value of EF 1% is 100, and the maximum value of EF 5% is 20. \n\nFrom the perspective of virtual screening tasks, this can be attributed to the increased difficulty in distinguishing between active and inactive molecules as more molecules are considered, which tends to dilute the enrichment factor. Increasing the screening percentage implies that a more diverse array of active molecules needs to be identified, which is often more challenging.\n\n**Impact of Soft Labels on Different Datasets**\n\nWe think this is caused by differences in the benchmarks. The molecules in DUD-E have more analogues and decoy biases,  making it crucial for the model to use soft labels to effectively distinguish between closely related molecules. The LIT-PCBA dataset ensures diversity in data representation, offers a broad distribution across chemical space, and effectively minimizes inherent biases, so the impact of soft labels is less pronounced.\n\n\n**Contributions of the Semi-Supervised Approach in Table 4 Compared to Fine-Tuning:**\n\nWe would like to clarify once again that the fine-tuning we refer to in Table 4 involves initial pre-training with contrastive learning on an unsupervised dataset, followed by contrastive learning-based fine-tuning using active supervised data. Compared to S-MolSearch, we believe that the fine-tuning approach does not optimally integrate the information from both the unsupervised and supervised datasets.\nThe performance improvements observed in Table 4 can be primarily attributed to the integration of unlabeled data through our semi-supervised approach, which enhances the model's ability to generalize beyond the limitations of fine-tuning.  \n\n**Extending the Method from Zero-Shot to Few-Shot Setting**\n\nExtending S-MolSearch from a zero-shot to a few-shot setting is feasible. We explored two few-shot settings. In terms of data division, we randomly selected 70% of the data from each target in DUD-E as the training set for few-shot learning. The remaining 30% of active molecules and all inactive molecules were used as test data. With the training dataset, we employed two settings. The first setting(random) considers the query molecule as part of the active molecule set bound to the target, then combines it with data bound to the same target as positive pairs and data bound to different targets as negative pairs. The second setting(fix query) fixes one molecule in the positive pair as the query molecule and selects another molecule from the active molecules to form positive pairs. The construction method for negative pairs is the same as in the first setting. ZS represents zero-shot in this table, and FS represents few-shot. The results are all obtained by S-MolSearch trained on data with a 0.4 similarity.\n\nBecause there is no universal setup for few-shot in this scenario, we do not compare it with other methods.\n\n| Configuration       | AUROC (%) | EF 0.5%  | EF 1%  | EF 5%  |\n|---------------------|-----------|----------|--------|--------|\n| 0.4,ZS, fix query   | 84.87    | 79.07   | 46.44 | 11.70  |\n| 0.4,FS, fix query   | 98.32     | 165.09   | 19.06  | 9.66   |\n| 0.4,ZS, random      | 85.38    | 79.08    | 47.11 | 11.82  |\n| 0.4,FS, random      | 97.21     | 154.90   | 86.00  | 18.48  |\n\n\nThank you very much for reading. We hope that our responses adequately address your concerns.\n\n*Reference:*\n\n[1] Taminau J, Thijs G, De Winter H. Pharao: pharmacophore alignment and optimization.\n\n[2] Atwi R, Wang Y, Sciabola S, et al. ROSHAMBO: Open-Source Molecular Alignment and 3D Similarity Scoring.", "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:
We sincerely appreciate the valuable feedback and insightful comments provided by each of you. Your input has been instrumental in refining our work and enhancing the clarity and depth of our manuscript.

In response to your suggestions, we prepare an additional PDF document. It includes qualitative examples of molecular embedding similarity and Tanimoto similarity, as well as experimental results tables containing AUROC and BEDROC.

Meta-review: All reviewers argued to accept this paper, with one raising their score up from weak accept after the rebuttal. There were a number of clarifying comments, and additional results and metrics, presented by the authors during the rebuttal period. The authors should please make sure to incorporate these elements of the discussion into the final revision of the paper.
Decision: Accept (poster)