BounDr.E: Predicting Drug-likeness via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
Authors: Dongmin Bang
Inyoung Sung
Yinhua Piao
Sangseon Lee
Sun Kim
Venue: ICML 2025 poster (2025)
Keywords: Drug-likeness
Expectation-Maximization
Multi-modal learning
AI Drug Discovery
Primary area: applications->health_medicine
TL;DR: Drug-likeness prediction framework based on EM-like one-class boundary optimization with multi-modal alignment of biomedical knowledge graph and structural space.

Abstract: The advent of generative AI now enables large-scale $\textit{de novo}$ design of molecules, but identifying viable drug candidates among them remains an open problem. Existing drug-likeness prediction methods often rely on ambiguous negative sets or purely structural features, limiting their ability to accurately classify drugs from non-drugs. In this work, we introduce BounDr.E}: a novel modeling of drug-likeness as a compact space surrounding approved drugs through a dynamic one-class boundary approach. Specifically, we enrich the chemical space through biomedical knowledge alignment, and then iteratively tighten the drug-like boundary by pushing non-drug-like compounds outside via an Expectation-Maximization (EM)-like process. Empirically, BounDr.E achieves 10\% F1-score improvement over the previous state-of-the-art and demonstrates robust cross-dataset performance, including zero-shot toxic compound filtering. Additionally, we showcase its effectiveness through comprehensive case studies in large-scale $\textit{in silico}$ screening. Our codes and constructed benchmark data under various schemes are provided at: https://github.com/eugenebang/boundr_e.

BounDr.E:
Predicting Drug-likeness via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
Dongmin Bang" 12
Inyoung Sung?
Yinhua Piao 4 Sangseon Lee² Sun Kim 1246
Abstract
1. Introduction
The expansion of deep generative models have reshaped the drug discovery landscape by rapidly producing vast li- braries of de novo compounds (Guan et al., 2023; Lee et al., 2023; Song et al., 2024), often conditioned by desired ac- tivity or pocket structure. However, evaluating which of these molecules are truly "drug-like" is yet an open problem. Traditional property-based metrics, such as Rule of five (Lip- inski et al., 1997), offer efficient preliminary screening but lack definitive criterion separate truly viable drug can- didates from non-drugs. Thus, in this era of generative AI, data-driven approach for precisely defining drug-likenes in terms of chemical or compound space is now required.
The advent of generative AI now enables large- scale de novo design of molecules, but identify- ing viable drug candidates among them remains an open problem. Existing drug-likeness pre- diction methods often rely on ambiguous neg- ative sets or purely structural features, limiting their ability to accurately classify drugs from non- drugs. In this work, we introduce BOUNDR. E: novel modeling of drug-likeness as a compact space surrounding approved drugs through dy- namic one-class boundary approach. Specifically, we enrich the chemical space through biomed- ical knowledge alignment, and then iteratively tighten the drug-like boundary by pushing non- drug-like compounds outside via an Expectation- Maximization (EM)-like process. Empirically, BOUNDR. E achieves 10% Fl-score improvement over the previous state-of- of-the-art and demon- strates robust cross-dataset performance, includ- ing zero-shot toxic compound filtering. Addi- tionally, we showcase its effectiveness through comprehensive case studies in large-scale in sil- ico screening. Our codes and constructed bench- mark data under various schemes are provided at: giihub.com/ugggmbbnn/bbudddeeee e.
Fundamentally, the approval of drugs depends on more than just structural validity. A candidate must exhibit favorable physicochemical properties and align with relevant biomed- ical context, including biological target interactions and disease pathway modulation. Yet, most existing predictive models ignore these requirements, depending heavily on structural features alone (Zhu et al., 2023).
Further complicating the problem, approved drugs are highly scattered in the chemical space, with fewer than two drugs typically sharing the same core scaffold. This dispersion makes it challenging to define compact decision boundary without including non-drugs, as observed in our initial studies (Appendix B). Specifically, defining such a boundary poses two major challenges: 1) the absence of definitive negatives, as any molecule could potentially be drug-like, and 2) the vast scale of chemical space, estimated to be up to 10e0 compounds (Polishchuk et al., 2013), mak- ing it impractical to sample representative set for training.
'Interdiciplinary Program in Bioinformatics, Seoul National University. Seoul, Republic of Korea 2 AAGGENDRUG Co., Ltd., Scoul, Republic of Korea 'BK21 FOUR Intelligence Com- puting, Scoul National University, Scoul, Republic of Korea *Department of Computer Science and Engineering, Scoul Na- tional University, Scoul, Republic of Korea Department of Arti- ficial Intelligence, Inha University, Incheon, Republic of Korea "Interdiciplinary Program in Artificial Intelligence, Seoul National University, Scoul, Republic of Korea. Correspondence to: Sun Kim <sunkim. arr>
Due to these challenges, supervised approaches that treat non-drug molecules as "hard negatives" tend to over-restrict the boundary (Sun et al., 2022), while purely unsupervised methods often become too broad (Li et al., 2024). Positive- unlabeled (PU) learning methods (Leee et al., 2022) also assume well-defined negative distribution, which is im- practical for the unbounded compound space, where defin- ing its representative set is challenging (Appendix A.7). Traditional one-class classifiers (Schölkopf et al., 2001; Tax & Duin, 2004; Ruff et al., 2018), though independent of neg-
Proceedings of the 42nd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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Predicting Drug-likeness via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
Step 1. alignment of drugs
Step 2. EM-like boundary construction
Knowledge graph space (XC; DREAMwalk)
DrugBank ZINC
Drug
Compound
DrugBark
Knowledge Encodor
Optimized
Uag Me
anzodar
Optimized drug boundary
Alignment frgast
Enooder
EM-like iterative optimization
B
E-step:
Unified embedding space (1I)
Boundary updale
Structure Encoder
Structural embedding space (5: Morgan Fingerprint)
M-step:
Lalent space updale
Figure 1: Overview BOUNDR.E. Step performs multi-modal mixup of two drug spaces:
knowledge graph and molecular
fingerprint spaces into a unified space U. Step 2 performs EM-like boundary optimization, where in E-step boundary B is updated and in M-step the latent space Z is updated by pushing the out-boundary non-drugs further while contracts drugs to the center.
ative samples, remain unused in drug-likenest prediction due to their static nature and overly broad boundaries which leads to high false positives.
efficiency and reliability of Al-driven drug discovery.
2. Related Work
In response, we propose BOUNDR.E E: a novel approach that frames drug-likeness prediction as constructing the chem- ical space of approved drugs using deep one-class bound- ary within a nhowledge-integrated embedding space. A desirable drug-like likeness space should form tight bound- ary around approved drugs, including only small fraction of existing compounds drug candidates. BOUNDR.E achieves this by iteratively refining the boundary through (EM)-like process, adaptively enclosing drug-like molecules while pushing non-drug-lin compounds outward. Furthermore, we integrate the essen- tial biomedical context via multi-modal mixup, merging molecular structure representation with biomedical knowl- edge graphs (Li et al., 2022) into a unified embedding space.
Computational Prediction of Drug-likeness Computa- tional identification of drug-like compounds has long been focus in drug discovery (Clark & Pickett, 2000). Early drug-liken likeelis prediction relied on descriptor like Ro5 (Lipinski et al., 1997) and QED (Bickerton et al., 2012), which serve useful filters but fail define clear decision boundary, as multiple studies have noted (Lee et al., 2022; 2023; Li et al., 2024).
metrics
an Expeecation-Maximivaaaii
More recent supervised GNN-based methods, including D- GCAN (Sun et al., 2022) and DeepDL. (Lee et al., 2022), treat drug-likeness prediction a binary classification PU learning problem, respectively. However, their assumptions tractable negative distribution makes them sensitive to the selected negative set, as reported in Beker et al. (2020), limiting their generalizability in open-world chemical space where no representative set exists.
Through extensive experiments, we show that our approach yields notable improvements in drug-likeness prediction task, with robust performance across time-based splits, ceaffold-based splits, and cross-dataset validation on three benchmark sets. Additionally, BOUNDR.E excels in zero- shot toxic compound filtering, with comprehensive case studies further showcasing its utility in large-scale screen- ing of Al-generated compounds.
In contrary, unsupervised approaches, such as DrugMetric (Li al., 2024) (VAE Gaussian Mixture Models), avoid re- liance on negatives but often yield overly broad, ambiguous boundarics that fail to precisely distinguish drug-like like from non-drug-like molecules. Most of all, existing approaches rely solely on structural input, overlooking the critical role of biomedical context in shaping drug-likenng likensss...
Our key contributions include: 1) Novel formulation of drug-likeness prediction as a one-class classification with- out reliance on negatives. 2) Proposal of deep EM-like optimization of both the drug-likeness boundary and the embedding space for accurate drug-likeness prediction. 3) Knowledge-integratee multi-modal alignment of structure and biomedical knowledge embeddings for defining drug- likeness with machine learning. These advances collectively establish BOUNDDR.E E as a dynamic, data-driven tool for initial screens of generated molecules, pushing the fron- tiers of drug-likenesy prediction and improving the overall
Deep Multi-modal Alignment Multi-modal alignment maps diverse data modalities, such as image, text and video, into a unified embedding space to enable effective joint learning and generalization (Girdhar et al., 2023). Notable advancements include contrastive learning frameworks such as CLIP (Radford et al., 2021). which align text descrip- tions with images. Recent methods have introduced im- proved alignment strategies, including Geodesic Mixup (Oh et al., 2024), which ensures that mixed samples from dis-
2

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Predicting Drug-likeness via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
Xramp
boundary Ber and its latent space Zg. Notations throughout this paper organized in Appendix D.
Dexemm
Xcmp x 1060
Dzme
Dprsg
Xamp Xprug
3.2. Knowledge-integrated Multi-modal Alignment
Yarug
Ccomp
Domp
Dpsackse
Xprug
Drruy
Each drug can be represented by two complementary em- beddings, which encode different aspects of molecular structure and biomedical context. The key ob- jective is to learn a structural encoder that can also map non-drugs, which have no corresponding biomedical infor- mation, into a biomedical context-ent -errichee space. The goal is to unify the two embeddings into a common latent space U. where both structural and knowledge representations of drugs are aligned and consistent.
Figure 2: Problem definition of drug-likeness prediction with compound spaces N' and datasets D.
tant modalities lie a geodesic path, maintaining robust representations on hypersphere.
In the biochemical domain, contrastive learning has been applicd to chemical- chemical-bioassay image alignment (CLOOME) SSanchez-Fernande et al., 2023), drug-target interaction prediction (Ye et al., 2021), element knowledge integration (Fang al., 2023) and knowledge graph completion (Hoang et al., 2024). However, no existing work has attempted to align knowledge graph embeddings of drugs with the structural embedding space for modeling drug-likeness.
To achieve this, we introduce a knowledge-integrate multi- modal mixup strategy. This involves softening the CLIP loss (Radford et al., 2021) to encourage alignment between the two embedding spaces based on semantic drug similarities as prior knowledge. The alignment is further augmented with geodesic mixup (Oh et al., 2024), which ensures that the interpolated samples lie on geodesic path between the embeddings. By employing this strategy, we create a uni- fied embedding space that leverages the contexts from both molecular structure and biomedical knowledge, capturing a richer representation of drug-like properties.
3. BounDr.E: Drug-likeness Boundary Optimization
Given the highly dispersed nature of drugs in chemical space and their approval based on both structure and biomedical knowledge, our framework combines these two modalities into unified space. followed by iterative refinement of hyperspherical one-class boundary to capture drug-like compounds (Figure 1). The alignment of the two modali- ties (Section 3.2) and the boundary optimization (Section 3.3) are the keys to addressing the challenges posed by an unbounded chemical space and the absence of explicit negatives.
We begin by aligning two key embedding spaces of biomed- ical knowledge graph embeddings Kanug E K. (Bang et al., 2023) and molecular structural embeddings Sarug E S (Mor- gan Fingerprint). This integration is crucial as it enriches drug representations by combining molccular structures with their biomedical contexts. We train two encoders: a knowledge encoder & K - U4 and a structural encoder &, S - U1 where both map their respective embeddings to unified latent space U C R2, The details of the aligned spaces are explained in Appendix C.2.
3.1. Problem Definition
3.2.1. SOFTENED CLIP LOSS WITH ATC SIMILARITY
We propose a new perspective on the problem of drug- likeness prediction as constructing a compact and adaptive one-class boundary B around drug-like compounds in a the- oretically unbounded chemical space (Figure 2). Let this space of all compounds be denoted Xeump, with subset Kang C Xeomp representing drug-like compounds. The ap- proved drug dataset Danug represents a subset of the Xanug while compound dataset Deump is a biased subset of Xcump- where its small yet unknown portion are potential drugs that are to be rescued (Appendix A.7). As visualized Figure 2, existing non-drug datasets Dcomp (e.g. ZINC, PubChem, ChEMBL) form a distinct distribution and can not be representative set of the compound space (Appendix C.5).
In this section, we propose a novel knowledge-integration strategy for multi-modal contrastive learning. We soften the CLIP loss (Radford et al., 2021) by incorporating semantic similarity (Jiang & Conrath, 1997) between drugs using Anatomic Therapeutic Chemical (ATC) classification. For batch of data D = ((s,, k:) i= given by:
M the original CLIP loss is
exp(s; ② k;/T) M Σ log
1 M
C(s,k)
Σj= exp (8: 3 kz/T)
LCUP (C(s, k) + C(k. s))
We define the drug-likeness boundary through 1) training encoders ε, and E, for alignment of drugs' knowledge space IC and structural space S into a unified embedding space U, followed by 2) EM-like iterative optimization of
where C(s,k) k) is the contrastive loss for structural and knowledge embeddings, 8; O K; = (s) (k) rep- resents their dot- product similarity, and T is the scaling temperature factor.
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Predicting Drug-likeness via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
To introduce prior knowledge of drug similarities, we in- corporate ATC code similarity matrix WATC = [ucgp] where Wij E [0, 1] measures the semantic similarity be- tween drugs and j. The modified loss incorporating WATC becomes a weighted sum over the soft labels (Eq. 1):
Knowledge-Structura Mix (KS-Mix) Interpolates the
knowledge and structural embeddings simultaneously:
CKs(s, =
1 M
EM log - exp(e,Cks/T)
(, kt WATC)= i Em Σラn was (- explac0ky/s) Ete (xplacoks/)))
1 CKS-Mix / (Oks(s, k) Oks(k,s)
(4)
LAACLIP = (CCoaa k. WATC) + Cson (k, 8, WATC)) (1)
Here, instead of assuming hard one-hot target where Wi;i = 1 and Ws.j 0 for i + j (as of the original CLIP loss), the soft labels Wi,j encourage similarity of drug pair embeddings to match their semantic similarity. Details of ATC similarity computation are provided in Appendix C.3.
These interpolations ensure the robustness of embedding space by smoothing the transitions between similar drugs and ensuring embeddings respect the 1.2-norm constraint of the hypersphere.
The final multi modiil alignment loss is a weighted sum:
3.2.2. GEODESIC MIXUP FOR EMBEDDING ALIGNMENT
Several studies have reported the problem of "modality gap" in contrastive learning frameworks including CLIP (Wang & Isola, 2020; Liang et al., 2022). To further improve align- ment of the two domains, we apply geodesic mixup (Oh et al., 2024) to interpolate between embeddings on a hy- persphere, ensuring the points are aligned uniformly in the latent space. Given two points ā and b, the mixup is per- formed along the geodesic path:
mmulti-modul = C CoM
We optimize the parameters of encoders &, and Ex using the Adam optimizer (Kingma, 2014). The trained structure en- coder &, is further utilized to project the chemical structural features into the unified embedding space  for downstream tasks including the drug- likgelikeness boundary generation.
(2 b) ā sin + sinn(( - A)0)
3.3. EM-like Iterative Optimization of Drug-likeness Boundary
sin(O)
where ca b), and Beta(a, a). Within the batch of length M, geodesic mixup interpolates information from data indices and = M - with À and À fraction, respectively. This allows smooth interpolation between data pairs, improving consistency within the latent space.
Once the multi-modal embeddings are aligned into the uni- fied space 44 we define a hyperspherical boundary tent space Z, which is generated by an encoder fe U4 - Z. This boundary is characterized by its center e and radius r, and the goal is to optimize B such that it encapsulates as many drug-like compounds as possible while minimiz- ing the inclusion of non-drug-like compounds, leading to decreased in mn-boundary compound ratio p.
a la-
With our formulation, we introduce three forms of mixup (visualized Figure 11):
Structural Mix (S-Mix) embedding space:
Interpolates within the structural
We formulate the optimization of this drug- diug-likenss bound- ary B an iterative process inspired by the Expectation- Maximization (EM) algorithm. The model adjusts the boundary parameters (a hypersphere with center c E Rd and radius r) in the Expectation (E)-step, while refining the embedding space Z and its encoder so during the Max- imization (M)-step. This allows the boundary to evolve throughout training, with each iteration improving the its compactness and reducing the aalse-positive rate. The full algorithm is provided in Appendix A.I.
1 M
exp(ma sv) o ki/T)
Cs(s,k) k) = M- 1=1
A Alog
ΣjA1 exp(s; 2 k2/T)
exp(mx(Bi,)) BR) ① kv /T)
- (1 - log
En exp(s; 8: @ TT)
Ls (C)(s, + Cs(ks
(2)
Knowledge Mix (K-Mix) Interpolates within the knowl- edge graph embedding space and has the same formula with S-Mix, except that it is applied knowledge embedding- side.
1. EXPECTATION STEP: BOUNDARY UPDATE
In the E-step, we update e and r to enclose x 100% of drug-like compounds, keeping the embedding function fo fixed. Given the set of embedded drug compounds Zdiug = (s(;; 0(0)) x E Xinuy) iteration time step f,
LKMM = (Cx((8)) + Cx 8))
(3)

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Predicting Drug-likenes via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
Drug
Compound
where Aor controls the strength of the out-boundary penalty. This loss iteratively improves the separation between drug- like and non-drug-like compounds, increasing the mar- gin Lamm Exkm Σ & Kamp di d((#comp) - d ((Zu)))) between drugs and compounds (Figure 3).
boundary
Margin
Figure 3: Schematic of latent space optimization during M-step. The margin between drug and compound increased through the update of embedding function using the Lioundry objective.
We show that minimizing the metric loss function (Eq. 5) leads to boundary that encapsulates drug-like com- pounds while excluding non-drug-like ones, improving drug- likeness prediction accuracy:
the boundary parameters are updated as follows:
Theorem 1 (Reduction of in-boundary non-drugs). Opti- mizing a neural network encoder with the distance-basee loss function reduces the number of non-drugs inside the boundary boin-boundary) belween two successive steps i < 12, where ((t1) (ta)) d Lanug and E(u)) (ta).
((+1)
Σ 2:
|Zdrug
# #E
,((+1)
(1 - -c(-((+()l))
(comp!
max
|| c((t2))12).
The proof is provided in Appendix A.2.
= E
Finally, convergence is determined by the in-boundary com- pound ratio P: = | in--boundyyy 1/Xoooyyy//////// The algorithm stops when the change in Pt. between iterations is smaller than a threshold e: |Pt+1 pal < e for Repatience consecutive itera- tions. In addition, a multi-initialization technique is applied to avoid the EM-like models' sensitivity to initialization, further detailed in Appendix A.6.
Here, c(I+1) is the center of the drug-like compounds at iteration ++1 1, ,((+1) is the radius of the smallest hyper- sphere containing Rz 100% of drug- like compounds de- fined by the a-th percentile (Q") of the set of distances ||-- ll=-c(++1] clt+ 112, and rcomp' captures the boundary of all com- pounds. Compounds outside the drug-like boundary are treated pseudo-negatives in the next M-step:
Overall, our EM-like framework iteratively refines the boundary and embedding space, resulting in compact boundary that effectively excludes non-drug-like com- pounds. The knowledge-aligned embeddings of further enhances the model's drug-likeness prediction capabilities.
Nou = for E Keump | d (x: 0) > ,((+2))
where (x; 0, c) = (I (()) - c(t+1))|2 2 is the Eu-
clidean distance from the boundary center.
3.3.2. MAXIMIZATION STEP: EMBEDDING FUNCTION UPDATE
4. Experiments
In the M-step, we optimize the embedding function fo U + Z with parameters 0 to reduce the inclusion of non- drug-like compounds inside the boundary while keeping drug-like compounds near the center. The total loss function consists of two metric terms:
4.1. Setup
Dataset Approved drugs are sourced from DrugBank v5.1.12 (Knox et al., 2024) and removed all withdrawn drugs. 100k non-drug compounds are sampled from ZINC20 (Irwin et al., 2020), limited to clean, annotated entries. We evaluate our model on drug-likenee predition under two split scenarios: scaffold- based and time-based. The scaffold-based split ensures the molecular scaffolds in train, validation, and test sets are mutually exclusive, using the Bemis-Mureko scaffolds (Bemis & Murcko, 1996). This evaluation scheme is applied to measure the models' gen- cralizablilty when an unseen scaffold compound is input, where approved drugs exist extremely sparse in the scaf- fold space (Appendix C.4.1). the time-based split, drugs are partitioned based on their approval year (e.g., drugs ap- proved post-2011 are in the test set), reflect the temporal evolution of approved drug properties (Appendix C.4.2).
1. Drug loss Lunug which encourages drugs to be located closer the center of the boundary:
Larug (8) ExExi, (z 0)
2. Out-boundary loss Lout. which pushes non-drugs la- beled as useudo-negativer during the E-step to the com- pound space boundary:
Coun(0) = EmEx,. max (roomp
(t+1)
(c).
The loss terms can be interpreted as reducing/increasing the samples' distances d(x)) to 0 and r(tt)) for drugs and out-boundary compounds, respectively. We then combine the two loss terms to yield a total loss described as:
Baselines We compare our model to established drug- likeness prediction models: DeepDI. (Lee et al., 2022),
Lavonndary (0) = Lanry(() (8) + Aout Loua (0)
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Predicting Drug-likeness via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
Table 1: Drug-lit like compound identification performance with time-split setting, Mean and standard deviation of 10 fold CV are provided. Best performance and its comparable results (paired t-test p < 0.05) are marked in bold, and second- broodd-bett are underlined. (Avg: Average)
F1 (t)
IDR (1)
ICR (1)
AUROC (1)
Avg. Precision (1)
JP-Similarity-cutolf FP-KNN classifier (Cover & Hart, 1967)
0.389 (0.0388)
0,415 (0.0647)
0.080 (0.0603)
0.681 (0.0041)
0.437 (0.0063)
0.297 (0.0134)
0,986 (0.0032)
0.476 (0.0251)
0.889 (0.0084)
0.331 (0.0208)
FP-SVM (Boser et al.. 1992)
0.665 (0.0126)
0.823 (0.0111)
0.067 (0.0052)
0.963 (0.0021)
0.724 (0.0174)
FP-XGB (Chen & Guestrin, 2016)
0.692 (0.0141)
0.815 (0.0205)
0.055 (0.0048)
0.966 (0.0026)
0.775 (0.0213)
FP-OCSVM (Schölkopf et al., 2001)
0.090 (0.0025)
0.274 (0.0000)
0.489 (0.0101)
0.331 (0.0030)
0,148 (0.0022)
FP-DeepSVDD (Ruff et al., 2018)
0.166 (0.0087)
0.834 (0.0350)
0.840 (0.0381)
0.494 (0.0532)
0.097 (0.0157)
FP-nnPU (Kiryo al., 7)
0.608 (0.0239)
0.789 (0.0367)
0.083 (0.0081)
0.944 (0.0049)
0.706 (0.0261)
FP-PU with NN (Li & Liu, 2003)
0.634 (0.0224)
0.791 (0.0296)
0.072 (0.0079)
0.949 (0.0045)
0.720 (0.0214)
DrugMetric (Li al., 2024)*
0.170 (0.0319)
0.767 (0.1271)
0.760 (0.2028)
N/A
N/A
D-GCAN (Sun et al., 2022)
0.669 (0. 1770)
0.942 (0.0337)
0.160 (0.2808)
0.918 (0. 1396)
0.613 (0.1874)
DeepDL (Lee et al., 2022)
0.740 (0.0584)
0.888 (0.0546)
0.054 (0.0225)
0.979 (0.0114)
0.886 (0.0374)
BOUNDR.E (ours)
0.846 (0.0165)
0.799 (0.0184)
0.009 (0.0031)
0.978 (0.0029)
0.908 (0.0096)
DrugMetric's GMM classifier fails to provide prediction prohabilities for AUROC and Average Precision calculation
D-GCAN (Sun et al., 2022), and DrugMetric (Li et al., 2024), as well as several general machine learning classi- SVM (Boser et al., 1992). XGBoost (Chen & Guestrin, 2016), Naive PU algorithm by Li & Liu (2003) implemented with neural network, nnPU (Kiryo et al., 2017), OC-SVM (Schölkopf et al., 2001), and DeepSVDD (Ruff et al., 2018). We further evaluated the difficulty of dike-liseness predic- tion using naïve nearest-neighbet baselines as lower bound, namely KNN classifier (Cover& & Hart, 1967) and similarity- cutoff approaches. The KNN classifier makes predictions based on k-nearest neighbors, and the similarity-cutoon base- line utilizes the distance to nearest approved drug in the training set, with the threshold value tuned during training. Each general baseline is provided with molecular finger- prints as input features. Implementation details are provided in Appendix C.7, along with discussion on the utility of count-based fingerprints.
well non-drug compounds are excluded. Reported AUROC further measures the models' capabilities in balancing the trade-off between TPR and FPR. In addition, Average Preci- sion (AP), Recall @k and Precision @k k evaluates the quality of recommended compounds (Appendix E.I).
fiers:
As result, our model consistently outperforms binary clas- sifiers, PU learners, and one-class classification models across both split settings. For the time-based split (Table 1), our model achieves the highest F1, AUROC, and AP, demon- strating its ability to adapt to unseen drug-like compounds. Results for the scaffold- based split (Appendix E.2) further confirm the robustness of our approach, highlighting its capacity to generalize across diverse molecular structures.
To further assess performance under more realistic and chal- lenging background distributions, we conducted an addi- tional experiment in which the ZINC-derived non-drug set was replaced with PubChem compounds. As described in Appendix C.5. this setting reflects a closer property distribu- tion to that of approved drugs, thereby posing harder clas- sification task. Across all models, performance degraded under this shift, validating the difficulty of property- matched background (Appendix E.3). Nevertheless, our model ex- hibited strong relative stability, reinforcing its robustness to distributional shifts, generalizing beyond background- specific biases.
4.2. Drug-Likenee Prediction Performances
We evaluate performance of models in distinguishing ap- proved drugs from ZINC compounds under both split strategies-time-bee split and seaffold-based split. We report the results using F1-score MCC, and two metrics: In-boundary Drug Ratio (IDR) and In-boundary Compound Ratio (ICR):
Drugs in boundaryl
IDR
TPR,
Cross-dataset Evaluation We further tested generaliz- ability through cross-compound dataset evaluation. Models are first trained on PubChem or ChEMBL compound sets then tested with the ZINC compounds, with the drug set (DrugBank) and its split setting fixed. As result, binary classifiers and PU-learning frameworks show heavy decline in performances whereas one-class classifers show no effect. BOUNDR.F E. demonstrate only moderate decline in both
Total drugs in test set]
|Compounds in boundaryl
ICR-
FPR.
Total compounds in test set
IDR, equivalent of True Positive Rate (TPR), reflects how well the boundary captures drug-like compounds, while ICR, representing False Positive Rate (FPR), measures how
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Predicting Drug-likeness via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
ZINC
FOMe-spproees
Center
Compound
Drug
2-
1-
0-
In-boundary compound:
un-boundary compound:
In-boundery compound:
In- In-boundary compound: 79/12,000 0. 0.66%
1..308/120000 85.90%
2,494/12 1494/12,00D 20.78%
138/12,000 1. 1.15%
200
200
-300 -200
200
400
-300 200
-100
200
400
-500
-100
100 200 300
(a) Epoch 0
(b) Epoch 33
(c) Epoch 66
(d) Epoch 99
Figure 4: PCA visualization of knowledge-allgneee embedding space and latent space at each epoch of boundary optimization. Box on the upper-left corner displays the space within the drug-like boundary based on PCI and PC2. Red circle and gray triangle display the movement of drug and zinc compound samples respectively, as training proceeds.
Table 2: False-positive rate of toxic compounds. Lowest and its comparable results (paired t-test p < 0.05) are marked in bold.
Table Drug-like compound identification with EM-like bound- ary optimization on embedding space aligned with different align- ment methods. Best and its comparable results (paired t-test < 0.05) are marked in bold.
Withdrawn
Hepatotoxic
Cardiotoxic
Carcinogenic
FP-XGB
0.96 (0.003)
0.96 (0.003)
0.85 (0.010)
0,93 (0.010)
FP-OCSVM
0.69 (0.002)
0.53 (0.003)
0.25 (0.006)
0.86 (0.001)
Alignment method
F1 (1)
ICR (4)
FP-noPU
0.95 (0.009)
0.94 (0.007)
0.87 (0.028)
0.86 (0.017)
No Aligament (only FP)
0.54 (0.032)
0.057 (0.0161)
DrugMetrie
N/A
0.77 (0.073)
0,76 (8.118)
0.82 (0.087)
Manifold Alignment
0.40 (0.045)
0.009 (0.0055)
DGCAN
0.91 (0.020)
0.85 (0.023)
0.88 (0.045)
0,95 (0.017)
CLIP
0.59 (0.022)
0.025 (0.0133)
DeepDL
0.91 (0.016)
0.92 (0.018)
0.85 (0.042)
0.84 (0.025)
Geodesic Mixup
0.69 (0.045)
0.025 (0.0133)
BOUNDR.E
0.51 (0.014)
0.54 (0.009)
0.20 (0.009)
0.19 (0.014)
Ours softCLIP
0.73 (0.037)
0.018 (0.0066)
DDruMMetric fails inler scaffolds present in training datasets
Ours
0.85 (0.017)
0.009 (0.0031)
scaffold-based and time-based splits (Appendix E.4). This result shows the generalizability of our one-class boundary approach by not relying on the non-drug set. Experimental details are available in Appendix C.5.
ingful negatives into the non-drug class. As a result, this intervention induced minor reductions in classification ac- curacy but yielded notable improvements in convergence efficiency and decision boundary structure. Traditional clas- sifiers exhibited heightened sensitivity to the induced class heterogeneity, whereas BOUNDR. E demonstrated greater ro- bustness under these conditions. The comprehensive results and methodological details are listed in Appendix E.5.3.
4.3. Zero-shot Toxic Compound Identification
To test our model's capacity to filter out potentially toxic compounds, we performed a zero-shot evaluation on toxic compound sets including DrugBank's withdrawn drug list and organ-toxicity groups (hepatotoxic. cardiotoxic, and carcinogenic compounds, (Wu et al., 2023)).
4.4. Embedding Space Visualization
As shown in Table 2, our model demonstrates lower false- positive rate compared to bascline models, consistently iden- tifying toxic compounds from diverse categories as out of drug boundary. Furthermore. eтror analysis on the with- drawn drugs reveal that among the 52% false-positive, most of them are withdrawn from some regions yet approved in others. These results indicates that our boundary, along with its integrated biomedical contexts, can effectively generalize to compounds with toxic properties, offering a promising tool for early-stage toxicity filtering. Full table of baseline model performances are provided in Appendix E.5.
Figure 4 displays the evolution of our embedding space as the EM-like boundary optimization proceeds. It is easy to spot that the compounds from ZINC database are be- ing pushed out of the boundary as FDA-approved drugs form more compact space as training epochs increase. The zoomed-in boxes of each epoch further visualizes how the density of ZINC-compounds decreases as the embedding space is optimized. This visualization effectively demon- strates our model's 's ability to iteratively refine the embedding space, making it increasingly more drug-focused over time.
4.5. Ablation Studies
Boundary Regularization via Partial Negatives To in- vestigate the effects of partial negative supervision on bound- ary formation, we introduced a subset of biologically mean-
Effect of Multi-modal Alignment with Softened CLIP Loss We compared our softened CLIP loss with alterna- tive alignment strategies, including CLIP (Radford et al.,
7

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Predicting Drug-likence via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
XGB SVM4 mnFU
Drug boundaly Median
0.5
Distance fron wwi.hhh.cco carccattee
12
0.4
ThrgetDIf
M00D
Investi-
Withdrown
Worls: approved
rDw-
1:1
1:5
1:10
1:50
1:100
getional
OrugCompoonn Rabio
Figure S: Change of Fl score with the decrease in drup-compound ratio of the test set.
Figure 6: Distribution of drug-like scores compound sets in different drug discovery stages.
Table 4: Drug-like like compound identification with different classi- fiers knowledge-aligned space. Best and its comparable results (paired I-test p < 0.05) are marked bold.
4.6. Distance Distribution of Compounds in Diverse Stages
To validate the effectiveness of our distance metric, we analyzed the drug-likeness scores for six compound sets spanning different stages of drug discovery: Al-generated compounds (Targetdiff (Guan et al., 2023) and MOOD (Lee et al., 2023)), investigational compounds and world- approved (ZINC20 (Irwin al., 2020),, withdrawn, and FDA-approved drugs (DrugBank (Knox et al., 2024)).
Aligned space
(f)
ICR (L)
MLP
0.77 (0.020)
0.046 (0.0053)
SVM
0.86 (0.012)
0.050 (0.0050)
XGGB
0.75 (0.012)
0.019 (0.0023)
naave PU
0.82 (0.011)
0.031 (0.0029)
+DeepSDDD
0.32 (0.079)
0.351 (0. 1148)
Ourrs-
EM
0.44 (0.162)
0.259 (0. (0.1931)
Ours
(0.017)
0.009 (0.0031)
Figure 6 shows a clear progression, with compounds mov- ing closer to the center of the drug boundary as they ad- vance through the drug development pipeline. The result reflects the increasing likelihood of drug-like properties as compound matures from early Al-generated candidates to approved drugs. Our model effectively differentiates Al-generated molecules from investigational and approved drugs. This ability to rank candidates based on drug likeless provides a valuable tool for in silico screening, accelerating etrly-stage compound prioritization.
2021), Geodesic Mixup (Oh et al., 2024), naive manifold alignment (Ham al., 2005), and unaligned space (i.e., molecular fingerprints) (Table 3). Our proposed method sigmificantly improves boundary quality due to the enriched representation that aligns molecular structure with biomedi- cal knowledge. The resulting embedding space produces a tighter drug boundary, leading to improved drug-like com- pound identification performances. The full ablation study results including each component of S-Mix, K-Mix and KS- Mix are provided in Appendix E.6, which also support the utility of integrating all the components.
4.7. Application to in silico Targeted Drug Discovery Pipelines
In this section, we demonstrate the utility of our model for initial screening and its potential real-world impact in target- based drug discovery pipeline. Utilizing three well-know anti-cancer targets, BCR-ABI,, EGFR and CDK6, we first generated 10k anti-cancer compounds with pocket-aware generative model (Guan et al., 2023). Then, we compared the filtering capability of our approach with property- -based filters, detailed in Appendix E. The results demonstrate the outstanding filtering ratio of our approach compared to others (Table 5). Additionally, by initially applying BOUNDR.E followed by all other filters yielded approx- imately 0.3% of screened compounds, very practical num- ber for wet lab validations (Figure 7). These outcome il- lustrates how BOUNDR, optimizes the workflow by min- imizing the initial candidate pool for downstream experi- mental validation and simultancously saving computational resources.
Effeet of EM-like Optimization We evaluated the advan- tage of our EM-like boundary optimization against tradi- tional binary classifiers, PU learners, and one-class models (Table 4). Our model achieves the lowest ICR (or FPR), showcasing the strength of iterative boundary refinement, which iteratively increases the out-boundary compounds (Appendix A.3). Figure shows the robustness of our method under increasing
syppound-toddruy ratios (from 1:1 to 1: 1:1))), maintaining performance in more realistic conditions of 1:50 and 1:100 ratios where non-drug com- pounds vastly outnumber drugs.
These ablations confirm the complementary nature of multi- modal aligmment and boundary optimization in improving diug-likeness prediction.
8

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Predicting Drug-likenes, via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
a
Conventional Filters
b
BounDr.E-Integrater Pipeline
12.5% for Experimental validation
0.36% for
Experimental validation
Pred. IC50
PAINS
BounDr.E
Pred. IC50
Ro5
PAINS)
Pocket-based
2,786
1,513
(12.5%)
1,320
300
114
52
(0.36%)
38
Generation (# 10,543)
10,543
10,543
Figure 7: Application case of BOUNDR.FF E in in silico drug discovery pipeline. Integration of BOUNDR. F. for filtering 10,543 pocket-based generated compounds yields realistic number for downstream validation compared to pipeline composed of conventional filters.
Table 5: Number of filtered compounds by different filters.
Table 6: Various traditional drug-likeness measures of Targetdiff generated molecules and filtered sets. Most desirable values are bold. (SAS: Synthetic Accessibility Score; Avg.: Average)
Filtering Method
BCR-ABL
EGFR
CDK6
Total Generated
10,543 (100%)
12,550 (100%)
11,496 (100%)
Target protein
BCR-ABI. (PDB: 1OPJ)
PAINS filter
10,078 (95.7%)
11,878 (94.6%)
10,996 (95. 6%)
Rule of Five
4,997 (47.5%)
6,520 (52.0%)
5,782 (50.3%)
Groups
SAS (L)
Avg. QED (t)
Ro5 ratio (1)
Predicted IC50
2,786 (26.5%)
1,018 (8. 10%)
4,734 (41.2%%
BounDr.E
300 (2.8%)
374 (3.00%)
264 (2.3%)
TargeDDiff 10k
4.956
0.425
0,474
Random sampled*
4,958
0,426
0,475
filters- BounDrFF
(12.588))
491 (3.9%)
2,710 (23.6%)
BOUNDR. filtered
4.930
0.433
0.532
All filters
38 (0.36%)
(0.15%)
(0.40%
RRpeatedd 100 times
Furthermore, downstream analyses reveal that the com- pound list filtered by BOUNDR E exhibits enhanced drug- like properties (Table 6). The filtered compounds show a more distinct distribution compared to the initially generated molecules, with improvements in traditional drug-likeness measures such as QED, Lipinski's s Rule of Five, and Syn- thetic Accessibility Scores (SAS). Additionally, the filtering process demonstrates a higher probability of identifying ex- isting approved drugs, including imatinib (targeting BCR), erlotinib (targeting EGFR), and ribociclib (targeting CDK6) (Appendix F.7.2). The structures of the filtered molecules, along with the most similar structured drugs for BCR-ABL target are provided in Appendix E.9.
utility as initial screen of drug candidates.
Several opportunities for improvement remain in our frame- work. The EM-like strategy still requires solid approaches and theoretical support for reaching global optima, and lower reliance to initialization points. Further experimental validation of the screened compounds, including efficacy, toxicity and PK/PD profiles, may provide more convincing results on the utility data-driven drug filters in drug discov- ery endeavours. In particular, the applicability of our model to specific therapeutic area can be further elaborated.
Extending to the applicability of our model, we believe it will action as reliable early-stage filter within well- characterized chemical spaces, such as me-too drug discov- ery. However, we acknowledge its limitations in general- izing to novel modalities (e.g.. PROTACS) or compounds for rare diseases lacking precedent. Machine learning ap- proaches, trained on historical data, may struggle with novel structures. In such cases, classical rule-based filters remain valuable complements, particularly for evaluating synthesiz- ability and basic drug-likeness, As the diversity of approved drugs expands, we expect machine learning models to im- prove in robustness and generalizability, broadening their applicability in future drug discovery efforts.
Lastly, to test our model's capabilities to be adapted for cancer drug discovery, we trained our model on a narrower training set containing only approved cancer drugs (Ap- pendix E.8). This anti-cancer variant, while showing strict- ness for toxic compounds, provided broader boundary for generated anti-cancer compounds, showcasing our model's potentials to be tailored for specific therapeutic area.
5. Conclusion and Future Works
In this work, we introduced BOUNDR.EE E, a novel frame- work for drug-likeness prediction that combines knowledge- aligned embeddings with EM-like one-class boundary optimization. By leveraging structural and biomedical knowledge through application of softened CLIP loss and Geodesic Mixup, BOUNDR.F E creates a robust multi-modal embedding space. Our experiments show that BOUNDR. consistently outperforms -fate-of-the-ar models, excelling at identifying drug-like compounds while effectively filter- ing out toxic molecules, with case studies demonstrating its
Overall, we believe our model is a promising complemen- tary solution for prioritizing drug-like compounds in early- stage development for efficiency in in silico drug discovery.
A Acknovledgements
The authors thank Jaemin Kim for his contributions during the formulation of this work. This study was supported by the Bio & Medical Technology Development Program of

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Predicting Drug-likeness via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
the National Research Foundation (NRF), funded by the Ministry of Science and ICT, Republic of Korea (RS-2022- NR067933), the NRF grant funded by the Korea government (MSIT, RSS-023-002557799 the Korea Health Technology R&D Project through the Korea Health Industry Develop- ment Institute (KHIDI, funded by the Ministry Health & Welfare, Republic of Korea (RS-2024-00403375)) and Insti- tute of Information & communications Technology Planning & Evaluation (ITTP) grant funded by the Korea government (MSIT, RS-2021-112111 11343, Artificial Intelligence Gradu- ate School Program (Seoul National University) (to S.K.). This work was partly supported by IITP grant funded by the Artifi-
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Impact Statement
This paper presents a novel framework for predicting drug- likeness, addressing critical bottlenecks in Al-driven drug discovery. There are many potential societal consequences of our work, none which we feel must be specifically high- lighted here.
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Predicting Drug-likeness via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
A. Details in EM-like boundary optimization
A.1. Algorithm of EM-like boundary optimization
Algorithm EM-like Training for Drug Boundary Optimization
Require: Dataset X' (æ: | Xdrug + Xcomp, Learning rate 1/o
Convergence tolerance
Ensure: Optimized embedding space parameters 6 and boundary parameters c* r
1: Initialize neural network parameters g(0), boundary parameters c(0), ,(0))
2: + &g (2) where & is pretrained multi-modal structure encoder
12: bousstan where 2 boundaryy : {ar (2com:: 010) c. 12 S r(
3: p(0)
Numol
4: Set =
5: while 1et+1 - pel do
6: E-step (Boundary update):
7: #ding f- f(ztarug (1())
8:
cli+1) [ssmul Σ Zdruug
9:
((++1) -mxx (I|Zarug e(t+
Tcomp <- max (1|2compp et++)) (2)
(b+1)
Identify Xout
11:
M-step (Embedding function update):
12:
Cirug(Ol) elt+1), ((+2)) + Aoo Loo (O(1) c(l-1) c((-1),x((+2) g(t+1) t 0(() To Adam (Vo((o(t), c((t1), ,,,,,, ,((+1)))
Lhreenday
13:
(((+1) 12
where (,( in-boundary : 100 | [ 0(++1)) - cllt2)l12 S p((t11
14:
Nomoll
15:
Increment + t+t+1
16:
end while
17:
Return Optimized parameters 0" r,,r"
A.2. Proof of Theorem
To recap, the M-step of the EM-like iterative optimizes the latent space with the following loss terms:
Langg (0)
Σ
(6)
xE
Lom (0) max
(++1) ccompp
(x 0, c)2
(7)
NE
Liboundary
(0)
Larnug (0) Aout Loul
(8)
where (x: = [[f (())
c(t++)) l2 is the Euclidean distance of samples from the drug center, and Aout is hyperparameter controlling the strength of the out-boundary penalty. The loss terms can be interpreted as reducing/increasing the samples' distances d(x:) to 0 and ((++1) for drugs and out- boundary compounds, respectively.
Theorem (Reduction of In In-boundary Non-drugs). Optimizing a neural network encoder with Euclidean distance loss regress distance of non-drugs toward radius of Teomp and drugs toward O leads to decrease in the number of non-drugs in boundary (iinduuudrryy between two successive time steps t < 1/ where Lrng > d
(t1)
(t2) and g(tt) > (122)
To prove this, we will break down the proof to show that the decreasing nature of r and the inconsistency that arises if the number points inside an arbitrary threshold v increases during the optimization of the Euclidean distance- loss.
Proposition 1 (Shrinkage of r): As the optimization of the Euclidean distance loss proceeds over time, the drug boundary radius defined as the maximum distance of drug-like like points from the center e, decreases.
Proof: Let Rang c d denote the set of drug-like compounds and c E IRd be a center point. The drug loss function Cane (Eq. 6) is given by:
Laigg
Σ d(x:)
Σ (15(;; c||2, NEn
13

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Predicting Drug-likeness via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
where d(x:) represents the Euclidean distance between point f((:;; 0) and c.
The objective of the optimization process is to minimize Lang by penalizing larger distances more severely with the square operation, while attracting points further away from more strongly, and since the Euclidean distance norm is a strictly convex function, any reductions in the loss Lang implies reduction in the distance [x; 0) c/ for each æ E Karug-
While Erug encourages all drug-like points to move toward the center c, this does not guarantee that the point defining the radius (i.e., the farthest point) also moves. However, under typical optimization dynamics and due to the stronger gradient signals applied farther points in convex losses, the maximum distance r' is often reduced. This trend is supported empirically in Figure 9 of Section A.3, where the relative drug radius consistently decreases over iterations.
Lemma 1 (Impact of Compounds Inside to Loai): The contribution to the out-boundary loss Low from points æ with d(æ) < V is greater than the contribution from points with d(æ) 2 V.
Proof: The out- boundary loss Lout (Eq. 7) is given by:
oou (0)
Σ EE
max (Teomp d)z)).0),
where d(x:) represents the Euclidean distance between the compound æ and the center c. Considering the loss contribution of a point x E Non with distance d(æ), the individual contribution to the loss for this point is
L a max (r ('cump d) 0).
So, for points such that a with d(x)) < V with given arbitrary threshold radius, we have
Tcomp d((r)=
Tcomp V.
On the other hand, for points where d((x) S V, we have
Toompp
d(x))= S 'comp" V.
Since the out-boundary loss four is the sum of the individual contributions for each point in Kemmps increasing the number of points for which d(x)) < v will increase the overall loss Leat more than increasing the number of points with d(x) 2 v. Therefore, the points with the threshold radius y contribute more to the loss than those outside. Thus, the contributions of points with d(x)) < is greater than that of points with d(x:) 2 v.
Proposition 2 (Decrease in Points Inside 1/): If the out-boundary loss Lour decreases with each iteration step, that is, ((ta) then the number of points such that d(xx) < v decrease between steps t and iz2 out
c(ta)
Proof: For given iterative steps 1 and 12, assume that the number of points such that d(xr) < v increases between iterative step t2 than at step t1. From Lemma 1, we know that the contribution to the out-boundary loss Lon from points within the threshold is greater than the contribution from points outside v. Specifically, for any point æ where d(x) < v, the contribution to the loss satisfies
steps, meaning that more points fall within the threshold
Toomp
d(xx)
Tcoopp V.
Thus, if the number of points such that d(x:) < increase at step 12, the out- out-boundary loss Lout step 122 should increase relative to its value at step 4, since the points inside v contribution more to the loss. This would imply that the loss at step t2 c(ta). is greater than or equal to the loss at step t1, e(tt).
However, this contradicts the assumption that ((tz) < <(tt) i.e., the loss decreases over steps. Therefore, our assumption that the number of points with d(x:) < v/ increases between iterations is false.
This reasoning suggests that, under the assumption of our loss formulation and typical optimization behavior, a decrease in Loor associated with fewer points falling within the threshold v. This aligns with the empirical trend observed in Figures 8 and 9 of Section A.3, where the in in-boundary compound ratio decreases as optimization progresses.
Corollary (Upper Bound of r): The radius (t1) serves as an upper bound on the maximum distance of drug-like points from the center at t2 where t1 < t2. As ((t:) > p(tz), fewer compounds lie inside this radius at tz implying that the boundary of the drug-like space shrinks and becomes more compact.
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Predicting Drug-likeness via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
Proof: By Proposition 1, the drug boundary radius r, defined the maximum distance of drug-like points from the center, decreases over steps. In other words, p(fz) < r(ti) for l2 > 11, meaning the boundary becomes tighter as the optimization progresses.
And then, by Proposition 2. the number of points such that d(x) < V is decreases over steps for any fixed threshold radius v. This implies that between steps 1 and 12- the number of compounds within the radius r((z)) decreases more than the number of compounds within the radius r(fx).
Since ((t)) encompasses all drug-like points time f and p(ta) < r(tt), we conclude that r(h) remains an upper bound on the maximum distance of drug-like points from the center time t2 even as the boundary shrinks. Therefore, as decreases with step, the drug boundary become increasingly compact, with fewer compounds lying within the shrinking boundary. D
Based on the above proofs, we now move on to the proof of Theorem 1.
Proof of Theorem 1: By Proposition 1, we know that the radius r. which represents the boundary of drug-like points, decreases over steps as the Euclidean distance loss is minimized. This shrinking boundary implies that the space enclosing the drug-like compounds becomes more compact as the optimization proceeds from t to 12-
From Proposition 2, we concluded that if the out-compound loss fou decreases over steps, the number of points inside an arbitrary radius v decreases. Thus, the number of non-drug points within the boundary shrinks as / progresses.
By Lemma 1, the contribution to the out-compound loss Lou from non-drug points inside given radius v is larger than from points outside. Hence, as the number of bo-uouddary points decreases, the out-compound loss decreases, consistent with the assumption that (ft)) (tz)
oou
According to the Corollary 1, the drug boundary radius ((h)) serves an upper bound on the maximum distance of drug-like like points from the center, and this boundary becomes more compact over steps. As (((2)) < r(tx), fewer non-drug points will lie inside the boundary at step 12.
Combining these results, we see that as the optimization proceeds, both the drug boundary shrinks and the number of non-drug points within this boundary decreases. Given that Lanug and Lou both decrease between steps to and i22 conclude that the number of non-drug points inside the boundary (oun-boundayy decreases well.
A.3. Evolution of Boundary Metrics During EM Optimization
The advantage of method lies in its iterative updates both the decision boundary and the encoder. Unlike other classifiers including MLP, which relies on fixed embeddings, our algorithm dynamically adjusts the feature space and boundary across multiple iterations as following:
Iterative improvement of out-boundary compoun
10-
Out-boundaary compounds ratio
0.8
0.6
1. An initial, coarse boundary is set using the contrastive embed- dings.
0.4
2. The encoder refines these embeddings based on feedback from the initial boundary, adjusting the representation.
0.2
3. A new boundary is established using these refined embeddings.
0.0
20
30
40
50
4. This process repeats, allowing the model to fine-tune both the decision criteria and the feature space.
Epoch
Figure 8: Iterative improvement of out-boundary com- pound ratio. Line shows mean over 10 trials; shaded area spans min-max values.
This iterative refinement can also be seen in Figure where the ratio of out-boundary compounds increases and converges over time with each EM iteration. This progressive refinement demonstrates the limitations of a static MLP approach, reinforcing the necessity of our iterative EM-like strategy for accurate boundary learning.
Furthermore, three plots in Figure 9 display the empirical development of boundaries and in-compound ratio per iteration of 10 repetitive experiments. The colored areas are between maximum and minimum values of the repetitions, while the bold line indicate the average value. The left panel display the decrease of relative drug radius (Rarug/ Reamp) over epochs.
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Predicting Drug-likeness via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
Development of Rave/ Resro during Trairing
Development of Rewep and Rang during Training
Development of In Compound Ratio during Training
Minhhax Average
Roce
1.0
Compoounn Rati
1730
Rang
1500
0.8
1250
280
1000
0.2
10
20
30
40
50
60
70
10
20
30
60
50
600
70
0
10
20
30
60
50
60
70
Tpoch
Spoch
Tpoch
Figure 9: Development of boundary radius and in-compound ratio per iteration.
Table 7: Performances of BOUNDR.E with two different convergence metrics. (ICR: In-boundary compound ratio, Avg.: Average)
Convergence metric
F1
IDR (1)
ICR (1)
AUROC (1)
Avg. Precision (1)
Avg. Epochs (L)
Time- split
ICR
0.826 (0.0486)
0.781 (0.0326)
0.012 (0.0086)
0.973 (0.0075)
0.877 (0.0419)
47.7 (4.20)
Looundery
0.833 (0.0463)
0.806 (0.0236)
0.014 (0.0098)
0.973 (0.0071)
0.885 (0.0463)
202.7 (99.20)
Paired t-test p-value
0.737
0.055
0.615
0.956
0.723
Scaffold-based split
ICR
0.655 (0.0209)
0.796 (0.0258)
0.063 (0.0079)
0.938 (0.0049)
0.590 (0.0369)
68.5 (4.39)
Léoundery
0.653 (0.0297)
0.793 (0.0348)
0.063 (0.0059)
0.941 (0.0084)
0.639 (0.0431)
174.2 (21.76)
Paired t-test p-value
0.892
0.594
0.937
0.158
0.040
The center panel display the increase of compound radius (Rcomp) over epochs. The right panel display the decrease of in-boundary compound ratio (ICR) over epochs. These results visualize the non-monotonic increase or decrease of each metric during EM-like drug-likeness boundary optimization.
A.4. Convergence criterion of FM-like optimization
For our EM-like optimization algorithm, we applied convergence criterion based the in-boundary compound ratio (ICR) metric. We initially considered using traditional foss-based convergence criterion, which would directly correspond to the model's objective of distance minimization. However, due to the nature of our distance metric, convergence using a loss-based criterion proved challenging; it occasionally led to expansions or contractions of the latent space that risked numerical instability (e.g., overflow/underflow issues). Consequently, we adopted the mn-oundary compound ratio as the convergence criterion with following reasons.
Theoretical Alignment Following the proof of theorem I in the Appendix A.2, optimizing the distance metric inherently results in decrease in the in in-boundary compound ratio. This proof establishes theoretical link between loss minimization and our chosen convergence criterion, indicating that both approaches are consistent with the model's objectives.
Empirical Stability We conducted experiments to empirically compare the performance of our model when using the loss-based criterion versus the in bo-nduddary compound ratio (Table 7). The results show no significant difference in final model accuracy, with a valuee of 0.737 which is greater than 0.05 based on a two-sided paired t-test, demonstrating that the two methods converge to similar solutions. Furthermore, the average number of training epochs needed for convergence was slightly reduced when using the -n-boundary compound ratio, indicating faster stabilization.
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Predicting Drug-likeness via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
A.5. Computational complexity analysis
In this section, we provide the detailed computational complexity analysis, further supporting our model's efficiency and scalability.
E-step (Boundary Update): The E-step in our model relies on computing the Euclidean distance from the center, with a time complexity linear in both the number of samples (N) and the dimensionality (D) of the data, resulting O(N x D). This ensures that the boundary update is scalable even for high-dimensional datasets.
M-step (Neural Network Optimization); In the M-step, the primary computational effort involves neural network optimization. we denote H as the number of layers, F, as the number of operations in layer ht and N as the dataset size, then the complexity for a forward pass is O(N Σx= Fr). Given that the backward pass approximately twice as computationally expensive, the overall complexity for each EM iteration is O(N x D) + O(N Σ Fa).
These complexities illustrate the model's linear behavior with respect to data size and dimensionality, making it efficient for large-scale drug discovery tasks. To validate these claims empirically, we trained our model with approximately 200 drugs and 2,000 non-drug compounds around 100 epochs using single NVIDIA RTX 3090 GPU, and the total training time was consistently under 5 minutes, demonstrating the alignment between theoretical analysis and practical performance.
A.6. Multiple-EN approach for avoidance of local optima
Avoiding local optima and searching for globally optimal parameters is the core challenge of machine learning. However, classical EM algorithms, including K-means clustering and GMMs, are prone local optima convergence due their deterministic and hill-climbing nature of monotonic increase in likelihood, which leads to the model's sensitivity to initialization conditions.
Our model is optimized through the Adam optimizer, a stochastic approach for gradient descent that allows flexibility in escaping EM algorithm's monotonic increases during training. On top of this, the biomedical knowledge-aligneed embedding space offers an informative initialization point; however, we aimed to develop more direct solution to address the initialization sensitivity of our framework.
Inspired by successful strategies in EM-based models, such as the Multiple Expectation maximizations for Motif Elicitation (MEME) gene motif search algorithm (Bailey & Elkan, 1995), we initialize our boundary optimization process multiple times from different random seeds (for our experiments, 0 ~ 9) and retain the best-performing model based on the validation set performance without any reliance on the test data. This approach has proven effective in enhancing performance by mitigating the risk of poor local optima.
A.7. Problem formulation details and comparison with PU learning
Our problem setting roots on the idea to rescue any non-drugs from the compound libraries by not treating any as 'negative drugs'. This motivation naturally led us to apply an one-class classification based approach.
On the other hand, PU learning typically assumes that the distribution of unlabeled data, Punlabeled, can be expressed as a mixture model: Punlabeled Ppocitive P Pneguiiee This leads training objectives rooted in empirical risk minimization that assume tractable and bounded space of both positive and negative examples with the dataset as representative subset of such space. In this context, PU methods often aim to minimize classification error with cross entropy- based loss functions by estimating the contribution of negative distribution, frequently relying on class prior (ratio of positive/negative in the dataset) estimates.
Conventional methods drug-likeness likeness prediction mainly employ binary classification and sometimes Dositive-Unlabeled (PU) learning frameworks, secking to classify compounds by minimizing the risk of misclassification between positive (drug-like) and negative (non-drug- -ikke examples with cross entropy- objectives. However, these approaches rely on defined negative sets or representative dataset from P Pregative distribution, which may not be feasible in the vast and partially known chemical space.
In contrast, our formulation of the drug-likeness prediction task does not assume a well-defined Pregative. The chemical space is vast, partially explored, and inherently complex. with any sampled "negative" set represspesete of the true distribution of non-drug compounds. Therefore, instead of attempting to estimate a boundary between positive and potential
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Predicting Drug-likeness via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
Table Key differences between binary classification, PU-learning setting and proposed definition rrug-likeness prediction.
Binary classification
PU-learning
One-class Frug-likeness prediction
Decision boundary between
Decision boundary between positive and unseen negative
Boundary around positives
Goal
positive and negative
(here, approved drugs)
Train set composition
Positive Negative
Positive Unlabeled
Drug. Compound
Positive data distribation
Positives (/p (Poomnive
Positives (P posttiie)))
Xanags as subset of X Xcompound
Unlabeled data distribution
(Only negative data)
positive + P negative (unseen)
X
Xcomponn
Assumption of unlabeled dataset
Representative of posiiie and Pregrive
Biased subset of intractable Xecepponnd
Strong reliance to negative set, lower generalizability
Reliance unlabcled set, lower generalizability
Low reliance to compound set, higher generalizability
Characteristics
Risk minimization with cross-entropy
Risk minimization with class prior cross-entropy
Objective
Metric learning (one-class hypersphere)
negatives, we propose a one-class classification framework that constructs a drug- ling-likeness boundary to capture the compact space of drug-like compounds directly, optimized based on distance-based metric learning terms. We summarize the key differences between binary classification, PU-learning and our proposed problem definition of likgliikeneess prediction in Table 8.
B. Initial Study Details
Scaffold-based distribution of approved drugs We analyzed 2,610 approved drugs from DrugBank using the Bemis- Murcko scaffold split, which partitions molecules into rings and the linker atoms between them. This decomposition resulted in 1,324 unique scaffold sets, with an average of 1.97 molecules per scaffold. These findings indicate a well-dispersed distribution of approved drugs in the chemical space, with minimal structural overlap. Notably, 1,074 scaffold sets (81.1%) contained only a single compound, further emphasizing the low scaffold redundancy among approved drugs.
Evaluating how models generalize to unseen scaffolds is crucial given the extreme sparsity of the scaffold distribution and its potential impact on model generalization, which encouraged us to perform a scaffold-based splitting scheme, further detailed in Appendix C.4.
2MC
Deaplonk
20
(a) Fingerprint
(b) GraphMVP
Figure 10: PCA visualization of embedding spaces of approved drugs (red) and 100k ZINC compounds (gray).
Distribution of approved drugs in representation spaces To explore the spatial distribution of approved drugs and non-drug compounds, we represented the structural features of 2,610 approved drugs and 100k ZINC compounds two distinct spaces: Morgan fingerprints and pretrained GraphMVP embeddings (Liu et al., 2022). Morgan fingerprints, a type of circular fingerprint, capture molecular structure by encoding atom environments within a specified radius. Each substructure, or circular neighborhood of bonds, is hashed into a bitstring, where each bit indicates the presence or absence of specific substruetures in the molecule. This approach creates fixed-length binary vector, efficiently capturing the molecular topology. In contrast, GraphMVP uses a GNN-based encoder, pretrained to align 2D and 3D molecular structures, to generate embeddings that reflect both graph-level and spatial information about molecules.
For each representation space, we calculated the center point of the drug embeddings (centroid) and defined the drug boundary as the maximum distance from the centroid to any drug. We then computed the distance of all 100k ZINC compounds from this centroid to determine the in-boundary compound ratio (ICR).
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Predicting Drug-likence via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
Table Distribution drugs compounds the two latent spaces. Max: Maximum; ICR: to-uoundary compound ratio.
Representation
Max. Drug distance
Max. Compound distance
ICR
GraphMVP
29.33
25.78
1.0
Morgan Fingerprint 12.02
10.01
1.0
Our results indicate that all 100k ZINC compounds were positioned within the drug hypersphere in both the Morgan Fingerprint and GraphMVP spaces. Specifically, the maximum distance of approved drugs from the centroid (i.e., the drug radius) was consistently smaller than the maximum distance of ZINC compounds, confirming that non-drug compounds are distributed further from the drug center in both embedding spaces (Table 9).
C. Experimental Details
C.1. Overview of Softened CLIP and Geodesic Mixup
CLIP
Softened CLIP
S-mix
KS-mix &
E
Ex
Knowledge graph embedding
1-1
1-A
0.4
0.1
1-A
Structural embedding
0.1
E
0.1
8.8
0.7
1-1
Label matrix
label matrix
WATC
21
(1 A31
Figure 11: Comparison of contrastive losses using structural encoder & and knowledge encoder & CLIP enforces pair-wise similarity between knowledge graph and structural embeddings from single entity. Softened CLIP allows pair-wise similarity between knowledge graph and structural embeddings to match prior similarity matrix (Wrr)). S-Mix (and -Mix), K--Mix performs antramoodaiiyy interpolation.
C.2. Multi-modal Alignment Spaces
Biomedical knowledge graph space To represent the biomedical context of drugs, we embeddings from DREAMwalk (Bang et al., 2023), which has shown efficacy in tasks of drug-disease association prediction and drug repurposing. DREAMwalk employs a heterogeneous skip-gram model to encode entities from the Multi-scale Interactome (MSI) network (Ruiz et al., 2021) into a 300-dimensional vector space. The MSI network integrates information on drugs, genes, diseases, and Gene Ontology terms, enriching each drug representation with biomedical knowledge. We utilize the embeddings of 1,449 approved drugs from DREAMwalk for alignment with their structural representations.
Molecular Fingerprint Space For the structural representation of drugs, we use Morgan Fingerprints, a widely adopted method that encodes molecular structures based on substructure patterns. this study, we employ 4,024-dimensional Morgan Fingerprints for multi-modal alignment, capturing the structural diversity of the molecules.
C.3. Semantic drug similarity calculation with ATC codes
The ATC classification system categorizes drugs based on their therapeutic, pharmacological, and chemical properties. Each drug is assigned a unique ATC code that reflects its primary mechanism of action and target area. The hierarchy naturally a tree-structured acyclic graph, and on the highest level (Level exists 14 foundational categories, including A (Alimentary tract and metabolism), B (Blood and blood forming organs), C' (Cardiovascular system), and more.
Anatomical Therapeutic Chemical Classification drugs
A direct modeling of such complex hierarchical structure as prior knowledge in model training is challenging. In order to retain the essence the hierarchical ATC relationships without complex adjustments to the architecture that may significantly increase computational overhead and complicate the model training process, we utilized the concept of semantic similarities between terms within the hierarchy and integrated them as prior knowledge to our softened CLIP loss.
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Predicting Drug-likeness via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
Information Content (IC) We adopt the semantic similarity measure introduced by Jiang & Conrath (1997). To quantify the semantic similarity of drugs within the ATC hierarchy, we first need calculate the Information Content (IC) of each entity. IC measures how informative entity is, based on its frequency position within hierarchical structure. For term c, IC is inversely proportional to the number of child terms Nehaa(C), meaning that terms with fewer descendants have higher IC, as they provide more specific information. The IC for a term in a tree-structured hierarchy is computed as:
IC(c) = 1 Mog(aNanna(e) + +1)
log( Vetata (root))
This formulation ensures that IC values are normalized within the range [o, 1], where the root entity has an IC of O.
Semantic Similarity Given two entities ei and 0g and their Most Informative Common Ancestor (MICA), the semantic distance between them is calculated as:
dist(c1, 02) = IC(a) ICC()) - IC(MICA(c) 02))
Since the maximum possible distance is 2 (when IC is 1 for both entities), normalize the distance into similarity score in the range [0, 1) using the following equation:
sim (1, 62) =1 ddist(en (1,
(0))diis(((cc 02)
2
We compute pairwise similarities for all drugs based on their ATC codes, generating similarity matrix S E RR**", where is the number of approved drugs.
C.4. Data splitting schemes
Two data splitting schemes employed to rigorously evaluate model generalizability to unseen compounds: a scaffold- based split, which ensures structurally novel compounds appear in the test set, and a time-based split, where drugs approved after a certain time point are assigned to the test set. Since the structural complexity of approved drugs tends to increase over time, with molecular properties diverging (Stegemann et al., 2023), the time-based split is considered a more challenging evaluation compared to scaffold- based splits.
To simulate real-world drug discovery conditions, where the chemical space is much larger than the number of approved drugs, we follow multi-step procedure: first, split the approved drugs into train- valid-tett sets in 8:1:1 ratio, then sample 10 times the number of test drugs from the 100k ZINC compounds to account for the larger compound space.
C.4.1. SCAFFOLD SCAFFOLD-BASED SPLIT
In drug discovery, scaffold diversity is a key concern, as new drugs often emerge from novel scaffolds that were previously untested. The scaffold-split evaluation aligns closely with these real-world scenarios, making it a more rigorous and realistic test of generalization than a random split, where similar scaffolds are likely to appear in both training and test sets.
Drugs are first grouped based on their scaffolds, defined using Bemis-Murcko scaffolds (Bemis & Mureko, 1996), which capture core molecular ring systems and linkers, ensuring that structurally similar drugs grouped together. Then, the scaffold sets are split into 10 parts for 10-fold cross-validation (CV), with an 8:1:1 ratio for train, validation, and test sets. Each fold ensures that test sets contain unseen scaffolds. The 100k ZINC compounds are also grouped by Bemis-Murcko scaffolds, then split similarly to match the number of drug scaffolds in each fold. For the test set, ZINC scaffolds are sampled to include 10 times the number of drugs.
Our pilot study demonstrates how prediction performance significantly decreases when using scaffold-split compared to randomly splitted setting (Table 10), indicating that the model's ability to handle unseen scaffolds is inherently more challenging. This underscores the necessity of scaffold-split as more appropriate evaluation scheme for understanding the impact of scaffold sparsity and further evaluate the models' generalizability.
C.4.2. TIME-BASED SPLIT
The properties of approved drugs have evolved over the past decades, particularly with the emergence of new therapeutic modalities and technologies. For example, tarnse-t drugs and biologies became prominent in the 2000s, leading
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Predicting Drug-likeness via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
Table 10:
Prediction performances of BOUNDR.E when applied on different split schemes. Our model displays significant decrease in prediction performances when applied with scaffold split, a splitting scheme to evalutate the models' generalizability in the sparse distribution of approved drugs' scaffolds. The best performance and comparable values (p-value < 0.05) are marked in bold.
F1
IDR
ICR
AUROC
Average Precision
soaffold-bused split
0.655 (0.0209)
0.796 (0.0258)
0.063 (0.0079)
0.938 (0.0049)
0.590 (0.0369)
Random split
0.689 (0.0142)
0.742 (0.0291)
0.041 (0.0060)
0.942 (0.0037)
0.663 (0.0379)
Paired t-test p-value
4.4E-4
4.6E-4
1.6E-04
0.082
0.008
to increase in molecular complexity, larger molecular weights, and drugs that often fall outside traditional Rulc-of-5 constraints (DeGoey et al., 2017). Additionally, the advancement of drug delivery systems has allowed for higher range of LogP values (lower solubility) among approved drugs (Vargason et al., 2021).
Drugs are first split based on their approval date, with approximate splits of 8:1:1 for train, validation, and test sets. The cut-off years are 2000 and 2011. Drugs approved before 2000 are assigned to the training set, those approved between 2000 and 2010 the validation set, and drugs approved after 2011 I to the test set. Then, The ZINC compound scaffolds are sampled following the same procedure the scaffold-based split, ensuring 10 times more compounds in the test set.
To validate that our time- based split reflects these temporal trends, we have conducted a detailed analysis of drug properties over the periods represented in our dataset (Table 11). Specifically, we tracked changes in key chemical characteristies (e.g.. molecular weight, LogP, polar surface area) across different temporal splits, observing clear shifts that align with known trends in drug development.
Table 11: Molecular properties averaged over drugs in the train set (approved before 201 and test set (approved since 2011). Drugs in the test set show significant difference from the train set drugs, according to the temporal evolution of approved drugs. (Ro5: Number of passed criterions with the Lipinski's Rule of Five)
Ro5
Molecular Weight
LogP
Polar Surface Area
Train (Before 2011)
3.652739
398. 120084
2.142421
100.041 105
Test (Since 2011)
3.379032
540.368339
2.937724
137.452177
Paired t-test p-value
0.000396
0.000583
0.024349
0.033635
C.4.3. INVESTIGATION ON DISTRIBUTION OF TRAIN/TEST SETS FOR THE TWO SPLIT SCHEMES
To assess the underlying distributional shifts between training and test sets under different dataset partitioning schemes, we analyze the similarity and molecular property distributions in the DrugBank dataset under two commonly used data splitting strategies: time-based and scaffold-based splits.
1.0
DrugBark tran similarity distribution
08-
Pan-
Figure 12 shows the distribution of pairwise Tanimoto similarities between training and test compounds for both splitting strategies. Despite the intuitive assumption that scaffold-based splitting would lead to more structurally distinct test compounds, the empirical similarity distributions are not significantly different (independent t-test = 0.568). This suggests that scaffold split may not always induce a larger domain shift than time split when fingerprint- based similarity is used as indicator for chemical relatedness.
0.27
.0.27
02-
00-
"Ime sp
Scaffild spit
Figure 12: Train-test set Tanimoto simi- larity distribution on DrugBank dataset.
To further explore potential distributional discrepancies, we compare the distribu- tions of key molecular descriptors in the training and test sets under the time- split (Figure 13). Eight uidely-used drug-like property metries are considered, including molecular weight (Mw), number of hydrogen bond donors (HBD), acceptors (HBA), rotatable bonds, aromatic ring count, quantitative estimate of drug-likeness (QED), and synthetic accessibility score (SAS).
The results highlight that, under the time-split setting, the test compounds tend to exhibit distinct physicochemical characteristics from those seen during training. This includes notable shifts in properties such as molecular weight, flexibility, and hydrogen bonding capacity. These shifts imply a latent distributional shift that may not be captured purely
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Predicting Drug-likeness via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
through structural fingerprint similarity. The only property without significant difference is SAS, suggesting that synthetic accessibility remains consistent over time, likely reflecting stable medicinal chemistry practices.
In addition, we investigate the extent of biological overlap between training and test drugs by analyzing their shared therapeutic annotations. Specifically, we quantify how many test-set positive examples (i.e., approved drugs) are associated with the same therapeutic targets or disease areas as those in the training set. Using Anatomical Therapeutic Chemical (ATC) classification codes as an approximation of therapeutic indication, we find that only 9.6% of test drugs share an ATC code with any drug the training set. This low rate of overlap indicates limited therapeutic redundancy across splits and highlights the biological distinctiveness of the test compounds.
Overall, this analysis emphasizes the need to consider multiple facets of molecular distribution-bont structural and physicochemical-wiie evaluating generalization performance. Apparent similarity under one metric (e.g., Tanimoto distance) does not preclude meaningful distributional shifts in other biologically relevant dimensions.
Molecular property distributions of drugs in Time-split Train and Test sets
Mw
AlogP
HBD
HBA
6000
60
5000
40
60
60
3000
40
40
2000
0
20
20
1000
-2
0-
Train
Train
Train
Rot bonds
Aromatic rings
QED
SAS
200
*2**
1.2
12
nn
1.0
150
0.8
8
100
4-
0.6
6
50
2-
2-
Train Test
Train
Test
Train
Test
Traiin
Test
Figure 13: Molecular property distribution of train and test set drugs in time-split setting. (Mw: Molecular weight; HBD: number of hydrogen bond donor, HBA: number of hydrogen bond acceptor, Rot bonds: numher of rotatable bonds, Aromatic rings: number of aromatic rings, QED: quantitative estimate of drug-likeness, SAS: synthetic accessibility score, ns: 5.00c-02 < 1.00c+00, 1.00e-02 < P S 5,00e-02, **; 1.00e-03 < p S 1.00e-02, s*t; 1.00e-04 < < S 1.00e-03, ***:;;; p S 1.00e-04)
C.5. Cross-compound dataset evaluation
We have further performed the performed cross-dataset validation using PubChem and ChEMBL. PubChem contains a vast array of bioassays covering numerous biological targets, while ChEMBL provides curated information on chemical compounds linked to bioactivity against biological targets. These external repositories are widely recognized for their breadth and diversity in assay-centric compound data. We have carefully examined how these datasets complement our original validation set, ZINC20, and their distributions compared with approved drug distribution.
Specifically, first measured the distributions of three key molecular properties in drug discovery: molecular weight (Mw), LogP and polar surface area (PSA) (Figure 14). The distances between the distributions were computed using 1-Wasserstein distance metric, which display the similarity between ChEMBL compounds and DrugBank approved drugs, followed by PubChem then ZINC20 compounds.
However, the pairwise Tanimoto similarity distribution of molecular fingerprint between DrugBank and other three compound sets reveal that PubChem molecules display the highest average similarity (0. 12) compared to ZINC20 11.111) and ChEMBL
22

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Predicting Drug-likeness via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
(0.013) (Figure 15) Overall, the dissimilarity between datasets demonstrate the uniqueness of each database, and these discrepancies necessitate cross-dataset evaluation for testing the generalizability of drug-likeness prediction models.
Mw
LogP
PSA
82.6
24.4
6098
1.0
105.8
1.28
2008
40
6:0
200
2039
80
Drughars
Drughase
Orugbanic
2NC
PutChum
Drugbark
PubChem
Drughantt
PutCham
Figure 14: Distribution of molecular properties of DrugBank, 7INC20, PubChem and ChEMBL datasets. The numbers hetween the distributions represent the Wasserstein distance between the two distributions.
Figure 15: Distribution of pairwise similaritics between DrugBank and compound datasets.
C.6. Model Parameterization and Training Details
The chosen hyperparameter search space (Table 12) aligns with prior work in drug-likeness prediction and molecular property prediction, where 2-3 layers with 256-1024 dimensions are commonly used due to their balance between expressiveness and computational efficiency. The selected configuration was validated through search on a validation set.
Multi-modal alignment Our multi-modal alignment encoders consists of 2-layer multi-layer perceptrons (MLPs) with LayerNorm and ReLU activation. The aligned space set to output wetpppuuddieensssee www.ddiiiiinn55... The model trained using the Adam optimizer (Kingma, 2014) with learning rate=0. 0011 and batch size=32.
EM-like boundary optimization For models requiring boundary optimization, we use 2-layer MLP architec- ture with LayerNorm, ReLU activations, and hidden dimension=512. When generating latent spaces, the nutput.cimension is set to 2. The model is trained with the Adam optimizer (Kingma, 2014) using a Learning 0005 and bat batchhsize==024.
Table Hyperparameter search space and selected values.
Parameter
Search space
Selected value
Alignment hidden dim
[512]
512
Alignment num layers
[2,3]
Alignment.drop.o
[None, 0.1]
0.1
Awoi (Soft CLIP loss weight)
[0.01, 0.1, 0.5, 1]
0.1
Boundary hidden_diin
[128,512,102]]
512
Boundary out dum
[2,16,128.512]
Boundary num layers
layers
[2.3.4]
Boundary _drop_outt
[None, 0.1]
0.1
Boundary learning rate
[le-4, 5e-4, 1e-3]
5e-4
Boundary Boundary_batch batch_size
[256, 512, 1024]
1024
(drug boundary percentile)
[90, 95, 99, 99.9, 100]
95
Aous (out-boundary loss weight)
[0.1, 1.5, 2]
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Predicting Drug-likeness via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
C.7. Baselines
C.7.1. DRUG-LIKENESS PREDICTION MODELS
DrugMetric DrugMetric' (Li al., 2024) an unsupervised drug-likeness prediction model based on JT-VAE (Jin al., 2018) and Gaussian Mixture Models (GMMs). JT-VAE encodes molecules tree-structured graphs of predefined substructures, with the VAE generating latent space that follows Gaussian distribution. Ensemble of GMMs are applied to model this latent space for predicting drug-likeness, and the drug-likeness score is computed using a Wasserstein distance-based metric.
DeepDL. DeepDD.2 (Lee et al., 2022) introduces two models: (1) an unsupervised LSTM-based model for drug-likeness scoring and (2) a PU learning-based Graph Convolutional Network (GCN) for binary drug-likenen classification. The LSTM model predicts the next token likelihood based on molecule's 's string representation, aggregating these probabilities into a drug-likeness score. As this method does not perform strict classification, we focus on the PU learning GCN for comparison.
D-GCAN D-GCAN² (Sun al., 2022) is graph convolution attention network designed for binary drug- likenliseness classification. The model encodes molecular subgraphs into atom-level vector embeddings using graph convolutional layers, followed by graph attention layers, global sum pooling, and dense layers to learn representations from molecular structures. We reproduce results using the official repository.
C.7.2. GENERAL CLASSIFIERS
To comprehensively evaluate our model's performance in drug-likeness prediction, we compare it against range of classifiers for binary classification, PU-learning, and one-class classification tasks. Each model is trained Morgan fingerprint vectors of dimension 1,024 as molecular input representations.
For comparisons with plain MLP-based architectures, we ensured that both our model and the baselines had identical numbers of layers and parameters. Specifically, each baseline was adjusted to match the total parameter count and architectural capacity of our model, ensuring comparable expressibility. For machine learning- based baseline models, we conducted limited search across range of hyperparameters, including number of estimators. This search was performed using cross-validation to ensure that the most effective configurations were applied consistently across all models.
Binary classifiers For binary classification of drugs and non-drugs, compare our model with traditional machine learning classifiers, including Support Vector Machine (SVM) (Boser et al., 1992) and eXtreme Gradient Boosting (XGBoost) (Chen & Guestrin, 2016). XGBoost is pradient-boosting framework that excels in handling structured data and is widely used for molecular property prediction tasks due to its ability to capture complex patterns in sparse input spaces. SVM constructs a hyperplane (or multiple hyperplanes) to separate data points in high-dimensional space, often using a Radial Basis Function (RBF) kernel to model nonlinear decision boundaries. Both models have demonstrated strong performance molecular property prediction, often surpassing neural network-based models for certain biological endpoints (Wu et al., 2023). For XGBoost model, we searched its number of est astimaoos parameter among [50, 100, 200] and chose 100 as the best parameter.
For both the XGBoost and SVM models, we conducted a hyperparameter search over class weighting factors for the positive class, using values in the range {0.5, 1, 2, 5, 10, 50, 1003. The resulting performance differences were marginal and did not yield consistent improvements. Therefore, we report results using the unweighted (i.e., standard) versions of the models as baselines.
PU-learning baselines -utabbled (PU) learning algorithms are well-suited for scenarios where only positive examples (drug-like compounds) and large set of unlabeled examples available. We benchmark our model against two PU-learning methods:
Naive PU (Li & Liu, 2003): This method uses the Rocchio classification algorithm, which computes centroids for
ggithub.com//hii Sun/D-GCAN
24

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Predicting Drug-likeness via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
the positive class and unlabeled set form decision boundary. We adapt this approach with a neural network classifier identical model capture more complex decision boundaries in molecular data.
nnPU (Kiryo et al., 2017): nnPU is an advanced PU-learning algorithm that mitigates overfitting by introducing a non-negative correction term in the risk estimator. This method has shown strong empirical performance in cases where positive and unlabeled data exhibit significant overlap, providing a more robust solution for PU-learning tasks drug discovery.
One-Class Classification Baselines One-class classification methods are designed to distinguish a single target class (e.g., drug-like compounds) from all other compounds without explicitly modeling the negative class. We evaluate the following one-class models:
OCSVM (Schölkopf et al., 2001): One-Class Support Vector Machines (OCSVM) estimate the support of high- dimensional distribution, fitting hyperplane that encompasses most of the positive (drug-like) examples. This is widely used in anomaly detection tasks, including outlier detection in chemical spaces.
SVDD (Tax Duin, 2004): Support Vector Data Description (SVDD) is an extension of SVMs for one-class classification, which minimizes the radius of hypersphere that encloses the positive data points. The method is partieularly effective in constructing compact decision boundaries around the positive class.
DeepSVDD (Ruff et al., 2018): DeepSVDD extends SVDD by utilizing deep neural networks to learn transformation of input data into a latent space, where the decision boundary is optimized. This method is well-suited for handling high-dimensional and non-linear representations of molecular structures, making it a strong baseline for drug-likeness prediction tasks in high-dimensional spaces.
C.7.3. NAÎVE DISTANCE- -AAAEE METHODS
To establish basic performance reference point, we implement two non- con-aaametrric, distance-bar based classifiers that do not rely on any learned representations or parameter optimization. These methods serve as lower-bound baselines and are useful for quantifying the intrinsic separability of the data in the input space defined by molecular fingerprints. Both methods use the Tanimoto distance computed on Extended Connectivity Fingerprints (ECFPs).
K-Nearest Neighbors (KNN) The K-Nearest Neighbors classifier (Cover & Hart, 1967) predicts the label of a test compound by majority vote among its nearest neighbors the training set. Similarity is assessed using the Tanimoto distance over ECFP representations. Although simplistic, this method captures local structure in the chemical space and provides a benchmark for evaluating more sophisticated, appresentationnbasedd models.
Similarity Cutoff (Sim-Cutoff) The Sim-Cutoff classifier makes binary predictions based on the distance between test compound and the most similar approved drug in the training set. Formally, given test compound z, compute:
dyn (I)
2f Etrain drugs d(x, 2'),z);
min
where .((,-) denotes the Tanimoto distance between ECFP fingerprints. The classifier assigns "drug" label if don (x) < Y and "'non-drug" label otherwise. The similarity threshold is hyperparameter, selected using validation set.
This method directly reflects how structurally similar test molecule is to known approved drugs. The Sim-Cutoff baseline offers clear and intuitive measures of out-t--distribution generalization.
D. Notation
Data Sets
Xcomp
the set of all chemical compounds
Xm boundary
the set of non-drugs inside the boundary the set of embodded drug compounds the set of batch data
Xang
the set drug-like compounds
Zang
Xout
the set nseudo-negatives
D
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Predicting Drug-likenes,, via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
Embedding Spaces and Arrays
S
the structural embedding space
uuomp
the structural embedding vector
I
the biomedical knowledge embedding space the unified latent space
Kdrog
the knowledge embedding vector
Z
the latent space at EM-like training
Functions
Eo
structural encoder from space S to U knowledge encoder from space K. to 24 an encoder from space 24 to 2
C(-)
the contrastive loss function
Ex
C())
the loss function
fo
O
the dot-product similarity operator
B
hyperspherical boundary
d(-)
the Euclidean distance from the boundary center
Parameters
the center of the drug-like compounds
P
the in boundary compound ratio the scaling temperature factor learning rate
r
the radius of the smallest hypersphere
T
I Teomp
the radius for compounds
"
t
the number of iteration steps
convergence tolerance arbitrary threshold radius
0
neural network parameters
E. Additional Evaluation Results
E.1. Rank-based evaluation
Since the core concept of our drug-likeness prediction problem lies in treating compound dataset potential drugs, using cessification-centti metrics including F1 score, is not perfectly fit for evaluation of miug-likeness prediction. Since our dataset does not have absolute negative samples, we here provide further evaluation of models using average precision, precision@1 k and recall @k metrics in Table 13. These metrics further measure how well models identify drug-like compounds among the vast chemical space.
Table 13: Drug-like compound ranking performance with time-based split setting. Mean and standard deviation of fold cross-validation are provided. Best performances marked in bold and second-best underlined.
Avg. Precision
Pr
Prec 100
Prec 200
Rec@50
Rec@ 100
Rec@200
FP-SVM
0.724 (0.0174)
0.852 (0.0160)
0.777 (0.0090)
0.540 (0.0067)
0,344 (0.0065)
0.627 (0.0072)
0.871 (0.0108)
FP-XGB
0.775 (0.0213)
0.868 (0.0458)
0.773 (0.0155)
0.538 (0.0117)
0.350 (0.0185)
0.623 (0.0125)
0.868 (0.0188)
FP-OCSVM
0.148 (0.0022)
0.280 (0.0000)
0.180 (0.0100)
0.132 (0.0023)
0. 13 (0.0000)
0.145 (0.0081)
0.212 (0.0037)
FP-SVDD
0.143 (0.0022)
0.240 (0.0000)
0.144 (0.0049)
0.108 (0.0040)
0.097 (0.0000)
0.1 16 (0.0040)
0.174 (0.0064)
FP-DeepVDD
0.097 (0.0157)
0.098 (0.0569)
0.106 (0.0420)
0.101 (0.0274)
0.040 (0.0230)
0.085 (0.0339)
0.164 (0.0442)
FP-nnPU
0.706 (0.0261)
0.846 (0.0457)
0.713 (0.0279)
0.500 (0.0101)
0.341 (0.0184)
0.575 (0.0225)
0.807 (0.0163)
FP-PU
0.720 (0.0214)
0.864 (0.0367)
0.712 (0.0248)
0.502 (0.0147)
0.348 (0.0148)
0.574 (0.0200)
0,810 (0.0237)
DeepDL
0.886 (0.0374)
0.976 (0.0233)
0.846 (0.0393)
0.513 (0.0172)
0.448 (0.0215)
0.777 (0.0390)
0.942 (0.0289)
DGCAN
0.613 1874)
0.512 (0.2461)
0.464 (0.2520)
0.499 (0. 1687)
0.217 (0.
0.393 (0.2126)
0.884 (0.2857)
BOUNDR.E
0.908 (0.0096)
0.988 (0.0098)
0.923 (0.0135)
0.569 (0.0070)
0.398 (0.0040)
0.744 (0.0108)
0.918 (0.0113)
26

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Predicting Drug-likeness via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
E.2. Drug-likeness Prediction with Scaffold Split
Drug-compound identification performances with scaffold split are provided in Table 14.
Table 14: Drug- like compound identification performance with scaffold-split setting. Mean and standard deviation of 10 fold cross-
validation are provided. Best performances marked in hold and second-hest underlined.
MCC (t)
F1 (1)
IDR (t)
ICR (L)
IDR/CCR (f)
FP -P-Similiartyy-cutoff
0.417 (0.1273)
0.567 (0. 1704)
0.114 (0.0536)
FP-KNN classifier
0.315 (0.0179)
0,991 (0.0091)
0.427 (0.0297)
FP-SVM
0.597 (0.0120)
0.597 (0.0090)
0,951 (0.0286)
0.122 (0.0061)
7.798 (0.2746)
FP-XGB
0.599 (0.0166)
0.602 (0.0181)
0,941 (0.0281)
0.118 (0.0112)
8.059 (0.6524)
FP-OCSVM
0.060 (0.1159)
0.179 (0.0582)
0.551 (0.2165)
0.446 (0.0172)
1,223 (0.4332)
FP-SVDD
-0.132 (0.0287)
0,151 (0.0033)
0.881 (0.0203)
0.970 (0.0022)
0.909 (0.0211)
FP-DeepSVDD
-0.120 (0.1607)
0.147 (0.0294)
0.834 (0.1787)
0.938 (0.0423)
0.890 (0.1871)
FP-nnPU
0.546 (0.0213)
0.550 (0.0182)
0.923 (0.0385)
0.146 (0.0110)
6.362 (0.4021)
FP-PU
0.549 (0.0239)
0.555 (0.0188)
0.907 (0.0491)
0.135 (0.0130)
6.776 (0.5185)
DrugMetric
-0.028 (0.0794)
0.160 (0.0238)
0.692 (0.2932)
0.690 (0.3452)
1.115 (0.3095)
D-GCAN
0.599 (0.0340)
0.594 (0.0456)
0.859 (0.0966)
0.109 (0.2808)
8.145 (1.9174)
DeepDL
0.528 (0.0298)
0.523 (0.0403)
0.889 (0.0608)
0.137 (0.0248)
6.661 (0.8857)
BOUNDR.E
0.626 (0.0211)
0.655 (0.0209)
0.796 (0.0258)
0.063 (0.0079)
12.808 (1.4438)
E.3. Drug-likeness Prediction on Time Split with PubChem as Background Set
We evaluate drug-likeness prediction under a temporal split using PubChem as the background compound distribution. Models are trained on the combined DrugBank-Pub PubChem training set and evaluated on a held-out PubChem test set (Table 15).
Compared to the ZINC background, molecules from PubChem exhibit physicochemical properties that more closely resemble those of approved drugs, as previously observed in our molecular profiling analyses. This increased similarity introduces a more challenging classification setting by reducing the distributional gap between positive (approved) and negative (non- -pproved) classes.
Table 15: Performance models on PubChem-time split, The mean and standard deviation of fold-CV on time-split setting are provided. Best performances are marked in bold and second-best underlined.
F1 (1)
IDR (t)
ICR (L)
AUROC (t)
Avg. Precision (1)
FP-XGB
0.364 (0.0174)
0.673 (0.0150)
0.208 (0.0122)
0.810 (0.0080)
0.375 (0.0195)
FP-SVM
0.351 (0.0132)
0.655 (0.0101)
0,213 (0.0114)
0.813 (0.0065)
0.320 (0.0122)
FP-PU
0.345 (0.0168)
0.639 (0.0301)
0.212 (0.0133)
0.791 (0.0118)
0.369 (0.0278)
FP-nnPU
0.311 (0.0168)
0.660 (0.0317)
0.268 (0.0224)
0.767 (0.0141)
0.280 (0.0284)
DeepDL
0.367 (0.0408)
0.804 (0.0473)
0.288 (0.0491)
0.796 (0.0273)
0.212 (0.0300)
DGCAN
0.289 (0.0235)
0.702 (0.0571)
0.255 (0.0365)
0.768 (0.0135)
0.213 (0.0167)
BOUNDR.F.
0.579 (0.2092)
0.685 (0.1 155)
0.199 (0.3540)
0.839 (0.1928)
0.552 (0.2341)
27

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Predicting Drug-likeness via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
E.4. Cross-dataset evaluation results
We extended our experiments to cross-dataset evaluation two additional well-established datasets: PubChem and ChEMBL as training background (non-drug) set, then applied the model to be tested test set with ZINC as background. Both datasets encompass a wide range of chemical scaffolds and molecular properties, making them suitable for testing our model's ability to generalize across varied chemical spaces. As shown in Tables 16 and 17, our model maintains stable prediction performance across these diverse datasets, demonstrating its ability to generalize effectively beyond the trained negative distribution.
Table 16: Drug-like compound identification performance on scaffold-spit setting with cross-dataset evaluation setting. Models are trained using PubChem or ChEMBI. as background, then tested on ZINC as background set. Mean and standard deviation of 10 fold cross-validation are provided. Best performances marked in bold.
PubChem DrugBank
ChEMBL + DrugBank
F1
IDR
ICR
Arg. Precision
AUROC
F1
IDR
ICR
Avg. Precision
AUROC
FPSSVM
0,268 (0.0194)
0.835 (0.0734)
0.434 (0.0174)
0.334 (0.1912)
0.795 (0.0759)
0.371 (0.0519)
0.681 (0.1422)
0,195 (0.0200)
0.494 (0.1982)
0.819 (0.0768)
FP-XGB
0.254 (0.0209)
0.810 (0.0800)
0.451 (0.0197)
(0.1188)
0.773 (0.0741)
0.358 (0.0589)
0.675 (0.141))
0.206 (0.0213)
0.469 (0.1839)
0.814 (0.0784)
FP-OCSVM
0.179 (0.0582)
0.551 (0.2165)
0.446 (0.062)
(0.2777)
0.576 (9.1949)
0.179 (0.0582)
0.551 (0.2165)
0.446 (0.0172)
0.366 (0.2717)
0.576 (0. 1949)
FP-SVDD
0.151 (0.0033)
0,881 (0.0203)
0.970 (0.0022)
0.055 (0.0019)
0.235 (0.0173)
0.151 (0.0033)
0.881 (0.0203)
0.970 (0.0022)
0.055 (0.0019)
0.235 (0.0173)
FP-DeeSVDD
0.147 (0.0294)
0.834 (0.1787)
0.938 (0.0428)
0.080 (0.0146)
0.415 (0.1224)
0.147 (0.0294)
0.834 (0.1787)
0.958 (0.0423)
0.080 (0.0146)
0.415 (0, (0.1224)
FP-enPU
0.244 (0.0182)
0.833 (0.0727)
0,504 (0.0637)
(0.0016)
0.749 (0.0556)
0.327 (0.0625)
0.666 (0.1337)
0.241 (0.0374)
0.360 (0.1999)
0.778 (0.0812)
FP-PU
0,241 (0.0265)
0.664 (0. (0.1219)
0,379 (0.0528)
0.228 (0.0556)
0.702 (0.0550)
0,311 (0.0485)
0.653 (0.1477)
0.250 (0.0311)
0.396 (0.1701)
0,778 (0:0674)
DeepDL
0.170 (0.0199)
0.764 (0.0754)
0.598 (0.0481)
0.092
0.590 (0,0233)
0.195 (0.0389)
0.681 (0.1329)
0.530 (0.1553)
0.102 (0.0196)
(0.0686)
DGCAN
0,213 (0.0232)
0,775 (0.06:43)
0,520 (0.0653)
0,1352 (0.0153)
0.685 (0.0436)
0.314 (0.0620)
0.652 (0.1288)
0.265 (0.2380)
0.211 (0.0601)
0.737 (0.1076)
Ours
0.501 (0.0232)
0.759 (0.0441)
0.126 (0.0148)
0.460 (0.0380)
0,875 (0.0157)
0.513 (0.0451)
0.746 (0.0281)
0.117 (0.0190)
0.435 (0.0889)
(0.0258)
Table 17: Drug-like compound identification performance on Time Split setting with cross-dataset evaluation setting, Models are trained using PubChem or ChEMBL as background, then tested on ZINC as background set. Mean and standard deviation of 10 fold cross-validation provided. Best performances marked in bold.
PubChem DrugBank
CLEMBL- DrugBank
Arg. Precision
ALROC
Arg. Precision
AUROC
EP-SVM
0,223 (0.0466)
0.576 (0.0115)
0.365 (0.0137)
0.177 (0,0085)
0.663 (0.0073)
0.252 (0.0068)
0.385 (0.0029)
0.171 (0.0085)
0,200 (0.0080)
0.624 (0.0077)
FP-XBB
02166 (0.005))
0.575 (0:0165)
0.382 (0.0241)
(0.056))
(0.0098)
0.248 (0.0108)
0.415 (0.0103)
0.198 (0.0139)
0.232 (0.0152)
(0.0123)
FF-OCSVM
0.136 (0.0028)
(0,0000)
0.248 (0.0052)
0.168 (0:0031)
0.371 (0.0025)
0,136 0028)
0,250 (0.0000)
0.248 (0.0053)
0,168 (0.0011)
0,571 (0.0029)
FP-SVDD
0.139 (0.0024)
0.766 (0.0000)
0.947 (0.0034)
0.143 (0.00220)
0.360 (0.0033)
0:139 (0.0024)
0.766 (0.0000)
0.947 (0.0034)
0.143 (0.0020)
0.360 (0.0037)
FP-DeepVVD
0.158 (0.0071)
0.810 (0.0439)
0,860 (0.0344)
0.096 (0.0132)
0,180 (0.0062)
0.158 (0.007))
0,810 (0.0439)
0.860 (0.0044)
0.096 (0.0132)
0,480 (0.0362)
FP-
0,212 (0.0116)
0.621 (0:0130)
0.430 (0.0235)
0.139 (0.0135)
0.632 (0.0144
0.229 (0.0153)
0.417 (0.0033)
0,253 (0.0246)
0.163 (0.0130)
0.616 (0.0215)
FP-PU
0.188 (0.0218)
0.491 (0.1036)
0.381 (0.0941)
0.151 (0.0348)
0.579 (0.0586)
0.217 (0.0285)
0.398 (0.0912)
0:234 (0.0318)
0.176 (0.0310)
0.608 (0.0300)
DeepLL
0,200 (0.0166)
0.786 (0.0618)
0.575 (0.0548)
0.108 (0.0090)
0.621 (0.0285)
0,207 (0.0362)
0.658 (0.0579)
0.506 (0.0707)
0,111 (0.0183)
0.617 (0.0106)
DGCAN
0.256 (0.0377)
0,810 (0.0707)
0.467 (0.1833)
0.155 (0.0267)
0,700 (0.0724)
0,318 (0.0691)
0.639 (0.1352)
0.251 (0.107))
0.220 (6477
0,739 (0.0732)
Ours
0.769 (0.0426)
0.796 (0.0137)
0.029 (0.0125)
0.760 (0.0492)
0,941 (0.0093)
0,816 (0.0149)
0.719 (0.0288)
0.009 (0.0035)
0,870 (0.0149)
0,950 (0.0047)
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Predicting Drug-likeness via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
E.5. Zero-shot Toxic Compound Identification
E. FULL TABLE MODEL PERFORMANCES
We provide the full table of zero-shot toxic compound identification performances on all baseline models in Table 18. DrugMetric in particular fails to yield predictions for withdrawn compound set since JTVAE is capable of encoding only the scaffolds present in the training set, in this case the combined set of ZINC and DrugBank approved drugs.
Table 18: False- False-positive rate of toxic compound groups. The best performances and the comparable values (paired t-test p-value < 0.05)
are marked in bold.
Withdrawn
Hepatotoxic
Cardiotoxic
Carcinogenic
FP-SVM
0.98 (0.001)
0.98 (0.001)
0.86 (0.006)
0.98 (0.002)
FP-XGB
0.96 (0.003)
0.96 (0.003)
0.85 (0.010)
0.93 (0.010)
FR-SVDD
0.95 (0.002)
0.93 (0.002)
0.92 (0.003)
(0.001)
FP-OCSVM
0.69 (0.002)
0.53 (0.003)
0.25 (0.006)
0.86 (0.001)
Fr-DeepSVDD
0.81 (0.022)
0.80 (0.020)
0.87 (0.032)
0.56 (0.063)
FP-PU
0.95 (0.007)
0.94 (0.005)
0.87 (0.021)
0.85 (0.009)
FP-nnPU
0.95 (0.009)
0.94 (0.007)
0.87 (0.028)
0.86 (0.017)
DrugMetric'
N/A
0.77 (0.073)
0.76 (0.118)
0.82 (0.087)
DGCAN
0.91 (0.020)
0.85 (0.023)
0.88 (0.045)
0.95 (0.017)
DeepDL
0.91 (0.016)
0.92 (0.018)
0.85 (0.042)
0.84 (0.025)
BOUNDR.E
0.51 (0.014)
0.54 (0.009)
0.20 (ULIM19)
0.19 (0.014)
"DrugMttric fails to infer scaffolds not present in approved drug and ZINC datasets
E.5.2. ERROR ANALYSIS ON WYTTHRAAWWWTH DRUGS
Partially-withhrrawn drugs ratio
0.7
We conducted an in-depth error analysis on the false- positivve withdrawn drugs predicted as nn-drrug-boundary by our model, identifying trend predictions involving drugs referred to as (partiallywwithdrann drugs that are approved in some regions but withdrawn in others, in contrary to withhrww drugs. This category represents complex cases where the criteria for withdrawal may vary.
Ratio of pathhaallywithhrraann drugs
0.5
0.3
Our analysis across 10 trials revealed significantly higher presence of partially- withdrawn drugs in the bouuudbbu predicted set (61.2%) compared to ones (38.8%) with p-value of 7.8E-3 (paired t-test) (Fig. 16).
0.1
This suggests that our model's predictions reflect real-world complexities in
drug-boundary Out drug-boundary
regulatory approval, while maintaining false positive ratio of 0.52, with 60% of these false positives falling into this murtiall-withhreen category.
Figure 16: Partially- withdrawn drug ratio between in- and out-drug-boundarry sets.
E.5.3. EFFECT OF PARTIAL NEGATIVE-DRIVE BOUNDARY OPTIMIZATION
Based on the idea that incorporating partial negative sets-such as known toxic scaffolds can provide valuable guidance for boundary refinement by encouraging the model to contract more meaningfully, we introduced toxic compounds (total 2,316 hepatotoxic, cardiotoxic, and carcinogenic compounds) into the non-drug training set. This adjustment aimed to influence the decision boundary more explicitly during training.
Interestingly, as shown in Table 19, while this strategy led to modest decrease in classification performance across all due to increased heterogeneity in the negative class it also resulted in significantly faster convergence during training (15% shorter training from average 47.7 epochs to 41.1 epochs). This suggests that even noisy but biologically meaningful negatives can serve as strong regularizers in the boundary contraction process. Furthermore, while ML classifiers (XGBoost and SVM) experienced severe performance drop when heterogeneous toxicity compounds were included in the negative set, our BOUNDR. model showcased its robustness to negative set with only a minor decline in overall
29

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Predicting Drug-likeness via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
metrics. Additionally, the drastic decrease of both IDR and ICR for ML models indicate the overly tight decision boundary formulated via inclusion of toxic compounds, yielding fewer test molecules predicted drugs.
Performances of comparison models with/without toxic compounds as negatives on Scaffold-split setting. Mean and standard Table 19:
deviation of 10-fold CV are provided.
Model (negative set)
F1 (f)
IDR (1)
ICR (L)
AUROC (T)
Avg. Precision (1)
BOUNDR.E E (unlabeled non drugs)
0.655 (0.0209)
0.796 (0.0258)
0.063 (0.0079)
0.938 (0.005)
0.590 (0.0370)
BOUNDR. E (with Tox negatives)
0.601 (0.0390)
0.756 (0.0369)
0.076 (0.0149)
(0.0124)
0,510 (0.0495)
Difference
-0.044
-0.04
0.013
0.028
0.08
FP-XGB (unlabeled non-drugs)
0.602 (0.0181)
0.941 (0.0281)
0.118 (0.0112)
0.972 (0.0120)
0.811 (0.0810)
FP-XGB (with Tox negatives)
0.341 (0.1664)
0.266 (0.1599)
0.023 (0.0060)
0.838 (0.0666)
0.424 (0.1573)
Difference
-0.261
-0.675
-0.095
-0.134
-0.387
FP-SVM (unlabeled non-drugs)
0.597 (0.0090)
0.951 (0.0286)
0.122 (0.0061)
0.971 (0.0120)
0.765 (0.1010)
FP-SVM (with Tox negatives)
0.287 (0.1958)
0.195 (0.1815)
0.004 (0.0019)
0.762 (0.0906)
0.420 (0.1737)
Difference
-0.31
-0.756
-0.118
-0.209
-0.345
E.6. Additional ablation study results
E. EFFECT OF MULTI-MODAL ALIGNMENT WITH SOFTENED CLIP LOSS
Our multi-modal alignment loss encompases four modules; softened-CLIP loss, S and K-mix, and KS-mix. While softened- CLIP loss is designed to integrate prior knowledge as ATC semantic similarity, geodesic mixup- inspireddddddd loss terms- terms-S-mix, the learning of the intermediate space between conflicting representations. Specifically:
K-mix, and
S-mix & K-mix: These loss terms focus on intra-space interpolation within the structural (S-mix) and knowledge-based (K-mix) embeddings, respectively. By encouraging the model to interpolate between known data points, it learns smoother and more continuous embedding space, reducing sensitivity to local conflicts.
This component specifically targets inter-space interpolation, blending structural and biomedical representa- tions. It creates synthetic data points that reflect balanced compromise between structural and biomedical features, enabling the model to harmonize inconsistencies and achieve a unified representation.
KS-mix:
We evaluated the performance of the model by selectively removing each component the final setup (Table 20). The results indicate that each component contributes uniquely to the model's performance. Replacing the softened CLIP loss with the original CLIP loss brought 10 percent point loss in Fl score, highlighting the importance of knowledge integration in our model's 's accurate performances. Removing both S-mix and K-mix resulted in drop of 36 percent points in F1
Table 20: Drug-like compound identification with EM-like boundary optimization on embedding space aligned with alignment method ablations on time-based split scheme. Best performance and comparable values in bold.
Alignment method
F1 (t)
IDR (1)
ICR (L)
AUROC (1)
Avg. Precision (1)
Ours w/ Original CLIP
0.727 (0.0365)
0.670 (0.0605)
0.018 (0.0066)
0.801 (0.0506)
0.755 (0.0481)
Ours w/o S,K-mix
0.466 (0.1705)
0.745 (0.1058)
0.270 (0.3446)
0.818 (0.1825)
0.420 (0.1995)
Ours w/o KS-mix
0.604 (0.2238)
0.858 (0.0734)
0.241 (0.3782)
0.849 (0.2091)
0.576 (0.2546)
No alignment (only FP)
0.539 (0.0324)
0.571 (0.0176)
0.057 (0.0161)
0.907 (0.0144)
0.557 (0.0461)
Ours (softened CLIP + -Si.
0.826 (0.0486)
0.781 (0.0326)
0.012 (0.0086)
0.973 (0.0075)
0.877 (0.0419)
Ours + Multiple-HM
0.846 (0.0165)
0.799 (0.0184)
0.009 (0.0031)
0.978 (0.0029)
0.908 (0.0096)
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Predicting Drug-likeness via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
score, indicating their contribution aligning embeddings across diverse drug classes and scaffolds in each of structural and knowledge spaces. Additionally, without KS-mix, the model showed reduction of 22 percent point in F1 score, underscoring the importance of balanced contribution from both structural and semantic features.
Overall, our results show that the combination of all three strategies yields the best performance, with a synergistic effect that improves both classification accuracy and stability, effectively integrating knowledge and simultaneously resolving conflicts between structural and biomedical spaces.
E.7. Filtering Al-generated anti-cancer molecules
E.7.1. DETAILS ON UTILIZED PROPERTY-BASEL FILTERING CRITERIA
PAINS filter The PAINS (Pan-Assay Interference Compounds) filter is designed to identify and eliminate molecules that are likely to produce false-position results in high-throughput screening assays. These compounds often interfere with biological assays through non-specific mechanisms such as covalent binding, redox activity, or fluorescence interference. The PAINS filter operates by detecting specific substructures known cause assay interference. In our pipeline, each compound is scanned against comprehensive library of PAINS substructure patterns. Compounds that do not contain any of these substructures are considered clean and retained for further analysis. This filter ensures that the remaining molecules have a reduced likelihood of assay-related artifacts, enhancing the reliability of downstream predictions.
Lipinksi's Rule 5
Lipinski's Rule of Five (Ro5) is a widely accepted guideline to assess the drug drug-likeness of molecule based on its physicochemical properties. The rule includes four criteria:
1. Molecular Weight must be less than or equal to 500 Daltons.
2. LogP (Partition Coefficient) must be less than or equal to 5, ensuring favorable lipophilicity.
3. No more than 5 hydrogen bond donors (sum of OH and NH groups).
4. No more than 10 hydrogen bond acceptors (sum of and N atoms).
Compounds that adhere to all four criteria are considered to have favorable pharmacokinetic properties, such as good oral bioavailability and permeation, and are retained for further consideration. By applying this rule, we effectively filter out molecules that are less likely to succeed in later stages of drug development due poor absorption or bioavailability.
Predicted IC50
Binding affinity prediction is critical step for assessing the potential biological activity of a compound. We employed XGBoost models to predict IC50 values, which represent the concentration of a compound required to inhibit a biological process by 50%. These models were trained on bioassay datasets from with IC50 values in ChEMBL database, specifically: BCR-ABL (CHEMBL20966118 18), EFGR (CHEMBL203), and CDK6 (CHEMBL2508) (accessed 16 November 2024).
The input features for these models were Morgan molecular fingerprints, which capture key structural and functional aspects of each compound. Compounds predicted to have an IC50 below 10 μM are classified as "active" and retained. This threshold was selected to balance the need for potent biological activity with the feasibility of further development, ensuring that only promising candidates proceed to subsequent stages of evaluation.
E.7.2. CHARACTERISTICE OF BOURDDYY COMPOUNDS
In this section, we provide detailed experimental results in investigating the potentials of our model as a complementary data-driven filter in a AI-driven rational drug discovery pipeline. To be specific, our model can serve as an efficient, carly-stage filtering tool that can significantly narrow down the search space large chemical libraries, thereby easing the computational burden on subsequent analyses.
We applied our model to filter 10,000 Al-generated compounds from TafgetDiff, using three widely-known anti-cancer targets: BCR, EGFR and CDK6, each targeted by cancer drugs imatinib, erlotinib and ribociclib, respectively. After screening with our drug boundary, we retained 300, 374 and 264 in- boundary compounds for each target. For comparison, we randomly sampled the equal amount of molecules (repeated 100 times) and measured key molecular properties of the filtered drugs, including polar surface area (PSA), molecular weight (Mw), and logP.
31

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Predicting Drug-likenee via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
Mw
PSA
LogP
1000
Imatinib
300
Imatinib
Imatinib
900
10
800
250
700
600
150
500
100
400
300
50
-2
Targetdiff Random
BounDr.E Filtered
Targetdirf 10k
Random sampled
BounDr.E E Filtered
Targetdiff 10k
Random
BounDr
10k
sampled
sampled
Filtered
Figure 17: Distribution of molecular properties of Targetdiff' generated molecules BCR protein pocket (PDB: 1OPJ) and its filtered sets. HOUNDR.E-filtett set shows more distant distribution molecular properties from original 10k molecules.
Table Various traditional drug likeness measures Targetdiff' generated molecules and filtered sets. Most desirable values are bold, (SAS: Synthetic Accessibility Score; Avg.: Average)
Target protein
BCR (PDB: 1OP))
EGFR (PDB: 4HJO)
CDK6 (PDB: 51.21)
Groups
SAS (J)
Avg. QED (1)
Ro5 ratio (t)
SAS ())
Arg. QED (?)
Ro5 ratio (1)
SAS ())
Avg. QED (1)
Ro5 ratio (f)
TargetDifff 10k
4.956
0.425
0.474
5.562
0.410
0.521
5.378
0.384
0.507
Random sampled*
4.958
0.426
0.475
5.586
0.409
0.514
5.353
0.382
0.508
BoUNDR.E filtered
4.930
0.433
0.532
5,477
0.413
0,546
5,523
0.392
0.532
Repeated 100 times
Figure 17 highlights a significant shift in key drug-like properties in the BOUNDR.E E-filterdd compounds compared to randomly sampled compounds generated for BCR. Furthermore, Table 21 shows a marked increase in average QED, Ro5-passing ratio and Synthetic Accessibility Score (SAS), implying the sampled compounds are more drug-like whens cross-measured through conventional metrics. detail, the Wasserstein distance of the three properties from the starting 10k compounds reveal that our filtering strategy significantly alters the distribution of the key molecular properties of filtered compounds (Table 22).
Table 22:
Properties of filtered Targeteiff-generateed generated molecules for three protein targets (BCR, EGFR, CDK6). (W-distance: 1- I-Wasserstein distance)
generated molecules and their distributional distance from to the original distribution of 10k
W-distance from BCR-10k
W-distance from EGFR-10k
W-distance from CDK6-10k
Groups
Mw
PSA
logP
Mw
PSA
logP
Mw
PSA
logP
Random sampled
6.122
2.205
0.058
6.882
2.566
0.099
5,997
5.584
0.266
BOUNDR.E filtered
17.695
1.979
0.187
16.834
2.298
0.168
10.903
5.032
0.135
Repeated times
In addition, the Probability Density Function (PDF) of approved drugs, imatinib, erlotinib and ribociclib among the three properties also increased, implying identifying the approved drugs among the filtered molecules more likely with our filtered set (Table 23).
The Wasserstein distance and Probability Density Function (PDF) of imatinib properties are measured using gaussian KDE, The properties of the approved drugs are computed with rdkit python package.
These findings demonstrate the practical utility of our model filtering Al-generated compounds, enabling efficient virtual screening and improving the quality of early-stage candidates.
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Predicting Drug-likenes, via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
Table 23: PDF of approved drugs with distribution three key molecular properties on different filtered sets, originated from 10k generated molecules for three protein targets (BCR, EGFR, CDK6). (Mw: Molecular weight; PSA: Polar surface area)
PDF of imatinib (BCR)
PDF of Erlotinib (EGFR)
PDF of Ribociclib (CDK6)
Groups
Mw
PSA
logP
Mw
PSA
logP
Mw
PSA
logl
TargetDiff lok
4.00E-03
1.0ZE003
2.26E-01
2.88E-03
5,10E-03
2.14E-01
3.64E-03
9,49E-03
2.06E-01
Random sampled
4.02E-03
1.33-03
2.27
2.841-03
5.05E:03
2.14F-01
3.68E403
9.57E-03
2.06F.01
BOUNDR.E filtered
3.94E-03
1.05E-03
2.32E-01
3,09E-03
5.32E-03
2.26E-01
3.49E-03
8.87E-01
2.18E-01
Repeated 100 times
E.8. Anti-cancer specific BOUNDR.E results
In this section, provide experimental results the anti-cance variant of our model, demonstrating our model's potential real-world impact in targeted drug discovery.
One of the strengths of our one-class boundary approach is its adaptability to domain-specific contexts by relying solely on the input positive labels. To explore this flexibility, we newly designed and conducted a concept study, using anti-cancer drugs. We first filtered our training set to include only drugs classified under the ATC code 'I.' (Antineoplastic and immunomodulating agents), which specifically targets the anti-cancer domain. This narrowed training set of 239 drugs allowed our model learn more focused boundary representative of the anti-cancer chemical space. We investigated this anti-cancer BOUNDR.E model with two scenarios:
Broader boundary for anti-cancer compounds When filtering the 10k generated compounds with anti-cancer target protein pocket as conditions, the anti-cancer-boundary obtained much higher ratio of drug candidates compared to the general drug boundary, which means the model adequately learned the protein target context of anti-cancer drugs (Table 24).
Table 24:
Filtering anti-cancer target-based based generated molecules with general BOUNDR. E and anti-cancee BOUNDR.E models. Approxi- mately 10k molecules were generated and filtered for BCR, EGFR and CDK6, three well kell-known mati-cancer targets. Compared to general BOUNDR.E model, Anti-cances Madi-cancer-BUNDR... model recommends more candidates, according the generated compounds' context.
Filtering Method
BCR
EGFR
CDK6
Total Generated
10,543 (100%)
12,550 (100%)
11,496 (100%)
Anti-cancer BounDr.E
434 (3.9%
434 (3.9%)
495 (4.9%)
General BounDr.E
300 (2.8%)
374 (3.0%)
264 (2.3%)
Strict boundary in toxic compound filtering On contrary and interestingly, false-positive ratio on toxic and carcinogenic compounds was significantly reduced when applying the aeti-cancer-spcffie boundary, highlighting the model's ability to filter out irrelevant or potentially harmful compounds more effectively (Table 25) with more compact boundary, while encompassing the contexts of anti-cancer drugs. The results imply that our model's anti-cancer variant, while providing broader boundary for anti-cancer generated compounds, shows strictness for toxic compounds, tailored for anti-cancer drug discovery.
Table 25: Toxic compound filtering comparison with best performances marked in bold. The anti-cancer BOUNDR.E model displays significant reduction in false positive rate compared to general BOUNDR.E model.
Withdrawn
Hepatotoxic
Cardiotoxic
Carcinogenic
General BounDr.F.
0.523 (0.0414)
0.541 (0.0284)
0.207 (0.0190)
0.208 (0.0436)
Anti-cancer BounDr.F.
0.195 (0.0363)
0.151 (0.029)
0.149 (0.0356)
0.148 (0.0321)
Paired (-test p-val
2.30E-09
6.80E-12
2.20E-04
1.00E-03
33

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Predicting Drug-likeness via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
E.9. Filtered Compounds
Figure 18 visualizes remaining 38 molecules after for BCR-ABL protein. The closest drug and Tanimoto similarity provided.
filtering pipeline TargelDifl-based generation
Mal
byeeretire (028)
Mal 2
Mutorettarnl (0.44
Mi
Mydrocertoone 22.21)
Mai
Lulgrootons (123)
CC
Mal
Momosetine (3.551
Mil
Dupropion (0.7)
Mail
bocalbosard (0:30)
Mail
Benaaepi (0.3)
Demouer (0.22]
Mydrocotsone 30244
Tebyoolio 20.27
Ciootaas (218)
Mol
Mol
Mol 17
Nandrolane (025)
Mel LS
Phone (o3n))
Mel :9
Tobreptan (025)
Mel 20
Lamateseore (2.2))
Mol
Viludoon (0355)
Mei 22
kow 13220
Mel
Meraimute (X24)
Mei 24
Capascon 12.33)
Fenstroend (025)
Keletten 1228)
Olipert J026)
Netpramdd (024)
Mel
3p
Mel
Cho
Mol 23
(B15))
Mcl 34
Mel 25
19321
Mel 35
Voupane (922)
Mel
Deprscaane 1222)
Mel 25
Ipteopen Juzt!
Figure 18: Structures of filtered molecules and their closest drugs molecules generated with Targetdiff using BCR-ABI, pocket structure.
34

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Predicting Drug-likeness via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
E.10. Statistical validation results
In this section, provide the statistical validation results for the tables in the main text (Tables ~ 5), computed with one-sided paired t-test to compare the significance compared to the best performing models (Tables 26 30).
Table 26: Statistical validation for drug-like compound identification performance with time-split setting (Table 1), Mcan and standard deviation of 10 fold CV are provided. Best performance and comparable results (paired t-test p < 0.05) are marked in bold
F1 (1)
IDR (1)
ICR ())
AUROC (1)
Avg, Precision (1)
SVM
1.0
1.0
1.0
1.0
1.0
XGB
1.0
1.0
1.0
1.0
1.0
OCSVM
1.0
1.0
1.0
1.0
1.0
DeepSVDD
1.0
0.9999
1.0
1.0
1.0
unPU
1.0
1.0
1.0
1.0
1.0
naive PU
1.0
1.0
1.0
1.0
1.0
DrugMetric
1.0
1.0
1.0
1.0
1.0
DGCAN
0.9947
Best
0.9311
0.9988
0.8841
DeepDL
0.9999
0.9905
0.9999
Best
0.4459
BounDr.F
Best
1.0
Best
0.07378
Best
Table 27: Statistical validation for cross-dataset evaluation drug-like compound identification performance on scaffold-split setting, trained on PubChem/ChEMBI..c and evaluated with ZINC20 compounds (Table 16). One-sided paired I-test p-values of 10 trials compared to the best model are provided. Best and its comparable performances (paired t-test < 0.05) are marked in bold.
PubChem DrugBank
ChEMBL DrugBank
Train
FI (f)
Average Precision (*)
AUROC (1)
FI (1)
Average Precision (1)
AUROC (1)
1.0
0.9981
0.9985
1.0
0,9204
0.9765
XGB
1.0
0.9714
0,9939
1.0
Best
0,9735
OCSVM
1.0
1.0
1.0
1.0
0.9997
1.0
DeepSVDD
1.0
1.0
1.0
1.0
0.9999
1.0
mnPU
1.0
1.0
0.9999
1.0
0.9976
PU
1.0
1.0
1.0
1.0
1.0
0.9957
DGCAN
1.0
1.0
1.0
1.0
0.9997
0.998
DeepDL.
1.0
1.0
1.0
1.0
0.9999
1.0
BOUNDR.E
Best
Best
Best
Best
0.560
Best
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Predicting Drug-likenes, via Biomedical Knowledge Alignment and EM-like One-Class Boundary Optimization
Table 28: Statistical validation for false-positive rate of toxic compound groups (Table 2). One-sided paired I-test p-values of 10 trials compared to best model are provided. Lowest comparable results (paired I-test < 0.05) are marked bold.
Withdrawn
Hepatotoxic
Cardiotoxic
Carcinogenic
XGB
1.0
1.0
1.0
1.0
OCSVM
1.0
Best
1.0
nnPU
1.0
1.0
1.0
1.0
DrugMetric
N/A
0.9616
0.9995
1.0
DGCAN
1.0
1.0
1.0
1.0
DeepDL
1.0
1.0
1.0
1.0
BOUNDR.E
Best
0.9875
Best
Best
DDrugMetric fails to infer scaffolds not present in approved drug and ZINC datasets
Table 29: Statistical validation for drug-like compound identification with EM-like boundary optimization on embedding space aligned with different alignment meth- ods (Table 3). One-sided paired I-test p-values 10 trials compared to the best model are provided. Lowest and its comparable results (paired t-test p < 0.05) are marked in bold.
Table 30: Statistical validation for drug-like compound identification with different classifiers on knowledge-alignel space (Table 4). Best performance in bold and second best underlined. One-sided paired t-test p-vuuues
model are provided. Lowest and its comparable results (paired t-test < 0.05) are marked in bold.
trials compared
A Aligned space
F1 (f)
ICR ())
Alignment method
(1)
ICR ())
MLP
1.0
1.0
+VV
Best
0.9863
No Alignment (only FP)
1.0
0.7489
XGB
1.0
1.0
Manifold Aligument
1.0
Best
naive PU
1.0
0.9999
CLIP
1.0
0.4685
DeepSVDD
1,0
1.0
Geodesic Mixup
0.9998
0.001325
+Ours EM
1.0
0.9978
Ours - SofICLIP
0.9992
8.50E-06
Ours
0.9816
Best
Ours
Best
9.86E-08
36


Reviews:
[{"review_id": "QTpNq2y02N", "reviewer": "Reviewer_Ha6n", "summary": "This paper proposes a method which predicts drug-like molecules by defining a hypersphere in a latent embedding space. They show promising results at predicting which drugs are clinically approved.\n\n### update after rebuttal\n\nThe authors performed additional experiments and answered my questions. I raised my score to a 4.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We would like to thank reviewer `Ha6n` for their time invested for such deep understanding of our work and also insightful comments. By reading the comments we were able to see how much time and effort you have taken to understand the intentions of our study. Below, we provide point-by-point responses, with all referenced Tables and Figures available in attached pdf at blind repo: https://anonymous.4open.science/r/boundr_e/R/R1.pdf\n\n> **Experimental Designs Or Analyses**  \n1. Thank you for suggesting the use of count-based fingerprints (FPs) (via `use_counts=True`). We additionally ran experiments under this setting for all our baseline and FP-ML methods. Interestingly, as shown in Table 1-1 of the attached link, the performance consistently dropped compared to binary fingerprints for all models. Visualization of FP spaces reveal approved drugs more compactly clustered in the binary FP space compared to the count-based space (Figure 1-1). While this result contrasts with prior expectations, we have not yet been able to fully explore the cause due to timely deadline. We appreciate your insightful suggestion and plan to further investigate potential optimizations or alternative settings in future work. \n\n2. Thank you for this excellent suggestion. We implemented the suggested 1-nearest-neighbor baseline (`Sim-cutoff`), classifying test compounds as drug-like if their maximum Tanimoto similarity to any training-set drug exceeded a tuned threshold γ, using count-based sparse Morgan fingerprints. Following best practices, we used similarity rather than distance since Tanimoto’s metric properties are debated [1]. As shown in Table 1-2, `Sim-cutoff` performed reasonably well, indicating the influence of structural similarity in classification. However, a noticeable performance gap remains compared to our method. We further tested with PubChem as a more challenging negative set and observed a notable performance drop, supporting your point that ZINC-based evaluations may overestimate generalization compared to the PubChem dataset (more discussion on `Questions For Authors` Q1).\n\n> **Other Comments Or Suggestions**\n\nWe appreciate your thoughtful concerns about potential spurious correlations and the possibility that some results may appear “too good to be true.” In response, we conducted additional analyses:\n\n**(1) Dataset Redundancy Analysis:** To quantitatively assess potential overlap in therapeutic targets, we analyzed the pharmacological class overlap using ATC codes. The results show that only 9.6% of test drugs share an ATC code with any training drug, indicating limited therapeutic redundancy. Additionally, the distribution of molecular properties differs significantly (t-test p-val < 0.05) between training and test drugs (Figure 1-2), suggesting low structural redundancy as well.\n\n**(2) Nearest Neighbor Experiments:** Following your helpful suggestion, we implemented a `Sim-cutoff` model and also a KNN classifier using count-based ECFP. Both yielded limited performance across splits (Table 1-3), suggesting this problem does not rely on compound similarity. Interestingly, they performed slightly better on scaffold-split, implying that longitudinal evolution in drug design introduces unique challenges not captured by chemical similarity alone.\n\n**(3) ZINC vs. PubChem Background Set:** Following your valid concern and to test against a more drug-like background, we evaluated our model on PubChem, a dataset with diverse molecular properties than ZINC. Despite the harder setting, our model remained robust (Table 1-4), supporting its generalization beyond simple structural similarity-based models.\n\n> **Questions For Authors** \n1. Thank you for this valuable suggestion. We did analyze the physical property distributions between ZINC and approved drugs (DrugBank), as previously presented in Appendix C.5 and Figure 10. However, we recognize that the appendix was dense and not easy to navigate, and we plan to improve its organization in future revisions.\n\n    The analysis revealed clear distributional differences between DrugBank and ZINC compounds in terms of molecular weight, logP, and atom-type frequencies. These distinctions likely contribute to the strong performance differences, as you noted. To address this, we evaluated our model using PubChem as a more drug-like negative set. As expected, performance dropped to more realistic levels across all models (Table 1-4). These results support your concern that ZINC is a relatively easier negative set, and we plan to include this analysis in the next revision.\n\n2. Yes, we retrained all baseline models using our exact evaluation framework to ensure a fair and consistent comparison. All methods were re-implemented or adapted to use the same training/test splits and molecular features (e.g., ECFP). We made the highest effort to align training conditions across models to support a meaningful evaluation.\n\n[1] Surendran, A, et al. \"Is Tanimoto a metric?.\" bioRxiv (2025).", "claims_and_evidence": "Yes, the claims and evidence seem well-supported.", "methods_and_evaluation_criteria": "Yes, they generally make sense, although I am concerned that the set of approved drugs is small, and there might be train-test set leakage that allows for \"cheating\" to some degree.", "theoretical_claims": "I did not look at the theoretical results in detail, but the claims did not clash with my knowledge about the EM algorithm.", "experimental_designs_or_analyses": "Generally, yes. I had only two concerns:\n\n1. I would like to see all fingerprint methods fit using _count_ fingerprints instead of binary fingerprints, since this reduces the amount of information loss and tends to improve performance in my experience. In `rdkit`'s fingerprint generator I believe you can just specify `use_counts=True`.\n2. I would be curious about \"distance to nearest approved drug in the training set\" as a method, ie $d_{nn}(x) = \\min_{x'\\in\\text{train drugs}} d(x,x')$. The distance function $d$ could be Tanimoto distance between ECFP fingerprints (count fingerprints, no compression, use use rdkit's sparse fingerprint object). The method would predict \"drug\" if $d_{nn}(x) < \\gamma$, otherwise not a drug. The method would have a single hyperparameter to tune ($\\gamma$), which you could fit on the validation set. I suggest this because it would very clearly show how much structural similarity there is between test and training set (this is not clear from the time split).", "relation_to_broader_scientific_literature": "The proposed algorithm has many parts, none of which are individually particularly novel, but the combination and application to drug-likeness is novel as far as I can tell.", "essential_references_not_discussed": "none that I am aware of", "other_strengths_and_weaknesses": "Overall this method is very complicated, but it is explained well and seems to work well for both time splits and scaffold splits. The paper is very thorough and contains a lot of extra experiments in the appendix- well done!", "other_comments_or_suggestions": "I am almost worried that the results are \"too good to be true\", since predicting approved drugs without knowing what the drug should treat should be very hard. I am suspicious that high performance is only possible due to spurious correlations in the dataset. Some possible ideas for correlations are:\n\n- \"me too drugs\": ie clusters of very similar drugs developed by different companies for the same disease\n- families of drugs which are very similar (eg different antibiotics containing rare substructures)\n- Since ZINC is used as the reference set of \"non-drug\" molecules, it is possible that this is not a challenging reference class. As far as I understand, ZINC has a relatively narrow range of molecular weights / logP / etc. Maybe any molecule with a very \"unusual\" feature is very easy to classify as not belonging to ZINC\n\nI suggested a nearest neighbor experiment above which I think could provide some insight into this, and hopefully would not be very much effort to implement.", "questions_for_authors": "- Did you do any analysis of the physical property distribution of ZINC vs approved drugs? Eg molecular weight, logP, atom type freqency\n- Did you retrain all the baseline methods on your exact evaluation dataset?", "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": "6bIrpy60QA", "reviewer": "Reviewer_KY6P", "summary": "This paper tackles the challenge of identifying drug-like molecules amid huge chemical libraries. Unlike previous methods that either rely on hard negative sets or purely structural filters, the authors propose BOUNDRE, an iterative one-class approach that defines a “drug-likeness” boundary around approved drugs. Two key innovations are: (1) Multi-modal embedding alignment of molecular structure and biomedical knowledge using a softened CLIP-style contrastive loss plus geodesic mixup, and (2) EM-like boundary refinement, which tightens or expands the hypersphere of drug-likeness by alternately updating the boundary parameters and the latent-space encoder. The authors demonstrate substantial gains over state-of-the-art baselines on multiple datasets, with better coverage of approved drugs and stronger exclusion of toxic or non-drug compounds. They also highlight real-world utility by applying BOUNDRE to filter AI-generated molecules, yielding a small but drug-favorable subset. Overall, the paper introduces a robust, knowledge-enriched approach for early-stage drug-likeness filtering in modern data-driven drug discovery pipelines.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "### Overall Response\nWe sincerely thank the reviewer `KY6P` for the insightful and constructive comments. We're especially grateful for your thoughtful summary and understanding of our iterative one-class framework, as well as the recognition of our method's contribution to early-stage drug-likeness filtering. Your interpretation of the boundary refinement and multi-modal embedding alignment is spot on, and your encouragement truly motivates us.\n\n> **Questions For Authors:** Have you tried combining partial negative sets (e.g., known toxic scaffolds) to accelerate boundary contraction or offset local optima?\n\nThank you for this excellent and thought-provoking suggestion. We agree that incorporating partial negative sets—such as known toxic scaffolds—can provide valuable guidance for boundary refinement by encouraging the model to contract more meaningfully.\n\nMotivated by your idea, we conducted additional experiments in which we introduced toxic compounds (total ~2,316 hepatotoxic, cardiotoxic, and carcinogenic compounds) into the non-drug training set. This adjustment aimed to influence the decision boundary more explicitly during training.\n\n**Table 2-1. Performances of comparison models with/without toxic compounds as negatives on Scaffold-split setting.** Mean and standard deviation of 10-fold CV are provided.\n|  | F1 (↑) | IDR (↑) | ICR (↓)| AUROC (↑) |Avg. Precision (↑)|\n|-|-|-|-|-|-|\n| **BounDrE** (original) | 0.655 (0.0209)  | 0.796 (0.0258)  | 0.063 (0.0079)  | 0.938 (0.005) | 0.590 (0.037) |\n| **BounDrE** (with Tox negatives) | 0.601 (0.0390) | 0.756 (0.0369) | 0.076 (0.0149) | 0.910 (0.0124) | 0.510 (0.0495) |\n| Difference | -0.054 | -0.040 | 0.013 | -0.028 | -0.080 |\n||\n| **FP-XGB** (original) | 0.602 (0.0181)  | 0.941 (0.0281) | 0.118 (0.0112) | 0.972 (0.012) | 0.811 (0.081) |\n| **FP-XGB** (with Tox negatives) | 0.341 (0.1664) | 0.266 (0.1599) | 0.023 (0.0060) | 0.838 (0.0666) | 0.424 (0.1573) |\n| Difference | -0.261 | -0.675 | -0.095 | -0.134 | -0.387 |\n||\n| **FP-SVM** (original) | 0.597 (0.0090)  | 0.951 (0.0286)  | 0.122 (0.0061) | 0.971 (0.012) | 0.765 (0.101) |\n| **FP-SVM** (with Tox negatives) | 0.287 (0.1958) | 0.195 (0.1815) | 0.004 (0.0019) | 0.762 (0.0906) | 0.420 (0.1737) |\n| Difference | -0.310 | -0.756 | -0.118 | -0.209 | -0.345 |\n||\n\nInterestingly, as shown in Table 2-1, while this strategy led to a modest decrease in classification performance across all models—possibly due to increased heterogeneity in the negative class—it also resulted in significantly **faster convergence** during training (15% shorder training from average 47.7 epochs to 41.1 epochs). This suggests that even noisy but biologically meaningful negatives can serve as strong regularizers in the boundary contraction process. \n\nFurthermore, while ML classifiers (XGBoost and SVM) experienced severe performance drop when heterogeneous toxicity compounds were included in the negative set, our BounDrE model showcased its robustness to negative set with only a minor decline in overall metrics. Additionally, the drastic decrease of both IDR and ICR for ML models indicate the overly tight decision boundary formulated via inclusion of toxic compounds, yielding fewer test molecules predicted as drugs. We plan to include these results, supporting the necessity of iterative one-class boundary optimization for minimizing reliance on negative set, in our future versions.\n\nWe truly appreciate your insightful question, which has opened up a promising new direction in our research.", "claims_and_evidence": "Several claims with their evidence:\n\nKnowledge integration via alignment of structural embeddings with a biomedical knowledge graph is crucial - Ablation shows performance drops significantly if the knowledge alignment or geodesic mixup steps are removed.\n\nIterative (EM-like) boundary approach consistently outperforms static classification (e.g., MLP, GCN） - visualizations of the embedding space show non-drug compounds increasingly pushed out with each iteration, and performance is stable even when negative examples are sampled from different databases.", "methods_and_evaluation_criteria": "make sense", "theoretical_claims": "no theory", "experimental_designs_or_analyses": "it is sound. pretty extensive.", "relation_to_broader_scientific_literature": "Builds on lines of GNN-based or VAE-based drug-likeness scoring (DeepDL, D-GCAN, DrugMetric).\nConnects to broad usage of one-class classification for anomaly detection, adapting it to a drug-likeness boundary context with iterative re-embedding.", "essential_references_not_discussed": "NA", "other_strengths_and_weaknesses": "Strength:\n- Data-driven solution for drug-likeness that avoids questionable negative sets.\n- Iterative boundary approach is intuitive and stable.", "other_comments_or_suggestions": "NA", "questions_for_authors": "Have you tried combining partial negative sets (e.g., known toxic scaffolds) to accelerate boundary contraction or offset local optima?", "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": "MGRMZg1aoK", "reviewer": "Reviewer_CLET", "summary": "This paper presents a novel approach for estimating the drug-likeness of compounds. Drug-likeness refers to a compound's potential to become a successful drug, factoring in its synthesizability, bioavailability, and safety. Many existing drug-likeness estimators rely on basic physicochemical properties or structural patterns. Some methods utilize machine learning models trained on datasets of drug-like and non-drug-like compounds. However, representing the negative class adequately poses challenges. To address this, the authors suggest employing one-class classification, labeling drug-like compounds as positive examples. The method involves two molecular representations that are integrated into a single representation space. The structural encoder uses Morgan fingerprints, while the knowledge-based representation employs DREAMwalk, developed from knowledge graphs of drugs, targets, and diseases. Following this, a one-class decision boundary is established using an EM-like algorithm that iteratively adjusts the boundary and pushes negative examples outside it. Experimental results indicate that this approach effectively identifies drug-like molecules within large compound libraries. Furthermore, the model can be applied in a zero-shot context to detect toxic compounds.\n\n## update after rebuttal\n\nThe Authors addressed all my comments and provided additional results. I decided to increase my score to 4.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you, reviewer `CLET`, for your time and thoughtful comments. We sincerely appreciate the depth of your understanding and the effort you invested in reviewing our work. Below, we provide point-by-point responses, with all referenced Tables and Figures available in attached pdf at blind repo: https://anonymous.4open.science/r/boundr_e/R/R3.pdf\n\n> **Methods And Evaluation Criteria** \n1. Thank you for raising this important point. To assess redundancy between drugs approved before and after the time cutoff, we computed pairwise Tanimoto similarity between test and training drugs in the time-split setting and found low median similarity of 0.27. As shown in Figure 3-1, the similarity distributions between time-split and scaffold-split were not significantly different (t-test p = 0.568), suggesting that high performance is not due to scaffold-level redundancy. Figure 3-2 also shows the discrepancy between train-test drug sets’ molecular property distributions. Further analysis (see `Questions For Authors` Q2) support the low redundancy of pharmacological overlap.\n2. We appreciate your insightful suggestion. Based on our prior analysis (Appendix 3, Figure 10), we identified PubChem as the non-drug dataset most similar to DrugBank in key molecular properties. Motivated by this, we evaluated our model using PubChem, instead of ZINC, as a negative set and observed a significant performance drop across all models (Table 3-1), confirming that property-matched negatives present a more realistic challenge. We plan to include these results and extend the evaluation to all baselines in the next version.\n3. Acknowledging this important point, we conducted additional experiments using class-weighted versions of XGBoost and SVM to mitigate class imbalance. We tested various weight ratios, and found that assigning 0.5 or 2.0 weight to the positive class yielded modest improvements in some metrics (Tables 3-2 and 3-3). While the improvements were not significant to change the overall performance ranking, this adjustment did help investigate the bias of models toward the majority class and effect of class weighting for balanced drug-likeness predictions.\n\n> **Theoretical Claims**\n\nThank you for carefully examining our theoretical analysis and highlighting these important points. We agree that the provided theoretical discussions are primarily intuitive sketches rather than rigorous proofs, and some scenarios indeed depend on the stochastic nature of our EM-like optimization arising from SGD-based neural network training. To *empirically* support these claims, we have now included experimental figures demonstrating the gradual shrinkage of the radius and the consistent decrease of the loss terms over iterations (Figure 3-3). We will tone down our manuscript from 'proofs', clarify these additional cases and emphasize more on empirical evidence in revised version.\n\n> **Other Strengths And Weaknesses**\n1. Thank you for highlighting this essential aspect. We have included the structures of the filtered molecules, along with the closest approved drug pair, in Figure 3-4 of the link. We also plan to integrate in the future versions of the manuscript.\n2. This is an excellent suggestion. To evaluate whether our method overfits to chemotype-specific features, we replaced Morgan fingerprints with Mordred descriptors, which include 697 general physicochemical and topological descriptors.\n\n    As shown in Table 3-4, this substitution led to a consistent performance drop across all models, including ours as well as other fingerprint-based baselines. This suggests that general descriptors may carry less discriminative signal for the task of drug-likeness prediction compared to substructure-based encodings. We appreciate your suggestion, which has helped broaden the scope of our evaluation.\n\n> **Questions For Authors**\n1. Thank you for raising this critical point, which aligns with the core challenges of data-driven drug discovery. We agree that models trained on known drugs may struggle to generalize to novel modalities, like PROTACs. Our approach is intended as a robust early-stage filter for well-established chemical spaces, such as me-too drug discovery. We view classical rule-based methods as complementary, especially for assessing compounds in unexplored spaces. As the field evolves and more diverse drugs are approved, we expect machine learning approaches to become more broadly applicable. We will incorporate this essential perspective in the Discussion section.\n2. We appreciate this excellent and specific suggestion. We agree that assessing similarity between training and test positives is key to evaluating generalization. Extending from Q1 of `Methods And Evaluation Criteria`, analysis on potential biological overlap show only 9.6% of test drugs shared an ATC code with any training drug, suggesting limited therapeutic redundancy. These results support that our model’s performance is not due to trivial similarity or duplication.", "claims_and_evidence": "The claims are convincing. Most experiments were conducted multiple times, e.g. using 10-fold cross-validation, and the standard deviations are reported. Most of the results are also supported by statistical tests, where all comparable results are marked together instead of just the highest number.", "methods_and_evaluation_criteria": "The proposed method presents an intriguing and novel approach for predicting drug-likeness. First, representations from two modalities are aligned using the innovative softened CLIP loss and geodesic mixup introduced by Oh et al. Next, a one-class classifier is trained by adjusting a hypersphere that separates drug representations from other compounds through an EM-like procedure.\n\nThe evaluation of the method is rigorous, and the datasets and metrics are selected carefully to address the problem. There are a few potential flaws in the experiment design that may reduce the impact of the presented results:\n1. In the time-split setup, the set of test drug-like compounds remains the same, while only the ZINC subset differs. It would be interesting to see how similar the testing drug-like compounds are to those known before the time cutoff.\n2. Given the vast chemical space represented by ZINC, most sampled compounds are likely unlike known drugs. A more challenging evaluation could involve sampling ZINC specifically around known drugs, e.g. further narrowing this space to compounds with comparable weight, numbers of rotatable bonds, and hydrogen bond donors and acceptors, among other factors, to those of known drugs.\n3. According to Figure 5, the class imbalance leads to a degradation in the performance of classical models such as XGB and SVM. However, it is unclear whether any class balancing strategies were utilized. The low F1-score of these models may result from their tendency to primarily predict one class when trained on imbalanced data.", "theoretical_claims": "I reviewed the proof for the theorem proposed in the paper. The intuition appears to be sound, but it functions more as a sketch of the proof. Some scenarios are not addressed. For instance, in Proposition 1, it is claimed that if $\\mathcal{L}_\\text{drug}$ decreases, the radius decreases as well. However, it is possible that all compounds except the one at maximum distance that defines the radius are moving toward the center, resulting in a decrease. Why are we confident that the farthest point is also moving toward the center? Depending on the selection of function $f$ and the joint optimization with $\\mathcal{L}\\_\\text{out}$, this point may remain in place.\n\nSimilarly, the proof of Proposition 2 does not describe some important cases. The proof is based on a vague term of \"greater contribution\" of points, for which $d(x)<\\nu$. However, these points may also not move while multiple points for which $d(x) \\geq \\nu$ move towards the radius. In that case, the assumption $\\mathcal{L}^{(t_2)}\\_\\text{out} < \\mathcal{L}^{(t_1)}\\_\\text{out}$ is not contradicted.\n\nPlease, clarify if my understanding is correct. Perhaps these cases could be discussed in the text.", "experimental_designs_or_analyses": "The experimental design is adequate to the posed research questions.", "relation_to_broader_scientific_literature": "Drug-likeness prediction remains an unresolved issue tied to a broader question: what defines a good drug? I believe the suggested on-class classification approach is sensible, considering the challenge of identifying negative examples. The results are promising and show that the proposed model can be useful in multiple setups. I am only concerned that machine learning methods may be biased towards the structures of a few known drugs and may fail to identify novel compounds that could be useful as drugs in the future (more details in Questions for Authors and Methods and Evaluation Criteria).", "essential_references_not_discussed": "Key references have been discussed.", "other_strengths_and_weaknesses": "Most strengths and weaknesses have been described in the other sections. Another strength of this work is the code shared along with the paper to ensure these results are reproducible. Some other potential weaknesses:\n1. The set of 34 compounds resulting from filtering the generated molecules has not been analyzed. These molecules could be presented in the supplementary materials as qualitative results, and their similarity to known drugs could be measured.\n2. The structural encoding is based on Morgan fingerprints. Other encodings using more general descriptors could be tested to see if this method is not overfitting to known chemotypes.", "other_comments_or_suggestions": "1. There is a typo in line 34: \"Dues to these challenges...\"\n2. Typo in line 609, \"in the loss $\\mathcal{X}\\_\\text{drug}$\" (should be $\\mathcal{L}\\_\\text{drug}$).", "questions_for_authors": "1. While the idea of using one-class classification is intriguing, I have concerns about the applicability of such methods. Machine learning techniques rely solely on known drugs, and in the future, molecules with entirely different structures may be proposed, including compounds for rare diseases that currently lack approved treatments. Ultimately, what matters for a molecule's success is its safety, efficacy, and, at the early stages of development, its synthesizability. Do you think machine learning methods will yield more robust results for novel chemical structures, or do classical filtering methods (like rules similar to the rule of 5) still need to be employed?\n2. Have you compared the training and testing sets of drugs to see how similar these compounds are to one another? This comparison could resemble Figure 11 in the supplementary material, focusing specifically on the positives from the training and testing sets in the time-based split. It would also be interesting to see how many testing positives were developed for the same target or disease as those in the training set.", "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:

Meta-review: The paper introduces BounDrE, a model for predicting drug-likeness which creates a hypersphere around known drug-like compounds, iteratively pushing non-drug-like compounds outside the sphere using a EM-like process. Experimental results point at the effectiveness of the approach in identifying drug-like molecules in large compound libraries.

The paper was well received by the reviewers: two of them improved their initial score to accept (4) after the rebuttal. Overall, the paper has been praised for the novelty of the approach, as well as the width and depth of experimental part.

I recommend acceptance.
Decision: Accept (poster)