I2Mole: Interaction-aware Invariant Molecular Learning For Generalizable Property Prediction
Authors: Wenjie Du
Jiahui Zhang
Xuqiang Li
Sihan Wang
Zhengyang Zhou
hongxin xiang
Jun Xia
Ye Wei
Yang Wang
Venue: ICLR 2026 Poster (2026)
Keywords: Molecular relationship learning; Drug-drug interaction; graph information bottleneck
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)

Abstract: Molecular interactions are a common phenomenon in physical chemistry field, which could produce unexpected biochemical properties harmful to humans, such as drug-drug interactions. Machine learning has the potential to deliver rapid and accurate predictions. However, the complexity of molecular structures and the diversity of molecular interactions could undermine model prediction accuracy and hinder generalizability. In this context, identifying core invariant substructures (\textit{i.e.}, rationales) has become essential for enhancing interpretability and generalization. Despite notable efforts, existing models often neglect the molecular pairs’ modeling, leading to insufficient capture of interaction relationships. To address these limitations, we propose a novel framework, \textbf{I}nteraction-aware \textbf{I}nvariant \textbf{Mole}cular learning (I2Mole), for generalizable property prediction. I2Mole meticulously models atomic interactions such as hydrogen bonds by initially establishing indiscriminate connections between intermolecular atoms, which are subsequently refined using an improved graph information bottleneck theory tailored for merged graphs. To further enhance model generalization, we construct an environment codebook by environment subgraph of the merged graph. This approach not only could provide noise source for optimizing mutual information but also preserve the integrity of chemical semantic information. By comprehensively leveraging the information inherent in the merged graph, our model accurately captures core substructures and significantly enhances generalization capabilities. Extensive experimental validation demonstrates the efficacy and generalizability of I2Mole. The implementation code is available.

Published as a conference paper at ICLR 2026
I2MOLE: INTERACTION-AWARE INVARIANT MOLEC- ULAR RELATIONAL LEARNING FOR GENERALIZABLE DRUG- DRUG INTERACTION PREDICTION
Wenjie Dul.2 Jiahui Zhang 1.2 Xuqiang Li Sihan Wang
Hongxin Xiang*
Jun Xia
Ye Wei Yang Wang
1 School of School of Software Engineering, University of Science and Technology of China (USTC)
2 Suzhou Institute for Advanced Research, USTC
3 State Key Laboratory of Precision and Intelligent Chemistry, USTC
4 Hunan University 5 Westlake University 6 City university of Hong Kong
(duwenjie, kongping, xuqiangli) J @ mail. .stc.e yeweiastronomer @mail..cmmmmmmmmmm xianghx @ @hnu.edu.cn xiajun @ westlake. end..nn angyan@ustc.edu.cn
ABSTRACT
Molecular interactions are common phenomenon physical chemistry, often resulting in unexpected biochemical properties adverse to human health, such as drug-drug interactions. Machine learning has shown great potential for predicting these interactions rapidly and accurately. However, the complexity of molecular structures and the diversity of interactions often reduce prediction accuracy and hinder generalizability. Identifying core invariant substructures (i.e., rationales) has become essential to improving the model's interpretability and generalization. Despite significant progress, existing models frequently overlook the pairwise molecular interactions, leading to insufficient capture of interaction dynamics. To address these limitations, we propose 12Mole (Interaction-aware Invariant Molecular learning), a novel framework for generalizable drug-drug interaction prediction. 12Mole meticulously models atomic interactions by first establishing indiscriminate connections between intermolecular atoms, which are then refined using an improved graph information bottleneck theory tailored for merged graphs. To further enhance model generalization, we construct an environment codebook by environment subgraph of the merged graph. This approach not only could provide noise source for optimizing mutual information but also preserve the integrity of chemical semantic information. By comprehensively leveraging the information inherent in the merged graph, our model accurately captures core substructures and significantly enhances generalization capabilities. Extensive experimental validation demonstrates 12Mole's ss efficacy and generalizability. The implementation code is available at https:/aaaooyymouu...oco/TToDooo
INTRODUCTION
The molecular interaction process can give rise to additional physical or chemical properties when two or more molecules are combined (Varghese & Mushrif 2019 Chen 2025 Low et al. 2022a] Chen &
Shi 2025). This phenomenon is common the fields of physies, chemistry, and medicine etc., such as changes in Gibbs free energy during dissolution (i.e., solute- pair) (Chung et al., 2022a Fang et al. 2024 Xia et al. 2023) and synergistic or adverse reactions between drugs (i.e., drug-drug pairs) (Lee et al. 2023b Klemperer 1992h. Due to the complexity of molecular structures and the diversity of molecular interactions, conventional modeling approaches are limited and susceptible to noise, undermining prediction accuracy. Meanwhile, they lack generalizability and reliability severely limits their applicability. Based on this, mining the invariant core substructures of molecules (i.e., rationale) has become a widely accepted strategy to enhance both interpretability and generalization like the CGIB (Lee et al. 2023a) and MoleOOD (Yang et al. 2022h).
"oorreponndng Author

---

Published as a conference paper at ICLR 2026
(a)
Drug pair
(b)
Independent
(c)
Interactive
PRO
VER
Rationale
Rationale
Cardiovascular Therapeutic Drugs
Affecting Neurons (effective)
Adverse effects (harmful)
An Example of molecular interactions. (a) Propranolol (PRO) and Verapamil (VER) are widely prescribed cardiovascular therapeutic agents; (b) each drug is influenced by distinct core substructures to achieve affect; (c) harmful effects human health occur by co-administered.
Figure 1:
Although current methods have attracted widespread attention in predicting the properties of molecu- lar pairs, two inherent shortcomings remain underexplored. The first is Insufficiency molecular interaction modeling. Existing methods demonstrate proficiency in elucidating essential structural characteristics for individual molecular models. However, when drug-drug interactions (DDI) occur, pivotal substructures may exhibit considerable variation. For example, Propranolol and Verapamil (Figure D (a)) are commonly prescribed drugs for the treatment of hypertension and cardiac ar- rhythmias, yet they through distinct pharmacological mechanisms that affect cardiovascular function. The aromatic ring and hydroxyl groups in Propranolol are critical for receptor binding and B-adrenergic inhibition, while the phenyl rings and amino moieties Verapamil mediate L-type calcium channel inhibition, as illustrated in Figure (b). However, when co-administered, the inter- action between Propranolol's 3-blocking pharmacophore and Verapamil's Aancium-channel-blle substructures may excessively suppress cardiac conduction, leading severe adverse effects such as excessive bradycardia or atrioventricular block (Figure (c)). Therefore, comprehensive modeling of intermolecular interactions is crucial for profound understanding of molecular interactions.
Some current models have noticed the aforementioned shortcomings (Behler 2013: 2016). However, they still lack consideration of model generalization. Given the diverse and complex nature of molecular species in real-world scenarios, the data used for training and testing may inevitably be sampled from different distributions, thus presenting challenges related OOD (Paul al., [02T Petrova 2013 Yang et al.) 2022b). While introducing integrated noise injection techniques to simulate diverse environmental distributions holds promise for enhancing model generalization and capturing core rationales, several drawbacks exist. Specifically, 1) The simulation of noise data may fail to accurately reflect authentic environmental vectors in chemical space. 2) Indiscriminate noise injection can distort semantic information and hinder model convergence, while random environmental vectors may inadequately represent the broad distribution molecular interactions; and 3) when the injected noise variance is too small, the noise effect may vanish, defeating its intended purpose.
In light of this, we introduce an Interaction-awwre Invariant Molecular learning framework, termed 12Mole, for generalizable DDI prediction. Spontaneous molecular interaction phenomena, tend to occur in spe- cific molecular structures -OH, =0, N), giving rise to stronger intermolecular interactions. We carefully design dynamic weighted relational edges to model the atom-atom interaction relationships. Conversely, for atomic pairwise interactions that rarely occur, we employ iterative truncation restrict their message passing processes, thereby reducing interference with the overall learning of the merged graph while moder- ately lowering graph complexity, as presented in Fig- u Given the vastness and largely unexplored nature of the chemical space, we further introduce the con- cept of vector quantization (VQ) (yan den Oord et al.) 2017| Razavi al.] 2019) for molecular interactions to construct a merged graph environment codebook. This codebook clusters the potential environments of
Merged Molecular Graph
Rationale
Figure 2: Diagram illustrating molecular interaction modeling to capture rationales. Molecular pairs will be constructed into merged graph by connecting atoms pairwise (dashed lines), Please note that to avoid ex- cessive complexity, some unimportant rela- tion edges will be removed (unconnected)
2

---

Published as a conference paper at ICLR 2026
molecules in the training set into predefined number of categories, and the learned environmental distribution also serves as a controllable noise source for mutual information optimization (Duncan 1970; Yu al. 2022b). Therefore, 12Mole which incorporates explicit molecule interactions and an improved environment codehook, effectively achieves generalizable property prediction on various DDI datasets.
PRELIMINARIES
2.1 PROBLEM FORMULATION
molecule can be depicted as a graph 9 whose nodes V denote the atoms and edges & act as the bonds Wen et al. (222I). U is the global feature vector which is extracted from each molecule (Appendix Dp. Given set of drug molecular graph pairs D {(C,, 9)), (Gh, 98), .... (9 ) and their associated target values Y= {Y), Y Y Y" }. our objective is to train model M that can classify the target values for arbitrary drug pairs in an end-to-end manner, i.e. Y MMG. g.).
2.2 GRAPH INFORMATION BOTTLENECK (GIB)
According to the GIB principle et et al. 2020 2022b Miao et al. 2022), we could get:
GIB arg min (Y; Gaub) + (G; Gaub).
Guab ES
Intuitively, S represents the set of Ssub, and GIB is the subgraph of 9, which discards information by minimizing the mutual information I[;; Gaub), while preserving target-relevant information by maximizing the mutual information / I(Y; Gsub).
2.3 INVARIANT LEARNING
Given the distribution shift between training and testing data, recent studies (Rojas-Carulla al. 2018a Arjovsky et al., 2019 Wu et al. 2022a propose the existence of a potential environment variable env express this problem:
min max V f Gun EE
Y) 9en
(2)
where E denotes the environment support, f() represents the predictive model, and R(::) is the risk function. The label Y is independent of the environment Genv, conditioned on the subgraph Gsub:
Y Il Genv
Gub:
where 1 denotes probabilistic independence. These principles collectively protect predictions from external influences, ensuring that the rationale comprehensively captures discriminative features. This is for a single molecule, and we would extend it to molecular pairs.
METHODOLOGY
we define the merged graph and the intermolecular message passing mechanism. Section the details of subgraph extraction by GIB theory. In Section 3.3 we describe how inject environmental embeddings into the rationales to enhance model generalization. Section 3.4 presents the total loss function of 12Mole.
In this section, we detail our proposed method. Section 3.1
3.1 MERGED MOLECULAR REPRESENTATION
Molecule Merging. The merged graph Č could be generated by establishing a weighted relational edge between two molecules which connects each atom pairwise.
ğ (R, E,,

---

Published as a conference paper at ICLR 2026
Marged graph constructed and message passing
Invariant Learning
Training Object
Sa
$18
MI
Retionalization
Rai
Sampling
So
Erw.
GIa
Merged greph (5i)
Message passing
Epre
Quary
Subgraph Discovery
rational
Sampling
Label
FC
Gin
Codabook
Pr Pa
Rational
Environment
Figure 3: Overview of our model. Initially, molecular pairs construct a merged graph to facilitate the message passing process. Subsequently, subgraphs are extracted based the GIB, and the environmental components are recorded in a codebook. During the invariant learning process, the rationale part concatenates different environment embeddings to achieve invariant representations.
The set of relation edges are
R = (Tig Cais Ubj kbi)]k=1 x
(5)
where E f1. bj E 2,......... N No No and N are the total number of atoms in drug molecular graph Go. Go. Mty represents the relation edge. And k is the index of R.
Intra-molecular message passing. Generally, in this merged molecular graph G, the message passing process is first executed intramolecule. In this process, eij is updated to e/y by aggregating the initial bond features, and the two atomic features, U, and Biy, and the global features u. addition, the feature vector i and updated E and ui respectively:
d = Byy LeakyReLU/FC(o; uy) + [FC(e.) + [FC(u)]].
(6)
a(e'y)
éi = Eyen, (eep) +
of = LeakyReLU/FC(u + Σ Ey @ FC(,,)) + FC(u), (7)
jEN:
N
= u Fea
Σ No
c + u)),
(8)
N
where FC is a fully connected layer. @ denotes the Hadamard product. a(-) is sigmoid activation function, and is fixed constant (0.0001). No and Ne are the number of atoms and bonds.
Intermolecular message passing. We utilize GAT network Veličković et al. 2017) for intermolecular message passing to calculate the weight of the relation edge Tij.
rsj LealyyeLLUFCC(WL.. Wol,)),
where W the learnable weight matrix. Based on the calculated attention coefficients (riz) for the relation edge, perform global sorting and retain the top_x% hyperparameter)::
Tij
if rf 2 X,
(10)
otherwise.
Here, X represents the threshold corresponding to the top_x% ranking of rij values. The selected attention coefficients are then normalized across the entire graph facilitate the intermolecular information information-passing process. The atomic feature v/ for is updated, also for v/g.
ai Enshl r 2i (1
Σ JeN,
aiy Maa
Σ aipehy JeN,
(11)
4

---

Published as a conference paper at ICLR 2026
3.2 CORE SUBSTRUCTURE EXTRACTION BASED ON GIB
We optimize the objective Equation 12 to detect the core structure in the merged graph:
OTB arg min (Y; + 3I(9; Gsub),
(12)
E
where S represents the set of Gaub. Each term indicates the prediction and compression terms respectively, which should be minimized during training, as outlined below.
3.2.1 EXTRACT TARGET-ORIENTED INFORMATION
Minimizing -Y GB.), which is to calculate upper bound -YYY; (IB). Given the merged graph
9. its label information Y, and the learned IB-graph GIB, we have:
- I(Y; S E v |- Po (YI)B)] Cpre:
(13)
where po( ((()))))) is variational approximation of p pY (iB). pe po(Y ( (IB) is a predictor parametrized by 0. Thus, we can minimize the upper bound of ((Y; 91B) by minimizing the model prediction loss Crre (Y, (I) with cross-entropy loss. Proofs are in Appendix C.1 (Sufficiency assumption (Yang al. 2022b)).
3.2.2 OPTIMIZE MINIMIZED G
Minimizing I( G. which is to calculate upper bound of I(:: GIB). Inspired by a recent approach on graph information bottleneck Yu et al. 2022b), we also minimize [(;; GIB) by injecting noise into node representations. Then, we dampen the information in by injecting noise into node representations with a learned probability. Let e be the noise sampled from parametric noise distribution. We assign each node a probability of being replaced by c. Specifically, for the i-th node, the k-th relation edge, we learn the probability p; and Pk: using a fully connected layer. Then, we apply Sigmoid function the output of fully connected layer to ensure p;, Pk: E [0, 1]:
p; = (FC()))(FC(h:)),,
(FC(m)
(14)
Next, a je-th relation edge is connected to the i-th node, we adjust the probability ps by adding Pk it, where N depends whether the i-th node in Ga Gb:
N
p: i E Gn and k-th edge is connected to i-th node, Pt +
Pc
(15)
if E G, and k-th edge is connected to i-th node.
We then replace the node representation h; by with probability ps:
= A,h4 + (1 A,).. h = (1 - 2,)
(16)
where X₂ ~ Bernoulli(p:), h is the irrelevant substructure node which would be used to construct
Gen. The transmission probability controls the information sent from h; to 2;. If p; 1, then all the information in h; is transferred z; without loss. On the contrary, when p: = 0, then z; contains no information from h; but only noise. We hope p; is learnable so that we can selectively preserve the information in GIB- However, A; is discrete random variable and cannot directly calculate the gradient of p:. Therefore, we employ the concrete relaxation (Jang et al. 2016) for A;:
X; Sigmoid( log
Pi
+ log
(17)
p
where t is the temperature parameter and Uniform(0.1 1). Another critical aspect of noise injection is the characterization of the injected noise. It is important that arbitrary noise can be detrimental to the semantic integrity of the input graph, leading predictions that deviate from the
5

---

Published as a conference paper at ICLR 2026
actual graph properties. Conversely, appropriately selected noise can provide variational upper bound the overall objective. Therefore, the minimizing the upper bound of T(91B; 9) as follows:
1 log Ag +
1 2mg
1(91n: 9) S Egg
Ag
+
B 2m
CMn(9IB, 9),
(18)
2
where A3 Eje 2j)² and B3
E As(he-Mu) on
More details are given in Appendix C.2
3.3 ENVIRONMENT INFERENCE
Based the above steps, we can identify the decisive substructure Gn in Equation relying solely on ÕIB may not ensure robust generalization across diverse distributions. To enhance its robustness, we incorporate principles from invariance learning theory, integrating features from various environments encountered across diverse distributions. The problem definition is as follows:
12 However,
min max E (()))) G.
[R((()), Y) Genv];
(19)
where E denotes the support of environments. The irrelevant substructures Gens be viewed as the environment, with each node embedding being h²- ((9em) is the distribution of data under environment Gene combined with various rationales, ʃ(-) is the prediction model and R(:--) is the risk function such as cross-entropy loss. Equation [9 aims to minimize the maximum errors across different environments, thus guaranteeing the capture of invariance across environments (Wu et al. b).
Directly solving Equation 19 is impractical due to limited training data across the various environ- ments E. Here, we introduce VQ yan den Oord et al. (2017): Razavi et al. (2019) to create a trainable environment codebook W {enu1, e7122 ................................ enuas J. defining latent embedding space env E IR M Here, M represents the number of discrete environments (i.e., enw),, and F denotes the dimension of each latent vector. A nearest neighbor lookup used in the shared embedding space E to find the closest latent vector enrm indexed by m. Additionally, the set2set network ( (Vinyals) et al. 2015) is utilized to pool GIB Genv. G. resulting in the substructure representation vectors Siu- Senv and 8g. This process acts as a specific non-linearity that maps the latent vectors Senv to one of the M embedding vectors:
for m = arg min || 3ea envyll2
q (m
Senv)
(20)
o otherwise.
To update the codebook and encourage the output of the encoder to stay close to the chosen codebook embedding, where the sg[-] denotes the sop-gradient and set to 0.25 Xia et al. (2022):
Lug = ||sg [Semv] - envm 11 + T sg(enum111
(21)
As Lug gradually converges, obtain stable codebook set W, which clusters the infinite possible environment space E into a discretized set of M finite environments represented by W. Subsequently, we traverse all potential environment vectors (env) and assign rationales to different environments achieve stable predictions. This ensures that the prediction results of the rationales are independent, thereby guaranteeing the independence (Invariance assumption Yang et al. (202bb)).
min Eene, E ((=(en)))())n:)) [R (f (3g), Y) env]].
(22)
This formula can be obtained by minimizing the weighted sum of cross-entropy losses across different environments. Assuming a total of C' classes, let Φ; denote the probability that enw belongs to enw, and let t represents the classification head that maps the molecular representation to the category labels. the encoder fenv and the classification head & together form the prediction model. So, the loss can be expressed in the following form, where ll denotes the concatenation operation:
M
Line =
Σ o
Σ Yog log (feno (5m (fmlleenu) lene;))
(23)
i=
70 FgEDEm c=)

---

Published as a conference paper at ICLR 2026
Table Performance of different methods in transductive setting. (Bold numbers are the best results,
while the nop-performing baseline is superscript cross. The standard deviations is in parentheses).
ZhangDDI
ChehMiner
DeepDDI
ACC
AUROC (1)
FI (7)
(TC
AUROC (1)
FI F1)
ACC (t)
AUROC (1)
F1 (1)
DeepDDI
83.35
91.13 ae)
80.24..4r2
90. 90.34.a.40
(8.71
(1.83
92.39
95. (5..40
SSI-DDI
86.97
93, 76).6.3)
82. 82.99
93.26 93.26
97.8 (o.a2)
93.11 (3.11
24.27(a.25
97.42 97.420.33)
95 (1.1
MDF-SA-DDI
(..89
94 94.0%
(3.67
94. 94.6%
98. 10
(4.17/011)
94.12 94.12
88 84,0.00
96. 13.13/1177
DSN-DDI
(7.65
91.63go 1e)
84.30
g4.25
98.31 98.31
(0.34
95.74ta.18 re:
98 (8.0
16.71.o.13
CGIB
37.32
94.43 oc)
84.53 os
94.37
98. any
95.44
95.76
96.53
CMRI.
87.78
94.08
84. 84.78
94.43/
98. 0..2
95.62.0.1)
95.4 95.49
98 98.03
96 22,
IE-HONN
(6.93
94.32,a 21)
36.361
(5.57
95,57
97. 97.9%/..a3
28
IGIB ISE
85.39 (2
94.92
(8.24
95.84
95.85
98.0220.00)
Ours
88.640034
95.34
18.84
(6.5
99.04...23
Table 2: Performance of different methods in inductive settings. (Bold numbers are the best results, while the oop-prfforming baseline is superseript cross. The standard deviations is in parentheses).
Typel
ZhungDDI
ChehMMiner
DeepDDI
ACC
AUROC (1)
(1)
(TC
AUROC (1)
(1
ACC (f)
AUROC (1)
F1
Despi>111
(.48
99.51 ue)
43.81
(1.51
67.67..20
64.39
69.52/u.55)
SSI-DI
(1.3)
69.56;1 2:)
47.59
(..94
27.61
(9.77
75.93
72.23 72.23/0.7)
MDF-SA-DDI
64,51 (4.51
70.99;
51.53
75.39
80.4 a0.47
79:83:1
11,13
80.5+0.04
71.61
DSN-DDI
67.68
72.49 0z)
53.64(am7)
78.94/a.7
85 85.93
83.81
73.35
83.11...0
75.68
CGIB
68.34
72.80go.am as)
67.29
79.75
86.41
73.86/a.o:
78.47.0.47
CMRI
68, (8.38
74.5% 74.5%;1
56.41caum
N0.54.0.000
87 (4/6440.4
86. 86.55
74.12(a.5:
84 34.96,0.5m)
77 (1:4))
IE- JE-HGNN
68.21
74.02
56.73/a.s)
60.21
87 (2.00
(6.21
73.5
85.07,0.71
77.12
IGIB ISE
a8.49
57.10
60.83
86.52 n0y
on
85.41
78.65 (as)
Ours
69.12
75.14p..0
5..8
81.5%
(8.51
(7.43
75.27
a5.62
78.96
Type2
ZlangDDI
ChebMliner
DeepDDI
(CC
AUROC (1)
(1)
(CC
AUROC (1)
F1
ACC(1) (f)
AUROC (T)
F1
DecpDDI
58.62
56.34;1
25.19/454:
63.78
(2.7
71.37
61.68
65.17
66.74:4.6)
SSI-DDI
57.24
59. 29.34
37. 37.16/5844
68.61
68 (..3
74.95
63.53
69.37
62. 68.18:394)
MDD-SA-DDI
(7.63
(5.97/1477)
33.94/2mm:
65.24
77.32
66.34/1.00
22.81
70.95;1.71)
DSN-DDI
(1.37
58.85;1 19)
39.09/2.00
68.36
69.34
77.52
68.17 se:
72.71
61.96
CGIB
58.39
57.24
28.83
68.7%
69 (2
78.46:200
68.26x
68.78
15.75
CMRL
60.78
60.02:20177
38.79/3.04)
(..4%
(2
75.76.1.29)
73.38
73.91:214)
IE-HGNY
60.47
61.18;1 a1)
38.92
68. (8.71
69. 69.47
78.92(1.0))
68. (32.00))
73.56
74.92/1.17)
IGIB ISE
59.96
59.71g
38.62
68.92 soy
69 69.94
79.32:1.007
68.41 say
74.10p
75.60) 0013
61.35
62.02
39.95(1.00
(9.23
70.02
(9.67
69.92
74.27
3.4 TRAINING OBJECTIVE
Finally, we train the model with the following objective:
Listal Lime + Lpre + 3LMI + 7fog
(24)
Here, Live and LMi are guided by the Gpe.Lpre is the cross-entropy loss for classification tasks. LMu represents the KL divergence between the core substructures and the non-core subgraph, encour- aging substructure compression. And Lim aims to minimize the disturbance loss across various environments. 3 and y are trade-off parameters that govern the weight of L and Liq.
4 EXPERIMENT AND ANALYSE
4.1 DATASETS AND SETUPS
Datasets. To evaluate the performance of our model, we conduct experiments based on three commonly used datasets in DDI event prediction task, including ZhangDDI (Zhang et al.) (017). DeepDDI (Ryu et al. 2018) and ChChMiner (Zitnik et al.)) Details are present in Appendix E. Baselines. In our extensive assessment, our model is compared with eight advanced DDI event prediction methods, all leveraging molecular graphs as input features. The compared methods include
DeepDDI (Ryu et al. 2018). SSI-DDI (Nyamabo al. 2021), CGIB (Lee et al. 2023a), CMRL (Lee)
et al. 2023c). MDF-SA SA-DDI (Lin et al. (2022). DSN DDI (Li et al., 2023). IE HGNN (Ye & Qian
2024 and IGIB-ISE (Zhang et al. 2025b). A more detailed description is in Appendix
H.2
7

---

Published as a conference paper at ICLR 2026
Table 3:
Performance on domain generalization experiments. Bold num- bers are the best results, and the standard deviations is in parentheses.
DeupOD1
Zhwn Siel
ChehMinnr
Deepiin
(CC
(UROC
(1
ACC
AUROC (f)
F1)
Dorp
60 60250
50. s0
65 m0:
400
SSI-nni
51 51,25
60477
62 24
49
67.2 47.20
MDF-SA-DDI
33554
65 3336
63.55
54.83pa
63.50 69.50
64.17 64.17
DSN-DDI
52.24
62458ua0
64 M0.0
54.86amm
68.25
65 54.4
CGIB
55.21
67.5k
64.53
55.32
63.48
65.44
CMRL
55.76
68.14
64 64.82a18)
56.431uu551
68.5
65 62
Figure 4: TSNE map for three DDI datasets (3000 drug pairs are respectively selected.)
LE HIGNN
56.48
68.32a44
65.01a
56.3510.31
68,03mas
65.48
KGIB ISE
170
68.63
65.11a.99
57.21aa2:
68.070031
05.57
Durs
89.25
69.22
68.25
88.12
6872
68.76
Metric. Three metrics are employed to evaluate the model performance: accuracy (ACC), area under the receiver operating characteristic (AUROC), harmonic mean of precision and recall (F1). All experiments are repeated eight times with the same dataset split, and average result is presented.
4.2 MODEL PERFORMANCE
Similar previous studies (Deac al. 2019 Nyamabo al. 2021) we first performed the transductive setting that is the common method evaluation scheme, where the entire dataset is randomly split and aims to predict the undiscovered DDI events among known drugs. We split the dataset into training (60%), validation (20%), and test (20%) parts. Key observations can be got:
Obs.1: 12Mole exhibits the excited predictive performance in transductive setting. The results of model and eight baseline models are presented in Table [ We observe that our model demonstrates the optimal predictive performance across three different scales of datasets. Regarding the ACC evaluation metric, it outperforms other models on the ZhangDDI and DeepDDI datasets, while its performance on the ChChMiner dataset comparable to IGIB-ISE.
Obs.2: 12Mole shows more pronounced performance improvements on the large-scale DeepDDI dataset. The model's performance across different datasets may be influenced by variations dataset characteristics, where larger datasets imply a greater diversity of drugs and more complex DDI relationships. Compared the second-best model, 12Mole has improved by 0.98% on the large-scale DeepDDI dataset, while only by 0.45% the medium and small-scal datasets in AUROC index.
4.3 GENERALIZATION TEST
In this section, evaluated 12Mole's generalizability by inductive settings and domain shifting tests. Type aims to predict potential interaction properties between known and unseen drugs, while Type 2 aims to predict potential interaction properties between unseen and unseen drugs as in Table 2
Obs.3: 12Mole demonstrates excellent generalization ability on inductive settings. We assessed the generalization capability on 12Mole unseen drugs, which holds significant practical and real-world implications. This process was implemented by partitioning drugs, and the testing results, compared with baseline models, are documented Table Evidently, when predicting with new drugs, the performance of all models experiences varying degrees of decline. However, 12Mole exhibiting excellent predictive performance has the minimized sensitivity to unseen drug pairs.
Obs.4: 12Mole shows robust performance on domain generalization experiments. To investigate the impact of domain shifting on generalization, we transfer a model trained on smaller dataset to larger one. Specifically, 12Mole, trained on the ZhangDDI dataset, is tested on two other datasets. Notably, ZhangDDI and DeepDDI exhibit entirely distinct distributions of molecular species, as depicted in Figure 4 12Mole outperforms other baseline models consistently across all conditions, underscoring its superior generalization capability, as recorded in Table
Obs.5: 12Mole demonstrates superior performance in scaffold and size splitting experiments. As presented in Table 20 (Appendix D). our proposed model consistently surpasses state-of-the-aas methods, achieving the highest accuracy in both scaffold and size splits. These results underscore the advantages our approach, enabling the model to effectively extract rationales with impressive generalization capabilities, and perform robustly across different test scenarios.
8

---

Published as a conference paper at ICLR 2026
(a)
Category
(b)
100
Category
Category
C Categary 7
Original cata
Original data Codebook embedding
Original
Codebook embedding
Codebook embedding
30
80
Popp/Son
TSNE
-30
20
10 0
TSNE
Element
Element
Figure 5: Environmental codebook vectors analysis. (a) TSNE dimensionality reduction plot of drug molecular pairs and the 10-class environment codebook vectors. Different colors represent the chosen codebook vectors, with red dots within clusters indicating the codebook vectors location. (b) Elemental composition of molecular pairs in clusters 5, 6, and 7 (colored) compared to the elemental composition represented by the codebook vectors (blank), along with an example pair molecules.
Table 4: Ablation experiment. Inter- molecular interaction denotes as A.
Table 5: Sensitivity analysis for and 7 (ACC indicator).
ZDangDDI
ZhangDDI
1E-5
1E-4
IE-3
0.1
ACC
AUROC
F1
85.71 (o.02)
85.84(0.05)
88.64(
86.83
56.46(0.00)
w/o VQ
(4.52
74.01 (4.01 (3
w/o A
84.51 84.51 (0.22)
87.21
80.21 (e.0))
2E-5
1E-4
2F-4
5E-4
1E-3
Ours
w/o GIB
88.64 88.64/0.24)
g4.72
95.12
81.07 87.21
83.87 (0.
88.31
88.64(0.12
88.21
88. (4,64))
88.32(0.01)
4.4 EXPLORING THE IMPACT AND EFFECTS OF ENVIRONMENT CODEBOOK
In this section, we provide an intuitive understanding through t-SNE analysis environment vectors and molecular embeddings from ChchMiner dataset, presented in Figure 5
Obs.6: Different environment embeddings in the environment codebook have clear boundaries in the visualization results. The 10 distinct environment embeddings exhibit clear distinctions (Figure (a)), ensuring that the model adcquately learns different types of environmental variables and thereby enhances its generalization. Moreover, different molecular substructure embeddings tightly centered around their corresponding environment embedding. This suggests that updating the codebook vector is essentially equivalent performing clustering on the molecular embeddings, with the environment embeddings serving as the clustering centers as shown in Figure 5 (a).
Obs.7: Different environment codes tend encode the local environments of various molecular pairs. Figure (b) shows the distribution of atom types for each environmental embedding, which is close to real-world data. Notably, significant differences exist between environment codes; for example, carbon is predominant in Category 7, while nitrogen and oxygen play important roles in Categories and These environmental embeddings represent the non-core substructures of molecular pairs. For each codebook category, we provide examples of molecular pairs in Figure 5 (b), illustrating the
types real-world substructures represented. More analysis are in Appendix M and N
5 ABLATION STUDY AND SENSITIVITY ANALYSIS
Ablation study, To further investigate the role of each component, we conducted a series of ablation studies. As shown in Table removing the GIB module reduced the model's ability to capture core substructures, limiting its performance. Similarly, the removal of intermolecular interaction disrupted accurate chemical modeling, degrading the model's capabilities. Notably, eliminating VQ module led to substantial performance drops, highlighting the importance codebook and vector quantization operation (more details in Appendix H and complexity are in Appendix andd
Sensitivity analysis. We investigate the sensitivity of and 7, which govern the trade-off between prediction and compression, and the codebook updating process, respectively. These parameters correspond to the weights of LMI and L:y in Equation Overall, the model demonstrates robustness to variations in 33 and 7, but performance degrades significanlly when / is sharply increased. More detailed sensitivity analysis results,are are presented in Appendix

---

Published as a conference paper at ICLR 2026
6 CONCLUSION AND FUTURE OUTLOOK
In this work, we introduce 12Mole, a novel framework for precise DDI prediction that aims to address the imbalance between training and testing data distributions commonly observed in real-word world scenarios. 12Mole constructs merged graph to capture complex molecular interactions and, through an enhanced information bottleneck theory to extract invariant subgraphs. Meanwhile, we design an environment codebook based on the molecular environments, which encodes environmental information and integrates it into data from diverse distributions, further improving the model's generalization capability. 12Mole enables the rapid identification of potential DDIs and reducing risks associated with drug misuse. The limitations of 12Mole are discussed in Appendix K
REPRODUCIBILITY
We provide the complete implementation in the repository along with guidance how re- produce our results. Our code is available at httts::/ 4open. science/r I2M61-C616
ETHICS STATEMENT
Our study does not involve human participants, personal data, sensitive information. The datasets and resources used are either publicly available or released under appropriate licenses. We confirm that our research does not raise any ethical concerns related privacy, safety, fairesss, or potential misuse. The contributions of this work are intended solely for advancing scientific research and are not designed or evaluated for harmful applications.
ACKNOWLEDGMENT
This paper partially supported by the National Natural Science Foundation of China (No. 12227901) ). The AI-driven experiments, simulations and model training were performed on the robotic Al-Scientist platform of Chinese Academy of Sciences., Anhui Science Foundation for Distinguished Young Scholars (No. 1N0.0000)))))),, Natural Science Foundation of China (No. (No.62502491).
REFERENCES
Alexander A Alemi, Ian Fischer, Joshua V Dillon, and Kevin Murphy. Deep variational information bottleneck. arXiv preprint arXiv:1612.00410 2016.
Martín Arjovsky, Léon Bottou, Ishaan Gulrajani, and David Lopez-Paz. Invariant risk minimization. CoRR, 0tos/1907.0289, 2019. URL http:::/aaxw...rc//////////////e wwwp/r///aabaa.oeeeeeeeeeeeaeeee 02893
Jörg Behler. Constructing high-dimensional neural network potentials: tutorial review. International Journal of Quantum Chemistry, 115(16): 1050, 2015. ISSN 0020-7608.
Jörg Behler. Perspective: Machine learning potentials for atomistic simulations. The Journal of chemical physics, (41(11)1 2016. ISSN 0021-9606.
Shiyu Chang, Yang Zhang, Mo Yu, and Tommi S. Jaakkola. Invariant rationalization. In Proceedings of the 37th International Conference on Machine Learning, ICML 2020, 13-18 July 2020, Virtual Event, volume 119 of Proceedings of Machine Learning Research, pp. 1448-1458 PMLR, 2020. URL http: httptt::/ppooeeennngeee
m.... htt.L.ppees///11/haaaaaee
html
Yeyun Chen. Relational invariant learning for robust solvation free energy prediction. 2025.
Yeyun Chen and Jiangming Shi. MIPT: Multilevel informed prompt tuning for robust molecular property prediction. In Aarti Singh, Maryam Fazel, Daniel Hsu, Simon Lacoste-Julien, Felix Berkenkamp, Tegan Maharaj. Kiri Wagstaff, and Jerry Zhu (eds.), Proceedings of the 42nd International Conference Machine Learning, volume 267 of Proceedings of Machine Learning Research, pp. 72228-2222722 72243. PMLR, 13-19 Jul 2025. URL https: hattps://proceedinntt mlr preas/v267 h0e.2///cheeeer html
10

---

Published as a conference paper at ICLR 2026
Y. Chung, F. H. Vermeire, H. Y. Wu, P. J. Walker, M. H. Abraham, and W. H. Green. Group contribution and machine learning approaches to predict abraham solute parameters, solvation free energy, and solvation enthalpy. Journal of Chemical Information and Modeling, 62(3):433- 446, 2022a. ISSN 1549-9596. doi: 10.1021 /ccm.//c....mm. 1031 URL (GotoTST>://w00
006745910500000
Yunsie Chung, Florence H Vermeire, Haoyang Wu, Pierre J Walker, Michael H Abraham, and William H Green. Group contribution and machine learning approaches predict abraham solute parameters, solvation free energy, and solvation enthalpy. Journal of Chemical Information and Modeling, 62(3):433-446, 2022b.
Andreea Deac, Yu-Hsiang Huang, Petar Veličković, Pietro Liò, and Jian Tang. Drug-drug adverse effect prediction with graph co-attention. arXiv preprint arXiv:1905. 00534, 2019.
Yifan Deng, Xinran Xu, Yang Qiu, Jingho Xia, Wen Zhang, and Shichao Liu. A multimodal deep learning framework for predicting drug-di drug interaction events. Bioinformatics, 36(15):4316-4222 2020.
Wenjie Du, Shuai Zhang, Di Wu, Jun Xia, Ziyuan Zhao, Junfeng Fang, and Yang Wang. Mmgnn: a molecular merged graph neural network for explainable solvation free energy prediction. In Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence, ICAA '24, 2024. ISBN 978-1-956792-006 10. 28.24993//20 / jcai. 2024 642
doi: http:6///ccai222246666
htthhttts///o.....
Wenjie Du, Shuai Zhang, Zhaohui Cai, Xuqiang Li, Zhiyuan Liu, Junfeng Fang, Jianmin Wang, Xiang Wang, and Yang Wang. Molecular merged hypergraph neural network for explainable solvation gibbs free energy prediction. Research, 8:0740. 2025a. doi: 00.34133/reeearch.777 0740. URL httph:ttsssppp
science. wwwp:/innwnnnnn//eeee//e..// /bo 34133/researeee 0740
Wenjie Du, Shuai Zhang, Zhaohui Cai, Xuqiang Li, Zhiyuan Liu, Junfeng Fang, Jianmin Wang, Xiang Wang. and Yang Wang. Molecular merged hypergraph neural network for explainable solvation gibbs free energy prediction. Research, 8:0740, 2025b.
Tyrone E Dunean. On the calculation of mutual information. SIAM Journal on Applied Mathematics, 19(1):215-220, 1970.
Junfeng Fang, Shuai Zhang, Chang Wu, Zhengyi Yang, Zhiyuan Liu, Sihang Li, Kun Wang, Wenjie Du, and Xiang Wang. Moltc: Towards molecular relational modeling in language models. CoRR, abs/2402.03781,, 2024.
Reza Ferdousi, Reza Safdari, and Yadollah Omidi. Computational prediction of drug-drug interactions based on drugs functional similarities. Journal of biomedical informatics, 70:54-64 2017.
Tianfan Fu, Cao Xiao, and Jimeng Sun. Core: Automatic molecule optimization using copy & refine strategy. Proceedings of the AAAI Conference on Artificial Intelligence, volume 34, pp. 638-645, 2020.
Assaf Gottlieb, Gideon Y Stein, Yoram Oron, Eytan Ruppin, and Roded Sharan. Indi: a computational framework for inferring drug interactions and their associated recommendations. Molecular systems systemsssssstemss biology, 8(1):592, 2012.
Mare W Harrold and Robin M Zavod. Basic concepts in medicinal chemistry, 2014.
Yue He, Zheyan Shen, and Peng Cui. Towards non-iid image classification: A dataset and baselines. Puttern Recognition, 110: 107383, 2021.
Patricia Jaaks, Elizabeth A Coker, Daniel J Vis, Olivia Edwards. Emma F Carpenter, Simonetta M Leto, Lisa Dwane, Francesco Sassi, Howard Lightfoot, Syd Barthorpe, et al. Effective drug combinations in breast, colon and pancreatic cancer cells. Nature, 603(7899) 2022.
Eric Jang, Shixiang Gu, and Ben Poole. Categorical reparameterization with gumbel-softmax. arXiv preprint arXiv: 1.01 144, 2016.
11

---

Published as a conference paper at ICLR 2026
Yuanfeng Ji, Lu Zhang, Jiaxiang Wu, Bingzhe Wu, Lanqing Li, Long-Kai Huang. Tingyang Xu, dataset curator and benchmark
Yu Rong, Jie Ren, Ding Xue, et al. Drugood: for ai-aided drug discovery- focus affinity prediction problems with noise annotations. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 37, pp. 8023-8031, 2023.
Jia Jia, Feng Zhu, Xiaohua Ma, Zhiwei W Cao, Yixue X Li, and Yu Zong Chen. Mechanisms of drug combinations: interaction and network perspectives. Nature reviews Drug discovery, 8(2):
111-128, 2009.
Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint 14X2::1412.6980 2014.
William Klemperer. Intermolecular interactions. Science, 257(5072):887-888 1992.
Namkyeong Lee, Dongmin Hyun, Gyoung S. Na, Sungwon Kim, Junseok Lee, and Chanyoung Park. Conditional graph information bottleneck for molecular relational learning. In ICML, volume 202 of Proceedings of Machine Learning Research, pp. 18852-18871. PMLR, 2023a.
Namkyeong Lee, Dongmin Hyun, Gyoung S Na, Sungwon Kim, Junseok Lee, and Chanyoung Park. Conditional graph information bottleneck for molecular relational learning. arXiv preprint arXiv:2305.01520, 2023b.
Namkyeong Lee, Kanghoon Yoon, Gyoung S Na, Sein Kim, and Chanyoung Park. Shift-robust molecular relational learning with causal substructure. arXiv preprint arXiv:2305.1844 18455, 2023c.
Zimeng Li, Shichao Zhu, Bin Shao, Xiangxiang Zeng, Tong Wang, and Tie-Yan Yan Liu. Dsn-ddi: an ac- curate and generalized framework for drug- drug interaction prediction by dual-view representation learning. Briefings in Bioinformatics, 24( 24(1):bbac597, 2023.
Shenggeng Lin, Yanjing Wang, Lingfeng Zhang, Yanyi Chu, Yatong Liu, Yitian Fang, Mingming Jiang, Qiankun Wang, Bowen Zhao, Yi Xiong, et al. Mdf-sa-ddi: predicting drug-drug interaction events based on multi-source drug fusion, multi-source feature fusion and transformer self-attention mechanism. Briefings in Bioinformattis, (bbD)bbb 2022.
K. Low, M. L. Coote, and E. I. Izgorodina. Explainable solvation free energy prediction combining graph neural networks with chemical intuition. J Chem Inf Model, 62(22))5457-544 -55-00 2022a. ISSN 1549-960X (Electronic) 1549-9596 (Linking). doi: 10.100///cs.jjimm2co000 2e00111 URL
https: www. ncbi...... n mmmmmmn. ii.iihh. gov hwtp://wwedddeeeo 3631 7829.
Kaycee Low, Michelle L. Coote, and Ekaterina I. Izgorodina. Explainable solvation free energy
prediction combining graph neural networks with chemical intuition. Journal of Chemical In- formation and Modeling, 62(22):5457-5470 2022b. doi: 10.1021/acs.jein sei.cscccim...0013.. URL
https://doo www./org.1... helgg//..111//aae. /acc/ jeim. 2c01 013
PMID: 36317829.
Dongsheng Luo, Wei Cheng. Dongkuan Xu, Wenchao Yu, Zong, Haifeng Chen, and Xiang Zhang. Parameterized explainer for graph neural network. In Hugo Larochelle, Mare Aurelio Ranzato, Raia Hadsell, Maria-Florina Balcan, and Hsuan-Tiee Lin (eds.), Advances in Neural Information Pro- cessing Systems 33: Anmual Conference Neural Information Processing Systems 2020, NeurIPS neuriss /C/
2020, December 6- 12. 2020, virtual, 2020. URL paper /0eer//220/haa httph//ewo00ddd0000 011e333111330ccbbbbee 71t.0/08000130000006666666668110
Fangrui Lv, Jian Liang, Shuang Li, Bin Zang, Chi Harold Liu, Ziteng Wang, and Di Liu. Causality inspired representation learning for domain generalization. In Proceedings of the IEEE/CVF conference on computer vision and paltern recognition, pp. 8046-8056, 2022.
Siqi Miao, Mia Liu, and Pan Li. Interpretable and generalizable graph learning via stochastic attention mechanism. In International Conference on Machine Learning, pp. 15524. PMLR, 2022.
Arnold K Nyamabo, Hui Yu, and Jian Yu Shi. Ssi-ddi: uubstructure--susstuunnet interactions for drug-dru interaction prediction. Briefings in Bioinformatics, 22(6):bbab133, 2021.
Debleena Paul, Gaurav Sanap, Snehal Shenoy, Dnyaneshwar Kalyane, Kiran Kalia, and Rakesh K
Tekade. Artificial intelligence in drug discovery and development. Drug discovery today, 26(1):80, 2021.
12

---

Published as a conference paper at ICLR 2026
Elina Petrova. Innovation in the pharmaceutical industry: The process of drug discovery and development. In Innovation and Marketing in the Pharmaceutical Industry: Emerging Practices, Research, and Policies, pp. 19-81. Springer, 2013.
Ali Razavi, Aäron van den Oord, and Oriol Vinyals. Generating diverse high-fidelity images with VQ-VAE-2. In NeurIPS, pp. 14837-14847, 2019.
Mateo Rojas-Carulla, Bernhard Schölkopf, Richard E. Turner, and Jonas Peters. Invariant models for causal transfer learning. Mach. Learn. Res., 1::::1,,,:34, 2018a. URL http://jmlz
wrg/papers/v13// 6- 432. html]
Mateo Rojas-Carulla, Bernhard Schölkopf, Richard E. Turner, and Jonas Peters. Invariant models for causal transfer learning. J. Mach. Learn. Res., 19:36:1-36:34, 2018b. URL http://jmlr
orq/papers/wl9//2 wwtpperrswww//eeeeee 432. html]
Karen A Ryall and Aik Choon Tan. Systems biology approaches for advancing the discovery of effective drug combinations. Journal of cheminformatics, 7(1):1-15, 2015.
Jae Yong Ryu, Hyun Uk Kim, and Sang Yup Lee. Deep learning improves prediction of trug-druu, and drug-food food interactions. Proceedings of the national academy of sciences, 115(18)EE434 E4311, 2018.
Zheyan Shen, Peng Cui, Kun Kuang, Bo Li, and Peixuan Chen. Causally regularized learning with agnostic data selection bias. In Proceedings of the 26th ACM international conference on Multimedia, pp. 41 411-419, 2018.
Zheyan Shen, Peng Cui, Tong Zhang, and Kun Kunag. Stable learning via sample reweighting. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 34, pp. 5692-5699, 2020.
Zhenchao Tang, Guanxing Chen, Hualin Yang. Weihe Zhong, and Calvin Yu-Chian Chen. Dsil- ddi: A domain-invariant substructure interaction learning for generalizable drug-drug interaction prediction. IEEE Transactions on Neural Networks and Learning Systems, 2023.
Aäron van den Oord, Oriol Vinyals, and Koray Kavukcuoglu. Neural discrete representation learning. In NIPS, pp. 6306-6315, 2017.
Jithin John Varghese and Samir H Mushrif. Origins of complex solvent effeets on chemical reactivity and computational tools to investigate them: review. Reaction Chemistry & Engineering, 4(2): 165-206, 2019.
Petar Veličković, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Lio, and Yoshua Bengio. Graph attention networks. arXiv preprint arXiv:1710.10003 2017.
Oriol Vinyals, Samy Bengio, and Manjunath Kudlur. Order matters: Sequence to sequence for sets. arXiv preprint arXiv:1511.0633 2015.
Tan Wang, Jianqiang Huang, Hanwang Zhang, and Qianru Sun. Visual commonsense r-cnn. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 10760- 10770, 2020.
Mingjian Wen, Samuel M. Blau, Evan Walter Clark Spotte-Smith, Shyam Dwaraknath, and Kristin A. Persson. Bondnet: a graph neural network for the prediction bond dissociation energies for charged molecules. Chemical science, 12(5):1858-1888 2021.
Qitian Wu, Hengrui Zhang, Junchi Yan, and David Wipf. Handling distribution shifts on graphs: An invariance perspective. In The Tenth International Conference on Learning Representations, ICLR 2022, Virtual Event, April 25-29, 2022. OpenReview.net, 2022a. URL /RL/atttp://ppeereee/
net /
Qitian Wu, Hengrui Zhang, Junchi Yan, and David Wipf. Handling distribution shifts graphs: An invariance perspective. arXiv preprint arXiv:2202.0244 2022b.
Ying-Xin Xin Wu, Xiang Wang, An Zhang, Xiangnan He, and Tat-Seng Chua. Discovering invariant rationales for graph neural networks. arXiv preprint arXiv:2201. /2872, 2022c.
13

---

Published as a conference paper at ICLR 2026
Yingxin Wu, Xiang Wang, An Zhang, Xiangnan He, and Tat-Seng Chua. Discovering invari- ant rationales for graph neural networks. In The Tenth International Conference on Learning Representations, ICLR 2022, Virtual Event, April 25-29, 2022. OpenReview.net, 2022d. URL htttps://openreet new. net forum? dd= j5r HWw
Jun Xia, Chengshuai Zhao, Bozhen Hu, Zhangyang Gao, Cheng Tan, Yue Liu, Siyuan Li, and Stan
Li. Mole-bert: Rethinking pre-training graph neural networks for molecules. In The Eleventh International Conference on Learning Representations, 2022.
Jun Xia, Yanqiao Zhu, Yuanqi Du, Yue Liu, and Stan Z Li. A systematic survey of chemical pre-trained models. IJCAI, 2023.
Nianzu Yang, Kaipeng Zeng. Qitian Wu, Xiaosong Jia, and Junchi Yan. Learning substruc- ture invariance for out-of-distribution molecular representations. In Sanmi Koyejo, S. Mo- hamed, A. Agarwal, Danielle Belgrave, K. Cho, and A. Oh (eds.), Advances in Neural Information Processing Systems 35: Annual Conference on Neural Information Process- ing Systems 2022, NeurIPS 2022, New Orleans, LA, USA, November 28 December 2022, 2022a. URL http: /ttp:://papene nips. cw/paper /ttpa//rrr..eeeeapppe////////// Comftrreett http://e.....t.eeeeeooeeeeeaaeaa
html
Nianzu Yang, Kaipeng Zeng, Qitian Wu, Xiaosong Jia, and Junchi Yan. Learning substructure invariance for oft-o--iisti molecular representations. Advances in Neural Information Processing Systems, 35: 12964-12978 2022b.
Wenbin Ye and Quan Qian. Forecasting the molecular interactions: A hypergraph- neu- ral network for molecular relational learning. Snowledge-Bassee Systems, 300: 2024. ISSN 0950-7051. doi: aet.apaccca.c..........aaarrraaa
121777. URL https::///// //www
sciencedirect.
Zhitao Ying. Dylan Bourgcois, Jiaxuan You, Marinka Zitnik, and Jure Leskovec. Gnnexplainer: Generating explanations for graph neural networks. In Hanna M. Wallach, Hugo Larochelle, Alina Beygelzimer, Florence d' Alché-Bue, Emily B. Fox, and Roman Garnett (eds.), Advances in Neural Information Processing Systems 32: Annual Conference on Neural Information Pro- cessing Systems 2019, NeurlPS 2019, December 8-14, 2019, Vancouver, BC, Canada, pp. 9240-9251, 2019. URL 6BCb7040b 9901 (ew.00eeddee22223ee333e
wwwpeddiiinnnn..uiii.oere.e http:///ws..erppppppep/////////e wwtpppper/2..///aaaaaaaaaaa /0t9//22//hhhh///// html
Hui Yu, Yu Zhao, and Yi Shi. Stnn-ddi: a substructure-awwree tensor neural network predict drug-drug interactions. Briefings in Bioinformatics, 23(4):bbac209, 2022a.
Junchi Yu, Tingyang Xu, Yu Rong, Yatao Bian, Junzhou Huang, and Ran He. Graph information bottleneck for subgraph recognition. arXiv preprint arXiv:2010.0556,, 2020.
Junchi Yu, Jie Cao, and Ran He. Improving subgraph recognition with variational graph information bottleneck. In IEEE/CVF Conference on Computer Vision and Pattern Recognition. CVPR 2022, New Orleans, LA, USA, June 18-24, 2022, pp. 19374-19383 IEEE, 2022b. doi: 10. 0W09CCVPRS2288.20222000 01879
URI https: htt.:/oooooooooooooooooooooooooo 10. 29T10/////PP/2222 2022
Dong Zhang, Hanwang Zhang, Jinhui Tang, Xian-Sheng Hua, and Qianru Sun. Causal intervention for weakly-supervised semantic segmentation. Advances in Neural Information Processing Systems, 33:655-6666 2020.
Peiliang Zhang, Jingling Yuan, Chao Che, Yongjun Zhu, and Lin Li. Subgraph information bottleneck with causal dependency for stable molecular relational learning. In James Kwok (ed.), Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence, IJCAI-25, pp. 7931-
7939. International Joint Conferences Artificial Intelligence Organization, 8 2025a. doi: 10.24963/ijcai.222555 2025/882. URL htLhhttp::/ddom wrt. 249 2025/882 Main Track.
Shuai Zhang, Junfeng Fang, Xuqiang Li, ALAN XIA. Ye Wei. Wenjie Du, Yang Wang, al. Iterative substructure extraction for molecular relational learning with interactive graph information bottleneck. In The Thirteenth International Conference Learning Representations, 2025b.
14

---

Published as a conference paper at ICLR 2026
Wen Zhang, Yanlin Chen, Feng Liu, Fei Luo, Gang Tian, and Xiaohong Li. Predicting potential drug-drug interactions by integrating chemical, biological, phenotypic and network data. BMC bioinformatics, 18:1-12, 2017.
Yi Zhong, Xueyu Chen, Yu Zhao, Xiaoming Chen, Tingfang Gao, and Zuquan Weng. Graph- augmented convolutional networks on drug-drug interactions prediction. arXiv preprint arXiv:1912.03370. 2019.
Yi Zhong, Gaozheng Li, Yang. Houbing Zheng, Yongqiang Yu, Jiheng Zhang, Heng Luo, Biao Wang, and Zuquan Weng. Learning motif-based graphs for drug- interaction prediction via local-global self-attention. Nature Machine Intelligence, 609):0994-1105, 2024.
Marinka Zitnik, Rok Sosič, Sagar Maheshwari, and Jure Leskovec. Biosnap datasets: Stanford biomedical network dataset collection. 2018. URL http:///sna.. stanford. edu/biodata.
15

---

Published as a conference paper at ICLR 2026
CONTENTS
Introduction
2
Preliminaries
Problem Formulation
2.2
Graph Information Bottleneck (GIB)
2.3
Invariant Learning
3
Methodology
3.1
Merged Molecular Representation
3,2
Core Substructure Extraction Based on GIB
3.2.1
Extract target-oriented information)
3.2.2
Optimize minimized G
3,3
Environment Inference
6
Training Objective
Experiment and Analyse
4.1
Datasets and setups
Model Performance
Generalization Test
8
Exploring the impact and effects of Environment Codebook
Ablation study and Sensitivity analysis
Conclusion and Future outlook
10
Reproducibility
10
8 Ethics Statement
10
9 Acknowledgment
10
Appendix
18
Regarding the Use of LLMs
18
Related Work
18
B.I Drug-Drug Interaction (DDI) prediction
18
B.2 OOD generalization
18
Proofs
19
Proof of L Lpre
19
16

---

Published as a conference paper at ICLR 2026
C.2 Proof of LMI
19
D The Detailed Features For Atoms, Bonds and Molecular Global
21
Experimental Settings
Datasets
21
Baselines
E,3 Parameter Setting
22
Results significance analysis
22
Sensitivity analysis
23
VQ module analysis
24
Data scalability analysis
24
Computational complexity
25
Limitation analysis
25
The scaffold and size splitting experiments result.
27
M Visualization analysis
27
Maximum Common Substructure (MCS) Analysis of VQ Environments
29
17

---

Published as a conference paper at ICLR 2026
A REGARDING THE USE OF LLMS
In this work, LLMs are used solely for polishing and refining the writing, All substantive content, ideas, and analyses are authored and created by the authors. The LLMs are only employed to improve clarity, grammar, and overall readability, and did not contribute the generation of scientific content or results.
B RELATED WORK
B.1 DRUG-DRUG INTERACTION (DDI) PREDICTION
In recent years, computational approaches, particularly employing machine learning and deep learning methods, have emerged indispensable tools for swiftly and economically predicting potential DDIs (Ryall & Tan 2013 Jaaks et al. 2022). Initially, DDI prediction models predominantly focused on drug attribute information, assuming that similar drugs would exhibit common interactions (Ryu et al. [018] Deng et al. (020). For instance, Goutlie et al. (2012) utilized seven types of drug features construct similarity vectors, forming a DDI prediction model based logistic regression, Ferdousi iet al. (2017) designed a deep neural network using drug molecular similarity vectors as descriptors for predicting potential DDIs. Recently, there has been a shift towards graph-based DDI prediction methodologies, Zhong et al. 2019) employed Graph Convolutional Neural Networks (GCNNs) for message aggregation and an eatention-bbsed pooling method for DDI prediction. Given that the interaction between two drugs is influenced by their specific substructures and functions, recent efforts have focused on substructure extraction and interaction [Harrold Zavod (2014); (2020). For instance, Yu et al. (2022a) utilized functional group information of drug molecules as their substructures, while Nyamabo et al. (2021) introduced the Substructure-Susttruuuu Substructure Interaction for Drug-Drug Interaction (SSI-DDI) method, employing graph attention network (GAT) layers to extract substructure representations and co-attention layers to model interactions among substructures.
4): [uu et al.)
Despite the proficiency of existing methodologies in elucidating essential structural characteristics of individual molecular models, considerable variation in crucial substructures may occur during molecular interactions (Tang et al. 2023, Lee et al. 2023c). Notably, while some pioneering work like DSIL-DDI (Tang et al. 2023) and CMRL. (Lee et al. 2023c) has provided foundational insights, noticeable gap remains in comprehensively modeling intermolecular interactions. CMRL (Lee et al.) 2023c) innovatively incorporates conditional graph information bottleneck theory to obtain rationales, simultaneously considering second drug as a conditional factor during drug subgraph generation (Lee) et al. 2023b). However, prevailing methodologies encounter limitations in adequately capturing molecular interactions, particularly at the atomic level. Moreover, integrating a comprehensive profile of interacting molecules into subgraph generation poses significant challenges. including overwhelming complexity and the risk of incorporating redundant information (Jia et al. 2009).
B.2 OOD GENERALIZATION
The susceptibility of deep neural networks to significant performance degradation under distribution shifts has spurred extensive research on out-of-distribution (OOD) generalization. In response, the invariant rationalization theory has been introduced, aiming to achieve an invariant representation across diverse environments (Chang et al. 2020 Rojas-Carulla et al. 20 8b). This theory involves rationalization module that discerns crucial subset within the input graph, referred to ratio- nale, essential for prediction (Ying et al. 2019 Luo et al., 2020). Subsequently, through invariant learning, these rationales are exposed to diverse environments, thereby fortifying the learned repre- sentation against environmental fluctuations and effectively bolstering the model's OOD capacity. 1) sufficiency: shows sufficient predictive power for the target, 2) invariance: contributes to equal (optimal) performance for the downstream tasks across all environments. Certain methods in computer vision Lv et al. (2022); Zhang et al. (2020); WWan et al. (2020) achieve OOD generalization by learning domain-invarinn
representations. Additionally, methods such as Shen et al. (2018); He et al. ): Shen et al. (2020) aim to achieve OOD generalization by decorrelating correlated and irrelevant features, considering the statistical correlation between these features as major factor for distribution shifts. In terms of molecular applications, DIR (Wu et al.) (202dd) introduces an inventive method to unveil invariant rationales by intervening in the training distribution, generating multiple
18

---

Published as a conference paper at ICLR 2026
interventional distributions, and identifying causal rationales consistent across varied distributions. Similarly, MoleOOD (Yng et al. (2022a) suggests that leveraging causal lata-generating invariance from substructures environments, linked specific properties, holds promise for enhanc- ing OOD generalization. However, learning a domain-invariant representation for intermolecular interaction remains open problem, and current discussions OOD issues are limited.
C PROOFS
C.I PROOF OF Cpre
Proof. Regarding I(Y;)), we consider Po (r) as the variational estimation of P (r g).
Therefore, we can proceed with the following derivation:
P ( Y Ø
I(::9) (r( log
P(Y)
Po (Y (Y10)
(25)
= B log
+
P(Y)
Eg log KL (P (P Ø) Po (Y [
Considering the non-negativity property of the Kullback-Leibler divergence, conclude that:
Po Y ( (Y10)
I(Y:ā) 2 (Y. log
P(Y)
(26)
(rIō)] + H(Y).
E (r log
Pa
As H (Y) remains constant across all data, it can be omitted, resulting in the final formulation of this
term:
Cpre B(yrō) log [Po (r [
(27)
C.2
PROOF OF LMi
Proof. We first use readout function obtain the graph representation 2ة of the perturbed graph Gm. And we assume these is no information loss in this process. Therefore we have (=am G) R
19

---

Published as a conference paper at ICLR 2026
(GIB: G). Now we bound (zōm" ())
using variational approximation:
I ( 20 (G)== 1| p 20
G)
log
dz
dG
P
Gm
= |]
2
G
log
dz8
dG
=Gin
+ /]
(= 2 G)log
log
dz
dG
(28)
E p(O)
[KL (pl
(2(2 2Gp
G 11
E p 18)
KL (p
(zmm))
E p(O) KL (p
(2(c (20
G
|| g
2
where q (=Gm. the variational approximation & And the inequality due the fact
that Kullback-Leilerr divergence is non-negative. We assume that g frmm noninformative
distribution following VIB Alemi al. (2016). That is, we obtain y = by aggregating the node
representations a fully perturbed graph. The noise eg ~ N (uh, of) is sampled from the Gaussian distribution, 1hh of
and variance of hy in G.
When we choose sum pooling as the readout function, we have:
9 (=Emm) =N (math, m3ok). mmot)
(29)
This is because the summation of Gaussian distributions is also a Gaussian distribution. Then, for p (2 G). we have:
p 2mm
a (1
(30)
=N
math
Xyhy
2,)2 oo
j=1
j=1
Plug Equation 29 and Equation into Equation 28 and we have:
I 2 G)
/ p(G) (-1 log Ag +
1
Ag +
1
B² dē
2m
2mg
(31)
+ / 1 G(( log my dō
= / p()) (-2 log Ag +
1
Ag + 2mg
By dō + +C,
2m
Σn (1a)
where Ag optimization process.
f (1 - 2,)² and B3
C' is a constant and can be ignored in the
20

---

Published as a conference paper at ICLR 2026
D THE DETAILED FEATURES FOR ATOMS, BONDS AND MOLECULAR GLOBAL
comprehensive overview of the selected atom, bond, and global input features presented in Table 6 The initial step involves the conversion of the SMILES string of both solute and solvent into graph structure using the RDKit package. This package is employed not only for graph creation but also for the computation of atom and bond features for each graph. The selection of features was restricted to those computable RDKit to mitigate the computational expenses associated with performing quantum mechanics calculations for the entire dataset. In order to standardize the lengths of the bond, atom, and global feature vectors, linear transformation is applied to each vector before the commencement of the pessagg-passingg steps.
Table 6: Atoms (nodes), bonds (edges), and global features for molecular representation
Atomic features (V)
Bond features (E)
Global features (L)
Atomic species
Bond type
Total No. of atoms
No. of bonds
Conjugated status
Total No. of bonds
No. of bonded H atoms
Ring size
Molecular weight
Ring status
Stereo-chemistry
Valence
Aromatic status
Hybridization type
Acceptor status
Donor status
Partial charge
E EXPERIMENTAL SETTINGS
In this section, we will provide a comprehensive overview our experimental setup. Section E. will provide detailed information about all the datasets utilized in the experiments. Subsequently, Section E.2 will offer a basic introduction the baseline methods incorporated our study. Following that, Section E.3 will delineate the diverse hyperparameters employed in the network architecture of our model. Additionally, it will elucidate the search space for hyperparameters and present the optimal hyperparameters.
E. DATASETS
ZhangDDI Zhang al. (2017) a small-scale dataset, including 548 drugs with 48,548 pairwise interaction data points, encompassing various types of similarity information for these drug pairs.
ChChMiner Zimik et al.) medium-scale dataset, comprises 1,514 drugs and 48,514 labeled DDIs, sourced from drug labels and scientific publications.
DeepDDI Ryu et al. (2018) is a larger-scale dataset with 1,704 drugs and 192,284 labeled DDIs, along with comprehensive side-effect information.
These datasets provide detailed drug information, including SMILES string representations, forming robust foundation for evaluating the proposed model.
E.2 BASELINES
In this chapter, will provide brief introduction to the baseline models mentioned in the experi- mental section. In our extensive assessment, our model is compared with eight advanced DDI event prediction methods, all leveraging molecular graphs input features.
DeepDDI. Ryu et al. (2018 is based on the structural similarity profile between input drugs and others.
21

---

Published as a conference paper at ICLR 2026
SSI-DDL. Nyamabo et al. (2021) it use 4-layer GAT network to extract substructures at different levels, and finally complete the final prediction based on the co-attention mechanism.
CGIB. Lee et al. 2023b Based on the graph conditional information bottleneck theory, conditional subgraphs are extracted to complete the interaction between molccules.
CMRL. et al.
(023c) it detects the substructure that is causally related to chemical reactions. we introduce a novel conditional intervention framework whose intervention is conditioned on the paired molecule. With the conditional intervention framework.
MDF-SA-DDL, [in et al. (2022) achieving DDI prediction by incorporating multi multi-source drug fusion, multi-source feature fusion and transformer self-attention mechanism.
DSN-DDI. Li et al. (023) it employs local and global representation learning modules iteratively and learns drug substructures from the single drug ('intra-view') and the drug pair ('inter-vie'') simultaneously.
IE-HGNN, Ye Qian 2024 It introduces interal-external bi-view hypergraph neural network, where cross-interaction message passing is applied to capture molecular relational patterns and reduce edge redundancy in paired molecular graphs.
IGIB-ISE. Zhang et al. (2025b) It integrates an iterative substructure extraction framework with the Interactive Graph Information Bottleneck, progressively refining interactive core substructures between drug pairs to improve accuracy and interpretability in molecular relational learning.
96.0
98.9
90.0
Zhang DDI
ChchMiner
DespDDCI
36.8
06
89.5
Accuunty C4
40.0
88.5
807
86.0
94.4
86
87.5
94.0
Number Codebooks Embedding
Number of Codebooka Embbddding
Number of Codeccolo Embeddinng
Figure 6: Test results of varying numbers of environmental vectors in the environment codebook in transductive setting.
E.3 PARAMETER SETTING
Model architecture. For intramolecular message passing, we employ 3-layer Gated Graph Convolutional Network (GatedConv). For intermolecular message passing, utilize 3-layer Graph Attention Network (GAT). As for the pooling layer, we opt for the set2set network. The detailed hyperparameters present in Table
Model Training. The model is trained using the Adam optimizer Kingma & Ba (2014) with an initial learning rate of 1 x 10-4, which is increased to 0.5, employing batch size of 32. Binary cross-entropy loss (BCE) utilized as the training loss function. Training is terminated the validation does decrease for 150 epochs if the maximum training limit of 300 epochs reached, 12Mole is implemented in the PyTorch framework and executed on Tesla A 100 40GB hardware.
F RESULTS SIGNIFICANCE ANALYSIS
In the transductive setting, which is conventional testing method where the dataset is randomly divided into training, validation, and test sets, we repeated the experiment 8 times and calculated the mean, variance, and value of the ACC, shown in the Table compared to the second-best model, 12Mole improved by 0.98% on the large-scale DeepDDI dataset, with an average improvement of approximately 0.05. The p-values are less than 0.05, proving that the improvements of our model
22

---

Published as a conference paper at ICLR 2026
Table 7: Hyperparameter
speciiicctitisssiiiiicaactiioo specifications.
Network layer hyperparameters
GatedCony
GAT
FC
Num-layers
3. 4.45
Num-layers Hidden size
3,4,5
Num-laaees
3, 3,4,5
Hidden
200, 600,
400,
Dropout Hidden-size
Layers
3. 4.5
Layers Activation
3, 4,5
300, 400, 500, 600
Activation
LeakyRelij
LeckyRetD
Training hyperparameters
Batch--izz
32
Learning rale
0.0001. 0.0005, 0.01, 0.005
3
0. le
$,1e
Environment codebook hyperparameters
Num cnvirenment S. 8, 10, 20, 30
2e f.1e"
statistically significant. Therefore, although this is limited improvement, the results are substantial and sigmificant.
In the inductive setting, which is a commonly used generalization testing method, molecule (type 1) or a molecule pair (type 2) is removed in the test set to verify the model's generalization ability. Notably, in the generalization tests, 12Mole achieved average improvement of 1.05% in type 1 scenarios and 1.20% in type 2 scenarios. This demonstrates 12Mole's ability to generalize to unseen molecules.
In domain generalization experiments, which is challenging testing method, we trained and tested on datasets from different domains to verify 12Mole's generalization ability. Clearly, 12Mole achieved the best generalization re- sults, with an average improvement of 2.71% % (Ace index), significantly outperforming the improvements in transductive and inductive settings.
Table 8: Significant difference analysis.
Model Performance
ZhangDD1
ChehMiner
DeepDDI
Second best model
88.08
94.92(0.21)
95.85
Our model
88 (8.64
(5.34
96.51 (o.14)
P-value
3.52E-04
2.13E-03
8.74E-05
G SENSITIVITY ANALYSIS
We conduct an in-depth investigation into the effect of varying the number of environment embeddings our model's performance, as depicted Figure The results demonstrate that altering the number environment embeddings has negligible impact on test performance across three different-sized test datasets, underscoring the robustness of our model. The optimal performance is achieved when the number codebook vectors is set to 10, which have adopted for our final model configuration.
Furthermore, we investigated the impact of varying the proportion of retained rela- tional edges during inter-molecular mes- sage passing on the model's performance, as illustrated in Table p The results indi- cate that gradually increasing the propor- tion of retained relational edges enhances the model's performance. However. be- yond a certain threshold, further increments lead noticeable decline performance. Consequently, selected 20% as the op- timal parameter for the proportion of re-
Table 9: Sensitivity analysis for retained relational edges ratio.
ZhangDDI
ACC
AUROC
F1
Top_s 5%
88.52 (a.08)
95.02
85.75
Top_s 10%
88.60
95. (0.10
85.80
Top s = 20%
88.64 88.64(0.24)
92.12
85.87
Top s 30%
88. 88.54 (
95.09
(0.53
Top s 50%
88.34 (8.34
94.87 (0.10)
(5.22
tained relational edges.
crucial parameter in this context is the number of environmental samples, denoted as 6. Increasing the number of sampled environments expands the range of simulated molecular interactions under various conditions, though it also introduces additional training overhead. To identify the optimal value of 0, systematically evaluated the impact of different sampling quantities, ranging from 2 to
23

---

Published as a conference paper at ICLR 2026
6, within the framework of environment codebook size of k 10, as shown in Table 10 Based on the results, we have determined the optimal value of 8 to be 4.
Table 10: Sensitivity analysis for the sampling numbers of environmental embedding.
7hangDDI
ChehMiner
DeepDDI
ACC (1)
AUROC (1)
F1 (f)
ACC (1)
AUROC (t)
F1 (t)
ACC
AUROC (1)
FI
0 2
88. (2
94.79(o.44
(..03
98. 98.61 (0.67
95.83
96.48.o.11)
(7.11
(7.277
(6)
94.74(0.10)
94.43(0.14) (5.07
08.68)0000
95.71.0.0)
(6.23(0.10)
97.93
97.37(0.10)
0
88 24)
95.12(0.22)
(5.87
95.34 (9.34
98. 98.84
(6.21
(6,51
99.04(u.2)
97.53
88. (8.299o.1))
(4.87(0.10)
85.41
94.38(0.18)
98.82(0.18)
95.61.a.0)
(6.18().12)
98.89(u.1)
97.28.
0 6
(8.24
94.85(o.a5)
(o.09
(4.577p.30)
98.76(u.0)
95.78
(6.34(a.2))
97.00
97.37
H VQ MODULE ANALYSIS
To further illustrate the role of the VQ module, we introduced extra variants for comparison: (1) RD Noise Variant: In this version, noise in the environment codebook is entirely random, mimicking the effects of random noise injection. (2) Serance--Deendenn (ID) Noise Variant: Here, we sampled new environments from the environment codebook and added them as small perturbations to the destance-dependent enviromment. The Gaussian distribution of this noise determined by the mean and variance of subgraph node vectors, emphasizing instance-dependent noisy perturbations.
Table 11: Performance comparison across different DDI datasets.
DD
ChchMiner
DeepDDI
Method
Acc (1)
AUROC (1)
Acc (f)
AUROC (f)
Ace (1)
AUROC (f)
RD noise
(7.21
93.76(0.13)
93.47(0..8)
97.52
92.39 (0.38)
(7.01(0.39)
ID noise
88.02(0.06)
94.47 (0.08)
94.27 94.27 (0.12)
98.54 (0.00)
94.56
(7.42
Ours
(8.64(
(5.12
95.34
98.84
96.51
99.04
Our experimental results demonstrate the superiority of the VQ module and the proposed optimization strategy, particularly in improving the model's robustness and ability generalize across diverse chemical environments.
I DATA SCALABILITY ANALYSIS
We have included the time and space complexity results for our model and various baseline models, along with comparison of model parameters in Table [2]nd and Table This table clearly showcases the results of various model parameters, time and computational complexity. Compared to other baseline models. 12Mole exhibits significantly larger number of total parameters, leading to substantially higher time consumption and computational complexity than the other baselines.
As the amount of training data increases and the test data decreases, the model's performance exhibits a notable improvement. is particularly worth mentioning that the model shows significant gains during the initial stages, but further increasing the training data yields only marginal improvements. Further, we evaluated the model performance under different training data sizes and model parameter conditions in Table [3 We control the model parameters by adjusting the number of message-passinng layers, dimensions of embeddings and feedforward NN.
12Mole also could naturally generalize other molecular relational learning tasks due to its pairwise merged-grae -raph design and interaction-forl focused information bottleneck theory. Therefore, we conducted an additional experiment to substantiate the model's applicability beyond classification-oni tasks. Specifically, we adapted 12Mole for regression by (1) replacing the final classification head with linear regression layer, (2) removing activation, normalization, and dropout, and (3) switching the loss function from BCEWithLogitsLos, to MSELoss. Without further hyperparameter tuning, we evaluated the model on five standard solute-solvent solvent datasets involving Gibbs free energy of solvation and hydration free energy (experimental and calculated) (Du et al. 2024 2025a). Despite minimal adaptation, 12Mole achieves competitive performance, comparable to strong baselines as present in Table 15
DDI
24

---

Published as a conference paper at ICLR 2026
J COMPUTATIONAL COMPLEXITY
Alongside increasing the model's complexity, there a clear rise in computational time, accompanied by performance improvements. This could be attributed the more intricate models being able to capture deeper inter-moleculat relationships, thereby enhancing performance. However, when the model's parameters are further increased, its performance starts degrade. This decline is likely due to overfitting, as the model becomes overly complex, leading to difficulties in convergence during training.
Table 12: Computational complexity analysis on 12Mole ZhangDDI dataset.
Model Parameter (M)
23.4
26.8
29.5
31.7
35.4
38.4
40.3
44.5
49
Time Consumption (h)
7.4
8.3
9.5
10.4
12.17
13.23
15.6
18.4
22.3
Performance (ACC)
83.61
85.94
87.43
88.27
88.64
88.64
88.35
87.91
86.87
Table Data scalability analysis on 12Mole on ZhangDDI dataset.
Training Data Ratio (%)
10
20
30
40
50
60
70
80
90
Test Data Ratio (%)
45
40
35
30
25
20
15
10
5
Performance (ACC)
53.27
65.27
72.34
80.34
88.27
88.64
89.01
91.34
92.25
The higher computational cost of 12Mole mainly arises from edge-level aggregation and message passing, as the constructed merged graph contains more relational edges, which are inherent to graph neural networks. We report two effective strategies that reduce cost while preserving most accuracy.
Improving the message-passing mechanism by using lightweight modules in certain layers. As shown in the Table [6] replacing the current MPNN layer with standard GIN backbone reduces the complexity to approximately one-fifth of the original, with only 44% drop in performance. consider replacing certain layers with GIN to reduce model complexity while ensuring performance.
Therefore,
By constructing a Molecular Merged Hypergraph Neural Network Du et al. (2025b) specific substructures of molecules, such functional groups, are defined as hypernodes, reducing the number of nodes the merged graph and thus lowering the model complexity. We have made preliminary attempts with the Hypergraph Neural Network (further optimizations is not within the scope of this work.), where the computational time can be reduced to approximately half of the original, and for larger molecules, the reduction in time consumption is even more significant, without sacrificing much predictive accuracy.
For further exploration, we consider replacing the current MPNN layers (Table 18 using layers) with GIN layers to better balance model complexity and performance. Our findings show that sub- stituting two the three layers with GIN significantly reduces model complexity (approximately 25% while resulting in only marginal performance drop of ~0.36%. Despite this slight decrease, the model still achieves SOTA compared the baseline. addition, integrating the model with a hypergraph neural network framework predefining functional groups or motifs hypern- odes can further reduce model complexity as present in Table [8] However, we observe that this strategy leads to lightweight GNN backbones and hypergraph frameworks to improve message aggregation and reduce the number of atomic nodes presents highly promising method, but further optimization and parameter tuning are needed.
noticeable decline in performance, about 33.5%% Therefore, employing
K LIMITATION ANALYSIS
I2Mole, based on the drug pair merged graph, achieves the extraction of rationale subgraphs in molecular interactions and combines the trained environment codebook, significantly enhancing generalization capabilities in domain generalization experiments. However, considering the rapid advancements in the pharmaceutical field and real-world prescription scenarios, we foresee improve- ments to the current framework in three key aspects:
25

---

Published as a conference paper at ICLR 2026
Table 14: Comparison of ZhI ChchMiner, and DeepDDI across different models.
Model
Metric
ZhangDDI
ChehMiner
DeepDDI
CGIB (Lee et al. 2023b
ACC
87.32
94.37
95.76
Time (h)
1.5
0.59
3.73
Memory (G)
5.1
3.9
7.4
Parameters (M)
11
11
11
CRML (Lee 2023c
ACC
87.78
94.43
95.49
Time (h)
1.3
0.47
3.24
Memory (G)
3.4
Parameters (M)
10
10
10
SSI-DDI (Nyamabo et al.
2021
ACC
86.97
93.26
94.27
Time (h)
1.77
0.65
4.08
Memory (G)
3.1
2.7
4.4
Parameters (M)
13
13
13
DSN-DDI (Li et al.
2023
ACC
87.65
94.25
95.74
Time (h)
1.2
0.43
3.08
Memory (G)
2.9
3.6
4.1
Parameters (M)
0.19
0.19
0.19
IGIB-ISE
(hhng et al. 2025b
ACC
88.08
94.92
95.85
Time (h)
8.7
2.9
22.8
Memory (G)
36.2
27.3
39.4
Parameters (M)
10.5
10.5
10.5
MMGNN (Du et al.
2024)
ACC
85.40
94.18
95.12
Time (h)
16.8
6.1
41.2
Memory (G)
38.1
30.4
39.7
Parameters (M)
389.10
389.10
389.10
Explainable GNN
(Low et al.
2022b
ACC
84.24
93.62
94.71
Time (h)
11.3
4.4
29.1
Memory (G)
20.1
15.3
18.6
Parameters (M)
39.10
39.10
39.10
MMHNN Duu et al.
2025a
ACC
86.17
94.55
95.43
Time (h)
9.6
3.8
25.6
Memory (G)
15.4
12.1
14.9
Parameters (M)
32.26
32.26
32.26
CasualIB (Zhang al.
2025a
ACC
88.14
94.94
95.86
Time (h)
15.4
5.4
33.8
Memory (G)
22.7
17.0
20.3
Parameters (M)
38.17
38.17
38.17
12Mole (Ours)
ACC
88.64
95.34
96.51
Time (h)
13.23
4.9
33.07
Memory (G)
17
13.3
11.7
Parameters (M)
35.4
35.4
35.4
We aim to acquire more comprehensive data on drug interaction processes and analyses between molecules, addressing the limitations of current research. In practice, patients often have multiple comorbidities requiring the concurrent use of various drug categories. Thus, the interaction system of multiple drugs remains a critical research area.
Constructing relationship edges in pairs, as previously done, is an effective strategy for predicting properties between molecular pairs. However, this approach significantly increases the graph's complexity, especially for large, intricate molecules, due to the substantial rise in degrees of freedom, leading to higher computational resource and time consumption.
26

---

Published as a conference paper at ICLR 2026
Table 15:
Test performance of different methods across eight independent runs, Mean values are reported, with standard deviations shown in parentheses. (The best result in each column is underlined, while the oo--performing baseline is marked with superscript dagger.)
MAR(U)
RMSE (i)
FrecSalv
CompSot
Abruhun
Comppoolty Exp
MNSSc
PreeSely
Compãol
Abcaham
CongSott- Exp
MINSi
D-MPNN
0.68
pa179
(4142
0.65%
166
0.343
0624ma20
0.667
Explairabie GNN
0.7244a
0.18haa12
3.686
0.321
0.367
0.633
SolvBEKT
0,585
0.167
6.3822
0.354
0.325o..0m
0.622aa2
0.472
GAT
0,675u
pu11))
(457
p.188
0.290
0.726pusm
0.100p.00))
GRUVER
0.625a
p.155
1.015ppes5)
0.332ax..
0.435mass
(.672
SMD
0.574g
0.162pato
(.574
1.113
0.317acm
0.516pass
1,023
(662
Uni-
0.565
0.164pam
0.322
(2214
p.002
0.303
0.373
Gem
0.584m
0.174pua1)
(.201
(.253
0.367
0.290
0.41mus
0.551pura)
(6675
CIGIN
0.56kar
0.164pua00
0.254
(.24
0.547
(.900)m)))
0.315
0.404mann)
0.1l
CGIB
0.156part
(.195
0.268
0.321
(.822
0.27%
0.391
a.35
I2Mole
0.535
p.158parr
g.189)
6.175
0.282
0.268 (.900
p.389
0.306
0,609
Table 16: Replacing the current MPNN layer with standard backbones.
GNN backbone
ACC (%)
Train time (s)
Test time (s)
Parameters (M)
GraphSAGE
80.26
514.80
50.88
21.3
GIN
91.35
188.10
19.27
21.4
GAT
87.42
376.40
36.12
22.4
Baseline
95.34
1020.62
90.61
35.4
An equally important aspect is that drugs often function only under specific conditions such as temperature and pH levels. Therefore, we anticipate future work to comprehensively consider the impact of external environments on the functionality of drug molecule pairs, thereby refining the model's capabilities.
L THE SCAFFOLD AND SIZE SPLITTING EXPERIMENTS RESULT.
The scaffold and size splitting experiments result are presented in Table 20
In the scaffold split, we follow the standard practice used in molecular OOD evaluation Chung et al. (2022b): Yang et al. (2022b). We first match all molecules against fixed set of SMARTS- defined scaffolds, consisting nine predefined core substructure patterns in Table [9] All molccules containing any of these scaffolds randomly divided into training and validation sets using a 9:1 ratio. This ensures that structurally distinct scaffolds appear exclusively in the test domain.
assigned to the test set. The remaining molecules are then
In the size split, following the procedure in Ji et al. (2023). we group molecules according to their atomic size (number of atoms). Molecules sorted in descending order of atomic size, and the ordered sequence is partitioned as follows: the largest 60% are assigned to the training set, the middle 20% the validation set, and the smallest 20% the test set.
M VISUALIZATION ANALYSIS
Acetaminophen, widely used medication for pain relief (analgesic) and fever reduction (antipyretic). frequently found in ther-the- formulations. However, unexpected drug-drug interactions (DDIs) between acetaminophen and compounds such as Fenoterol, Fosphenytoin, and Ethanol can pose significant threats to patient safety, as depieted in ( Specifically, the aromatic ring of acetaminophen, along with its surrounding functional groups, is capable of interacting with target molecules, particularly at the central carbon atom bonded to the carboxyl group. This key interaction has been effectively captured by the 12Mole model. Additionally, the core subgraphs extracted by 12Mole exhibit good connectivity and consistent distribution across regions, although the associated weights may vary.
As demonstrated in Figure (b). In the case of aspirin, a widely used anti infilmmmfmmtory drug that also serves analgesic, antipyretic, and, low doses, antiplatelet agent, its interaction with
27

---

Published as a conference paper at ICLR 2026
Table 17:
Comparison of ChehMiner across Hypergraph Neural Network (HGNN) and 12mole. AM: average number of atoms per molecule.
Model
Params (M)
AM=340
AM=549
AM=638
AM=722
AM=1934
ACC(%)
I2Mole
35.40 13.225
780.74
871.57
962.28
1012.22
1274.38 499.75
95.34
HGNN
350.27
437.63
456.94
478.81
92.37
Table 18: Comparison of ChchMiner across different models.
GIN layer
ACC (%)
Decrease
Train time (s)
Test time (s)
Params (M)
layer
95.07
0.27
757.79
70.38
31.40
2 layer
94.98
0.36
450.10
47.91
26.50
3 layer
91.35
3.99
188.10
19.27
21.40
2layer+HGNN
92.19
3.15
278.81
43.74
9.874
Baseline 95.34
1020.62
90.61
35.40
Table 19: SMARTS-definee scaffold patterns used in the scaffold split.
[ CI=CCCCI
C#[C&HI] clccc20(-.cel Jocc NS(= clccccc//N&++][550000)
C[C&H2JCI CICOCCNI O[N+[[O-I)=O
molecules like Ibrutinib, Eluxadoline, and Glipizide notably influenced by specific structural features. The aromatic branch of aspirin (excluding the carboxyl group region) is more prone to forming interactions with the during DDI events, the merged graph substructures of these molecules have enhanced propensity for direct interaction, leading to increased DDI potential. These observations provide important insights into the structural determinants of DDIs, further emphasizing the predictive capability of the 12Mole model in capturing complex inter-molecular relationships.
heterocycles of other molecules. This suggests that,
To further validate the interpretability of our model, designed evaluation strategy inspired by Zhong et al.) (2024) to benchmark the alignment between model-identified substructures and experimentally supported chemical knowledge. Specifically, curated dataset of 73 chemicals (perpetrators) known to inhibit metabolic enzymes through well-defined functional groups, thereby inducing metabolism-mediatee DDIs. These chemicals 13,786 DDI instances. We evaluate the model at three complementary levels. DDI-level matching examines the classification performance across all 343,036 MMDDI pairs in the dataset, comprising 171,518 true interactions- number reverse-order negative samples generated by flipping the semantic roles of the two drugs. The model must determine whether the predicted mechanism and direction for each pair are correct, i.e., whether drug truly affects drug Perpetrator-level matching further tests whether the model can correctly identify which drug in the pair acts as the perpetrator and which serves as the victim. Finally, Frequent Functional Groups Matching assesses substructure-leval interpretabilityy using a manually curated set of 73 chemicals known from the literature to cause metabolism-meddin mediated DDIs through specific functional groups or reactive substructures.
paired with other drugs to generate
drug A inhibits or induces the metabolism of drug B-and an equal
Using 12Mole, conducted interpretability analysis by comparing the substructures highlighted by our model with enzyme-inhie inhibition functional groups reported in the literature. The results demonstrate that model achieves DDI-level matching rate of 60.63%. a perpetrator-Ievel matching rate of 90.35%, and a frequent functional group matching rate of 78.42%, indicating that 12Mole captures key pharmacological substructures consistent with experimentally validated mechanisms.
28

---

Published as a conference paper at ICLR 2026
Table 20: The scaffold and size splitting experiments result.
Model
ZhangDDI
Chchminer
DeepDDI
Scaffold (1)
Size (1)
Scaffold (t)
Size (1)
Scaffold (T)
Size (1)
SSI-DDI
(3.34)
70.15 (2.47)
(1.22)
76.89 .82)
(2.22) (2.12)
(4.75().32)
MDF-SA-DDI
(9.34(1.37)
(0.46
(0.47)
84.23(0.63)
(0.32)
(0.37)
DSN-DDI
82.16(1.21)
80.38 (1.23)
(2.144
(1.92
(2.99
(6.53
CGIB
83.32
(0.8)))
89.47 89.47;1.10)
(1.43
89 89,56(2.22)
89.4 89.44(2.02)
CMRL
(2.25
(o.77
(9.78(1.24)
(1.49
90.76(2.a1)
90.77
IE-HGNN
83.05(0.88)
81.67 (0.69)
89.96; 1.12)
89.02(1.37)
91.02
(1.05(1.14)
IGIB-ISE
83.22
82.01 (0.73)
90.11 (1.05)
89.37
91.25 (1.77)
(1.32
Ours
83.45 (0.92)
82.55 (1.12)
90.32 1.71)
89.95(1.00)
91.76(2.63)
91.89 (1.42)
(a)
Acctaminophen
Aspiri
Fenoterol
Fasphenytain
Etannl
lbnutinib
Eluxadoline
Gipizide
Figure 7: Visualization of the important substructure pairs in six drug pairs, (a) Acetaminophen with Fenoterol, Fosphenytoin, and Ethanol drug ligands. And (b) Aspirin with Ibrutinib, Eluxadoline, and Glipizide drug ligands. The darker the color means the greater the weight.
N MAXIMUM COMMON SUBSTRUCTURE (MCS) ANALYSIS OF VQ ENVIRONMENTS
We further assess whether the learned VQ codebook captures meaningful structural patterns by performing an MCS exemplar analysis. In particular, we examine environment categories 5, 6, and 7, which contain 4,556, 20,278, and 7,666 molecular pairs, respectively.
To evaluate the structural coherence of each VQ environment, we computed both inter-category and intra-category MCS similarities. Since MCS is computed at the molecular level and the overall number of molecules large in our setting, the exact computation is computationally expensive. Therefore, we adopted a sampling-bass evaluation strategy:
Inter-category analysis: For each pair of categories, we randomly sampled 200 SMILES from each category. This yields 40,000 (200x200) cross-category molecular pairs. From these, we randomly selected 1,000 pairs and computed their MCS similarity. The resulting distribution reflects the structural overlap between the two categories.
Intra-category analysis: For each of the three categories, we randomly sampled 200 SMILES from all molecules assigned that category. From these 200 molecules. we randomly selected 500 molecular pairs and computed their MCS similarity. These 500 values characterize the structural consistency within the category.
Table 21: Interpretability evaluation results.
Evaluation Aspect
Hit-Rate (%)
DDI-level Matching
60.63
Perpetrator-level Matching
90.35
Frequent Functional Groups Matching
78.42
29

---

Published as a conference paper at ICLR 2026
The MCS similarity between two molecules G1 and G2 is defined as:
|MCS| SMcs min [G1l.
(32)
For each category, we report the mean and variance the intra-category and inter-category MCS similarities, and for each pair of categories. The results are in Table 22
Table 22: Inter-category and intra-category MCS similarity (mean variance).
Inter-Category
Category vs
Category vs
Category 6 vs 7
MCS similarity
0.2523 1224)
0.2366 11014)))
0.2491(0.1144)
Intra-Category
Category
Category
Category 7
MCS similarity
0.3458 12559)
0.3921(0..172)
0.3423((.1109))
Our MCS-based analysis shows that the inter-category and intra-category structural similarities differ substantially. This indicates that the VQ-based clustering not merely direct grouping of molecules by shared substructures. Instead, the VQ codebook is learned in a latent embedding space, initialized from distinet environment vectors env, and each environment substructure vector Senv is mapped through non-linear projection layer into the discrete code space as Equation 20) As result, although the learned codewords reflect meaningful structural patterns, they are not expected to correspond one-to-one to
structural clusters. As Lug converges, the model obtains stable codebook W, which clusters the infinite possible environment space E into discretized set of M finite environments represented by W.
Furthermore, we extracted representative MCS structure for each category. Specifically, for each category we randomly sampled 300 candidate molecules and computed the full 300x300 Tanimoto fingerprint similarity matrix. We then identified the "central" molecule, i.e., the one with the highest average Tanimoto similarity within the category and selected its top-40 nearest neighbors. Using RDKit, we computed the MCES shared by these molecules. The resulting representative MCS patterns exhibit clear qualitative differences across categories: Category 5 tends to capture exocyelic C-C motifs, Category is enriched in aromatic ring structures. and Category is dominated by non-ring nitrogen atoms. These differences further confirm that the learned VQ codebook organizes molecular environments into semantically coherent and structurally distinct groups.
Table 23: Representative MCS exemplars extracted for each VQ environment category.
Category
MCS exemplar (SMARTS)
Illusion
5
[466R]-611 [#66!R]
Exocyclic C-C
6
6-member aromatic ring
Aromatic rings
7
[#7& a !R]
Non-ring nitrogen atom
Overall, the VQ clustering results and the MCS analysis are not expected to align perfectly. Although the intra-category MCS values within each VQ cluster relatively small, indicating that molecules in the same VQ category do not necessarily share large explicit common substructures, it is interesting observe that each category nevertheless exhibits distinet representative MCS pattern, and these patterns differ clearly across categories. This behavior is consistent with the fundamental difference between the two approaches: VQ clusters substructures based on learned semantic similarity in the latent embedding space, whereas MCS groups molecules purely according to graph- graph-theoretic structural overlap. As result, VQ could capture higher-level or functional similarities that may not correspond to large MCS fragments.
30


Reviews:
[{"review_id": "DZvWHW2ph9", "reviewer": "Reviewer_vk1e", "summary": "This paper proposes I2Mole, an interaction-aware, invariant molecular relational learning framework for predicting properties of molecular pairs (with a focus on drug–drug interactions).\n\nThe key ideas are:\n1. build a merged graph that explicitly connects atoms across the two molecules and run intra- and inter-molecular message passing to model atomic interactions\n2. extend the Graph Information Bottleneck (GIB) idea to extract an invariant rationale (core subgraph) from the merged graph via controlled noise injection\n3. learn a discretized environment codebook (via vector quantization) that represents non-core environmental contexts and is used to encourage invariance / domain robustness.\n\nThe authors evaluate on three DDI datasets (ZhangDDI, DeepDDI, ChChMiner) and report consistent gains over baselines in transductive, inductive and domain-shift experiments.", "questions": "* Could you add some kind of error metrics (such as the standard deviation)  to the reported performance numbers, by training and inferencing the models multiple times with different seeds?\n* Could you include parameter-matched baseline comparisons or lighter model variants to better assess the cost–performance tradeoff?\n* There are many typos and grammatical errors throughout the text. A careful proofreading could help.\n* Please fix the styles for citations (do use `\\cite`, `\\citet` and `citep` wisely).", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "* Well-motivated idea. Explicitly modeling inter-molecular atomic interactions addresses a real limitation of existing single-molecule GNNs in pairwise tasks.\n* Novel combination of techniques. Extending GIB with a learned VQ codebook for structured noise injection is conceptually interesting and empirically effective.\n* Thorough evaluation. The experiments are comprehensive, including multiple datasets, settings, ablations, and statistical significance checks. The fact that performance gains are consistently observed on all settings is especially impressive.", "weaknesses": "* Marginal performance improvement. The proposed model is relatively heavy compared with baselines, and some gains (especially on larger datasets) are modest. It’s unclear whether improvements stem mainly from architectural bias or model capacity.\n* Presentation quality. The paper is dense and difficult to follow in several parts. Important design choices are buried in the appendix or described briefly. A clearer, higher-level walkthrough and cleaner notation would greatly improve readability. There are also some typos and grammatical errors throughout the text, such as 98-99 \"moderately and moderately\", 182-183 \"$u_i^{\\'}$\", etc.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "ZsqlivnNkF", "reviewer": "Reviewer_E6Gc", "summary": "This paper proposes I2Mole, a DDI-focused framework that builds a merged intermolecular graph with atom–atom links, applies a GIB-style subgraph extractor, and augments invariance via a learned environment codebook (VQ) for robust generalization. On three DDI benchmarks, the method reports consistent gains in transductive, inductive, and domain-shift settings, with ablations supporting the roles of intermolecular interactions, GIB, and the codebook.", "questions": "- There are two “moderately” words on p.2 line 99 (typo).\n\n- What exact pair embedding is used for the t-SNE plots?\n\n- Which dataset underlies Figure 5a?\n\n- Please list the bond/edge features used for intermolecular connections.\n\n- Model names are missing in Tables 12 and 13—please restore.\n\n- How exactly are scaffold and size splits implemented?\n\n- For interpretability, specify the matching criteria for “DDI-level, perpetrator-level, frequent functional group,” and how key substructures are selected.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "- The paper’s formulation—merged graph + GIB-based rationale + VQ environment codebook—is clearly specified theoretically and experimentally ablated. \n\n- Results span transductive/inductive/domain-generalization regimes with competitive numbers and reasonable sensitivity analyses.", "weaknesses": "- Please streamline the paper’s scope to drug–drug interaction prediction. The architecture (pairwise merged graph, DDI benchmarks) is DDI-specific; claims about “molecular property prediction” (generally single-molecule, regression) or broader molecualr interaction tasks (e.g., DTI) feel overstated without evidence.\n\n- Many DDIs arise from shared or convergent pathways rather than direct atom–atom contacts. This is not well captured by purely structural intermolecular edges.\n\n- Although the authors state I2Mole “models van der Waals and hydrogen bonds,” Eq. 5 effectively creates fully connected cross-molecule edges and top-x% pruning; without 3D interatomic geometry, this is not an explicit physical interaction model. This is an another overstated claim in this study.\n\n- The top-x% selection for intermolecular edges is non-differentiable; it would be suggested to use a differentiable sorting relaxation (e.g., NeuralSort/SoftSort) to avoid potential gradient issues, or justify why straight-through works here.\n\n- Several tables/figures appear inconsistent (e.g., optimal I2Mole performances on ZhangDDI differ between sensitivity and ablation/comparison tables). Please reconcile and ensure one canonical set of results across Tables 4–5/9/10/12/13 and the main comparison tables.\n\n- For interpretability, Figure 5’s element-level analysis is coarse. Consider adding maximum common substructure (MCS) exemplars per environment to indicate whether the codeboook can actualy learn and clustering chemical structures or not.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Xucnmy3fdc", "reviewer": "Reviewer_WU3y", "summary": "The paper proposes the I2Mole framework, aiming to improve model generalization and interpretability in drug–drug interaction (DDI) prediction scenarios. The framework constructs merged molecular graphs, applies an enhanced graph information bottleneck, and develops a molecular environment codebook to model atomic-level interactions and extract core substructures. By performing invariant learning on these substructures, the method enhances the model’s capability to generalize across different data distributions.", "questions": "See the weaknesses.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 1, "contribution": 2, "strengths": "1. The experiments are relatively comprehensive, and the reported results demonstrate strong performance.\n2. The paper provides extensive visualizations, which are beneficial for achieving a clear understanding of the proposed methodological design.", "weaknesses": "1. The scientific significance of the problem addressed in the manuscript is not clearly and specifically articulated. The lack of generalization in previous methods within this domain is a common issue across many fields; however, it would be preferable if the manuscript could provide a more concrete and well-defined scientific contribution.\n2. The manuscript lacks strong observational analysis. Most of the nine observations presented are general descriptions without in-depth or insightful examination. Highlighting these observations in bold as if they were substantial analyses appears inappropriate.\n3. There are typographical errors in the manuscript, such as the misspelling “realted work” on page 15.\n4. In the initial modeling stage, the authors establish models for every possible atom pair between the two molecules, and then perform filtering to characterize hydrogen bonds and van der Waals forces. I would like to know whether the authors have reliable justification ensuring the correctness of the hydrogen bond modeling (as this likely involves some specific filtering steps).\n5. Regarding the “molecular environment codebook” mentioned in the manuscript, I would like to know what exactly is meant by “molecular environment” in this context, and what its precise definition is within the field of chemistry.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "xdq1GMbJhB", "reviewer": "Reviewer_qi4Q", "summary": "I2Mole predicts drug–drug interactions by constructing a dense merged molecular graph that connects every atom in one drug to all atoms in its partner, followed by attention-guided pruning to retain only the most informative inter-molecular edges. A Graph Information Bottleneck (GIB) module then compresses the pruned graph into an invariant “core substructure”, while a vector-quantized environment codebook captures contextual variations across molecular pairs. Trained end-to-end, I2Mole jointly optimizes node embeddings, attention-based pruning, information compression, and codebook assignments. Experiments show strong performance across various DDI benchmarks, especially in out-of-distribution settings.", "questions": "See Weaknesses.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1.\tThe approach introduced in this study is well-structured, with clear methodology.\n2.\tThe experimental section is comprehensive and solid, encompassing benchmark evaluations, interpretability analyses, and detailed examinations of the codebook module.\n3.\tUsing GIB and invariance learning to model inter-molecular interactions makes the model more interpretable. \n4.\tCompared to many existing approaches, the proposed method shows stronger performance and better generalization across three DDI prediction benchmarks.", "weaknesses": "1.\tThe work does not report results on widely used DDI benchmarks, such as DrugBank and TWOSIDES. \n2.\tThe evaluation is scoped to DDI only: results are limited to DDI, with no experiments on other interaction tasks. \n3.\tHow much do you expect external physicochemical factors such as pH or temperature to alter the significance of your results？\n4.\tIncluding an analysis of the physicochemical mechanisms underlying the modeled interactions could be added further validate the effectiveness of the proposed model.\n5.\tThe manuscript contains a few typographical errors, which do not affect the overall quality of the work. For instance, Howevew->However ，REALTED WORK -> RELATED WORK.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)