Iterative Substructure Extraction for Molecular Relational Learning with Interactive Graph Information Bottleneck
Authors: Shuai Zhang
Junfeng Fang
Xuqiang Li
hongxin xiang
ALAN XIA
Ye Wei
Wenjie Du
Yang Wang
Venue: ICLR 2025 Poster (2025)
Keywords: Molecular Relational Learning
EM Algorithm
Substructure Extraction
Interactive Graph Information Bottleneck
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)

Abstract: Molecular relational learning (MRL) seeks to understand the interaction behaviors between molecules, a pivotal task in domains such as drug discovery and materials science. Recently, extracting core substructures and modeling their interactions have emerged as mainstream approaches within machine learning-assisted methods. However, these methods still exhibit some limitations, such as insufficient consideration of molecular interactions or capturing substructures that include excessive noise, which hampers precise core substructure extraction.
To address these challenges, we present an integrated dynamic framework called Iterative Substructure Extraction (ISE). ISE employs the Expectation-Maximization (EM) algorithm for MRL tasks, where the core substructures of interacting molecules are treated as latent variables and model parameters, respectively. Through iterative refinement, ISE gradually narrows the interactions from the entire molecular structures to just the core substructures.
Moreover, to ensure the extracted substructures are concise and compact, we propose the Interactive Graph Information Bottleneck (IGIB) theory, which focuses on capturing the most influential yet minimal interactive substructures. In summary, our approach, guided by the IGIB theory, achieves precise substructure extraction within the ISE framework and is encapsulated in the IGIB-ISE}
Extensive experiments validate the superiority of our model over state-of-the-art baselines across various tasks in terms of accuracy, generalizability, and interpretability.

Published as a conference paper at ICLR 2025
ITERATIVE SUBSTRUCTURE EXTRACTION FOR MOLEC- ULAR RELATIONAL LEARNING WITH INTERACTIVE GRAPH INFORMATION BOTTLENECK
Shuai Zhang Junfeng Fang!* Xuqiang Li Hongxin Xiang*
Jun Xia
Ye Wei? Wenjie Du 33,47 Yang Wang!.3.4
1 University of Science and Technology of China (USTC)
2 School of Computer Science and Technology. USTC
3 Suzhou Institute for Advanced Research, USTC
4 State Key Laboratory of Precision and Intelligent Chemistry, USTC
5 Hunan University 6 Westlake University T City university of Hong Kong
(shuaizhang. xuqiangli, duwenjie @ mail.ustc.edu.cn [[angjf1997, yeweiastronomer/ @ gmail.com angyan@ustc.edut
xianghx @ hhnu.ddu.n Xiajun westlake.edu.co
ABSTRACT
Molecular relational learning (MRL) seeks to understand the interaction behaviors between molecules, pivotal task domains such as drug discovery and materials science, Recently, extracting core substructures and modeling their interactions have emerged mainstream approaches within machine learning-assisted methods. However, these methods still exhibit some limitations, such as insufficient consid- eration of molecular interactions or capturing substructures that include excessive noise, which hampers precise core substructure extraction. To address these chal- lenges, we present an integrated dynamic framework called Iterative Substructure Extraction (ISE). ISE employs the Expectation Mitiiiontiiiiiztiioonnn (EM) algorithm for MRL tasks, where the core substructures of interacting molecules are treated as latent variables and model parameters, respectively. Through iterative refinement, ISE gradually narrows the interactions from the entire molecular structures to just the substructures. Moreover, to ensure the extracted substructures concise and compact, we propose the Interactive Graph Information Bottleneck (IGIB) theory, which focuses capturing the most influential yet minimal interactive substructures. In summary, our approach, guided by the IGIB theory, achieves precise substructure extraction within the ISE framework and is encapsulated in the IGIB-ISE. Extensive experiments validate the superiority of our model over state- of-the-art baselines across various tasks in terms of accuracy, generalizability, and interpretability. Our code can be found at http://hhww..oommooongui//////a/
INTRODUCTION
Molecular relational learning (MRL) Rozemberezki et al. (2021 Fang et al. (0244) Du et (024)
aims to represent interaction properties between molecules, such as potential drug-drug interactions (DDI) Xiong et al. (2022), chromophores Ye al.) (202T) different solvents etc., which has gained significant attention. The core substructure of molecules embodies the essence of their physicochemical properties in molecular interactions Chi et al. (2010); Bender & Glen (2004). As shown in Figure (a)), styrene oxide exhibits primarily blue fluorescence in hexane due its epoxide moiety, while in acetonitrile, the fluorescence shifts to a yellowish hue due to the influence of its vinyl group. For capturing interaction behavior between molecules, current models often rely the chemical prior that core substructures encapsulate key characteristics of molecular, i.e. the linchpin Book 42014); Jerry (T992).
"quual Contribution
Corresponding Author

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(a)
[D]
[c)
M0
Styrene (Sclute)
Core substructure
Category|
Category
Category (Ours)
Hexane (Sovent)
G1
Inital state
Dissoution
Homogeneous solution
Styrene oxide (Sclute)
Core substructure
G+1
GZZ
Gst
GA
G
G
Acetonirila
(So vent)
Intal state
Dissoution
H Homogeneous solution
Predictin
Prediction
Prediction
Figure 1: (a) shows the differences in fluorescence emission of styrene oxide in various solvents, while (b), (c), and (d) compare different paradigms for MRL. Best viewed in color.
In order to accurately mine these vital substructures, prevailing methodologies can be broadly categorized into two categories. Category I (Figure (b)) exemplified by models such as SSI-DDI Nyamabo et al. (nd STNN-DDI Yu (2022a) which individually obtain substructures from each molecule before subsequent interaction. However, such methods present notable limitations. Primarily, the isolated extraction of substructures from each molecular neglects the potential interplay between different molecular substructures. This overlooks the fact that the selection of substructures for one molecule can be significantly influenced by another, depending on the specific task Lang let al. (2021). This leads to somewhat superficial understanding of MRL, failing to fully grasp the dynamic and interconnected nature of molecular interactions in the biochemical context Sillvermnn & Holladay 2014); Böhm et al. (2004); Schneider al. (2018).
In sight of this, Category II (Figure (c)) Li et al. (0033) have pivoted towards a more holistic
approach address these limitations. These methods simultaneously consider a second molecule as a conditional factor during the generation of a molecular substructure Lee et al. (2023)) This paradigm shift ensures that the substructure generation is not an isolated event but an interactive process. However, such methods also present their challenges. Considering that core substructures 2009)::yamabbo
Lee
often play a crucial role molecular interactions Jia et al. (2009); Nyamabo et al.] (202T), integrating the complete profile of an interacting molecule into the substructure generation can be overwhelming, carries the risk of compromising generalizability and the inclusion of redundant information Lee eet al. (2023b); Tang et al. (2023), particularly for molecules that share similar structures yet exhibit significant functional divergence in specific combinations, e.g., Activity Cliff' Tamura et al. 2023)
Van Tilborg al. ) Schneider et al. (2018).
Considering these factors, we aim to harness the interaction effects of core substructures to fa- cilitate the process of interactive substructure extraction. In this paper, we propose the Iterative Substructure Extraction (ISE) framework. As shown in Figure ISE employs the Expectation- Maximization Dempster al. (977) (EM) algorithm iteratively uncover core interactive substruc- tures between molecular pairs, where two molecular core substructures are regarded as latent variables and model parameters, respectively. Under the premise of molecular interactions and inherent symme- try. ISE facilitates iterative interaction and substructure selection between the two graphs, ultimately identifying the optimal core substructure combination. This ensures that the extracted substructures depend solely on the core substructures of another molecule, thereby minimizing the influence of extraneous structures and enhancing alignment with the essence of molecular interactions.
Furthermore, to ensure that the ISE framework obtains concise and compact interactive substructures, we draw inspiration from the Graph Information Bottleneck (GIB) theory Wu et al. (2020a). method used to extract core cubstructure-based compressed variable information from single input graph. We introduce the Interactive Graph Information Bottleneck (IGIB) to ensure comprehensive consideration of substructure information from another graph during the process of substructure compression, achieved through the introduction of conditional mutual information. IGIB lays down theoretical foundation and establishes precise optimization goal for the analysis of biochemical molecule interactions and the mining of interactive substructures.
Our contributions can be summarized as follows:
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We identify and articulate the limitations of existing Molecular Relational Learning methods in addressing the problem of core substructure extraction. For the first time, we redefine this problem in the context of the Expectation- -aritattinn-Maiiizzttioon (EM) algorithm and propose the ISE framework, which employs iterative coupling of substructures to optimize the extraction process.
We introduce IGIB as theoretical foundation for Molecular Relational Learning, more consistent with chemical principles. IGIB-ISE is highly compatible with our ISE framework, representing a paradigm shift that emphasizes the importance suter-substrecture dynamics in capturing the essence of molecular interactions more effectively.
The superiority of our approach is empirically validated through extensive experiments multiple Molecular Relational Learning datasets. Our method outperforms existing approaches in terms of accuracy, generalizability, and interpretability in MRL. Notably, our ISE framework revitalizes the interpretable research of core substructures, shedding light on the selection process of essential interactive substructures.
2 PRELIMINARIES
In this section, first formally describe the problem formulation (Section 2.
Then, introduce
the Graph Information Bottleneck (GIB) theory Wu et al. (2020b) (Section 2.2 Finally, we introduce the key variables and the execution process in the EM algorithm (Section
2.1 PROBLEM PREDEFINITION
A molecule can be naturally represented as graph, G = (V,E), E), where V represents the set of nodes and & denotes the set of bonds. the context of MRL, for each data point the dataset, we receive pair of molecular graphs, 91 and G2 as input, along with their associated label Y. The label Y is scalar value, i.e., Y (-o0, oo), for molecular interaction prediction tasks, while is a binary class label, i.e., Y E {0, 1}, for the binary classification task. G. and G.2 represent the subgraph of Gi and G2 respectively, with subgraphs corresponding to the molecular substructures.
2.2 GRAPH INFORMATION BOTTLENEEC
In graph-related tasks, discerning which substructures within a graph are significant and which are not is essential. The GIB method addresses this challenge by learning bottleneck graph GIB for given graph G. This approach compresses the source graph to retain the structures pertinent to predicting the target random variable while discarding those irrelevant to the target Yu et al. (2020) 2022b); Miao et (2022).
Definition 2.2 (GIB): Given an input graph & and label Y, GIB aims to extract compact subgraph GIB. while keeping the information relevant for predicting Y by optimizing the following objective:
arg min (m; - (G; GmB)
9IB
where ((--)) denotes the mutual information Tishby et al. (2000) between random variables. | is Lagrangian multiplier for balancing the two mutual information terms.
2.3 EXPECTATIOO-MMXXIMIATTOOO MAXIMIZATION ALGORITHM
The ISE framework utilizes the EM algorithm Dempster et al. (197). The EM algorithm is designed to handle situations involving observed variables. latent variables. model parameters, and their distributions. It iteratively estimates parameters in probabilistic models, with particular focus on latent variables. This iterative process consists of two steps: the E-step, which computes the posterior probabilities of latent variables, and the M-step, where model parameters updated by maximizing the likelihood using expected values obtained from the E-step.
3 METHODOLOGY
In this section, we introduce our proposed method. First, we define the Interactive Graph Information Bottleneck (IGIB) (Section 3.1). Then, detail the application of the EM algorithm within the ISE
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Molecular Graph Encoder
Meertiive Substructure Extractor
Interactive Graph Information Bottlenack
heomt
Selector
Graph
Encodits
Prediction
f2
Interadtion
Kyot
Label
Selector
fecou
Label
Prediction
912
Gsa
Lup
EM Framework
Noise vector
Figure 2: The overall framework of our proposed IGIB-ISE. Best viewed in color.
(Section 3.2). Next, we present the architecture of interactive substructure extraction (Section 3.3 Finally, we describe the entire model optimization process based on IGIB (Section
3.1 THE THEORY OF INTERACTIVE GRAPH INFORMATION BOTTLENECK
We introduce the IGIB theory to guide interactive substructure extraction in MRL tasks. Specifically, for two input graphs G1 and G2 and their interaction label Y. IGIB posits that the generation process of the interactive substructures 9s1 and 922 should not only maximize the mutual information between the substructures and the target output Y, but also minimize the mutual information between G.1 and the original graph 91 when conditioned on 92 (and vice versa for 922). Notably, the condition here is based the substructure rather than the entire original graph as in CGIB Lee et al. (2023a), thereby mitigating the influence of redundant and irrelevant information. We formalize this theory as Definition 3.1 and refer to it as IGIB.
Definition 3.3 (IGIB): Given a pair of graphs G1 and G2 and their label information Y, IGIB aims to extract pair of compact yet maximally informative substructures Ga1 and Ga2, which related to each other by optimizing the following objective:
arg min I (Y: Go2) I1I (91: G.1 922) + B2I (92; 9s2 9m1), 9.2
(2)
where 31 and B3 are trade-off parameters. Note that the two parameters 31 and B3 incorporated by the above equation designed to adapt to the unique scenarios in MRL where the interaction between two molecules is not entirely symmetrical.
By focusing on the essential information within the substructures and minimizing extrancous features, IGIB provides a more efficient and task-specific way of handling the complexities inherent in molecular interaction modeling.
3.2 EM ALGORITHM FOR ITERATIVE SUBSTRUCTURE EXTRACTION
The assignment of variables: From the perspective of the EM algorithm, we re-examine the relationship between input molecular graphs G1, G2, substructures GsL, Gs2, and label Y. Firstly, 9. 92. and can be directly provided by the dataset. Therefore, Yg is regarded as the observed variahles, including G1 G2. and Y. Secondly, because most interactions between molecules arise from the interactions between core substructures, the contribution of G1 and G2 to Y is through G.1 and G.2 (substructures). We designate G.2 as the latent variables. For G.I. considering that the core interacting substructures between molecules influence each other, the latent variables Go2 are influenced by the substructure G.1. Thus, G.1 1 is regarded as the model parameters (vice versa).
Iterative process: E-step: Estimate the latent variables G.2 while freezing the model parameters G.t. then utilize it to calculate the Evidence Lower Bound (ELBO), M-step: Refine the optimal model parameters G.1 which maximizes the ELBO obtained in the E-step. The procedure marked by green lines in the EM framework of Figure represents regure2repr the E-step, while the process indicated by blue lines corresponds to the M-step. Their optimization targets are defined as follows, where (t) is denoted by the iteration step.
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Initialization:
Given two molecular graphs 91 and 92, set 9 91.
E-step: Estimate the substructure 9/2 according to - and then calculate the ELBO:
P(g Yg 9
ELBO +
g Yo.gf
flog
(3)
P(g Yg. Gg. g
M-step: Find the corresponding substructure (1+1) that maximizes the above ELBO:
P Yg 9.. P Yg, (f)
arg max E 9x1 Yo.s
g [log
Output: Iteratively execute E-step and M-step, then output the interactive substructures G.1 and G.2.
For the detailed derivation of E-step and M-step, please refer to Appendix B.2 and B.3 proof of ISE framework is provided in Appendix B.4
Convergence
3.3
ARCHITECTURE OF INTERACTIVE SUBSTRUCTURE EXTRACTION
The architecture of interactive substructure extraction consists of the molecular graph encoder and iterative substructure extractor.
Molecular Graph Encoder. For the molecular graphs G1 = (V),E) and G2 (V2, E2), we employ GNN for their encoding:
E))
P2 GNN(V2, &2)
(5)
where F(1)) N and F((1) (1) N xd the node embedding matrices for 91 and G2, respec- tively. Next, we focus on expanding node features. This expansion is based on the interaction architec- ture of CIGIN Pathak et al. (2020). To facilitate the interaction between two graphs, the graph-graph interaction map I E N x is computed by using the following equations: Lij = sim
((() F())
1r
where sim(.)) :) denotes the cosine similarity. Here, N and N2 represent the number of nodes in Gi and G2, respectively. Next, we compute the embedding matrices F(2) E R and F:(2) R each embedding matrix incorporating information from its paired graph. These matrices are derived based the interaction map as follows:
F(()) I F,,,", F/(3) IT F(", where (-) denotes matrix multiplication. Based on these, the aggregation operation of node features can be completed follows: H1 features of G1 and G2, and denotes the concatenation operation.
H₂ F | where H2 and H2 are the final node embedding
Iterative Substructure Extractor. Initially, we initialize (0 91 and H Hi, where H.1 represents the node embedding features of G.1-
E-step: The interaction operation employed in molecular graph encoder along with a two-layer Multi-Layer Perceptron (MLP) is utilized to assess the importance of each node in G2 as expressed by:
( st
(t-1) H22), p(t) Sigmoid (MLP (I H.)).
(6)
Inspired by the theorys of information bottlenecks Tishby et al. (2000) and focusing on node significance, we introduce random noise into nodes to facilitate substructure extraction, suggested by Yu et al. (2022h). This process involves the following operations:
1 h1 + (1
{ log
A Sigmoid
p
+ log
(8)
P
where i represents the node number in G2. h4 represents the embedding feature of node i, X is drawn from Bernoulli distribution with probability ( To ensure differentiability in the sampling
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process, adopt the Gumbel sigmoid Maddison et al. (2016); Jang et al. (2016) for the discrete random variable x The transmission probability P;
(c) regulates information flow from h; to h
The parameter adjusts sensitivity to noise randomness, and is drawn from uniform distribution, Uniform(0, 1). Thus, the interactive substructure 9 from G2 is successfully extracted because nodes excluded in this process have been injected with noise, diluting their inherent information.
The interactive substructure 0.1-1) is obtained based 9 achieve maximum likelihood. Due to the symmetric nature of molecular interactions in MRI,, we employ the same network architecture in the E-step to determine ((t+1)) Finally, upon completion of the iterations, the set2set network Vinyals et al. (2015) utilized to pool the substructures Gs1 and g22, resulting in the substructure representation vectors 2G,, and =G.2- These vectors
M-step:
compact representations that encode the essential information of the substructures for further prediction.
3.4 MODEL OPTIMIZATION BASED ON IGIB
We provide the upper bound of the intended Definition 3.1 which should be minimized during training.
Minimizing - (Y; 9Y1 922): We consider Pg (Y 941. 922) as the variational estimation of P(Y 9s.. 922). Thus, we derive:
Pe (Y Gsl)
2 9.199))) log
P(Y)
= E S.2) log Pa (Y Ga1, Ga2)l + H(Y) == Spres
where H(Y) is constant across all data, will be omitted the model optimization process.
Minimizing (91; 9s1
9s2): Based the chain rule of mutual information, decompose it into:
I (91; Gat G22) = ( - (G.1i
(10)
For I(Gs1; : 91, 9s2), 2g., represents the encoding of G.1. Minimizing [Ge1 91, Go2) is equivalent to minimizing (zg., G1, 9.2). We approximate I (2g.. G1 9s2) using a variational inference approach ((25,)) ) as an estimate for p(=g..).
pp (zg.1 11 Gs2)
I (zg.1 91, 9s2) = (e0, (1.0 log
(2gg.)
(11)
pv (zg., 191 Go2)
(.) log
E, (=0,,, 01.922)
KL (p (zg.1) [lg (zg,,)).
q (2q.1)
Here, the function pa refers the objective of the process described in Section 3.3 which is based on the EM algorithm and aims to generate G.1. Given the non-negativity of the Kullback-Leibler divergence, it follows that:
I ( 91, < Egg, KL (po (zg., (1,9 ||q (zq..) Leom
(12)
For the term 7 (G.1; G.z), it is necessary to augment the mutual information between G.1 and Gaz- To achieve this, we employ contrastive loss function Tian al. (2020); HHjelm al. (2018). which has been demonstrated to effectively increase mutual information. The contrastive loss is defined as:
1 K
exp(sim(2)) G. 1/T)
Lcont
log
(13)
بز= exp(sim( =(..)/T)
where sim(.-) denotes similarity function, the superscript denotes different pairs of molecules, and 7 is a temperature parameter employed to adjust sensitivity to the similarity between samples.
Minimizing (G2; 9o2 Ga1): The upper bound of the objective function is obtained similarly to minimizing I (91:0 G.1 9.2). leading to the derivation of additional loss functions Leom2 and Lconz:
Loomz E.GG....) KT. (po (Eg.a G2, Ga1) (=G.2)),
(14)

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1 K
exp(sim( " G.gr (/,1
Lcon2
log
(15)
k مز=يير (up(sim(z)) (/,,, )/T)
1/T)
In summary, our overall loss function equation I6 serving as an upper bound for equation 2 constructed by combining these components to optimize our IGIB-ISE:
is
Suum Cpre + 31 (feoml + feom1) ) + B2 (foom Leowz) + Soups
(16)
where 81 and B2 is the trade-off parameters. Ssup is the prediction loss between label Y and the pair of input graphs (91, G2). Here, Cpre can be modeled as the cross entropy loss for classification and the mean square loss for regression. Lcom1 and Leom2 represent KL divergence between extracted interactive substructures and the noise graph, encouraging substructure compression. Ceon and Leon2 denote contrastive loss between two substructures reinforce their relationship. The detailed proofs for Lpre and Leoml will be provided in Appendix [B.3 B.6
4 EXPERIMENT
In this section, we conduct extensive experiments to answer the following questions:
RQI:
Can our model enhance the performance of molecular relational learning tasks?
RQ2: Does the interactive extraction of substructures improve the performance of IGIB-ISE?
RQ3: How effective the ISE module terms of interpretability?
4.1
EXPERIMENTAL SETTINGS
In this section, we briefly introduce the datasets, baselines, and evaluation metrics. More details on experimental settings, dataset descriptions, baseline introductions, hyper-parameet selection, and the performance of the models on additional evaluation metrics are provided in Appendix [D3 and 7
Datasets. To evaluate the performance of our model, conduct experiments based nine datasets. For the molecular interaction prediction task, we utilize the Chromophore dataset et al. (2020), including absorption, emission, and excited state lifetime. Additionally, MNSol Marenich al. (202)), FreeSolv Mobley & Guthrie (2014), CompSol Moine et al. (2017), Abraham Grubbs et al. (20T)), and CombiSoly Vermeire & Green (021a) are also considered, which describe the solvation free energy for colute-solvent pair. For the drug-drug interaction prediction task, we incorporate three DDI datasets, including ZhangDDI Zhang et al. (2017), ChChMiner Zitnik al. (2018) and DeepDDI Zitnik et al. (2018). which record the adverse reactions between drug-drug pairs.
Vermeiir
Baselines. For both tasks, we compare our method with the diverse SOTA models that could be regarded as three categories, as shown in Figure CGIB et al. (2023a). CMRL et al. (2023b), and CIGIN Pathak et al. (2020) have widely proven their superiority on MRL. For the drug-drug interaction prediction tasks, we chose routine SSI-DDI Nyamabbo al. 2021), GoGNN Wang et al. (2020), DSN-DDI Li et al. (2023) and MHCADD Deac el al. (2019). For the molecular interaction prediction tasks, chose additional models D-MPNN Vermeire & Green (202 Explainable GNN Low et al. (2022), and UNI-MOL Zhou et al. 2023), due to the single-task nature of these baseline models.
Evaluation metrics. The performance of the molecular interaction prediction task is evaluated by RMSE Pathak al. (2020), while the DDI prediction task is evaluated in terms of classification accuracy Wang et al.
2021
4.2 PREDICTION PERFORMANCE (RQ1)
The empirical performance our model is summarized in Table and Table 2 respectively. Our observations follows:
Obs.1: IGIB-ISE outperforms other baselines in both molecular interaction prediction and drug-drug interaction prediction tasks. The experimental results in Table Tnd Table illustrate
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Table I: Performance on molecular interaction prediction task (regression) in terms of RMSE.
Chromophore
Model
MNSol
FreeSolv
CompSol
Abraham
CombiSoty
Absorption
Emission
Lifetime
Category 1
Explainable GNN
(1.0
28.00 (.43)
0.834 (o017))
0.673 00024)
1.258 yous4)
0.353 01202)
0.751 (00244)
0.417 coumy
UNL-MOL.
0.637
1.210
0.339
0.672
0.629
CIGIN
19.47 0134)
25. 17 0123)
0.815 mont
0.644 (oazz)
1.013 ao
0.301 01205)
0.435 (oona)
0.498 co
D-MPNN
24.08
29.34 (053))
0.829 (iu02))
0.667 (0d17)
1. 1.107 00
0.303 m..03)
0.608 (0030)
0.559 100000
Category II
CGIB
18. 15.05 0134)
21.62 01229
0.783
0.613
0.918
0.279 00.05)
0.386
0.4
18.2 01333
25.69 00.37)
0.791 (oaae))
0.623 (o009))
0.927 10104)
0.274 00.204)
0.375 (00008)
0.423 c0
Category III
ISE
17.81 (03t)
24. 06 w.4t)
0.773 mab0
0.607 mo00:
0.825 co0)
0.205 (0.013)
0.300 (0014))
0.400 000000
IGIB-ISE
16. 12y
23. 83 (0:700
0.747 m011)
0.572 01.014
0.713
0. 262 on 010
0.343 (1204))
0.394 (oo00))
Table 2: Performance drug-drug interaction prediction task (classification) in terms of ACC.
(a) Transductive
(h) Inductive Setting I
(c) Indiective Setting
Model
ZhangDi
ChChMiner
DeepDDI1
ZhangDDi
ChChMiner
DeepDDI
ZhangDDI
ChChMiner
DeepDDI
Category I
GoGiNN
84. mon
91-17 0:50
93.35 54 0:95
51 (1.4)
67.48 ( 5o
67. 53 5%
67.37 coer
64:27 (1:0)
63.96.066
CIGIN
85.98 wnr
02.71 aus
93. 29 amm
05.27
76.30 942
71.84 moss
67.11
64.25 (2.3)
65.54 (299)
SSI-DDE
86.97
93.26
27
02.38
76.94
69.77
57. 67.24.0
65.61
66.53
MHCADDI
oum
(094)
87.01 (07))
61.81
65.77 (076)
63.94 (008)
57.84 (2.00
(9.21
01.17 (2m))
Category
CMRL
87 oum
94.13 m225)
96, 99 (034)
68, 58
$0.54 su.0
74. 12 (u55)
59: (1.3)
07:09 (1.54)
08. 29 (171)
CGIB
67.69
91.68
95. 76
68.3
80.67
74.29
58.
68.75
26
DSN-DDI
0026
0034)
79.96 50/23
59. 10.11... 11:20
(1.24)
69.
Category III
ISE
88. 45 mu-z
91.82 man
96.15 is
67 66 (uzz
80.20 suss
74. duss
56. 11:40
69.27 (1,00
12:422m (124)
IGIB-ISE
88.84 0u30
95. 56
96. 65
66. 75
81. 15
75. 28
59 96,96-11 (1.29
70. 31.34 50
70.54
significant improvements. We argue that our model architecture, which iteratively extracts interactive substructures, can extract more accurate substructures. This ensures that more precise information can be provided in subsequent prediction tasks, thereby enhancing the performance of the model.
Obs.2: Our model also demonstrates excellent generalization performance in various inductive settings. We conducted additional experiments in two inductive settings: Setting I ensures that at least one drug is unseen in the test dataset while Setting 2 ensures that both test molecules are unlearned (as shown in Table 2 (b) and (c)). IGIB-ISE achieves higher prediction accuracy across three datasets, showcasing its superior generalization capabilities. This heightened performance can be attributed to the extensive interaction among captured core substructures, underscoring IGIB-ISE's practical utility, especially in handling emerging drug molecules.
Obs.3: The performance exhibits a clear ascending order for Category I, Category II, and our model. Compared models lacking intermolecular interactions (Category I), models considering molecular interactions exhibit clear superiority. Furthermore, the performance of IGIB-ISE surpasses all evaluation metries for models of Category II across all datasets. This suggests that considering substructure interactions between molecules significantly enhances model performance. The introduc- tion of the EM algorithm enables the substructure to evolve dynamically through interactive iterations. The substructure can be accurately represented during the iterative process, and detailed analysis of its dynamic iteration process is provided Appendix E.6
Obs.4: The IGIB theory effectively improves model performance. Specifically, results from the IGIB-ISE framework demonstrate superior performance compared to using ISE alone. Guided by the IGIB theory, the ISE framework's 's ability to extract generalized and accurate interactive substructures is significantly improved. This enhancement is attributed to IGIB's ' proactive nature, which promotes the compression of substructures to their fullest extent. This compression process yields more concise structures, substantially enhancing the model's 's capabilities. Detailed results and analyses are provided in Appendix E.2
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(a)
[b)
[c)
AGD reaut
0.57
0.001
30
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0.02
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ZhangO0i
Optiaal
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Cithkliner
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ZhangDtt ChahNiner
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Abraham
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1E-4
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Taration number (N)
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Figure 3: Hyperparameter experimental results. (a) Test results under different values of 31 and B2. (b) Test results under different iteration numbers (IN); (c) the optimal-IN on various datasets.
4.3 ABLATION AND SENSITIVITY EXPERIMENT (RQ2)
In this section, we analyze the core hyperparameters, including $1, 82, and iteration numbers (IN) of the EM algorithm, as illustrated in Figure
Obs.5: There exists the optimal point of 31 0.0001 and 82 0.0001 in terms of the model performance. 31 and B2 govern the delicate balance between prediction accuracy and information compression within the two molecular graphs. As shown in Figure 3 (a), setting $1 0.001 and 82 0.001 results in suboptimal model performance. This can be attributed to the aggressive compression encouraged by these values, resulting in the model inadequately capturing the molecular information crucial for the target task. Conversely, the reduction of 31 and 83 implies preservation of more original graph information. However, does not consistently guarantee improved performance. This is because, in such scenarios, the model may struggle to identify the precise interactive substructure necessary for accurate predictions, thereby compromising its generalization capabilities.
Obs.6: The performance of the model closely related to the IN. In Figure 3 (b), we observe that as IN increases, the model's performance gradually improves on all datasets. This improvement can be attributed to our iterative extraction method, which enhances the accuracy of the extracted substructures. However, as IN becomes larger, the performance on the test set begins to decline. This is because excessive iterations lead to the extraction of 'locally optimal' substructures, thereby diminishing generalization performance.
Obs.7: The optimal IN value for the model increases with the size of the dataset. As illustrated in BigureJcc., (), the optimal IN value this phenomenon to the distributional error during the dataset partitioning process. When the dataset smaller, the distributional error is larger, whereas it would decrease as the dataset size increases. Therefore, by dynamically adjusting the iteration times of the ISE framework, model to achieve different levels of fitting and generalization capabilities, demonstrating the robust adaptability of our model to diverse datasets.
model increases with the size of the dataset. We attribute
enable the
4.4 INTERPRETABILITY ANALYSIS (RQ3)
In this section, we visually analyze the DDI prediction process based on IGIB-ISE. We conducted random selection of four drug pairs, all of which could generate a DDI reaction. The dynamic nature of substructure identification renders the ISE module distinctly remarkable.
Obs.8: IGIB-ISE exhibits distinct core substructure recognition in molecule pairs interaction. Illustrated in Figure 4 (a) and (b), each graph demonstrates the substructure selection results for Theophylline and Hydroxyurea molecules when interacting with different molecules produce DDI. Taking the example of the molecular pairs formed by Theophylline with Domperidone and Atazanavir, significant differences the selection O and are observed. This reflects that the model extract core substructures for different molecular combinations.
Obs.9: Dynamic iterative substructure extraction enhances core substructure learning. For different numbers of iterations, the iterative updates continue along with the iterative selection of substructures, the learning process of ISE towards core substructures is enhanced. As depicted in Figure (c), the acyl group gradually phased out, while other groups progressively manifest their

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(s)
Theophylline
Domperdone
Hydronyurea
prepitant
Iterate
Theophy'lime
Atazanavir
Hydroxyursa
Eszopiclone
Figure 4: Interpretability analysis interactive substructure. The visual representation of the interaction between (a) Theophylline molecules and different molecules. And (b) Hydroxyurea molecules. (c) Substructure visualization results under different iteration numbers. The darker the color means, the greater the weight.
importance. This evident the gradual clarification and stabilization of substructures, accompanied by the gradual removal of redundant nodes.
LIMITATION AND FUTURE OUTLOOK
ISE implements the dynamic substructure extraction process of molecular pairs based on the EM algorithm and has achieved significant improvement in the MRL experiment. However, considering the diversity and complexity of the real chemical molecular space, we expect to improve the current framework in three aspects in the future: 1) Expect to obtain more molecular interaction processes and analyses between molecules, which limited by the limitations of current research, we only verified it during the interaction process of two molecules. However, the interaction system of multiple molecules is still a research hotspot that cannot be ignored. 2) It is expected to obtain a more efficient iterative pruning strategy. For larger data sets, ISE requires more IN times, which will undoubtedly increase the consumption resources and time; 3) Anticipated to be effective in verifying large molecular data sets, focus extends beyond the tested molecular interaction tasks. Interactions between macromolecules such as protein-protein, protein-peptide, and drug-protein also represent significant molecular interaction tasks. Acknowledging the differences in macromolecule modeling methods, we aim to delve into the exploration of macromolecular interactions in our future work.
CONCLUSION
This paper presents significant advancements in the field of molecular relational learning through the introduction of the ISE framework and IGIB theory. These methodologies address the crucial limitations of existing methods, particularly those pertaining core substructure extraction. These advancements provide much-needed paradigm shift in the understanding and analysis of molecular interactions, emphasizing the importance of the dynamic interactions between substructures. The ISE framework, firmly supported by experimental validation, has shown superiority in accuracy, generalizability, and interpretability. The framework's generalizability suggests potential appli- cation in numerous areas, expanding the boundaries of the field. Moreover, the introduction of the IGIB theory has revitalized the interpretative study of core substructures. This theory, guided by the philosophy of effective information utilization, provides valuable insights into the selection process of essential interactive substructures. These insights facilitate more nuanced understanding of nuanced understanding of molecular dynamics,
molccular dynamics. These insights facilitate which has the potential to reshape our approach to molecular relational learning, stimulating more in-depth and insightful research the future.
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7 ACKNOWLEDGMENTS
This paper is partially supported by the National Natural Science Foundation of China (No. 12227901, No.62202427), the Project of Stable Support for Youth Team in Basic Research Field, CAS (No. (No.YSBR-OOK) YSBR-005), Academic Leaders Cultivation Program, USTC.
REFERENCES
Andreas Bender and Robert C Glen. Molecular similarity: key technique in molecular informatics. Organic & biomolecular chemistry, 2(22):3204 -2118, 2004.
Hans-Joachim Böhm, David Banner, Stefanie Bendels, Manfred Kansy, Bernd Kuhn, Klaus Müller, Ulrike Obst-Sander, and Martin Stahl. Fluorine in medicinal chemistry. ChemBioChem, 5(5): 637-643, 2004.
Gold Book. Compendium of chemical terminology. International Union of Pure and Applied Chemistry, 528, 2014.
Zhenxing Chi, Rutao Liu, Bingjun Yang, and Hao Zhang. Toxic interaction mechanism between oxytetracycline and bovine hemoglobin. Journal of hazardous materials, 180(1-3)7411-77, 2010.
Andreca Deac, Yu-Hsiang Huang, Petar Veličković, Pictro Liō, and Jian Tang. Drug-drug adverse effect prediction with graph co-attention. arXiv preprint 0005:4, 2019.
Arthur P Dempster, Nan M Laird, and Donald Rubin. Maximum likelihood from incomplete data via the algorithm. Journal of the royal statistical society: series B (methodological), 39(1): 1-22, 1977.
Wenjie Du, Shuai Zhang, Jun Xia Di Wu, Ziyuan Zhao, Junfeng Fang, and Yang Wang. Mmgnn: molecular merged graph neural network for explainable solvation free energy prediction. In Proceedings of the Thirty-Third International Joint Conference Artificial Intelligence, pp.
5808-5816, 2024.
Junfeng Fang, Shuai Zhang, Chang Wu, Zhiyuan Liu, Sihang Li, Kun Wang, Wenjie Du, Xiang Wang, and Xiangnan He. Molte: Towards molecular relational modeling in language models. arXiv preprint arXiv:2402.03781, 2024.
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.
Laura Grubbs, Mariam Saifullah, E Nohelli, Shulin Ye, Sai Achi, William Acree Jr, and Michael H Abraham. Mathematical correlations for describing solute transfer into functionalized alkane solvents containing hydroxyl, ether, ester or ketone solvents. Fluid phase equilibria, 298 (1):48-5) 03,8-53,77 2010.
Mare W Harrold and Robin M Zavod. Basic concepts in medicinal chemistry, 2014.
R Devon Hjelm, Alex Fedorov, Samuel Lavoie-Marchile Karan Grewal, Phil Bachman, Adam Trischler, and Yoshua Bengio. Learning deep representations by mutual information estimation and maximization. arXiv preprint /rXiv:/808. 0667006670, 2018.
Edward J Hu, Yelong Shen, Phillip Wallis, Zeyuan Allen-Zhu, Yuanzhi Li, Shean Wang, Lu Wang, and Weizhu Chen. Lora: Low-rank adaptation of large language models. arXiv preprint
271.v.2006.09685, 2021.
Qihe Huang, Lei Shen, Ruixin Zhang. Shouhong Ding, Binwu Wang, Zhengyang Zhou, and Yang Confronting noisy multivariate time series via cross interaction refinement. Advances in Neural Information Processing Systems, 36, 2024.
Wang. Crossgnn:
Eric Jang, Shixiang Gu, and Ben Poole. Categorical reparameterization with gumbel-softmax. arXiv preprint 161 1.01 144, 2016.
11

---

Published as a conference paper at ICLR 2025
March Jerry. Advanced organic chemistry: reactions, mechanisms and structure, 1992.
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.
Joonyoung F Joung, Minhi Han, Minseok Jeong, and Sungnam Park. Experimental database of optical properties of organic compounds. Scientific data, 7(1):16,, 2020.
Thomas Kipf and Max Welling. Semi-supervised classification with graph convolutional networks. 2016.
arXiv preprint
Jennifer Lang, Ludwig Vincent, Marylore Chenel, Kayode Ogungbenro, and Aleksandra Galetin. Reduced physiologically-basee pharmacokinetic model of dabigatran ciexilate-dabigatran and its application for prediction of intestinal p-gp-mediated drug-drug interactions. European Journal of Pharmaceutical Sciences, 165: 105932, 2021.
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:2305.00150, 2023a.
Namkyeong Lee, Kanghoon Yoon, Gyoung Na, Sein Kim, and Chanyoung Park. Shift-robust molecular relational learning with causal substructure. arXiv preprint arXiv:2305. 18451, 2023b.
Zimeng Li, Shichao Zhu, Bin Shao, Xiangxiang Zeng, Tong Wang, and Tie-Yan Liu. Dsn-ddi: ac- curate and generalized framework for drug-drug interaction prediction by dual-view representation learning. Briefings in Bioinformatics, 24(1):bbac597, 2023.
Zhiyuan Liu, Yanchen Luo, Han Huang, Enzhi Zhang, Sihang Li, Junfeng Fang, Yaorui Shi, Xiang Wang, Kenji Kawaguchi, and Tat-Seng Chua. NEXT-MOL: 3d diffusion meets 1d language modeling for 3d molecule generation. In The Thirteenth International Conference on Learning Representations, 2025. URL httpthtsss:pppeeeeeeeee
net. forum wtreee/ooooridmeeeeeee 2ddpprm0002220665000000000
K. Low, M. Coote, and E. I. Izgorodina. Explainable solvation free energy prediction combining graph neural networks with chemical intuition. / Chem Inf Model, 62(22):545755770, 2022. ISSN 1549-960X (Electronic) 9599 (Linking). doi: 1..00///cs.ccim220000033
URL
https: hwtp://www............m m1m. nih. http://umedd/333113/e/ 36317829
Chris J Maddison, Andriy Mnih, and Yee Whye Teh. The concrete distribution: A continuous relaxation of discrete random variables. arXiv preprint arXiv:1611.00m) 2016.
Aleksandr V Marenich, Casey P Kelly, Jason D Thompson, Gregory D Hawkins, Candee C Chambers, David J Giesen, Paul Winget, Christopher J Cramer, and Donald G Truhlar. Minnesota solvation database (mnsol) version 2012. 2020.
Siqi Miao, Mia Liu, and Pan Li. Interpretable and generalizable graph learning via stochastic attention mechanism. In International Conference on Machine Learning, pp. 15524-15543. PMLR, 2022.
David L Mobley and Peter Guthrie. Freesolv: database of experimental and calculated hydration free energies, with input files. Journal of computer-aided molecular design, (107):711-7201 2014.
Edouard Moine, Romain Privat, Baptiste Sirjean, and Jean-Noël Jaubert. Estimation of solvation quantities from experimental thermodynamic data: Development of the comprehensive compsol databank for pure and mixed solutes. Journal of Physical and Chemical Reference Data, 46(3): 033102, 2017.
Arnold K Nyamabo, Hui Yu, and Jian-Yo Shi. Ssi-ddi: substructure-suusstruuuree interactions for drug-dn interaction prediction. Briefings in Bioinformatics, 22(6):bbab133, 2021.
Yashaswi Pathak, Siddhartha Laghuvarapu, Sarvesh Mehta, and Deva Priyakumar. Chemically interpretable graph interaction network for prediction of pharmacokinetic properties of drug-like like molecules. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 34, pp. 873-880, 2020.
12

---

Published as a conference paper at ICLR 2025
Benedek Rozemberczki, Stephen Bonner, Andriy Nikolov, Michael Ughetto, Sebastian Nilsson, and Eliseo Papa. A unified view of relational deep learning for drug pair scoring. arXiv preprint arXiv:2111.02916, 2021.
Jae Yong Ryu, Hyun Uk Kim, and Sang Yup Lee. Deep learning improves prediction of drug drug and drug- food interactions. Proceedings of the national academy of sciences, L15(18):E4304-BA4 2018.
Nadine Schneider, Richard A Lewis, Nikolas Fechner, and Peter Ertl. Chiral cliffs: investigating the influence of chirality on binding affinity. ChemMedChem, 13(13):1315-132, 2018.
Richard Silverman and Mark W Holladay. The organic chemistry of drug design and drug action. Academic press, 2014.
Shunsuke Tamura, Tomoyuki Miyao, and Jürgen Bajorath. Large-scale prediction of activity cliffs using machine and deep learning methods of increasing complexity. Journal of Cheminformatics, 15(1):4, 2023.
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.
Nicholas P Tatonetti, Patrick P Ye, Roxana Daneshjou, and Russ B Altman. Data-driven prediction of drug effects and interactions. Science translational medicine,
- 2012.
Yonglong Tian, Dilip Krishnan, and Phillip Isola. Contrastive multiview coding. In Computer Vision-ECCV 2020: 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part XI 16. pp. 776-794. Springer, 2020.
Naftali Tishby, Fernando Pereira, and William Bialek. The information bottleneck method. arXiv preprint physicx/0004057, 2000.
Derek Van Tilborg, Alisa Alenicheva, and Francesca Grisoni. Exposing the limitations of molecular machine learning with activity cliffs. Journal of chemical information and modeling, 62(23): 5938-5951, 2022.
Florence H Vermeire and William H Green. Transfer learning for solvation free energies: From quantum chemistry to experiments. Chemical Engineering Journal, 1293077 2021a.
Florence H Vermeire and William H Green. Transfer learning for solvation free energies: From quantum chemistry experiments. Chemical Engineering Journal, 418:129307 2021b.
Oriol Vinyals, Samy Bengio, and Manjunath Kudlur. Order matters: Sequence to sequence for sets. arXiv preprint arXiv: 15X1v:5511.06391 2015.
Hanchen Wang. Defu Lian, Ying Zhang, Lu Qin, and Xuemin Lin. Gognn: Graph of graphs neural network for predicting structured entity interactions. arXiv preprint 2rX1v:2005.05537, 2020.
Yingheng Wang, Yaosen Min, Xin Chen, and Ji Wu. Multi-view graph contrastive representation learning for drug-drug interaction prediction. In Proceedings of the Web Conference 2021, pp- 2921-2933. 2021.
Tailin Wu, Hongyu Ren, Pan Li, and Jure Leskovec. Graph information bottleneck. In NeurIPS. 2020a.
Tailin Wu, Hongyu Ren, Pan Li, and Jure Leskovec, Graph information bottleneck. Advances in Neural Information Processing Systems, 33:20437-20448 2020b.
Guoli Xiong, Zhijiang Yang, Jiacai Yi, Ningning Wang, Lei Wang, Huimin Zhu, Chengkun Wu, Aiping Lu, Xiang Chen, Shao Liu, et al. Ddinter: an online drug-drug interaction database towards improving clinical decision-making and patient safety. Nucleic acids research, 50(D1): D1200-D1207, 2022.
Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka. How powerful are graph neural networks? arXiv preprint 18X.v01810.00826, 2018.
13

---

Published as a conference paper at ICLR 2025
Wenpeng Ye, Huili Ma, Huifang Shi, He Wang, Anqi Lv, Lifang Bian, Meng Zhang, Chaoqun Ma, Kun Ling, Mingxing Gu, et al. Confining isolated chromophores for highly efficient blue phosphoreseence. Nature materials, 20(11):1539-1544 2021.
Hui Yu, SuiYu Zhao, and JuanYu Shi. Stan-ddi: substructure-awwre tensor neural network predict drug-drug interactions. Briefings in Bioinformatics, 23(4):bbac009, 2022a.
Junchi Yu, Tingyang Xu, Yu Rong, Yatao Bian, Junzhou Huang, and Ran He. Graph information bottleneck for subgraph recognition. arXiv preprint arXiv:2010.05563, 2020.
Junchi Yu, Jie Cao, and Ran He. Improving subgraph recognition with variational graph informa- tion bottleneck. In Proceedings of the IEEE/CVF Conference Computer Vision and Pattern Recognition, pp. 19396-19403) 2022b.
D. Zhang. S. Xia, and Y. K. Zhang, Accurate prediction of aqueous free solvation energies using 3d atomic feature-based graph neural network with transfer learning. Journal of Chemical Information and Modeling, 62(8)) 1840-18888, 2022. ISSN 1549-9596. doi: 10.1021/acc.jeo sti....ccm..200266 URL
<GoteIsI> :/tp:s/s////o0s00001111330000
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):1-12, 2017.
Yudong Zhang, Xuan Yu, Xu Wang, Zhaoyang Sun, Chen Zhang, Pengkun Wang, and Yang Wang. COFlownet: Conservative constraints flows enable high-quality candidate generation. In The Thirteenth International Conference on Learning Representations, 2025. URL https
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:1912.03702. 2019.
Gengmo Zhou, Zhifeng Gao, Qiankun Ding, Hang Zheng, Hongteng Xu, Zhewei Wei, Linfeng Zhang, and Guolin Ke. Uni-mol: universal 3d molecular representation learning framework. 2023.
Marinka Zitnik, Rok Sosic, and Jure Leskovec. Biosnap datasets: Stanford biomedical network dataset collection. Note: http://snap.. stanford. edu/biodata Cited by. 5(1), 2018.
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A RELATED WORK
A.1 MOLECULAR RELATIONAL. LEARNING
Molecular research Liu et (025); Zhang al. 2025 is a critical task in the field of natural sciences, and molecular relationship learning (MRL) is a crucial branch of this area. However, it still faces a variety of challenges, including drug-drug interaction (DDI) prediction and solvation-free energy prediction for solute-solven vent pairs. The rapid emergence of graph neural networks Kipf & Welling (2016); Huang et al. (2024) (GNNs) has ignited considerable interest employing graph- based methodologies for MRL. For instance, Zhong et al Zhong al. (019)) harnessed Graph Convolutional Neural Networks (GCNNs) for message aggregation and utilized an attention based pooling method to forecast DDIs. Jones et al Zhang al. (2022) employed GNN to accurately predict water solvation Gibbs free energies for over 100,000 organic compounds, achieving an impressive error rate of 0.4 kcal/mol. The intricate relationship between two molecules is inevitably influenced by their specific substructures and functionalities Harrold & Zavod (2014); Fu et al. (2020).
As consequence, research has shifted towards substructure extraction and the interplay between these substructures. Yu et al. Yu et al. (2022a) integrated functional group information of drug molecules as substructures, further exploring the interactions among them. Nyamabo et al. (2021) introduced the Sesstructuur-SSbstruutht
Interaction for Drug-Dre -rug Interaction (SSI-DDI) method Nyamabo et al. (202T), employing Graph Attention Network (GAT) layers for substructure extraction and co-attention layers for modeling interactions among substructures.
However, prevailing methodologies typically encode two molecules separately or extract substructures independently, thereby overlooking their interaction for specific tasks. To capture the interaction be- tween molecules during substructure extraction, Lee et [ee et al. (2023a) introduced the Conditional Graph Information Bottleneck (CGIB) model. This model, inspired by Information Bottleneck theory, identifies core substructures between pairs of graphs and predicts interaction behavior. Aligned with the Structural Causal Model (SCM), Lee et al et al. (2023b) introduced conditional intervention framework where interventions are conditioned on paired molecules. This framework enables the model effectively glean insights from causal substructures and mitigate the confounding effects of spuriously correlated shortcut substructures in chemical reactions. Despite its demonstrated superior- ity over prior methods, the interaction mechanism remains rudimentary. Direct interaction between entire graphs introduces excessive redundant information, hindering the extraction of interacting substructures. This is because molecules often operate through one or several core substructures. In contrast, our method focuses on leveraging the interaction of key substructures, particularly under task-specific conditions, during the exploration process.
A.2 GRAPH INFORMATION BOTTLENECK
The GIB theory offers precise method for obtaining subgraphs and has been widely applied in the field of extracting subgraphs from a single graph. PGIB Yu et al. (2020) proposes a Graph Information Bottleneck (GIB) framework for recognizing informative yet compact subgraphs from the original graph, addressing key graph learning problems like graph denoising and compression. To optimize the challenging GIB objective, it introduces mutual information estimator for irregular graph data, a bi-level optimization scheme, and a connectivity loss to stabilize the process. VGIB Yu al. (2022b) further stabilizes the subgraph recognition process by injecting Gaussian noise into node representations, modulating the information flow from the original graph to the perturbed graph.
Additionally, Lee et al. Lee et al. (2023a) expanded the graph information bottleneck to the field of molecular relational learning, proposing the Conditional Graph Information Bottleneck (CGIB) theory, which aims to retain as much relevant information as possible with paired graphs while obtaining compressed subgraphs. The CGIB theory addresses the issue of extracting independent subgraphs in GIB for MRL tasks, but considering all information from another graph during interaction can introduce excessive noise. To address this limitation, this paper proposes the IGIB theory, which fully considers the detailed molecular interactions in molecular relational learning to ensure precise extraction of interaction subgraphs.
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B PROOFS
In this section, we provide detailed derivations for the theoretical aspects and equations presented in this paper. First, we explore the impact of redundant substructures on the extraction of core substructures in Section B.I. Additionally, we describe two Derivation Proof's of the E-step and M-step for ISE in Section B and B33 In Section [3.4] we analyze the convergence of ISE. Section B.5 and B.6 focus on providing detailed proofs for the Cpre and Lcom1 loss formulas of the IGIB theory.
B.I IMPACT OF REDUNDANT SUBSTRUCTURES ON CORE SUBSTRUCTURE EXTRACTION
Let G.1 denote general substructure of G1. G1B1 the substructure of G1, 91B2 the substructure of G2 and Gu2 the redundant substructure of G2.
Objective Function in Existing Methods: The extraction of the core substructure GIBI often involves minimizing mutual information. Specifically, this can be formulated as the following optimization problem:
arg minl (G.1: 91 92),
(17)
G.
where 7 (.) represents the mutual information between variables.
2. Decomposition of G2: The structure G2 can be decomposed into two components:
The core substructure Grz2, which contains essential and valid information.
The redundant substructure Gn2, which primarily introduces noise or irrelevant information.
Thus, G2 can be expressed as:
92 - G1BZ + 9n2-
(18)
Substituting this decomposition into the objective function, we obtain:
arg min/ (9
Grmz + 9n2).
(19)
G.
Assume that Gn2 is conditionally independent of GI as the redundant substructure does not directly influence the core substructure's 's information. Using the chain rule of mutual information, we can expand the objective function as:
3. Conditional Independence Analysis:
(9 91B2 + 9..2) = (9.1:91 91B2) + (G.1; 91 (n2).
(20)
4. Impact of Redundancy: The term 7 (G Gn2) captures the influence of the redundant structure Gu2 on the extraction process. However, as G.2 mainly introduces noise or irrelevant information, this term interferes with the actual optimization target, leading to suboptimal results. Ideally, the objective function should exclude the redundant substructure, focusing solely on the core substructure GIB2:
arg min/ (G.1: G1 G1B2).
(21)
9x1
Incorporating the redundant substructure Gu2 into the optimization process intro- duces an additional mutual information term, I (G.1 91 9n2), which interferes with the extraction of core substructures. To achieve more accurate and efficient extraction, the optimization should rely exclusively on the core substructure G1 thereby eliminating the influence of redundant information.
5. Conclusion:
B.2 DERIVATION PROOF OF THE E-STEP AND M-STEP FOR ISE
Proof. Objective: Given two graphs Gi and G2 and label Y, we aim identify the substructures G.1 and G52 most relevant to label Y. Yg is the observed variables. Additionally, Yg is determined by the model parameters 0 as follows:
Y g arg max log P P ()).
(22)
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Latent Variables: In molecular interactions, core substructures frequently exert significant influence. Consequently, 92 primarily influences through latent variables G22, where:
{ PYY,, 9s2 0) 2g
P(Yg ()
(23)
992
Bayes' Theorem Application: Applying Bayes' theorem, derive:
s(Y,, Ga2 0)
P(Yg 0) = PG,2 Yg,
(24)
Logarithmic Transformation: Taking the logarithm on both sides and introducing probability distribution of Gs2 (GG2),, while ensuring Jq.2 9 (9e2) dGæ2 1, arrive at:
log (YY 10) 10)=
P P(Yo, Gs2 0) log PG Y), (9x2)
(25)
log
9 (9,2)
Expectation Calculation: By taking the expectation with respect to G22 on both sides and converting into integral form, we obtain:
1 (GG2)) (olol0dde dG
6.2
1 (9x2) log
P(Y., 9s2 ()
dg.2
(26)
q
(9,2)
9,2
(9 Yg, 0) dg.2.
(9 log
(G
G.2
ELBO Derivation: Simplifying leads to:
log P P(g 10)
( a (9.2) log g.2
P P(Yg, 9o2 0)
(27)
9 (9,2)
+KL (g (G22) (G Yg, 0))
ELBO Inequality: Due to the non-negativity of the Kullback-Leiller divergence, we establish:
P (Yg, Go2 (0)
log P 0) 2 g (G+2) log
(28)
(Gx2)
G22
ELBO Optimization: By setting the KI. divergence term zero, we aim to maximize the expectation,
leading to:
f q (G.2))
P9 Yg (0) q (9
P (G.2. Yg
P P 0) log
d9.2
P 0, Y))
G.2
(29)
P (G,2, Yg ())
Eg, log (G,2 Yg)
Eg..10.Yo Yo [log P (9,2, Yg 0)]
E [log P ( 8, Ya)--
We proceed by meticulously examining the model parameters 9, with a particular focus on its components within the MRL task. The parameter set consists of only two constituents, 01 and 62. In this context, 0 governs the selection of G.1 from the set G,, while 02 regulates intermolecular interactions to determine G.2 based on G.1- Notably, the supervision of molecular interaction,
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indicated by the label Y, is independent of the EM iteration process, rendering it negligible for analysis. Consequently, our focus narrows down to 81, which exclusively influences G.1- However, concerning 9s2. 9.1 emerges as the determinant parameter. Thus, redefine 0 Gs1- Consequently, at the current time step (t), the E-step can be succinctly expressed as follows:
P ( Yg 9
log P ( Yg Yg.0.)
(30)
02 Yo.gh!
Subsequently, we aim to maximize this expectation, leading to:
P p y 9 log
((++1) arg max
(31)
9x1
P
P Yg, g(t))
B.3 DERIVATION PROOF 2 OF THE E-STEP AND M-STEP FOR ISE
Proof. Introduction of Latent Variables: We introduce latent variables using the Law Total Probability:
(
log P(Yg (9.1) = log
P(Yg. 9s2 9s1)d9,2
(32)
1g.
Incorporating Probability Distribution: Assuming the probability distribution of 9.2 as ((922).
we rewrite the equation as:
/
P(Y o. Go2 G.1) g(Gx2)dG.2
log P(Ys (. log
(33)
Jo.
(9w2)
Expectation Calculation: The integral inside the log the expectation
P(Ya. ((9.a)
with respect
to 9.2:
P(Y Go2 Gal)
log P(Y. G.1) log EG,,,
(34)
((9,2)
Jensen's Inequality Application: Since the logarithm function is strictly concave, according to Jensen's inequality:
P(Y 9x2 (n1)]
P(Y 9,2 9m1) ((G22
log Bg.a
2 Eg.a
log
(35)
(9022
ELBO Derivation: This implies:
log P(Y g, 9x2 141)
P(Y N.2.
191)
log P(Yg) (a1) 2 Eg..
(G
=
((9x2) log
(9
dgw2 (36)
G.2
Equality Condition of Jensen's Inequality: The equality holds when
C:
915.2)
((G.2) ] P(Y G.2 Ga1)
(37)
Normalization:
Integrating both sides with respect to G22:
[
1
(G = =
? P(Ys Gal) =
(38)
Final Inference: Hence, P(Yg (.1) C. Replacing C:
((92)) = P(Yg, Go2 9.1)
(39)
P(Y a G.1)
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ELBO Formulation: Clearly, this expression is the Evidence Lower Bound (ELBO) we mentioned earlier.
[ P(gs Yg 9s1) log P(Yg, Ge2 Gar) P(gs2 9x)
P(Yg, Ge2 9a1) P(g,2 Yg, G.1)
dGs2 BgaalYo. log
(40)
Su2
Iterative Procedure: Since the ISE framework is iterative, in each iteration, first estimate the posterior 9/22 yg.9%1 based on the previous iteration's g(t) and the samples y, and then compute the expectation in the E-step:
P ((g Yg 9
log P
(41)
9 Yo.g!!
( y 9.1
Maximization Objective: Subsequently, we aim to maximize this expectation, leading to:
P ( Yg g
(1+1) arg max E S.1 g(0) Yo.g.
log
(42)
P (( Y 0(1
B.4 PROOF OF CONVERGENCE OF THE EM ALGORITHM
Proof. The objective of the EM algorithm is to find suitable model parameters G.1 such that P(Y Ga1) is maximized. Since EM is iterative algorithm, prove its convergence, it suffices show that P
Yg g((+t)) >
P Ygg G.f))
holds.
As we know:
log P(Y (a1) = log P(Y 9s2 9.1) log P(g,2 Yg, Ga1)
(43)
Taking the expectation with respect to (G.2 Yg,
(()) (())
both sides, have:
E
g!! [log P(Yg (n1)
(44)
E Y.alY (log P(Y G22 Ga1)] - E 6 yo.of [log P(gx2 Yg, Ga1)
For the left-hand side of the equation, since log P(Y Ga.) is independent G.2, we have:
E
B [log P(Yg / (a1)l
- P (Gs2 YE, G log P(Y. Ga1 dG log P(Y G.1)
(45)
For the right-hand side, let's first consider the first term. actually the Q ( (c.. from our E-step, as:
g((++)) = arg max Q (9s1.99)
(46)
G.t
Therefore, it follows that:
Q (g (g(t)) ,.ti) 2 Q (g... g
(47)
Since 9.1 is variable, we can set G.1 = ((t) thus:
Q (g (++1) g(tl > Q ( 9
(48)
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Next, let's consider the second term. Since we aim to prove log ( g z
log Yg ( and we have already demonstrated Q (g:1 "ott",..)) 2 Q (os) 0 we only
need ensure that the second term satisfies
6 Yoool log P (g Yg g )
Y g ] [og P (9%
(49)
S R 9 TY
0
Thus, is proven
log P Ygs g((t1)) 2 log P Yg 0
(50)
B.5
PROOF OF Lere
Proof. Regarding I (YY 9s2), we consider Pe (Y 991 922) as the variational estimation of P(Y Ga. 922). Therefore, we can proceed with the following derivation:
P ( 9.1 922)
I (Y: 952) E(r.G. log
P(Y)
Po (Y
Gs1.9s2)
(51)
-E(Y.G.I.Sa)) log
P(Y)
B 9.2) log (P Ga,, G22 Considering the non-negativity property of the Kullback-Leibler divergence, we can conclude that:
IPo (Y 9.1, 9s2))
Po Y 901, 922)
I (Y; Gs1. Go2) 2 B( log
P(Y)
(52)
= -E log Po (Y
G.19G22) + HYY).
As HYY) remains constant across all data, can be omitted, resulting in the final formulation of this
term:
Lyre == EY log [Po (Y) Ga1, Ge))
(53)
B.6
PROOF OF Leom
Proof. For (9.1: G1, (e2), zg., is employed to denote the encoding of Gs1, and we approximate (=g.. 91, G22) using variational inference approach ((=G.)) ) as estimate for p(=g..):
po (=g.. 11, Gs2)
I :eg..:11.00 G.2) B( G1.022 log
p (2g.1)
pa (zg.,
91, G.2
(54)
=E(or. log
q (2g..) E [F Sr G.2) KL (p KL
(zg.n) l1q (2GH))
With the non-negativity property of the Kullback-Leibler divergence, we can conclude that:
I : 922) S E(G. G.) KL (po (zg,, G1, G.2) [lg (2g.)) == Lcomi-
(55)
Adopting the VIB framework, we postulate that the latent representation g(zg.)) is derived by aggregating node representations within fully perturbed graph. The perturbation is introduced
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through noise e, which follows Gaussian distribution (( or The parameters μad and d represent the mean and variance of H1, encapsulating information from both 91 and 92. By selecting sum pooling the aggregation mechanism, and considering the additive property of Gaussian distributions, we formulate the following relationship:
((c,,)) NNNNNNNN M.NNHH N'
(56)
where N denote the number of nodes in G1. Then for po (=g.. equation:
9.2). we have the following
N² +
N
N
pb (zg., 91. (.2 N (NN +
Hn,
X
Σ (1- 11) o
(57)
j=1
j=1
Finally, we have following inequality by plugging Equation equation 56 and Equation equation 57 into Equation equation 55
B²
(2g.191, (2, S 8 log A + 2NT
A +
+
(58)
2N1
Σド where A = 1 (1 A, ENI Ay(Ha, and C' is constant term that is ignored during optimization.
011
C FEATURES OF MOLECULAR MODELING
As illustrated in Table
our study leverages carefully curated set of atomic and bond features.
Table Atomic and bond features used in our study.
Atomic Features
Bond Features
Atomic number
Bond type
Degree (number of bonds)
Conjugated status
Formal charge
Ring status
Chiral tag
Stereo-chemin
Number of bonded atoms
Hybridization type
Aromatic status
Mass (scaled by 0.01)
D EXPERIMENTAL SETTINGS
In this section, provide detailed explanation of experimental setup. Section D.I offers information on all the datasets used in the experiments. Section D.2 presents a basic introduction the baselines involved in our paper. Section D.3 describes the various hyperparameters used in the model's network architecture and illustrates the hyperparameter search space and the optimal hyperparameters.
D.1 DATASETS
molecular interaction prediction task: For the molecular interaction prediction task, the datasets concerning solvation free energies include MNSol, FreeSolv, CompSol, Abraham, and CombiSolv. In addition, we also selected the chromophore dataset:
Marenich et al. 20200 features 3,037 experimental free energies of solvation transfer energies across 790 unique solutes and 92 solvents. We analyze 2,275 combinations following previous work [Le et al. 2023a).
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FreeSolv Mobley & Guthrie (2014) offers 560 experimental and calculated hydration free energies of small molecules in water.
CompSol Moine et al. (2017) explores how solvation energies are influenced by hydrogen- bonding association effects. It comprises 3,548 combinations encompassing 442 unique solutes and 259 solvents.
Abraham Grubbs et al. (010)) presents 6,091 combinations featuring 1,038 unique solutes and 122 solvents.
CombiSoly Vermeire & Green 2021a amalgamates data from FreeSolv, CompSol, and Abraham, totaling 8,780 combinations.
Chromophore Joung et al. (2200) encompasses 20,236 combinations of 7,016 chromophores and 365 solvents SMILES string format. We predict key optical properties like maximum absorption wavelength (Absorption), maximum emission wavelength (Emission), and excited state lifetime (Lifetime), taking care filter out NaN values. Due to skewed distribution, we opt for log- normaalzzd target values for Lifetime following previous work Lee et al. (2023a).
drug-drug interaction prediction task: For the drug-drug interaction prediction task, we selected the drug-drug interaction dataset. We employ positive drug pairs from MIRACLE Wang et al. (2021) and generate negative counterparts through complementary pair sampling. Detailed descriptions of each dataset are as follows:
DDI Zhang et al. drugs.
2017 contains 113,972 pairwise interaction data points with 544 unique
ChChMiner Zitnik et al. 2018 includes 33,669 pairwise interaction data points with 997 unique drugs.
DeepDDI Ryu et al. 2018 encompasses 316,595 pairwise interaction data points with 1,704
unique drugs.
D.2 BASELINES
We present concise overview of the foundational models discussed in the experimental section, categorizing them based on the nature of the molecular interactions they consider. Category includes models where substructure extraction is completed before any interactions occur. Some of these models capture atomic-level interactions, treating individual atoms as distinct substructures. This category emphasizes atomic interactions and ensures that the encoding of substructures remains invariant to molecular interactions. Category II comprises models where substructure extraction influenced by the holistic graph representation of another molecule, highlighting the broader molecular context in which interactions occur. Category III encompasses models that consider the influence exerted by the substructure of another molecule on substructure extraction. This nuanced approach accounts for specific structural features within molecular interactions. For the task of drug-drug interaction prediction, we adopt the following baseline models:
GoGNN. Wang et al. (2020) GoGNN extracts features from structured entity graphs and entity interaction graphs in hierarchical manner. It propose dual attention mechanism that enables the model to preserve the importance of neighbors at both levels the graph.
MHCADDI Deac et al. (0199) A gated information transfer neural network is used to control the extraction substructures and then interact based on an attention mechanism.
SSI-DDI. Nyamabo et al. 202 It uses 4-layer GAT network to extract substructures at different
levels, and finally completes the final prediction based on the co-attention mechanism.
CGIB. Lee et al. substructures are extracted to complete the interaction between molecules.
(023a)) Based on the graph conditional information bottleneck theory, conditional
CMRL. et al. (2023b) CMRL detects the core substructure that is causally related to chemical reactions. It introduce a novel conditional intervention framework whose intervention conditioned on the paired molecule.
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DSN-DDI. et al. (2023) It employs local and global representation learning modules iteratively and learns drug substructures from the single drug ( ('intraview") and the drug pair ('inter-view) simultaneously.
CIGIN. Pathak et al. (020) is a method based on graph neural networks. The proposed model adopts an end-to-end framework consisting of three essential phases: message passing, interaction, and prediction. In the final phase, these stages are leveraged to predict solvation free energies.
For the molecular interaction prediction task, we additionally employ the following baselines:
D-MPNN Vermeire & Green (021 employs a transfer learning approach to predict solvation free energies, integrating quantum calculation fundamentals with the heightened accuracy of experimental measurements through two new databases, CombiSolv-QM and CombiSolv-Exp.
Explainable GNN Low et al. (0022 introduces a graph neural network (GNN) for predicting sG incorporates atom and bond-level features, semi-empirical partial atomic charges, and solvent dielectric constant into the featurization process. Solute- solueet interactions are visualized through an interaction map layer, enabling the examination of solubility-enhancing or -decreasing interactions.
Uni-Mol Zhou et al. 2023) incorporates two pre-trained models featuring the SF(3) Transformer architecture: molecular model pre-trained on 209 million molecular conformations and a pocket model pre-trained on 3 million candidate protein pocket data. Additionally, Uni-Mol integrates various fine-tuning strategies to effectively apply these pre-trained models across diverse downstream tasks.
D.3 PARAMETER SETTING
Model Architecture. For the molecular interaction prediction task, the molecular coding layer, we configured the GIN network Xu et al. (2018) with layers. Since the two molecules asymmetric, each molecule has its own graph encoder and readout network. However, for DDI tasks, where the two molecules are symmetric, they share the same graph encoder and readout network.
Model Training. We employed the Adam optimizer for model optimization in both molecular interaction prediction and drug-drug interaction prediction task. For drug-drup interaction tasks, the learning rate was decreased by a factor of 10 after 10 epochs of reaching a plateau, and training was terminated when the optimal accuracy on the validation remained unchanged for 20 consecutive epochs. Similarly, for the molecular interaction prediction task, we adopted a comparable strategy: the learning rate was reduced by factor of 10 after 10 epochs of reaching a plateau, and training concluded when the optimal accuracy on the validation set did not change for 50 consecutive epochs. For the DDI task, we divided the dataset into training, validation, and test sets a 6:2:2 ratio. For the molecular interaction prediction task, we employed 10-fold cross-validation to partition the dataset. Our model and all baselines used the same random seed and were evaluated across five random experiments.
Hyperparameter Tuning. To ensure fair comparisons, we adhered to the embedding di- mensions and batch sizes of the state-of-the-art baseline for each task. Detailed hyper- parameter specifications are provided in Table 4 For our model, hyperparameters were fine-tuned within specified ranges: learning rate 7 in [5e-5 3. 5,5e -4 5e -lee4,5e 5,5-_5. 51, 81 in [1e-1, le-2 1e-3, le le 1e-6 1 le 1e-10), [, B2 in [e le-2, le-3 le 1e-6 le-s, 16-10), in 0.5, 0.2], and IN in [3, 5, 10, 20, 30, 40, 50, 60).
The model implementation was conducted in PyTorch, and the execution was performed on hardware consisting of an Intel(R) Xeon(R) CPU E5-2620 v4 @ 20 and Nvidia Tesla A A100 40GB. This robust hardware configuration ensures efficient processing and execution of the model.
E ADDITIONAL EXPERIMENTS
In this section, we carry out additional experiments to demonstrate the effectiveness and interpretabil- ity of our method. In Section 7
validate the superiority of our model using two additional
classification metrics. In Section E we conduct supplementary ablation experiments to gain a more comprehensive and clear understanding of the loss function derived based the IGIB theory.
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Table Hyperparameter specifications (+: Inductive Setting I and **; Inductive Setting
Embedding Dim (d)
Batch Size (K)
Epochs
Ir
B1
TN
Bg
Absorption
52
256
500
5e-3
le-2
20
le-2
1.0
Emission
256
500
5e-3
le-3
20
le-3
Lifetime
52
256
500
5e-3
le-7
20
lc-7
1.0
MNSol
52
32
200
le-3
le-7
10
1e-7
1.0
FreeSolv
52
32
200
le:3
le-9
3
lc-9
1.0
CompSol
500
le-3
le-7
1e-7
Abraham
52
256
500
le-3
le-11
5
le-11
1.0
CombiSoly
52
256
500
1e-3
lc-7
10
1c-7
0.5
ZhangDDI
300
512
500
le.4
le-4
40
le-4
0.5
ChChMiner
300
500
le-4
le-4
30
le-4
DeepDDI
300
512
500
1e-5
lc-8
50
lc-8
1.0
ZhangDDI*
300
512
500
5e-5
le-4
30
le-4
1.0
ChChMiner
300
512
500
5e-4
le-4
20
le-4
1.0
DeepDDI
300
512
500
5e-5
1c-8
40
1c-8
1.0
ZDa
300
512
500
5e-5
le-4
20
le-4
1.0
ChChMiner"
300
512
500
5e-4
le-4
20
le-4
1.0
DeepDDI
300
512
500
5e-5
1e-8
20
1c-8
1.0
In Section E.6 substructures.
we provide more detailed illustration of the dynamic process of selecting core
E. THE PERFORMANCE OF OUR MODEL ON ADDITIONAL. METRICS FOR THE DDI TASK.
We conducted additional experiments comparing model with the baselines using the AUROC and FI Score metries. As demonstrated Table 5 and Table IGIB-ISE achieved superior results compared to the other baselines.
AUROC (Area Under the Receiver Operating Characteristic Curve): AUROC measures a binary classifier's ability to distinguish between classes across all threshold values, with higher values indicating better performance.
The Fl Score is the harmonic mean of precision and recall, providing a single metric that balances both false positives and false negatives.
F1 Score:
Table 5: Performance of different methods in transductive setting (Bold numbers are the best results).
DeepDDI
ZhangDDI
ChehMiner
Method
AUROC
F1
AUROC
FI
AUROC
Category
GoGNN
92.7 12.71 (0.27)
(0.1))
92.35 (0.45
(1.54(0.12)
96.64
82.35
CIGIN
95.35
91.32
91.47
82.68
97.29 (0.33)
89.37
SSI-DDI
97.42 (0.31)
95.41 (0.19)
(0.34)
82.99 (0.30)
97.81 (0.22)
93.11 (0.19)
MHCADDI
88.640.833)
(8.54
86.94/o.68 (0.68)
73.67
89.33 (0.72)
83.21 (0.53)
Category
CGIB
98.66
(7.24
(5.03(0.54)
(4.98
98.45 (0.31)
95.44
CMRL
98.73
96.82
94.78
84.78
98.67 (0.12)
95.62
DSN-DDI
97.87 (0.14)
96.2 (o.13)
94.37 (0.16)
84.30
97.31 (0.10)
(0.38
Category III
ISE
98.75 (0.46)
97.38 (0.31)
94.97 (0.39)
85.34 (0.53)
98. (4.274
95.85 (0.32)
IGIB-ISE
98.97 (0.37)
97.79 (0.26) (0.26)
95.47 (0.21)
85.93 (0.17) /5.93
(0.19)
(..
E.2 SUPPLEMENTARY ABLATION EXPERIMENTS
We conducted additional ablation experiments on three DDI datasets (ZhangDDI, ChChMiner and DeepDDDI) and three solvent-solute datasets (FreeSoly, Abraham, and CombiSolv). These experiments
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Table Performance of different methods in inductive settings (Bold numbers are the best results).
Interaction
DeepDDI
ZhangDDt
ChehMiner
Method
Category
AUROC
FI
AUROC
FI AUROC
FI
Inductivv Setting
GoGNN
71.34(1.24)
67.16
63. 63.17(1.42)
69.52 (1.28
69.22
CIGIN
(2.64(1.77)
(9.55(1.45)
68. 38.39 (1.07)
44.39
(1.49
(1.92(1.48)
Category I
SSI-DDI
(1.93(1.14) (2.23(o.77)
69.56
47.59
(1.64(1.58)
(1.61
MHCADDI
68.18
(1.37
62.52
44,51 (4.51
(1.38)
70.92
75.15
CGIB
(0.80(
78.47 (0.57)
72. (0.04:
$7.29
86.41 (0.98)
85. 85.13
Category II
CMRL
(4.96(..87)
(a.74)
(1.5)
56.41
(7.64
86.55(a.07)
DSN-DDI
(o.7))
(8.68
(1.49(
56.64(0.77)
86.93
85.81
ISE
(3.86
(1.55
75. 16.166)
(8.27
87.52
86.63(o.74)
Category III
IGIB-ISE
85.01 (0.41)
80.08 (o.56)
(0.32
58.96
87.88 (0.62)
87.37 (0.54)
Inductive Setting 2
GoGNN
(3.0)
(3.53)
(2.37
(4,92
(2.19(4.29 (3.73
CIGIN
68 (8.67)3.54)
(9.34(4.53)
(2.67)
33.68 (4.35)
65.36(2.98)
71.73(3.54)
Category I
SSI-DDI
(4.37
67.18
(3.23
(7.16
68.39 (1. (1.4)
74.95(2.17)
MHCADDI
(3.89(3.12)
(5.57
(6.47
(3.53
63.57
64.51
CGIB
68.78(1.67)
75.72
57.24(1.97)
(4.83)
69.82
78.46((2.8)
Category II
CMRL
73.38
(3.91
(0.02
(3.73
69.62
75.76
DSN-DDI
(1.7)
77.9611.64)
61.88
(2.49
(1.34)
(1.52(1.21)
ISE
(1.92().64)
(2.17)
(2.42
(2.38
69.67 (1.52)
71.73
Category III
IGIB-ISE
(1.51(1.54)
79.64(1.67)
63.24(1.72)
(2.03
70.09 (1.46)
80.12(1.48)
were designed to demonstrate the contribution of each model component across various data scales and task types. We ensured that all experiments followed the same setup (except for the ablated components) and repeated them five times to provide robust results. The results are reported as Mean (Variance).
Table 7: Results on DDI datasets (Evaluation Metric: ACC (%))
Dataset
31 =
82 = 0
w/o KL Loss
w/o Contrastive Loss
Baseline
ZhangDDI
88.34 (0.41)
88.39 (0.27)
88.37 (0.39)
88.59 (0.24)
88.84 (0.32)
DeepDDI
96.27 (0.34)
96.33 (0.31)
96.12 (0.28)
96.41 (0.19)
96.65 (0.37)
ChChMiner
94.86 (0.37)
94.82 (0.11)
94.93 (0.17)
95.33 (0.26)
95.56 (0.28)
Table 8: Results Solvent-Solute datasets (Evaluation Metrie: RMSE)
Dataset
31 0
B2 0
w/o KL Loss
w/o Contrastive Loss
Baseline
FreeSolv
0.921 (0.058)
0.886 (0.029)
0.986 (0.030)
0.921 (0.033)
0.713 (0.034)
Abraham
0.353 (0.002)
0.419 (0.009)
0.414 (0.001)
0.366 (0.001)
0.343 (0.009)
CombiSolv
0.411 (0.004)
0.397 (0.004)
0.413 (0.001)
0.411 (0.001)
0.394 (0.008)
As shown in the Table 7 and Table g with all components active, our model achieved the best performance across all datasets. When the KL divergence loss (Ccoml and Lcom2), which facilitates the compression of interactive substructures, was removed, the performance declined on all datasets, with FreeSolv and Abraham experiencing the most significant drops. This highlights the critical role of KL divergence loss in guiding the model towards more precise substructure selection, particularly in regression tasks.
On the other hand, removing the contrastive loss (Lom and Loom2) resulted in marginal performance reduction for most datasets, except for FreeSolv. This phenomenon could be attributed to the robust interaction modeling of our iterative interaction module, which reduces the reliance contrastive loss. However, for the FreeSoly dataset, where fewer IN were used, the contrastive loss played a more pivotal role, demonstrating the dataset-dependent utility of this component.
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Then, evaluated the impact of setting 31 and B2 to zero. For DDI datasets, the results indicate that 31 and B2 have similar contributions, as evidenced by the small margin performance differences. Nevertheless, for solvent-solute datasets, 31 and B2 exhibited distinct impacts. This divergence may stem from the inherent asymmetry in solvent-solute interactions, suggesting that the choice of Bi and 82 requires careful consideration when dealing with asymmetric molecular interactions.
Finally, We explain the objective function under each ablation experiment. The original objective function is:
arg min T 9,1 9.2) + 31 (91: G22) + /327 (92; 9s2 Ga1) Gar
When 81 The objective becomes
arg min (Y; 922) + B21 (G2; 9s2 9.1)
$..9.2
When B2 0: The objective becomes
arg min (Y; + 317 (G); Gs1 (22)
G.1
Without KL loss: The objective becomes
arg min / 9s,, 311 (9.1; Bel (9.2; 9s1) G.1.2.
Without Contrastive loss: The objective becomes
arg min 1 (.1 + 311 ( (1:1911922)) + Bel (9s2: 9..1
G,1.0s2
E.3 PERFORMANCE LARGER DATASET
To validate the scalability and effectiveness of our method, we performed experiments on larger datasets. For solvent-solud dataset, we used the containing I million solvent-solute combinations from 284 solvents and 11,029 solutes. The solute molar masses range from 2.02 g/mol to 1776.89 g/mol. For the DDI task, we extended our evaluation using the Twosides Tatonetti et al. (012) dataset and combined it with ZhangDDI, ChChDDI, and DeI datasets to create a benchmark of 843,964 unique drug-drug pairs.
Green (202Tb) dataset,
Table 9: Performance on Solvent-Solute Dataset
Table 10: Performance DDI Dataset
Model
ACC
F1
AUROC
Model
RMSE
CRML
84.33%
74.86%
92.76%
CGIB
0.0976
CGIB
84.14%
74.69%
92.41%
CRML
0.0983
IGIB-ISE
84.92%
75.14%
93.89 %
IGIB-ISE
0.0912
As shown in Table IGIB-ISE achieves the lowest RMSE of 0.0912, outperforming CGIB and CRML, and highlighting its ability effectively capture complex solvent-solute interactions. Similarly, Table [0 demonstrates that IGIB-ISE consistently surpasses CGIB and CRML in accuracy (84.92%). F1-score (75. 14%), and AUROC (93.80 (3.8%)). underscoring its robustness identifying intricate drug- drug interactions while maintaining high predictive accuracy. These results underscore IGIB-ISE's superior performance on large datasets, with the lowest RMSE for the solvent-solute task and leading metrics for the DDI task, showcasing its robustness and scalability for real-world applications.
E.4 OPTIMAL IN FOR DIFFERENT MOLECULAR SCALES
This section investigates the relationship between IN and molecular scale. We combined multiple datasets, including ZhangDDI, ChChDDI, DeepDDI, and Twosides Tatonetti et al. (2012). into
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Table 11: Model performance (ACC) for various IN and AM values.
IN
AM 340
AM 549
AM 638
AM 722
AM 1934
78.85%
72.52%
69.57%
69.00%
84.08%
10
79.38%
74.93%
70.98%
69.45%
84.77%
20
78.98%
75.47% %
73.47%
70.65
85.02%
30
78.25%
75.14%
72.13%
68.90%
85.24%
40
78.03%
74.83%
72.34%
69.13%
85.11%
larger, consolidated dataset. The dataset was categorized into five groups based the molar of the molecules, with each group containing 50,000 drug- wuggddug pairs. We then determined the optimal IN for each group by assessing model performance using ACC. The results are summarized in the Table II where AM represents the average molar mass for each group.
The results demonstrate clear trend: larger average molar masses (AM) require higher iteration numbers (IN) to achieve optimal performance. For small molecules (AM = 340), an IN value of 10 strikes a balance between computational cost and accuracy. Medium-sized molecules (AM 549 to 638) benefit most from an IN value of 20, which effectively improves performance without incurring significant computational overhead. For larger molecules (AM A 722). an 20 remains optimal, increasing IN to higher values (e.g.. 30) can degrade performance. Meanwhile, for very large molecules (AM R 1934), an IN value 30 fully leverages the model's 's capability to handle the increased complexity. This flexible approach enables the tailored selection of IN based molecular scale, ensuring an optimal balance of performance and computational efficiency.
E.5 SCALABILITY OF IGIB-ISE ACROSS MOLECULAR SIZES
To further assess the scalability of IGIB-ISE, we utilized the dataset from for performance evaluation. The results presented in the Table 12
Table 12: Performance comparison of IGIB-ISE, CGIB, and CMRL across AM.
Model
AM = 340
AM = 549
AM 638
AM 722
AM 1934
IGIB-ISE
79.38%
75.47%
73.47%
70.65
85.24
CGIB
78.14%
74.31%
72.59%
68.91%
84.62%
CMRL
78.42%
74.19%
72.68%
69.72%
84.43%
The results reveal that IGIB-ISE consistently outperforms both CGIB and CMRL across various molecular scales, demonstrating its robustness and scalability. For small molecules (AM 340), IGIB achieves an accuracy of 79.38%, surpassing CGIB and CMRL by 1.24% and 0.96%, respectively. In medium molecule categories (AM 549 to 638), IGIB attains accuracies of 75.47% and 73.47%, with improvements of approximately 1 1.2% and 0.8% over the baselines. For large molecules (AM as 722). IGIB achieves 70.65% %, outperforming CGIB (68.91%) and CMRL (69.72%). Notably, for very large molecules (AM 1934). IGIB reaches remarkable accuracy of 85.24%, exceeding CGIB (84.62%) and CMRL (84.43%). These findings underscore IGIB's ' effectiveness as a reliable method for analyzing diverse molecular sizes, making it robust tool for molecular-scal applications.
E.6 DYNAMIC ITERATION PROCESS OF THE INTERACTIVE SUBSTRUCTURE EXTRACTION
As illustrated in Figure 5 we present schematic diagrams depicting the substructure interaction pro- cesses Pentazocine and Aminocaproic acid drugs over 40 iterations. Notably, for the Aminocaproic acid drug, it is evident that the amino group more significant in the early iterations. This observation raises the possibility that, algorithms selecting substructures based on original molecular graphs, the amino group might be chosen In contrast, our ISE framework, through iterative steps, selectively identifies the core interaction substructures of Pentazocine. This process determines the insignificance of the amino group, leading
substructure, thereby impacting the final prediction.
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Iteratione1
Iteration=2
Iterationnd
lteration:8
Meration=33
Itemt on:35
Itaration=388
Boration=40
Figure 5: Schematic diagram of the substructure interaction process of Pentazocine (upper) and Aminocaproic acid (lower) drugs.
its removal in later iterations, and gradually stabilizing the results. Additionally, we also observe that after the EM algorithm finds the optimal substructure, it continues to exhibit slight fluctuations around the converged result.
Table 13: Comparison time and memory usage during the training phase.
Model
Metric
ZhangDDI
ChChMiner
DecpDDI
MNSol
FreeSolv
CompSol
Abraham
CombiSoly
Memory (GB)
7.41
2.13
2.11
2.14
2.42
2.31
CGIB
Time (hours)
1.52
0.63
3.75
0.042
0,0034
0.081
0.164
0.153
CMRL
Memory (GB)
3.45
6.12
2.12
2.12
2.13
2.45
2.33
Time (hours)
1.34
0.53
3.24
0.041
0.0032
0.072
0,142
0.121
IGIB ISE
Memory (GB)
36.2
27.3
39.4
2.12
1.83
2.25
2.64
2.42
Time (hours)
8.73
2.91
22.8
0.083
0,0037
0.153
0.225
0.257
Table 14: Comparison time and memory usage during the inference phase.
Model
Metric
ZDangDDI
ChChMiner
DeepDDI
MNSol
FreeSoly
CompSol
Abraham
CombiSoly
CGIB
Memory (MB)
277.5
303.2
296.7
85.34
38.41
84.97
103.4
103.8
Time
24.8
6.81
94.7
1.69
0.94
2.62
3.64
4.76
Memory (MB)
236.2
254,2
252.3
72.37
34.21
71.43
93.87
92.34
CMRL.
Time
23.5
5.89
77.3
1.49
0.88
2.31
3.43
4.37
Memory (MB)
274.8
301.3
294.2
81.28
37.33
75.31
100.8
98.45
IGIB-ISE
Time
22.6
74.9
1.62
2.22
3.53
4.55
F
TIME AND SPACE COMPLEXITY
F.1 TRAINING PHASE
In this work, we evaluated IGIB-ISE in terms time and space complexity, dividing the analysis into the training and inference phases across multiple datasets and comparing it with several existing methods. For training phase, as shown in Table [3] while our method effectively reduces redundant information, it incurs higher time and memory overhead compared to baseline models. This is attributed to the extensive use of interaction networks in our iterative substructure selection process, which is integrated with end-to-end optimization achieve superior performance. This design leads to redundant storage and prolonged gradient computations, contributing to the observed overhead.
Time Complexity:
The primary contributor to extended training time is the repeated gradient computations within the interaction network during substructure iterations.
Space Complexity: The redundant storage of interaction network parameters across itera- tions is the main factor for increased memory usage.
F.2 INFERENCE PHASE
In real-world applications, inference efficiency is critical. Once trained, the core substructure extractor directly applied for molecular interaction predictions. For inference phase, shown in Table 14
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IGIB-ISE demonstrates competitive efficiency. For instance, large datasets like ZhangDDI, it completes inference in just 22.6 seconds, outperforming CGIB and CMRL. Its memory usage during inference is low and comparable to the baseline methods (e.g.. 274.8 MB for ZhangDDI compared to 277.5 MB for CGIB). These results highlight IGIB-ISE's practicality for real-world applications without incurring significant resource overhead.
F.3 ENGINEERING OPTIMIZATIONS FOR TRAINING EFFICIENCY
In this section, we outline three potential engineering optimizations to improve the efficiency of the training phase:
Interaction network parameters, unchanged during iterations, can be globally stored and reused for gradient computation. This reduces redundant storage while maintaining functionality.
Optimization of Computation Graph Storage:
Core Substructure Initialization: Reducing iterations by initializing substructures based on prior chemical knowledge (e.g., functional groups) can accelerate convergence and reduce training overhead.
Efficient Parameter Fine-Tuning (e.g., LoRA Hu et al. (2021)); Using low-rank matrices for fine-tuning allows freezing the interaction network and adapting it with minimal compu- tational cost, significantly reducing both memory and time requirements. The pre-trained parameters of the interaction network can be obtained from baseline models such as CGIB.
29


Reviews:
[{"review_id": "mIiFla2fYM", "reviewer": "Reviewer_xkpA", "summary": "To alleviate the problems in current methods of molecular relational learning: insufficient consideration of molecular interactions and failure to capture high-quality substructures, this paper introduces an IGIB (Interactive Graph Information Bottleneck)-ISE (Iterative Substructure Extraction) method. Their work achieves better performance than current SOTA models in terms of accuracy, generalizability, and interpretability.", "questions": "1. Please justify your assumption stated at line 161.\n2. For Line 1224 Figure 5, why do you only choose to conduct the ablation study on the ChChMiner dataset? Ablation studies on larger datasets are needed.\n3. Following your design, IGIB-ISE should effectively identify the core substructure of molecules, why did the model not improve the classification accuracy more? As it reduces redundant information, why does it occupy a larger space? More analysis is needed to identify factors that may limit the improvement. What are the potential enhancement may be introduced to address these limitations?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "1.\tThis paper has good clarity. It is well-written with a clear structure. In a concise but informative style, readers would find it easy to understand the key concepts, backgrounds, and methods.\n2.\tTheir work also brings new insights into the MRL area. They noticed the inefficiency of current methods, where using the complete profile of an interacting molecule could not only be unnecessary but also comprises generalizability. And they proved the effectiveness of their method through experiments. \n3.\tIn general, they bring new ideas to the MRL area: Interactive Graph Information Bottleneck (IGIB). Bottleneck-based methods are widely used in many areas and receive satisfactory results. In this paper, they integrated it into the ISE framework for further optimization. It is also the method that leverages the model’s performance to outperform all baselines.", "weaknesses": "1.\t(General Assumption) Most molecule interactions may depend on each molecule’s substructures, but does this apply to all molecule interactions? If not, the assumption at line 161 is somewhat arbitrary, where some edge cases could be ignored by this model. This assumption needs to be further justified. \n2.\t(Time and Space Complexity) While the model outperforms all the baseline models, it spends much more time processing DDI Datasets. Compared to CMRL, with around 1% accuracy improvement, this model costs 5.8 ~ 7.1x more time and 6.4 ~ 9x more space. This may lead to expensive computation. The trade off between the performance and computing cost needs to be examined. \n3.\t (Ablation Experiment) Most experiments are designed well, but the experiment in line 1224 is less persuasive. Among all the datasets for the drug-drug interaction prediction task, ChChMiner has the fewest data points. Besides, since molecular interaction prediction tasks are different from DDI, a separate experiment would be good. \n4.\t (Improvement) While IGIB-ISE achieves good performance, ISE fails to outperform all Category II methods in Table 1 (line 324) and some Category II methods in Table II (line 378). Also, the improvement of IGIB-ISE is not that noticeable in the classification task.", "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": "GiVgm869L7", "reviewer": "Reviewer_WivT", "summary": "The paper describes a method to improve molecular relational learning using information theoretical loss functions on a subgraph of the molecules. The technical contribution lies in the coupling of graph information bottlenecks with expectation maximization. The results show the approach's superiority both in deductive and inductive scenarios. The method is well-motivated, and the experiments are solid.", "questions": "In general, the paper is a solid contribution but the presentation should improve. Please answer to my questions above.", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "(S1) The paper solves a timely problem and presents a sound solution that fully exploits the relationships among substructures.\n\n(S3) Due to its substructure alignment, IGIB-ISE outperforms previous techniques on several datasets.\n\n(S3) The method is well-motivated and builds on previous graph information bottlenecks, ELMO and expectation maximization.", "weaknesses": "(W1) Missing explicit objective function: The paper first explains the solution and then reaches the objective in Equation 8. I find this presentation counterintuitive. Why not present the objective first and then explain how to compute it?\n\n(W2) In the modelling of the graph there is no feature vector associated with nodes/edges. Are the graphs without attributes? Molecules should have information about the type of bonds among atoms.\n\n(W3) Notation without introduction: The paper uses notation without introducing it. Examples include:\n\n- $\\mathbf{Y}_\\mathcal{G}$\n- Line 216: the symbol *, is it a matrix multiplication?\n- $\\||$ in line 218\n\n(W4) If sim is symmetric cosine similarity, what is the need for computing both $sim(F_1, F_2)$ and $sim(F_2, F_1)$?\n\n(W5) It is not clear how Eq. 5 ensures that the two structures are aligned since $H_1$ and $H_2$ refer to two different embeddings spaces, or is the alignment enforced by the two matrices $I_{12}, I_{21}$? Please explain and motivate.\n\n(W6) What is the Gumbel sigmoid and how does it help in this case?\n\n(W7) It is not clear whether Eq. 16 is a lower bound on Eq. 8 or what is the relationship with Eq. 8? Is that an approximation or a heuristic? This aspect should be clarified in the text.\n\n(W8) In Figure 4, the focus of the network substantially changes over iteration. This seems to indicate that the method struggles with convergence. Is that expected or is it a sign of instability?", "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": "DJEiL7DLnZ", "reviewer": "Reviewer_spWZ", "summary": "This paper introduces the Iterative Substructure Extraction (ISE) framework for molecular relational learning, addressing how molecules interact through their core substructures. The framework combines an Expectation-Maximization algorithm for iterative refinement with a new Interactive Graph Information Bottleneck (GIB) theory to ensure extracted substructures are minimal yet influential. Through experiments on datasets covering both regression and classification tasks, the combined IGIB-ISE approach demonstrates improved accuracy and interpretability compared to existing methods for predicting molecular interactions.", "questions": "**1. The discussion of the limitations of Category II methods is confusing.** \n- It is understandable that core substructures often play a crucial role in molecular interactions. But, Figure 1 (a) does not deliver a relevant message to support this argument. \n- In addition, from Figure 1 (a), it is unclear why integrating the complete profile of an interacting molecule into the substructure generation can be overwhelming. \n- It's unclear why Category II carries the risk of compromising generalizability. After reading the cited paper [1], it's still very confusing. There is no clear evidence from [1] to support this statement. \n- It's unclear why the authors mention \"Activity Cliffs\" here. \n\n**2. Limited Discussion of Method Robustness.**\nAs an interactive method, what happens if the EM algorithm finds optimal solutions during iteration? The lack of guidelines for selecting optimal iteration numbers based on dataset characteristics leaves important practical questions unanswered.\n\n**3. Technical Clarity Issues.** \n- Line 160, what is Y_G? Should it be Y?\n- In Tables 6-7, your method should be named ISE-IGIB or IGIB-ISE?\n\n**4. Computational Overhead.** \n- Tables 6 and 7 show IGIB-ISE takes more than 700% execution time and 1000% memory compared to one baseline DSN-DDI, with around 1.5% DDI performance improvement. I don't appreciate such results. The authors do not sufficiently address this limitation or propose potential optimizations. \n- The experiments focus on relatively small molecules. There is no discussion or analysis of how the method scales with molecular size, which is important for applications involving larger molecules. \nThe memory requirements (Table 6-7) suggest potential scaling issues.\n\n[1] Mechanisms of drug combinations: interaction and network perspectives", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "- The paper presents a novel approach to molecular interaction learning. Rather than handling entire molecular structures or extracting substructures independently, it introduces an iterative refinement process guided by molecular interactions. \n\n- Using EM algorithms for substructure extraction is creative, treating substructures as latent variables that get refined through iterations. This is a fresh perspective on the molecular interaction learning problem.\n\n- This work has a substantial potential impact on drug discovery and materials science. The ability to identify and understand interacting substructures between molecules is crucial for these fields.", "weaknesses": "The discussion of the limitations of Category II methods is confusing.\n\nLimited Discussion of Method Robustness. \n\nTechnical Clarity Issues. \n\nComputational Overhead.", "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": "9WRuNak7qX", "reviewer": "Reviewer_Vr3G", "summary": "This paper introduces a framework called ISE to improve MRL by focusing on the interaction between core substructures of molecules. The model iteratively refines the core substructures using the EM algorithm. Additionally, the IGIB theory is proposed to capture minimal but most influential substructures, enhancing the efficiency and generalizability of the extraction process. Through extensive experiments, the IGIB-ISE framework demonstrates superior performance compared to existing methods in terms of accuracy, generalizability, and interpretability for molecular interaction prediction tasks.", "questions": "1. Can the authors validate the interactions between multi-molecule interactions?\n\n2. Why the interaction is computed as $H_1=F_1^{(1)}||F_1^{(2)}$?\n\n3. The way to extrapolate the core substructure is **very similar to [1]**. What's the difference between this paper and [1]?\n\n4. What's the complexity of the method? Can you compare the training and inference time with baselines?\n\n5. Can you validate your method on larger datasets?\n\n[1] Capturing substructure interactions by invariant Information Bottle Theory for Generalizable Property Prediction", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "1. This paper introduces an innovative method for core substructure extraction using the EM algorithm, which effectively captures molecular interactions.\n\n2. IGIB theory ensures a precise and compact extraction of interactive substructures.\n\n3. The method is extensively validated across various molecular relational learning tasks, including drug-drug interaction and solvation energy prediction, showing clear improvements over state-of-the-art methods.", "weaknesses": "1. **Some parts of this work is very similar to [1]**. The key idea and many formulas are similar. For example, they all utilize similar methods to extrapolate core substructures (Section 3.4 in this paper and Section 3.2 in [1]). The only difference here seems to be this paper extrapolates the core substructure from a pair of graphs while [1] extrapolates the core substructure from one graph.\n\n1. The framework is validated on interactions between two molecules. It does not extend to more complex scenarios like multi-molecule interactions, which are important in real-world biochemical environments.\n\n2. The method requires more iterations, increasing resource consumption and time. This may limit its scalability for very large datasets or complex molecular systems.\n\n\n\n[1] Capturing substructure interactions by invariant Information Bottle Theory for Generalizable Property Prediction", "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)