CheapNet: Cross-attention on Hierarchical representations for Efficient protein-ligand binding Affinity Prediction
Authors: Hyukjun Lim
Sun Kim
Sangseon Lee
Venue: ICLR 2025 Poster (2025)
Keywords: Protein-Ligand Binding Affinity
Hierarchical Representation Learning
Cross-Attention Mechanism
Drug Discovery
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
TL;DR: We propose CheapNet, an interaction-based model with hierarchical representations and cross-attention for protein-ligand binding affinity prediction, achieving state-of-the-art performance across benchmarks with efficient complexity.

Abstract: Accurately predicting protein-ligand binding affinity is a critical challenge in drug discovery, crucial for understanding drug efficacy. While existing models typically rely on atom-level interactions, they often fail to capture the complex, higher-order interactions, resulting in noise and computational inefficiency. Transitioning to modeling these interactions at the cluster level is challenging because it is difficult to determine which atoms form meaningful clusters that drive the protein-ligand interactions. To address this, we propose CheapNet, a novel interaction-based model that integrates atom-level representations with hierarchical cluster-level interactions through a cross-attention mechanism. By employing differentiable pooling of atom-level embeddings, CheapNet efficiently captures essential higher-order molecular representations crucial for accurate binding predictions. Extensive evaluations demonstrate that CheapNet not only achieves state-of-the-art performance across multiple binding affinity prediction tasks but also maintains prediction accuracy with reasonable computational efficiency. The code of CheapNet is available at https://github.com/hyukjunlim/CheapNet.

Published as a conference paper at ICLR 2025
CHEAPNET: CROSS-ATTENTION ON HIERARCHICAL REPRESENTATIONS FOR EFFICIENT PROTEIN-LIGAND
BINDING AFFINITY PREDICTION
Hyukjun Lim', Sun 233,5, Sangseon Lee
l Department of Materials Science and Engineering, Seoul National University
Department of Computer Science and Engineering, Seoul National University 3 IInterdisciplinary Program in Bioinformatics, Scoul National University
"Interdisciplinaryy Program in Artificial Intelligence, Scoul National University AIGENNDRG Co., Ltd., Seoul, Republic of Korea
6 "Department of Artificial Intelligence, Inha University (hyuk junl im, sunk imm.mm...... bioinfo @nuu. ac. kr, as lee@ beeiini iha ac kr
ABSTRACT
Accurately predicting protein protein-ligand binding affinity is critical challenge in drug discovery, crucial for understanding drug efficacy. While existing models typically rely on atom-level interactions, they often fail to capture the complex, higher-order interactions, resulting in noise and computational inefficiency. Transitioning to modeling these interactions at the cluster level is challenging because it is difficult to determine which atoms form meaningful clusters that drive the protein-ligand ligand interactions. To address this, we propose CheapNet, a novel interaction based model that integrates atom-level representations with hierarchical cluster-level interactions through a cross-attention mechanism. By employing differentiable pooling of atom-level embeddings, CheapNet efficiently captures essential higher- order molecular representations crucial for accurate binding predictions. Exten- sive evaluations demonstrate that CheapNet not only achieves state-of-the-art per- formance across multiple binding affinity prediction tasks but also maintains pre- diction accuracy with reasonable computational efficiency. The code of CheapNet is available at
com/ hyuk jun ChChhapeeeett
INTRODUCTION
Predicting protein-ligand binding affinity-the quantitative measure of interaction strength between protein and ligand-is fundamental challenge in drug discovery with major implications for therapeutic development. This measure, often expressed as the dissociation constant (K₂) or inhibi- tion constant (K2). directly determines drug efficacy. Traditional wet-lab methods. though accurate, are consuminn, costly, and difficult to scale (Schirle & Jenkins 2016 Lee & Lee 2016 Yang let al. 2022), necessitating the development of computational approaches faster, scalable alterna- tives in the drug discovery pipeline. However, computational modeling of binding affinity remains highly challenging due to the intricate and variable nature of molecular interactions, presenting sig- nificant hurdles for deep learning approaches (Dhakal et al. 2022).
Recent advances in deep learning have shown promise in predicting binding affinity by learning atom-level representations of proteins and ligands (Öztürk et al., 2018 Yang et al. 2022 Jiang al. 2021: Townshend et al. 2020 Yang et al. 2023] Feng et al. 2024), modeling their interac- tions as sets of atom-to-atom re relationships. While this atom-centric approach captures fine-grained details of local interactions, has notable limitations. Modeling solely at the atom level results in excessive computational complexity, as many atom pairs contribute negligibly to overall binding affinity (Nguyen et al., 20233 Tan et al., 2024] Abdelkader et al. 2023). Moreover, treating all atoms equally introduces noise, irrelevant atoms can interfere with accurate predictions (Jin et al. 2023 Shen et al. 2024).
"Corresponding author.

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Published as a conference paper at ICLR 2025
Beyond the limitations of atom-level model- ing, binding mechanisms often involve hierar- chical relationships that atom-level approaches alone cannot fully capture. Clusters of atoms often interact collectively with specific protein regions, such as aromatic rings targeting bind- ing pockets to inhibit HIV protease (see Fig- T.. These clusters exemplify the importance of identifying groups of atoms that act syner- gistically. a key factor in established binding paradigms like the lock-and-key and induced fit models (Du et al. 2016 Zhao al. 2021 Fatmi
Figure 1:
Protein-ligand complex (PDB ID: 1HVR) of HIV protease and its inhibitor. The ligand's aromatic ring and its corresponding con- tact region on the protein are highlighted in match- ing colors. Cyan dashed lines represent all contact points between the ligand and protein.
et al. 2009) [Schatz et al.) 2022 Liu et al. 2017a). The primary challenge lie in developing mech-
anism that identifies meaningful clusters dynamically and ensures their relevance to the binding process.
Effectively addressing this challenge involves learning subgraphs- within the protein- ligand complex- that encode both local and global structural features (Yuan & Ji 2020). Unlike traditional methods that focus exclusively on atom-level interactions or predefined clusters with geometric constraints (Du al., 2024 Kong al. 2024), this requires model capable of adaptively identifying relevant clusters based on their contributions to binding interactions. Such a model should aim learn these clusters through end-to-end training, capturing both local interactions and their broader structural context to provide a comprehensive understanding of ligtiinnligadd binding.
To address these limitations, propose CheapNet, a novel interaction-based model that dynami- cally identifies cluster-level representations of protein-ligand complexes through end-to-end train- ing. By leveraging differentiable pooling mechanism, CheapNet aggregates atom-level embed- dings into higher-level clusters, reducing noise and computational complexity while focusing on groups atoms that contribute significantly to binding interactions. Next, cross-attention mecha- nism is applied between protein and ligand clusters, enabling the model to focus on the most relevant moter-molccular interactions, thereby improving prediction accuracy and computational efficiency, In summary, the key contributions of CheapNet are as follows:
We propose hierarchical model that integrates atom-level and cluster-level interactions, improving the representation of protein-ligang complexes.
Our model incorporates a cross-attention mechanism between protein and ligand clusters, focusing relevant binding interactions in the cluster-level.
CheapNet achieves -tate-of-the-at performance across multiple binding affinity prediction tasks while maintaining computational efficiency.
RELATED WORKS
Protein-ligane ligand binding affinity prediction has traditionally focused atom-level approaches. Re- cently, cluster-level frameworks have emerged, emphasizing the importance of capturing higher- level interactions. Additional details representative methods provided in the Appendix
2.1 ATOM-LEVEL PROTEIN-LIGANU BINDING AFFINITY PREDICTION
Atom-level approaches to protein protein-ligand binding affinity prediction are categorized as interaction- free or interaction- Interaction- ligands independently. failing to capture critical interdependent interactions (Öztürk al. 2018
models, while computationally efficient. treat proteins and
Nguyen et al. 2021 Yang et al.) 2021 Rifaioglu et al.) 2021 |Huang et al., (021] Yang et al. 2022
Yuan et al. 2022). Interaction-
models address this by modeling atomic-level relationships
using 3D structural data (Townshend al. 2020: Jiang et al.) 2021 Yazdani-Jahromi et al. 2022 Yang et al. 2023; Wang et 2023 Nguyen et al. 2023 Feng et al. 2024). but they often overlook hierarchical mechanisms, such group-level cluster-leve interactions. Our model fills this gap by integrating a cluster-attention mechanism, capturing interactions at both atom and cluster levels for more comprehensive representation.
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Bluster-Atlentin M Mechanism
(a)
(b)
(c)
ligand
ligand clusters
ligand
protein
clusters
W
Seftome
W2
proteon
protein
Protein-ligand complex
Functionality- based Clustering
GNN encoder
Cross-attention
Figure 2: Architecture of CheapNet for protein-ligand binding affinity prediction. (a) A graph encoder learns atom-level embeddings of the protein-ligand complex. (b) A differentiable pooling mechanism clusters the embeddings into cluster-level representations. (c) A cross-attention mecha- nism applied between the protein and ligand clusters to capture key interactions.
2.2 CLUSTER-LEVER PROTEIN-LIGAND BINDING AFFINITY PREDICTION
Recent studies, including GemNet (Gasteiger et al. 2021), Equiformer (Liao & Smidt 2022). LEFT- Net (Du et al. 2024), and GET (Kong al., 2024), > have leveraged geometric and hierarchical repre- sentations enhance protein-ligand binding affinity prediction. GemNet and Equiformer focus on local and global molecular interactions using geometric and equivariant features. LEFTNet and GET build this by incorporating hierarchical frameworks that integrate block-level and atomic details. However, these models often depend on predefined clusters or geometric constraints. CheapNet addresses these limitations with data-driven approach, utilizing soft clustering of atoms based learned embeddings and cross-attention to dynamically model diverse protein-ligant interactions.
3 METHODS
In this section, we present the architecture of CheapNet, a model designed for protein-ligand binding affinity prediction. CheapNet first employs a graph encoder to learn atom-level embeddings of the protein-ligand complex (Figure 2 a)). Subsequently, differentiable pooling mechanism is used to aggregate atom-level embeddings into cluster-level representation (Figure 2[b)). Next, a cross- attention mechanism introduced between the protein and ligand clusters, allowing the model to focus on the most relevant interactions for binding affinity prediction (Figure ())
3.1 PROBLEM DEFINITION
In this study, aim to predict the binding affinity of piotein-ligand complexes. Each complex is represented as graph g = (V. E) = (VUV, U Ep. Eip), where Vi and Vp denote the set of nodes corresponding to atoms in the ligand and protein, respectively. Each node v; E V is associated with a feature vector I; E Rd representing atomic properties (which may vary across datasets), and 3D coordinate r; IR3 The edge sets Ei and Ep represent intra-molecular covalent bonds within the ligand and protein, while Eip denotes inter-molecular, non-covalent interactions between ligand and protein atoms within distance of 5A. The target variable, R, represents the binding affinity of the complex, expressed as log (Ka) - log(K)), where Kạ and K; are the dissociation and inhibition constants, respectively. The objective is to train predictive model f that estimates the binding affinity ý = f() by minimizing the error between ý and the true affinity y.
3.2 ATOM-LEVEL EMBEDDING VIA GRAPHI ENCODING
Before clustering the atoms, we first update the embeddings of the protein and ligand nodes to capture both local atomic properties and interactions within the protein-ligand complex. For each node v; E V. representing an atom in either the protein or ligand, we employ an interaction- graph neural network with geometric information (GIGN) (Yang al. 2023). This model updates
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node embeddings by aggregating information from neighboring nodes, incorporating both structural and geometric data while ensuring translation and rotation invariance the 3D coordinate space. h; GN, ru,))(u;) where h; E R is the updated embedding for the node et. .V(u,) de- notes the set of neighboring nodes, and d is the embedding dimension. While this work utilizes GIGN, other graph neural networks, such as GCN (Kipt & Welling (2066). or SE(3)-eqiivariant encoders like EGNN (Satorras et al. (202I) and SE(3)-Transformet (Fuchs et al. 2020), can also be applied. The embeddings h, produced in this step serve as inputs for the subsequent cluster-level representations, ensuring that both local and global interaction patterns are effectively captured.
3.3 CLUSTER-ATTENTIE FOR PROTEIN-LIGANT COMPLEX
Traditional models often focus on atom-level interactions, which can lead to excessive computational complexity. To address this, propose novel cluster-attention mechanism that clusters atoms using a differentiable pooling mechanism and applies cross rros-attentioon at the cluster level.
3.3.1 CLUSTER-LEVER PROTEIN-LIGANT INTERACTION
In protein-ligand complexes, is often unclear which atoms interact most significantly. To address this, we employ differentiable pooling method (Ying et al. 2018 to group atoms into clusters, capturing interaction patterns at a higher level of abstraction. By learning soft cluster assignment matrices and generating cluster embeddings, reduce the complexity of the graph while preserving critical structural and interaction information.
First, soft cluster assignment is performed separately for the ligand and protein atoms. This allows the model to aggregate atoms with similar representations. The soft cluster assignment matrices for the ligand and protein, S E R V and Sp E IR [V,l,,,, are computed as:
S softmax (GNN,, (H, Ei) Sp = softmax (H Ep)
where H, E R Vi and H, E R are the atom-level embeddings for the ligand and protein, respectively, with Eg and E, as their intra-molecular edges. cj and c, denote the numbers clusters for the ligand and protein.
Once the cluster assignments are obtained, we compute the high-level cluster representations by aggregating the atom embeddings within each cluster. The cluster-level embeddings for the ligand and protein are given by:
Z ST ST Hi, Z, ST
where Zi E Raxd and Zp xd represent the cluster embeddings for the ligand and protein, respectively. The cluster adjacency matrices, which capture the interactions between clusters, are updated based on the original graph structure follows:
A Sf A,S,
S
where A, and A, denote the adjacency matrix of F, and Epp, respectively. A, Raxa and Á, [ X represent the cluster-level adjacency matrices for the ligand and protein, respectively.
Next, we finally update the cluster-level embeddings based on the cluster representations and clus- ter adjacency matrices. Formally, the final cluster representations for the ligand and protein are computed as follows:
Z Rnal GNN,G ve At), Ziiaal GNN (p:AA)
(4)
where Zffnal Raxd and Zign R. denote the final cluster-level feature representations for the ligand and protein, respectively.
3.3.2
MECHANISMS CLUSTERS
After obtaining cluster- representations, we apply a cross-attention mechanism (Vaswani 2017 Chen et al. 2021 Lin al. 2022 between the protein and ligand clusters capture the critical inter- molecular interactions. This mechanism serves not only to capture key interactions between clusters but also filter out irrelevant noisy clusters, allowing the model to focus on the most biologically
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meaningful binding interactions. By dynamically adjusting the attention weights, CheapNet effec- tively selects the clusters that are most predictive of the binding affinit,, thereby enhancing both efficiency and accuracy.
We first compute the query, key, and value matrices for the seaandto--poteinn (L2P) and protein-to- ligand (P2L) attention mechanisms. For the L.PP attention, the query, key, and value matrices given by (for simplicity, we omit the superscript final)::
Q12p WQ Zi,
Kt2p
W Kiap 2p.
Vi2p WVa,, 2p
(5)
where W Qrap" W Kiay: and W Vizg are learnable weight matrices. Similarly, for the P2I. attention,
p2l
W Wa Zp K WKya Zr V221 WV, Z
(6)
The attention weights and representations for both directions are computed using the scaled dot- product attention:
Q12p K
2p2 softmax Ppzi KT 221
12p softmax(
12p
Vipp:
p21
Vd
vd
The representations of ligand-to- toppoetto-protein Zea and protein-to-ligand 2 are combined to form the final representation Zeomplez of the complex with multi-layer perceptron (MLP) and residual con- nection:
12
d2
Zcopplex MLP
(3)
p21
Finally, this combined representation is passed through MLP--based classifier fal to predict the binding affinity: ÿ = faif complex))
3.4 PERMUTATION INVARIANCE OF CLUSTER ORDER FOR CROSS ATTENTION
An essential property of the proposed cluster-level aross-attention mechanism its permutation in- variance with respect to cluster ordering, ensuring consistent model outputs regardless of the order of ligand and protein clusters. This property enhances the robustness and reliability in processing cluster-level representations. The detailed proof is provided in Appendix [A.3] Additionally, Cheap- -equivrana encoders, enabling CheapNet to
Net's modularity allows for the integration address broader range of symmetries in protein-ligand interactions.
3.5 LOss FUNCTION FOR OPTIMIZATION
To optimize our model, we employ the mean squared error (MSE) loss function, which quantifies the 1.2 distance between the predicted binding affinity and the actual value. The MSE loss is defined as: LASE = >i= (i) 32 where vi represents the predicted binding affinity for the i-th protein- ligand complex, Yt the corresponding ground-truth truth value and is the total number of samples.
We explore incorporating additional loss functions, such as link prediction and entropy regular- ization losses proposed by Ying et al. (2018). to guide clustering based geometric proximity. However, ablation studies in Appendix A. show no significant performance improvements. This suggests that clustering atoms based geometric proximity does not align with our goal of dynam- ically identifying biologically meaningful clusters. Thus, we retain the MSE loss for its simplicity and effectiveness in optimizing binding affinity predictions.
4 EXPERIMENTS
In this section, evaluate our CheapNet various protein-ligand affinity tasks including ligand binding affinity (LBA) prediction, ligand efficacy prediction (LEP). Detailed hyperparameter setting and experimental setup provided in Appendix Al We provide comprehensive comparisons with offtte-f--he-ant art methods, as well as ablation studies to assess the contributions of individual components. The code is available at https///ghhhhhcoollyyyuiiinnnnnn
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Table 1: Performance comparison of CheapNet and baselines the cross-dataset evaluation with parameter counts, The top results are shown in bold, and the second-best are underlined, respec- tively. The complete results, including all baselines with standard deviations are Appendix
2013 set
+201 set
x2019 holdout set
RMSE
Pearson
RMSE
Pearson
RMSE 1
Pearson
Interaction-free
DecpDTA (zzürk al.
2018
L93M
1,639
0,718
1.357
0,785
1,485
0.586
GraphTTA-Gaa GAT-GG (eeyeeh at
4.75M
1.645
0.711
1,434
0.754
1,705
0.474
MGrapDDTA Yang et ar.
2024
3.05M
1,600
0.696
1.439
0.753
1,553
0.538
Interaction-husee
PotentialNei Feimbere
2018
0.08M
1.607
0,773
1.503
0,772
1,514
0.564
SchNet (Schdit or 7
0,28M
1.570
0.754
1,390
0.787
1,522
0.560
GNN-DIT Lam
2019
0.22M
1.533
0.767
1.384
0,779
1,446
0.614
IGN Jiane 0r 3 2021
1660M
1.428
0.807
1,269
0.821
1,410
0.630
EGNN Silfomss m 2021
I ..99M
1 .498
0.782
1.289
0.816
1,399
0.628
GIGN Yang cf 2025
0.62M
L.380
0.821
1.190
0.840
1.393
0.641
Interaction-bused (atlention mechanism)
AllentionSiteDD11 Yazdaui-Jahhomm et 2022
42. 66666
1.444
0.792
1.352
0.784
1.539
0.563
CAPLA Din
2025
0.31M
1,409
0.816
1,306
0.841
GAABind Tan et al. 2024
17.95M
1.488
0.772
1.297
0.803
DEAttiationDIAA CClene
2024
2.32M
1,470
0,800
1,266
0.827
Interaction-baaed (custer-altentionn mechanism)
CheapNet (ours)
1.33M
1.262
0.857
1.107
0.870
1.343
0.665
4.1 LIGAND BINDING AFFINITY
Task. The Ligand Binding Affinity (LBA) task aims to predict the strength of interaction between protein and ligand. This regression task estimates the binding affinity of protein-ligand complex.
Dataset & Evaluation. We evaluate CheapNet on the widely-used PDBbind dataset (Liu et al, 2017b), which contains 3D structures of protein-ligand complexes with experimentally measured binding affinities. For a fair comparison, we follow the experimental settings, including data splits, used in existing works. CheapNet is evaluated in settings:
. Cross-datasel evaluation: Following the protocol in GIGN Yang et al. 2023). we train and validate CheapNet on the PDBbind v2016 general set and test on three independent datasets: PDBbind v2013 core set, v2016 core set, and v2019 holdout set. This configura- tion assesses CheapNet's generalization across different dataset versions.
Diverse Protein evaluation: As Atom3D (Townshend et al., 2020), the PDBbind v2019 refined set (Liu et al.] 2017b) is divided based protein sequence identity thresholds 30% (LBA 30%) and 60% (LBA 60%), ensuring that the test proteins have reduced similarity to those in the training set. This setup is designed to assess the model's robustness to structurally diverse proteins.
The number of clusters for both protein and ligand predefined as a constant through hyperpa- rameter tuning, with the median number of nodes in the training set chosen to balance overfitting and generalizability (see Appendix 10). We report RMSE and Pearson correlation coefficient for both settings, with the addition of Spearman correlation in the diverse protein evaluation. Each experiment is conducted three times with different random seeds for reliability.
Baselines. We compare CheapNet against diverse range of baselines of interaction-free methods and interaction-based methods. We also include pre-training models that are trained on large-scale data with significantly larger model parameters; interaction-fre models (e.g., DeepDTA (Ōztürk) et al. 2021
2018), GraphDTA (Nguyen et al. 2021)), interaction-based models (c.g.. IGN (Jiang et al.) GIGN (Yang et al. 2003)) ), cluster-level models (c.g.. LEFTNet (Du et al. 2024). GET (Kong
et al.
2024 and pre-training models (e.g., BindNet (Feng et al. 2024
Performances. Tables I and summarize the results for the LBA task. CheapNet demon-
strates significant improvements across both evaluation settings. outperforming interaction-free free, interaction-basee and even pre-trained models. Notably, CheapNet achieves the best results in terms of RMSE and Pearson correlation coefficient for the cross-dataset evaluation, showcasing its

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Table 2: Performance comparison of CheapNet and baselines the diverse protein evaluation with parameter counts. The top results are shown in bold, and the second-best are underlined, respec- tively. The complete results, including all baselines with standard deviations Appendix A.6 A
LBA 30%
LBA 60%
Model
RMSE 1
Pearson 1
Spearman
RMSE
Pearson 1 Spearman
Interaction-Fres
DeepDTA (Oztirk 2018
1.93M
1,866
0.472
0.471
1.762
0.666
0.663
SSA Bepler & Berger 2019
8M
1.985
0.165
0.152
1.891
0.249
0.275
TAPE 2019
93.0M
1,890
0.338
0.286
1.633
0.568
0.571
Interaction-basel
Atom3D-GNN (Jownshend et
1.601
0.545
0.533
1.408
0.743
[BConv (ermosilla aL 2021
5.M0
1.554
0.414
0.428
1.473
0.667
0.675
ProNet Wang all
0.765
0.761
Cluster-level
GemNet (asteiier et 202
1.37M
OOM
Equiformat (L:B Smatl
2072
1.10M
OOM
LEFTNee Da al M024
0.85M
1.366
0,592
0.580
GET Kong
0.69M
1.327
0.620
0.611
Pre-training
LGNN-PPM
2025 Gan
650M
1.403
0.565
0.646
Uni-Mol (Zhoü araie 2025
47.61M
1.434
0.565
0,540
1.357
0.753
0.750
0.762
BindNet Feng
47.66M
1.340
0.632
0.620
1.230
0.793
0.788
Interaction-hase (clsste-atteenioon)
CheapNet (ours)
0.642
0.639
1.238
0.789
Adapted from GET Kong al. 20244 which used hicracchical approschses from hovel to block-level. parameter cstimation for ProFSA BindNet
due insvallability pre-training model checkpoints. However, parameter count likely higher than that of Uni-Mol, both models are bused on it.
ability to capture complex protein-ligant interactions. For the diverse protein evaluation, although CheapNet achieved a comparable result on the LBA 60% dataset, slightly trailing BindNet, it is particularly noteworthy that it demonstrates exceptional first-place performance lenging LBA 30% dataset, where there is lower similarity between the training and test sets. Despite using far fewer parameters and requiring no pre-training, CheapNet consistently outperforms more complex models, highlighting its efficiency and robustness.
the more chal-
4.2 LIGAND EFFICACY PREDICTION
Table 3: Comparison results of CheapNet and baselines on LEP datasets. The top results are shown in bold, and the second-best underlined, respectively. The complete results, including all baselines with standard devia- tions are at Appendix A.7
Task. Ligand Efficacy Prediction (LEP) is a bi- nary classification task that predicts whether lig- and activates or inactivates a target protein. This task is crucial in drug discovery, it helps identify potential drug candidates that either enhance or in- hibit protein activity.
AUROCT
AUPRCT
Interaction-fee free
Dataset & Evaluation. For a fair comparison, evaluate CheapNet using the LEP dataset and experimental setting derived from the Atom3D benchmark (Townshend al. 2020). The dataset contains protein-ligand complexes labeled for ac- tivation inactivation. For evaluation, we report Area Under the Receiver Operating Characteristic Curve (AUROC) and Area Under the Precision- Recall Curve (AUPRC). Each experiment is run in- dependently with different random seeds.
DepDTA Oztiik
Interaction- based
Atee3D GNX Townshend et 2021
0.68
0.598
GVP-GNN [ing
2021
0.628
ProNec-All- Wailg 2025
Claster-Jevel
SchiNer (Schar al 2017
0.736
0.731
Salooras
0.724
GET
Kong ci 2i 2004
0.761
0.751
Pre- Pre-training
GeoSSL [Luu et 2020
0.776
0.694
Uni-Mol
ProPSA
Can et 2013
0.840
0.806
BindNet Fong
03882
0.700
Interaction-Base (claster-atennioonn
CheapNet (ours)
0.935
0.924
Baselines. We compare CheapNet against range of models, including interaction-fres meth- ods such DeepDTA (Öztürk et al. 2018); interaction- methods such as ProNet (Wang et al. 2023); cluster-leve approach such as GET (Kong al. 2024); pre-treining methods such BindNet (Feng al. 2024).
Adapted from GET Kong et 20144 which reed hicnanchical approaches from aton-level bovk--evel.

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Table 4: Ablation study results showing RMSE, Pearson correlation coefficient, and performance improvement (A) for different graph encoders on the PDBbind v2013 core set, v2016 core set, and v2019 holdout set. The top results are shown in bold, and the second-best are underlined. respectively. Standard deviations are at Appendix A.8
v2013 core set
v2016 core set
v2019 holdout set
Model
RMSE
Pearson
RMSE
Pearson
Pearson
GCN (Kipf & Welling 2016
1.385
0.819
1.295
0.809
1.460
0.593
CheapNat-GCN
1.368
0.820
1,246
0.823
1.391
0.635
(
+1.935
+0.122
+4.726
EGNN Satorras al. 2021
1.498
0.782
1,289
0.811
1.399
0.628
CheapNar-BGNN
1.321
0.843
1,161
0.856
1.343
0.664
(%)
+11.816
+7.801
+9.930
GIGN (Yang et al. 2023
1,380
0.821
1.190
0.840
1.393
0.641
CheapNar-GiGN
1,262
0.857
1.107
0.870
1.343
0.665
A (X)
+8.551
+4.385
Performances. As shown in Table CheapNet achieves state-of-the-art performance on the LEP task, significantly outperforming all baselines, including larger pre-training models. For AUROC, CheapNet achieves a score of 0.935, surpassing the previous best by BindNet (0.882), as well as other models like Uni-Mol (0.823) and GcoSSL (0.776). For AUPRC, CheapNet also achieves the best score of 0.924, outperforming BindNet (0.870). This performance is attributed to CheapNet's cluster-attention mechanism, which effectively captures complex protein- relationships.
4.3 ABLATION STUDIES
To demonstrate the effectiveness of CheapNet components, we conduct ablation studies: (1) adapt- ability of cluster-attention, (2) hierarchical representations and attention mechanism, (3) number of clusters, (4) auxiliary loss function, (5) atom selection & grouping approaches. Due to the limited space, experimental results of (3)-(5) are reported in Appendix A. 10 A.I1 and A.12 respectively.
4.3.1 ADAPTABILITY CHRAPNET WITH DIFFERENT GRAPH ENCODER
In this section, we demonstrate the adaptability of CheapNet by evaluating its performance when combined with different graph encoders. Specifically, we assess how adding CheapNet's cluster- attention mechanisms impacts models using GCN, EGNN, and GIGN base encoders.
Table 4 shows that CheapNet consistently improves performance across all encoders, regardless of the underlying architecture. While GIGN achieves the highest overall performance, both EGNN and GCN also benefit from notable improvements when paired with CheapNet's 's hierarchical repre- sentation and cluster-level attention mechanisms. Notably, GCN, which does not 3D structural information, achieves substantial gains, demonstrating CheapNet's flexibility in enhancing atom- level encoders and improving accuracy datasets.
4.3.2 HIERARCHICAL REPRESENTATION AND ATTENTION MECHANISMS
We perform an ablation study to evaluate the impact of hierarchical representations (Cluster) and attention mechanisms (Attention) on CheapNet's performance. Table S presents the RMSE and Pearson correlation coefficient across the PDBbind v2013 core set, v201 6 core set, and v2019 hold- out set.
The results show that both hierarchical representations and cross-attention work together to im- prove CheapNet's performance, Cluster-level representations are particularly effective on the v2019 holdout set, where larger protein-ligand complexes benefit from reduced computational complexity and better interaction modeling at higher scales (see Appendix A.5 for details). Otherwise, Cross- attention mechanisms enable CheapNet to focus biologically meaningful interactions by filtering out irrelevant clusters, which is reflected in the sharp performance drop when this component is removed.
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Table 5: Ablation study results for the effect of using hierarchical representations (Hierarchical), and type of attention mechanism (Attention) on the PDBbind v2013 core set, v2016 core set, and v2019 holdout set. The top results are shown in bold, and the second-best are underlined, respectively. Standard deviations are at Appendix A.9
v2013 core sel
v2016 core set
+2019 holdout sel
Cluster
Attention
RMSE
Pearson
RMSE
Pearson
RMSE +
Pearson
1,345
0.844
1.189
0.851
1.360
0.652
Self
1.305
0,850
1.166
0.854
1.367
0.650
Cross
1.293
0.853
L.551
0.857
1.362
0.653
1.330
0,840
1.161
0.853
1.348
0.662
Self
1.327
0.841
1.168
0.853
1.348
0,662
Cross
1.262
0,857
1.107
0.870
1.343
0.665
4.4 EVALUATION ON EXTERNAL BENCHMARKS
To demonstrate CheapNet's 's robustness and generalization, we evaluate its performance on three ex- ternal benchmarks on protein-ligand related tasks: the CSAR NRC-HiQ dataset (Dunbar Jr et al., 2013), the CASF-2016 dataset (Su et al. 2018), virtual screening on DUD-E dataset (Mysinger al. 2012). These benchmarks assess the model's predictive power on unseen, structurally diverse protein-ligand complexes, testing its real-world applicability. Furthermore, we extend the scope of CheapNet to Mootein-Protein Affinity (PPA) prediction on Protein-Protein Affinity Benchmark Version2 (Vreven et al. 2015) to evaluate its generalizability. Due to the limited space, the evalu- ations the CASF 2016 dataset, the DUD-E dataset, and the PPA prediction are presented in the A.15 and A.20
Appendix A.14
4.4.1 CSAR NRC-HIQ DATASET
We evaluate CheapNet on the CSAR NRC-HiQ dataset (Dunbar Jr et al. (2013), an external bench- mark for ligae binding affinity prediction. After removing complexes that RDKit could not process and overlaps with the training data, 14 samples remained for evaluation. compers CheapNet with other interaction-basee methods.
Table Performance comparison of Cheap- Net on the CSAR NRC-HiQ dataset. The top results are shown in bold, and the second-best underlined, respectively. Standard devia- tions are at Appendix A.13
Model
RMSE
Pearson
Interaction-baase
PotentialNet (Feinherg et al. 2018
1.730
0.718
CheapNet achieve the best performance, with an RMSE of 1.381 and a Pearson correlation coef- ficient of 0.901, outperforming all other models. These results highlight CheapNet's ability to han- dle complex mooeein-lignn interactions, especially in the external dataset.
GNN-DII (Lm
1.675
0.855
IGN (Jiane & al. 202
1.647
0.846
EGNK (Saleras
0.866
GIGN
Yang el 21/4
1.827
0.766
Interaction-best (cluster-attcntion mechanism)
CheapNet (ours)
1.381
0.901
4.5 MEMORY FOOTPRINT ANALYSIS
Memary Footorint Expertment of Actentoor-baeee bas-baoed Modes
GAMilid DEVetentinn6A
Figure
compares the memory usage of CheapNet with other attention-based models, GAABind Tan et al. 2024) and DEAtten- tionDTA (Chen al. 2024), across different batch sizes and complex sizes.
3
GAABind, which uses atom-level all-pairwise attention, consumes substantial memory and can only handle small batch sizes for small complexes. In contrast, DEAttentionDTA is more memory-effiiient with residue-level pro- tein representations but still requires significant memory for larger complexes due to residue-to- atom attention caleulations.
Setch Complex Sec
50 Large Complex
Small Compe
Figure 3: Memory footprint analysis. Com- parison of CheapNet, GAABind, and DEAtten- tionDTA across different batch sizes for small (50-100 atoms) and large (400-450 atoms) com- plexes. 'OOM' indicates out-of-memory.

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@
bb)
Ligand
in Chopdee 212
Uagasa Atue lose
0.5
23
40
60
103
Figure 4: Visualization of CheapNet interpretation and cross-attention map of protein-ligand complex (PDB ID: 4kz6). (a) The high-attended pairs of ligand and protein atoms are highlighted in the red box, with yellow dashed lines representing interactions. (b) Cross- map between ligand and protein atoms. The high-attention regions marked in yellow within the red box.
In comparison, CheapNet maintains consistently low memory usage across varying batch and com- plex sizes, even handling large protein-ligand interactions efficiently without OOM issues. This effi- ciency underscores the advantage of CheapNet's s cluster-level attention mechanism, which captures the essential binding interactions without the memory overhead typical of atom-level approaches. These results highlight CheapNet's scalability and suitability for handling large, complex interac- tions. Detailed experimental setups can be found in Appendix A.16
4.6 INTERPRETABILITY
CHEAPNET
This section analyzes the interpretability of CheapNet using the protein-ligand complex in PDBbind v2016 core set (PDB ID: 4kz6). Figure provides key insights into how CheapNet focuses atten- tion on critical binding regions. Further visualizations and details on how the attention scores computed are provided in Appendix 17.7
CheapNet's cluster-attention mechanism enables the identification of significant interactions be- tween ligand and protein, by focusing on the most relevant clusters involved in binding. As seen in Figure 4 CheapNet assigns higher attention to clusters that known to be critical for binding, while assigning low attention weights to less relevant clusters, thereby demonstrating its ability to filter noise.
Therefore, by accurately capturing key atomic interactions through its cluster-attention mechanism, CheapNet only achieves rear-perfect binding affinity predictions but also offers clear visual evidence of the interactions driving these affinities. This interpretability makes CheapNet powerful tool for understanding the molecular mechanisms behind pooeeinlligand binding, which crucial for drug discovery applications.
CONCLUSION & DISCUSSION
In this paper, we propose CheapNet, a novel interaction-based model that captures protein-ligand binding affinity by integrating hierarchical cluster-level representations with cross-attention mech- anisms. By leveraging differentiable pooling approach, CheapNet effectively balances capturing intricate inter-molecular interactions with computational efficiency. Extensive evaluations demon- strate faate-of-the-as art performance across diverse datasets, suggesting that hierarchical modeling of molecular interactions is promising direction for enhancing binding affinity prediction.
Although CheapNet achieves strong results, several directions remain for further exploration. Its performance beneñits from strong protein and ligand encoders, and integrating SEuiivequivariant encoders could enhance its ability to handle global and local 3D symmetries. While CheapNet can operate without 3D structural data (as shown in Table 4 optimal performance relies on 3D informa- tion. Advances like AlphaFold3 AAramsson al., 2024) now provide access to predicted structures, and CheapNet could be further developed to remain robust even with noise in these predictions (see Appendix A.1 Finally, extending the use of 3D information to cluster-level attention or adopting awarenessssesss framework that combine atom- and cluster-level features offers exciting potential for future work (see Appendix A.19
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ACKNOWLEDGMENTS
This paper was partly supported by the Basic Science Research Program through the National Re- search Foundation of Korea (NRF) funded by the Ministry of Education (RS-2023-00246586) the Bio Medical Technology Development Program of NRF funded by the Ministry of Science & (CTNRF-2022MB553300677 Institute of Information and communications Technology Plan- ning and Evaluation (IITP) grant funded by the Korea government (MSIT) [NO. 2021-0-01 2021-0-01343, 343, Ar- tificial Intelligence Graduate School Program (Seoul National University), W..RS-2022-0015555
Artificial Intelligence Convergence Innovation Human Resources Development (Inha University)), the ICT Scoul National University, and AIGENDRUG Co. Ltd., by Korea Institute for Ad- vancement of Technology (KIAT) grant funded by the Korea Government (Ministry of Education) sawiicondduuto--ppccaaiiiie University).
(P0025681-G02P2223000 -0020222500000000000000000
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A APPENDIX
A.1 ADDITIONAL EXPLANATIONS OF RELATED WORKS.
In this section, we briefly introduce several representative approaches including interaction-free, interaction-based, cluster-level, and pre-training models for protein-ligand binding affinity predic- tion.
A.1.1 INTERACTION-FRE MODELS
DeepDTA Öztürk et al., 2018 uses convolutional neural networks (CNNs) to analyze SMILES representations of molecules. This approach demonstrates the potential of deep learning to capture molecular features effectively. Instead, the focus is primarily on learning molecular representations independently for proteins and ligands.
GraphDTTA (Nguyen al. 2021) and MGraphDTTA (Yang al., 2022 extend DeepDTT by representing molecules as graphs, using various graph neural network (GNN) architectures such as Graph Convolutional Networks (GCN), Graph Isomorphism Networks (GIN), and Graph Attention Networks (GAT). These approaches capture the structural information of molecules more effectively compared SMILES-baie based representations.
A.1.2 INTERACTION BASEDD MODELS
IGN (Jiang et al. 2021) introduce significant advancement by employing both intra- graph and inter-graph convolutions to capture pairwise atomic interactions. This allow the model to account for both local and global interactions within the protein-ligand complex, leading to more accurate binding affinity predictions.
Equivariant Graph Neural Networks (EGNN) (Satorras et al. 2021) addresses a critical challenge in molecular modeling, ensuring that predictions invariant changes in the orientation or position of the protein-ligand complex. This geometric invariance ensures that predictions remain physically meaningful, regardless of how the complex is rotated or translated.
Geometric Interaction Graph Neural Networks (GIGN) (Yang et al., 2023) further advances this concept by incorporating both intra- and inter mnter-molecular geometric information, al- lowing the model to capture complex 3D spatial relationships within the protein-ligand complex.
A.1.3 CLUUSTE--LEEL MODELS
GemNet (Gasteiger et al. 2021) employs directional message passing capture both local and global molecular interactions using geometric features such as distances and angles. focuses on fine-grainee spatial relationships, achieving high accuracy in molecular property prediction tasks.
Equiformer (Liao & Smidt 2022) combines Transformer architecture with SE(3)/E(3)-
equivariant features to handle 3D molecular graphs. integrates spherical harmonics and tensor products to represent complex interactions while preserving rotational and transla- tional symmetry.
LEFTNet (Du et al. 2024) introduces hierarchical representations for 3D molecular graphs, utilizing predefined clusters (e.g., residues motifs) encode higher-order interactions. It emphasizes computational efficiency while maintaining expressiveness.
GET (Kong et al. 2024) models molecular complexes geometric graphs of sets using a bilevel design. It captures block-level sparsity and atom-level density through bilevel attention mechanisms, ensuring adaptability across diverse molecular domains.
A.1.4 PRE-TRAINING MODELS
GeoSSL (Liu et al. 2022) introduces a 3D coordinate denoising pretraining framework de- signed model the dynamic behavior of 3D molecules, where their continuous movement
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within the 3D Euclidean space generates smooth potential energy surface. Extensive periments, including quantum mechanics and force prediction as well as binding affinity prediction, validate the effectiveness and robustness of this proposed method.
ProFSA (Gao et al. 2023) introduces a novel pocket pretraining approach that harnesses knowledge from high-resolution atomic protein structures, supported by effective pre- trained small molecule representations. By segmenting protein structures into drug-lit like fragments and corresponding pockets, ProFSA simulates ligand-receptor interactions, gen- erating over 5 million complexes. The pocket encoder is then trained contrastively to align with pscudo-ligand representations from pretrained small molecule encoders.
BindNet (Feng et al., 2024) emphasizes discerning intricate binding patterns from fine- grained interactions. This self-supervised learning problem is formulated as predicting the final binding complex structure given pocket and ligand through a Transformer-basee interaction module, which naturally emulates the binding process. To ensure the represen- tation of rich binding information, two pretraining tasks are introduced: atomic pairwise distance map prediction and masked ligand reconstruction, comprehensively modeling fine- grained interactions both structural and feature spaces.
A.2 PSEUDOCODE OF CHEAPNET
In this section, provide the detailed pseudocode for CheapNet, which outlines the step-by-step process for predicting protein-ligand binding affinity (Algorithm(]) D] The algorithm starts by initial- izing atom-level embeddings for both the protein and ligand components.
Initialization: The initialization process of the atom representation follows that of GIGN (Yang et al.] 2023) for Cross-Dataset Evaluation, and Atom3D (Townshend et al., 2020 for Diverse Protein Evaluation and Ligand Efficacy Prediction. Both methods initial- ize each node's ' features using one-hot encoding based on atom types (c.g., elements like H, O, ). In addition, for GIGN, the degree of an atom, hybridization, and number of valence electrons are considered. For Atomãl,, co-crystallized metals considered (e.g., elements like Zn, Na, Fe, etc.) for proteins. Finally, linear layers are applied to obtain the initial embedding, refining the atom representation.
2. Atom-Level Embedding: Each atom's 's embeddings are updated using Graph Neural Net- work (GNN), capturing intricate local interactions within the protein and ligand structures.
3. Cluster-Level Representation: Soft cluster assignment matrices are computed using the GNN outputs, enabling the model to form hierarchical, cluster-level representations. This step allows CheapNet capture more abstract, functionally relevant features beyond the atom level. Finally, using the soft cluster assignments, cluster-level representations and adjacency matrices are derived. These cluster embeddings are further refined via a GNN, incorporating higher-level structural information.
4. Cross-Ar Attentiotnn Mechanism: The core CheapNet involves a cross-attention mechanism that models interactions between the protein and ligand clusters. The model computes query, key, and value matrices to perform scaled dot-product attention, ensuring that critical inter-moled moleculo interactions are accurately captured. This step also filters out irrelevant clusters by focusing on those with higher attention weights.
5. Final Representation: The output of the cross-attention mechanism is combined and pooled to form a comprehensive representation of the protiin-igaad complex, which is then passed through an MI. to predict binding affinity.
A.3 PERMUTATION INVARIANCE OF CLUSTERS ORDER FOR CROSS ATTENTION
An important aspect of the proposed cross-attention mechanism cluster-level representations is the permutation invariance cluster ordering. This property ensures that the model's output remains consistent regardless of the order of ligand and protein clusters. Maintaining this invariance is crucial for the robustness of the model, as it prevents the network from being sensitive to arbitrary orderings of atoms clusters, which should not influence the physical properties of the complex. By ensuring that the model's 's predictions are unaffected by cluster permutations, we preserve the reliability of our dluster-ttention mechanism.
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Algorithm 1 CheapNet for Protein-Ligand Binding Affinity Prediction
Require: Protein-ligand complex graph = UVi V,, Ei U Ep U Elp) Predicted binding affinity
Ensure:
1: Initialization: Atom embeddings H₃ E Rill H, E RIVlIa obtained by one-hot encoding
followed by a linear transformation.
2: Atom-Level Embedding:
3: for each node V E Vi U V do
4: hy = GNN(2;, (T,s))
5: end for
6: Cluster-Level Representation:
7: Compute soft cluster assignment matrices
> dynamically group together atoms by their embeddings
S softmax (H, E.), Sp o Ex)
8: Obtain cluster-level representations:
Z: Hi,
Zp = S Hp
9: Obtain cluster-level adjacency matrices:
À A,S,
A, = S S
Final update the cluster-level embeddings:
> learn cluster-level interactions for each ligand and protein before cluster-attention
Z iinal
GNN vi (Zi, Ai), Zp
GNN vi (Zpr Ap)
Cross-Attention Mechanism:
12: For ligand-to-protein attention, compute query, key, value matrices:
Q12p W2 Zfimal
Ki2p
Wx Zfial
Vi2p
Wv Zfmal
13: Apply scaled dot-product attention:
B filters irrelevant clusters by focusing on those with higher attention weights
Q12p KT
Zz softmax
12p
Viap
Vd
14: For protein-to-ligee -igadd attention, perform similar computations L12-13:
(qai KT p21
2p21 = softmax
Vpa1
Vd
15: Final Representation: Combine outputs:
C
41
Gp
Z complex
MIP
(i:))
Z
(ith p2l
(6:3)
Z
(1:)
12p
17: Prediction:
MLP (ML((ccomllll complex)
Consider the ligand-to-protein attention mechanism (for simplicity, we omit the subscript 12p). As- sume permutation matrices P& and P, for the ligand and protein, respectively. The permuted cluster- level representations of the ligand and protein are given by:
2 Pa Zt,
Zz P.Z
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The corresponding permuted query, key, and value matrices are then:
Q W - Po P
(10)
K' W WxP,Zp P,W P.K
(1I)
V W.Zg WvP.Zpp = W, P.V
(12)
The attention weights for the permuted representations, denoted by 0',, are computed as:
QKKK)) softmax Po P
a. softmax
Vd
vd
(13)
QKT
softmax Po
Vd
Since Ps and P. are permutation matrices, they simply reorder the rows and columns of the attention matrix. The softmax function is applied row-wise and is invariant to row permutations. Therefore:
QK
S.p Ps softmax
P
(14)
Vd
Next, the attention output is computed as:
QKT
2 = OPP Pe softmax
)P!
P.V.
Vd.
(15)
QKT P
Ps softmax
Finally, we apply sum pooling over the cluster dimension c,. Since the summation is invariant to the order the elements, the sum pooling of the permuted attention output is:
(9)
(16)
Thus, the output of the sum pooling for the ligand-to-protein attention is permutation-innaaiian with respect to the ligand clusters.
The same reasoning applies the protein-to-ligand attention mechanism. Therefore, since both the figand-to-prott and protein-to-lignnn outputs are pooled in a permutation- intioonnivariant manner, the final representation Zcomplez will remain unchanged regardless of the order in which the ligand or protein clusters are arranged.
Geometric Symmetries Protein-Ligand Complexes and Their Treatment in CheapNet: CheapNet's cluster-attention mechanism is designed to be permutation invariant with respect to the ordering of clusters in the graph representation, ensuring consistent outputs regardless of how ligand and protein clusters are indexed. However, this invariance pertains the graph-level discrete ordering of clusters and should be distinguished from geometric symmetries (translation, rotation, and permutation of 3D coordinates) inherent to protein-ligand complexes.
When addressing symmetries in 3D coordinates, CheapNet's ability to handle translation, rotation, and permutation invariance relies on the properties of the atom-level encoder used compute em- beddings for proteins and ligands. In this study, we employed GIGN (Yang et al.) 2023). which enforces translation and rotation invariance and is permutation equivariant by the nature of GNNs. properties propagate to the cluster-level representations and outputs of CheapNet, ensuring global translation, rotation, and permutation invariance. However, CheapNet's cluster-attention mechanism itself operates graph representations derived from these embeddings and does not directly enforce additional symmetries.
These symmetry-preseet
In local coordinates (e.g., within specific cluster), rotation and permutation invariance depend en- tirely on the encoder's properties. For global coordinates (e.g., protein-ligand complex as a whole), the translation and rotation invariance of GIGN ensures that CheapNet can handle these symmetries
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effectively. To further enhance its ability to capture symmeetry-awee -aare features, integrating (S)E(3)- cquivariant encoders (Satorras et al. 2021: Fuchs et al. 2020) into CheapNet's 's modular framework is promising direction for future improvement.
This modularity allows CheapNet to flexibly adapt to tasks and datasets with varying symmetry requirements. However, the cluster-attention mechanism itself does not enforce additional sym- metries, its performance might depend on the quality of the embeddings provided by the encoder. Future work could explore extending the use of 3D information within the cluster-attention mecha- nism itself to improve its ability to handle local symmetries dynamically.
A.4 DETAILS OF HYPERPARAMETER
EXPERIMENT SETTINGS
In table A1 we present the hyperparameter search space used to optimize CheapNet's performance across pross-dataser evaluation, diverse protein evaluation (LBA 30%, LBA 60%). and LEP. For LEP task, combine the results of CheapNet for active and inactive complexes, we applied multi-layer perceptron (MLP) and trained models using binary cross-entropy (BCE) loss. All experiments were conducted on two separate NVIDIA RTX 3090 GPUs (24GB each), with each model running on single GPU. Each model was trained with early stopping based on validation RMSE.
Table Al: The search space of hyperparameters for cross datased,, LBA 30%, LBA 60%, LEP task. The optimal hyperparameters shown in bold.
Hyperparameters
Cross-dataset
LBA 30%
LBA 60%
LEP
Activation function
SiLU, GELU, Mish 64, 128
Mish
Mish 8, 16
Mish
Batch size Cutoff-intra
8, 16
4,
3
3
3Á
Cutoff-inter
SÅ 0.1. 0.2, 0.3 800
5
5
5
Dropout rate
0,
0.1
0.
Epach
10,
500, 600
10, 15
Hidden
64, 256 5e-3, le-4, 1.5c-4 Reducee..Rnnllteen Adam, AdamW 1e-7, 1e-6, le-5, le-4
64, 256
64,
64, 256
Learning rate scheduler
5e-3, le-4, 1.5e-4
5e-3, le-4, 1.5e-4
5e-3, Ic-4, 1.5e-4
Peducel.ROnPlatee Adam, AdamW 1e-6
Optimizer
Adam, Adam le-6
Adam, AdamW 1e-6
Weight decay
Number of clusters
Protein
156 28
372
362
312
Ligand
25
24
49
Number layers
Message Passing
1,
1,2.3
1,
1,2,3
Diffentiable pooling
1,2
1,2
1.2
Prediction MLP
1,2,
1.2.
1.2,3
1,2,
A.5 STATISTICS OF THE DATASETS AND EVALUDATION SCHEMES
Table A2 provides detailed statistics of the datasets used for cross-dataset evaluation, diverse protein evaluation (LBA 30%. LBA 60%), and ligand efficacy prediction (LEP). The table summarizes the total number of complexes, as well as the quartiles (Q1-Q4), averages, and standard deviations for the number of atoms in proteins, ligands, and overall complexes across these datasets.
For cross-dataset evaluation, the PDBbind v2016 general set used as the training and validation dataset, while the v2013 core set, v2016 core set, and v2019 holdout set serve as test datasets. Among these test sets, the v2019 holdout set contains the largest and most diverse complexes, with an average of 191.36 atoms per complex and a standard deviation of 48.31, indicating wide variety in protein-ligand sizes.
For diverse protein evaluation, the PDBbind v2019 refined set is used, with the LBA 30% and LBA 60% datasets split based on protein sequence identity thresholds of 30% and 60%, respectively. These datasets, along with LEP dataset consist of larger and more diverse ligands and proteins com- pared to the cross-datase, evaluation sets. For example, the average number of atoms in protein struc- tures in the LBA 30% and LBA 60% dataset is 371.6 1.66, and in the LEP dataset, it's 327. .6, reflecting
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the complex and varied nature of these datasets. These characteristics highlight the challenging and comprehensive nature of the evaluation benchmarks used to assess CheapNet's performance.
Ligand Binding Aflinity / Cross-data Evaluation Test Dataset To ensure fair comparisons across all 19 models, including CheapNet, we adopted the same test datasets as described in GIGN Yang et al. )023):
PDB v2013 core set (N=107)
PDB v2016 core set (N=285)
PDB v2019 holdout set (N=,4366)
These datasets were consistently used to evaluate all models' generalization capabilities, with dif- ferences in training and validation datasets depending the baseline model's protocol.
Ligand Binding Aflinity Cross-data Evaluation -Training and Validation Details
GIGN (Yang al. 2023) Protocol (16 Models, including CheapNet)
Training Set: 11,904 samples from the PDBhind v2016 general set.
Validation Set: 1,000 samples from the PDBbind v2016 general set.
All 16 models followed the protocol established in GIGN for training, validation, and test- ing.
2. CAPLA (Jin et al. 2023), GAABind (Tan et al., 2024), DEAttentionDTA (Chen et al., 2024) These models provided pre-trained checkpoints based on training and validation datasets derived from the PDBbind v2020 general set (CAPLA: v2016 general refined sets). Their test evaluations included only the PDB v2013 and PDB v2016 core sets, as their respective original papers limited comparisons to these benchmarks.
Ligand Binding Affinity Diverse Protein Evaluation and datasets ensure consistency in evaluation protocols, the following two steps:
We carefully reviewed the original papers
1) Dependency Mapping. Previous studies are mentioned while citing two main references: Holo- Prot (Somnath et 2021 and Atom3D Townshend al. (221))
ProNet (Wang al. 2023 references the dataset protocol from HoloProt (Somnath al. 2021}.
ProFSA (Gao et al.
2023 BindNer (Feng al. 2024 and GET (Kong al. 2024 follow
the dataset splits established by Atom3l (Townshend et al., 2021
2) Dataset Consistency. To verify dataset consistency, we compared datasets using public reposito- ries provided by HoloProt and Atom3D, and found that the datasets are identical:
Sequence identity 30%:
Training Set: 3,507 samples
Validation Set: 466 samples
Test Set: 490 samples
Sequence identity 60%:
Training Set: 3,563 samples
Validation Set: 448 samples
Test Set: 452 samples
Baseline Results
The baseline results were directly adopted from the following sources:
HoloProt (Somnath et al.
2021): DeepDTA, SSA, TAPE, IECony, MaSIF. Holoprot-Full Surface, Holoprot-Superpix.l ProtTrans
Atom3D (Townshend et al.
2021): Atom3D-3DCCN, Atom3D-ENN, Atom3D-GNN
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ProNet (Wang et al.
2023
ProNet-Amino Acid, ProNet-Backbone, ProNet-All-Atom
ProFSA (Gao et al.
2023
EGNN-PLM, ProFSA
NindNet (Feng et al.
2024)
DeepAffinity, SMT-DTA, GeoSSL, Uni-Mol, BindNet
GET (Kong et al. Net, GET
2024
SchNet, GemNet, Equiformer, TorchMD-Net, MACE, LEFT-
Ligand Efficacy Prediction All 17 models were evaluated using the same training, validation, and test splits defined in the Atom3D benchmark (Townshend et al. (021))
Baseline Results. The baseline results were directly adopted from the following sources.
Atom3D (Townshend et al.
2021): Atom3D-3DCNI Atom3D-ENt Atom3D-GNN
ProNet (Wang et al.
2023
GVP-GNN, ProNet-Amino Acid, MooNet-Backbone, ProNet-
All-Atom
ProFSA (Gao et al.
2023
ProFSA
BindNet (Feng et al.
2024):
DeepDTA, GeoSSL, Uni-Mol, BindNet
GET (Kong al.
2024): SchNet, EGNN, TorchMD-Net, GET
Dataset statistics for cross-dataset evaluation, diverse protein evaluation (LBA 30%, LBA 60%), and LEP. The table summarizes total number of complexes, as well as QI-Q4 quantiles, averages, and standard deviations for the number of atoms in proteins, ligands, and complexes across the datasets.
Table A2:
Statisties
Cross-dataset
Diverse protein
LEP
v2016 general
v2013 core
v2016
v2019 holdout
LBA 30%
LBB 30%
of complex
12904
107
285
4366
4463
518
127
282
Q2
156
159
152
153.5
360
325
Protein
Q3
186
186.5
178
183
462
372
Q4
500
280
454
650
Avg
160 84
160.87
153.53
157.77
371.63
327.96
71.25
Q1
20
21
42
Q2
51
Ligand Atom #
Q3
37
31
30
37
32
59
161
147
Avg
32.65
25.41
24.55
33.59
25.43
$1.47
Stdl
21.61
1120
9.81
21.97
11.24
15.24
Q1
154
149.5
147
153
286
324
Q2
186
184
378
Complex Atom
Q3
224
218
205
220
488
430
Q4
595
332
332
533
1085
796
Avg
193.50
186.25
178.08
191.36
397.06
379.43
Std
60.51
49.34
45.10
61.29
145.22
83.21
A.6 PERFORMANCE OF CHEAPNET ON LBA TASKS WITH PARAMETER COUNTS AND STANDARD DEVIATIONS
Tables A3 and A4 provide a detailed breakdown of the parameter counts and standard deviations for all models evaluated on the LBA tasks in both the cross-dataset and diverse protein evaluations. These tables reinforce the efficiency of CheapNet, as it consistently delivers superior performance with significantly smaller parameter count compared other models, especially pre-trained mod- els like BindNet, which utilize orders of magnitude more parameters.
Moreover, CheapNet demonstrates smaller standard deviations in its predictions across all datasets, indicating greater stability and reliability. This consistency is particularly noteworthy given that CheapNet does not rely on large-scale pre-training, further emphasizing its robustness in handling diverse mooeiin-ligant interactions. These findings affirm that CheapNet achieves state-of- ff--th-art art performance with a reasonable computational footprint, making it highly practical and effective solution for protein-ligand binding affinity prediction tasks.
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To measure the statistical significance of performance differences between models, used Z-tests, as paired t-tests were not feasible due to relying on reported results from previous studies. With the available means, standard deviations, and sample sizes, Z-tests provided suitable alternative.
We compared CheapNet's performance against the second-best model in terms of RMSE, Pearson correlation coefficient, and Spearman correlation coefficient on the LBA task. The p-values corre- sponding to the Z-statistics are indicated at the end of the table. The results show that CheapNet's improvements over the second-best model are statistically significant (p-value < 0.001) compa- rable.
Table A3: Performance comparison of CheapNet and baselines with parameter counts and standard deviations on the cross-dataset evaluation. The top results are shown in bold, and the second-best underlined, respectively.
Model
Params
x2013 cure set
Y2016 core set
Y2019 holdout set
RMSE
Pearson
RMSE: L
Pearson
RMSE:
Pearson
Interaction-tree
DeepDIX (zzliik et all 2018
193M
1,339 1: 0.025
0.718 = 0.014
1.357 2: 0.015
0,785
0,007
1,485
0.025
0.586 :: 0,012
GraphDTA-UU
3021
2.66M
1,749 + 0.062
0.662 - 00832
1,513 + 00048
0.719
0.003
1,763 + 0.099
0.439 + 0.021
GraphDTA GAT
1.46M
2,03 1 0.029
0.176
0.022
1,768 0.019
0.591
0.010
1,663 0.027
0.432 1. 0,016
GraphDTA-GIN (aager
1.30M
0.124
0.084
0,743
0.027
0.022
0.021
GraphDTA-GAT.A
4.75M
1.655- 0.085
0.11
1.434
0.754
1.705 +00075
MGruphDDA Yong et
3.05
1,600
0.093
0.696
1,439
0.753
0.022
1,553 0.028
1 0.013
Interaction
Pafiney
2018
0.014
0.785
1.450
0.700 0.019
0.016
0.622 0.014
QuionNa Papon 2017
130M
0.079
0.741
1.399
0.770 0.027
1.510 00034
0.014
Putentis|Nix [imiiee
2018
0.8M
1,607 1: 0.027
0.773
0.010
1,503
0.033
0.772 0.007
1.514 0.028
0.564
0.014
Schieet
Schirer 2017
0.88
1,570 1: 0,029
0.754 = 0.030
1,390
0.023
0.757
0.016
1.522 0.01
0.560
0.028
GNN-D T
1p Mi 4m19
0.2M
1.533 + 0.084
0.767 0.840
1.884-
0.013
0.779 0.008
1.466 0.066
0.614
0.007
IGN June 21 KM
1.66
1,228 1 0.020
0.807 0.001
1.269
0.000
0,821
0.01.
1.400
1 0.015
0.630 0,008
BGiN Sahoras
2021
1.59M
1 +: 0.025
0.782 =: 01015
1,289
0.021
0.866
0.011
1,399
0.033
0.628 = 0.010
GIIN
0.6M
1 1.800-1 + 0.089
0.821 - 0.003
1,190
0.017
0.840
0.007
1,301
0.007
0.641 + 0,006
Interaction--usee -assd (attentionn mechunien)
AltendinN Yogaan Jihromi al. 2012
42.66M
1,44 0.057
0.792 0,014
1.352
0,784
0,008
1.539 0.015
0.563 0.004
CAPLA
0.31M
1,409
0,816
1,206
0.841
GAABiil
17.5M
1,488
0.772
1.297
DEAnemieDTs
0,500
Interaction--aee bused (duster-atteniion mechunism)
CheapNet (ours)
133M
1.262 0.017 0.857 = 1.107
0.011
0,870 0,002
1,343 0.007
0.00L
Surteiial Signifieunce (p-valae)
Suticaad was pofoomaal worming seno sinderd the unanddisbillty the standal desiation poralie (000)
A.7 PERFORMANCE OF CHEAPNET ON LEP TASK WITH PARAMETER COUNTS AND STANDARD DEVIATIONS
Table A5 provides comparison of CheapNet and baseline models the LEP task, including stan- dard deviations for AUROC and AUPRC metrics. Notably, only GeoSSL, Uni-Mol, and ProFSA report standard deviations based on repeated experiments. Consistent with its performance on the LBA tasks, CheapNet demonstrates smaller standard deviations compared to other methods, re- flecting its stable and reliable performance across multiple runs. These results further emphasize CheapNet's efficiency and robustness in modeling ligand efficacy, making it an effective solution for capturing complex protein-ligand interactions. 7-tests were also performed as in Appendix AA6 to compare CheapNet's performance against the second-best performing model in terms of AU- ROC and AURPC on the LEP task. The results demonstrate that CheapNet's improvement over the second-best model is statistically significant (p-value < 0.001).
A.8 ABLATION STUDIES (1): ADAPTABILITY OF CHEAPNET WITH PARAMETER COUNTS AND STANDARD DEVIATIONS
Table A6| presents the detailed results of the ablation study with standard deviations for RMSE and Pearson correlation coefficients across the PDBbind v2013 core set, v2016 core set, and v2019 hold- out set. Despite only modest increase in the number of parameters. CheapNet combined with vari- ous graph encoders (GCN, EGNN, and GIGN) demonstrates consistent and substantial performance improvements across all datasets. This highlights CheapNet's is ability to enhance predictive accuracy effectively while maintaining parameter efficiency, making it a scalable choice for pootiin-ligani binding affinity tasks.
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Table A4: Performance comparison of CheapNet and baselines with parameter counts and standard deviations on the diverse protein evaluation. The top results are shown in bold, and the second-best are underlined, respectively.
Model
Params
LBA 30%
LBA 60%
RMSE 1
Peurson 1
Spearman
RMISE 1
Pearson 1
Spearman
Interaction-free
DeepD/1A (Ouurk et al 2018
193M
1,866
0.080
0,572
0,022
0.471 0.024
1.762 à 1.266
0,566
0.012
0.663
0.015
(eeplr
48.5M
1.985
0.165
0.006 0,358
0.024
18891 0.004
0.349
0.275
0.008
TAP
(corecal
93/0M
0.124
0.568
0.021
Interaction-bseed
Alom3D-- DD-DDNN (Tonsheml et al
2.22M
1416 0.021
0.550
0.021
0.553
0.009
1621 +: 0.025
0.608
0.000
0.615
0.028
Atom3D ENN
Johon:o Se 3l20
0,66M
1 1,568 4: 0.012
0.359
0,024
0,808 1. 0.021
1.620
1: 0.049
0.623
0.015
0.633
0.021
0.3
1,40 + 0.048
0.545
0.027
0.583
0.083
1.408 + 0.069
0.743
0.022
0.743
0.027
IECam- [Tlem/hiii of 1 2023
5.80M
1.554 1 0.016
0.414
0.053
0.428
1 0.032
1.473 1 0.024
0.667
0.01
0.875 1 0.019
MaSilt (iiii of dig 2020
BAZM
1 + 0.018
0.407
0,000
02455 = 0.014
1.426 +: 0.017
0.709)
0.001
0.701 = 0.001
Holopn Surmer Smimiith ml 302
144M
1.64 + 0.006
0.500
0,002
0,500
0,005
1.365 + 0.038
0.749
0.014
0.742 0.011
Hollopro Supernitel
1.66
1.491 0.001
0.491
0.014
0.482
0.052
1416 0.022
0.724
0.011
0.715 0.006
ProNes-Aatiae Acid
1455
0.536
0.012
0.012
1.397
0.741
0.009
ProNat-Buclbvte
1.3
1458
0.546
0,550
0.008
3.34 1:001
0.764
ProNet All-Atmm Wante
139M
1
0.001
0.551
0.005
0,351
0.008
1.443 0.025
0.705
0.009
0.761 0.003
Salieer (Shiill
B21M
1.370
0.028
0,500
0.017
0.571
0.028
GemNer Com h01l
1.7MM
00M
Equitormis Land & Sany Puzz
1.JOM
00M
TurchMD Ncc T1o0 V Puchnii 2022
0,30M
1.383 1: 0.009
0.590 a: 0,008
0.564 1: 0.004
MACE Begalinrr
391M
1.372 + 0.021
0.612 0,010
0.592
+ 0.010
LEFTN
0.85M
13366 0.016
0,592
0,014
0,580
1 0,011
(Kon
0.6PM
1.327
0,620
0.004
0.005
Pre-training
DeepA Rinily KKrimi
1,803 + 0.650
0:426
SMT D/A P Mi24
1.574
0.447
1.347
0.758
GeoSSL (Lmre Fi14
1451 + 0.030
0.577
0,020
0.572
0.010
ProxTrame LII E
2.4M
1.544 :: 0.015
0,438
0.053
0.434
0.058
1611
:: 0016
0.505
0.04
0.588
0.009
BGNN PLAT We e 31 M64
650M
1
:: 0.010
0.563
0,020
0.564
: 0.010
1,559
1: 0.000
0.544
0,020
0.646 =: 0.020
Uni-Moa Zhxu ai 9123
47.61M
1.434
565
0.540
1.357
0,753
0.750
ProFSA
NFFA
347.61M*
1.77 1. 0.100
0,628 0,010
0.620 1 0,010
1.377 1 1.1000
0.764
0.000
0,762 0,010
RindNe Fong
24761M*
1,340
0.620
1,230
0.788
Interaction-haee (chsler-attentionn mechanism)
CheupNat (ours
1.39M
1.31
0.642 0.001
0.010
1.238
0,002
0.001
Striitical Significance (p-value)
Addpped from GET Koogetal etal. [001 which used heeaachiccl approaches from atom level to Mock level.
Accanae panameter Giimatos for BindNet not possibl due Bhe muvaiabblll of the pae irining model chockpoirr, but Hally higher thas Mad sines hael
performed mosming doadand unone bhiliy standant
p-vals B005
..: -potlle 0.001
"; non-iigtificnt
A.9 ABLATION STUDIES (2): HIERARCIIICAL REPRESENTATIONS AND ATTENTION MECHANNSMS WITH PARAMETER COUNTS AND STANDARD DEVIATIONS
Table A7 shows CheapNet's performance under various configurations for RMSE and Pearson cor- relation coefficients across the PDBbind v2013 core set, v2016 core set, and v2019 holdout set, showing the effects of hierarchical representations and cross-attention mechanisms. The results show that the combination of cluster-level representations and cross-attention yields the best perfor- mance, highlighting the significant improvements achieved by integrating both components.
1. ABLATION STUDIES (3): EFFECTS OF NUMBER OF CLUSTERS
We investigate how varying the number of clusters, defined by quantiles of the number of complex nodes (Q1-Q4), affects CheapNet's 's performance. The model uses differentiable pooling mecha- nism to cluster atoms based on functional similarity, and the number of clusters can influence both accuracy and efficiency. To evaluate this, experimented with four different cluster sizes (Q1, Q2, Q3, Q4) and summarized the results in Table A8
The results show that cluster size q2 consistently provides the best balance between RMSE and Pearson correlation coefficient across the datasets. While q4 shows slightly better results on the v2019 holdout set. q2 performs optimally on the v2013 and v2016 core sets. This suggests that q2 strikes the best balance between computational efficiency and capturing key molecular interactions, making it the most suitable cluster size for most applications in CheapNet.
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Table A5:
Comparison results of CheapNet and baselines LEP datasets. The top results shown in bold, and the second-best are underlined, respectively.
Model
Params
AUROCT
AUPRCT
Interaction-free
DeepDTA Oztüikk et
Interaction-based
Atom3D-3DCNN Townshend et
2020
97.51M
0.589
0.483
Atom3D-ENN Tolnsseen èl
0.663
0,55
Alom3D-GNN Townseen ef al.
2020
1.21M
0.681
0.598
GVP-GNN (Jing 2021
0.628
ProNet-Amitoo Acid Wane 0t 2023
0.646
ProNet-Backhone WWang et 2025
0.687
ProNet-All Wain
SchNet [Schiirt et al. 7077
0.20M
0,736
0.020
0.731 + 0,048
EGNN
0.056
NDT Tholke & Fabritis 2022
0.29M
0,717 0.033
0.724 1 0.055
KKng et
0.761
0.751 0.012
Pre-traluing
GeoSSI [Lu et 2022
0.776
0.050
0.694 0.060
Uni-Mol Zhou cra
P025
47.61M
0,782
0.020
0.695 : 0.070
ProFSA Lao et m
A0743
>47.6M
0,840 0.040
0.806 + 0.040
BindNet (1 TTeng el
247.61M*
Interaction-based (clnster-attentoon)
CheapNet (ours)
1.45M
0.924
Statistical Significance (p-value)
Adapted from GET Kong al 2024 which used hierarchical approaches from ztom-level bloek-level.
Accurate parameter estimatin BindNNet is possible due the unmailability of the pre-training higher Uni-MMl since hased Unii- Iin--Mol.
checkpoinr, hut
Statistical test performed assuming zero
the unavailabiliry standard deviation.
p-value 0.001
Table A6: Ablation study results showing RMSE, Pearson correlation coefficient, and performance improvement (A) for different graph encoders with parameter counts and standard deviations on the PDBbind v2013 core set, v2016 core set, and v2019 holdout set. The top results are shown in bold, and the second-best are underlined, respectively.
Model
Params
v2013 sce
v2016
v2019 holdout
RMSE
Pearson
Pearson 1
L
Pearson
(Krr& Welling 2016
6.033
0014
0.004
0.593
ChespNerGCN
109
1,368
0.039
0.800 0.122
1216
0.04
0.823
1 0.014
1,311
0.018
0.655
0.110
((%)
+1.935
+0.122
+3.784
+1.731
+4.726
+7.083
RGNN Smtrras et al, 1021
1.50
1.498
6.025
0.782 + 0015
1.289
0021
0.16
0.011
1,999 + 0.013
0,68
0.100
CheapNer DUNNY
243M
1.321 1 0,027
0.843
1 0.012
1.161
1 0.100
0,856
0.000
1,33
1 0,009
0.664
1864410000 0.008
(55)
+11.316
+7,801
+9.930
+5.549
+4,000
+5.732
GIGN Yang al 2023
0.62M
1,380 à 0,009
0.821
= 0.003
1.190
0017
0.840
0,007
1,393
a 0,007
0.641
0.006
133
1,262 + 6.017
0.87
+ 0.084
107
0011
0,800
0.002
1,343
+ 0.007
0.665
0.083
(5))
48.551
+4.385
46975
43.571
+3.580
43.744
Table A7: Ablation study results for the effect of using hierarchical representations (Hierarchical), and type of attention mechanism (Attention) with parameter counts and standard deviations on the PDBbind v2013 core set, v2016 core set, and v2019 holdout set. The top results are shown bold, and the second-best are underlined, respectively.
Hierarchical Attention
Params
RMSK
Pearson
RMSK
Pearson
RMSE.
Pearson
0.49M
1,345
0.017
0.844 4: 0.003
1.189
0.005
0.851 2: 0.001
1.360
0.001
0.652 J: 0.001
Self
1.22M
1,305
0.030
0880
+ 0.004
1.166
0.005
0.854
0.002
1.367 + 0.000
0.650 0.002
Cross
1.02M
1,95
0.022
0.853 1 0.0002
1,111
0.003
0.857
0.001
1.362 1 0.0011
0.653
1 0.004
x 0.81M
1,350
0.017
0.840
4: 0.006
1.161
= 0.012
0.853 - 0.003
1.348 0.005
0.662
:: 0.005
Self
1.33M
1.327 0.044
0.811 1 0.015
1.168 0.003
0.853 1 0.001
1,348
0.004
0.662
0.012
1,262
1.107
0.011
A.11 ABLATION STUDIES (4): EFFECTS OF ADDITIONAL AUXILIARY Loss
We considered incorporating auxiliary losses, including link prediction loss and entropy
regularization loss, as proposed by |Ying et al. (2018). The link prediction loss is defined as
Tup ||A S where || means Frobenius norm. The entropy regularization loss is
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Table A8: Ablation study results of CheapNet for different number of clusters with parameter counts and standard deviations on the PDBbind v2013 core set, v2016 core set, and v2019 holdout set. The top results are shown in bold, and the second-best are underlined, respectively.
Chuster size
Params #
x2013 set
v2016 set
v2019 holdout set
RMSE
RMSE.
RMSE |
Q1
L32M
1303
0.016
0,850
0.005
1,53 0.015
0.856
0.004
1,356 0.009
0.657
0.006
Q2
133M
1,262 0.017
0857
0.000
1,007 0.011
0,870
0.002
1.343 0.007
0.655
0.003
Q3
1.34
1.274 +: 0.029
0.862
0.011
1.142 0.025
0.863
0.007
1,340
0.008
0.665
0.004
Q4
1,6MM
0.052
0.847 + 0.011
1,147 + 0.002
0,859 0.002
1,334 0.009
0.669 0.005
Table A9: Ablation study results of CheapNet for auxiliary loss with standard deviations on the PDBbind v2013 core set, v2016 core set, and v2019 holdout set. The top results are shown in bold, and the second-best are underlined, respectively.
auxilliary loss
v2013 core set
v2016 core set
v2019 holdout set
RMSE 1
Pearson 1
RMSE
Pearson
RMSE
Pearson
X
1.262 0.017
0.877 + 0.004
1.107 + 0.011
0,870 + 0.002
1.343
0.007
0.665 + 0.1013
1,288
0.017
0.858 0.003
1.143 + 0.007
0.861 0.004
1.348
0.002
0.661 0.001
Table A10: Ablation study results for the effect of using various pooling methods compared to the differential pooling of CheapNet with parameter counts and standard deviations on the LBA 30% dataset of Diverse Protein Evaluation.
Model
Params #
RMSE J
Pearson
Spearman
TopKPooling (Gao & Ji. 2019
1.03M
1.478 + 0.048
0.578 + 0.013
0.574 0.030
ASAPooling Ranjan 2020
1.16M
1.419 + 0.040
0.592 + 0.017
0.594 0.020
SAGPooling (ao et al. 2023
1.03M
1,514 + 0.020
0.582 + 0.013
0.590 = 0.007
CheapNet (ours)
1.39M
1.311 + 0.003
0.642 + 0.001
0.639 0.010
given by LE Ei H(S:), where H is the entropy function, and S; represents the i-th row of S.
As shown in Table A9 the use of auxiliary loss does not consistently improve performance. While provides a marginal boost Pearson correlation coefficient on smaller dataset such ac v2013 core set, it tends to degrade results larger datasets. This indicates that clustering atoms based on geometric positions is less effective compared to clustering based purely on features, particularly when used with cross-attention mechanisms.
A.12 ABLATION STUDIES (5): COMPARISON OF ATOM SELECTION & GROUPING APPROACIES AND CLUSTER- ATTENTION MECHANNISM OF CHEAPNET
To further analyze the impact of soft-clustering approaches in CheapNet, we evaluate different atom selection or grouping approaches by replacing CheapNet's differential pooling method with alter- native strategies. Specifically, we tested hard node selection methods such as TopKPooling (Gao)
& Ji 2019) and ttructure-based pooling methods like ASAPooling (Ranjan et al. (020) and SAG- Pooling Leee et al. ) As presented in Table CheapNet consistently demonstrated superior performance in the LBA 30% dataset on the Diverse Protein Evaluation. Unlike hard selection or structure-based clustering approaches, CheapNet's cluster-attention mechanism prioritizes cluster- ing by atom embeddings, rather than relying on geometrie properties, offering complementary perspective clustering.
A.13 PERFORMANCE CHEAPNET CSAR NRC-HIQ DATASET WITH PARAMETER COUNTS AND STANDARD DEVIATIONS
Table ATI summarizes the detailed performance of CheapNet and various interaction based models on the CSAR NRC-HiQ dataset, including parameter counts and standard deviations. CheapNet not only achieves the best RMSE and Pearson correlation coefficient but also exhibits the smallest stan- dard deviations across both metrics (except RMSE of EGNN), indicating its consistent and reliable
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Table A11: Performance comparison of CheapNet and various interaction-based models with pa- rameter counts and standard deviations on the CSAR NRC-HiQ dataset. The top results are shown in bold, and the second-best are underlined, respectively, with standard deviations.
Model
Params
RMSE 4
Pearson 1
Interaction-basee
PotentialNet (Feinherg al.
2018
0.08M
1.730 + 0.119
0.718
0.056
GNN-DTI (Lim et al. 2019
0.22M
1.675 + 0.256
0.855
0.123
IGN (Jiang et at. 2021
1.66M
1.647
0.265
0.846
0.052
EGNN Satorras ét al. 2021
1.59M
1.640 0.068
0.866
0.031
GIGN Yang
2023
0.62M
1.827
0.166
0.766
0.086
Interaction- based (cluster-attention mechanism)
CheapNet
1.33M
1.381 + 0.089
0.901 = 0.016
(8)
Ranking Power
(b)
Scoring Power
0.01
DCP1:10
6.711
Ax (10
182
Au
RAC
ALT
Hy dadddme
8/012
ECN
0.040
Chan
2012
Sur
Autodoo Wha
Chemdor
Chendcanng
155
Upford
dev uSe
00511
201
Ugione
1.100
414
1.0
0.2
0.0 Cotrelation Coaffiic
Spearman Inttonttioooo Confficntt
Figure A1: Comparison of (a) ranking power and (b) scoring power of CheapNet and various other models based on Spearman correlation coefficient and Pearson correlation coefficient.
performance. Despite using more parameters than some models, CheapNet's cluster-attention mech- anism offers significant improvements, demonstrating its robustness in handling complex protein- ligand interactions.
A.14 PERFORMANCE OF CHEAPNET ON 2ASF-2016 DATASET
We assess the ranking power and scoring power of CheapNet using the CASF-2016 dataset (Su cet al. 2018). To evaluate ranking power, we calculate the Spearman correlation coefficient for ligands, averaged over 57 complexes. As shown in Figure a)), CheapNet ranked first with correlation of 0.761, outperforming all other models. For the scoring test, we assess the Pearson correlation coefficient for 285 complexes. As illustrated in Figure [T[,), CheapNet is the best- performing model among those evaluated. These excellent results demonstrate CheapNet's potential to significantly advance protein-ligand ranking in pharmaceutical research.
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Table A12: Performance comparison of models with and without the cluster-attention mechanism on the DUD-E dataset. The integration of the cluster-attention mechanism significantly improves performance with fewer parameters. The top results are shown in bold, and the second-best are underlined, respectively.
Model
AUROC1
EFuux ?
EF
EFax f
GCN Kipf & Welline
2016
DURM
0.677 0.030
9.951 + 0,084
5.062
0.353
4.148
0.865
3,200
0.626
EGNN Santras MP
0.03M
0.771 00.017
11,368 = 5.423
9.202 #: 4.079
7.393 4: 2.714
5.534 +: 1.418
GIGN Yang
DDUM
0.780 0.017
11.079 5.09
8,689
7.992
5,00
1.538
Attenions 187T
42.59M
0820
0.012
13,985
7,580
11,694
7,418
9.447
5.861
6,846
2.635
CheapNer (ouS)
DO3M
0.826
0.011
24,646
10.922
16.249 # 7.617
12.549 + 5.032
8,109 2.144
A.15 APPLICATION TO WORLD SCENARIO: EXAMPLE OF VIRTUAL SCREENING TASK
In drug discovery, accurately predicting whether ligand will bind to a receptor protein-a process known as virtual screening- essential. To demonstrate the effectiveness CheapNet in capturing the relationship between a protein and a ligand, we curated a dataset from the well-established DUD- dataset (Mysinger al. 2012) and processed its 3D structures using RDKit. For each active ligand, pockets were extracted, and corresponding graphs were constructed. Undersampled decoys were then generated in equal numbers, resulting in 1 11,109 actives and 10,987 decoys. The number of target proteins is 52. With CheapNet, we compared GCN (Kipf& & Welling 2016). EGNN (Satorras) ct al. 202T), GIGN (Yang et al.) 2023), and AttentionSiteDTI (Yazdani-Jahrom et al. 2022) as baselines. A 3-fold cross-validation was applied, and the averaged results reported. For fair comparison, a hidden dimension of 35 is adopted.
Table clearly shows that CheapNet notably enhances performances of the virtual screening task. Importantly, y, this improvement is achieved with greater parameter efficiency, as the cluster-attention mechanism boosts performance while reducing the parameter count.
Furthermore, to demonstrate the interpretability of CheapNet, we performed a case study using the Tyrosine Protein Kinase SRC protein (SRC) with one of its active ligands from the DUD-E dataset. SRC is a disease-causing protein that promotes the growth of cancer cells, making it an important target for cancer treatments (Luo et al. 2022).
As shown in Figure A2 CheapNet showed high confidence in the activity of the ligand with SRC, with a predicted score of 0.9998. Notably, the interpretability of CheapNet in this scenario was impressive, as it successfully pinpointed the regions of critical interaction between the ligand and the protein. Using cluster-level cross attention, CheapNet effectively identified key molecular in- teractions, demonstrating its potential to enhance Al-based drug development by improving both accuracy and interpretability.
A.16 DETAILS OF MEMORY FOOTPRINT ANALYSIS
The memory usage in attention-basee based models is significantly influenced by the number of atoms in -rggin complex, due to the quadratic complexity of attention matrices. To assess CheapNet's 's memory efficiency, we compared it against GAABind and DEAttentionDTA using varying numbers of atoms and batch sizes.
We divided the PDBbind v2016 core based on the number of atoms in the complexes, ranging from 50 to 450 in increments of 50. For each interval, 128 complexes were randomly sampled to en- sure fair comparison. For the smaller atom interval (50-100 atoms, "small complex"), experiments were conducted with batch sizes of 2 and 4. For the larger interval (400-450 atoms, "large com- plex"), batch sizes of 32, 64, and 128 were used. Although we tested a wider range of intervals and batch sizes, Figure Bin in the main text focuses representative settings to highlight the differences in memory efficiency.
Each model was trained for 20 epochs, with memory usage monitored via nvidia-smi. CheapNet consistently required less GPU memory compared to GAABind and DEAttentionDTAA, owing to its cluster-attention mechanism, which reduces the burden of large attention matrices by leveraging hierarchical representations. Notably, CheapNet's memory usage remained stable even with larger batch sizes, demonstrating its scalability for protein-ligand binding predictions.
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Protain SRC
Thue: 1
CheepNiet: 0,9998
10
0
Crops Arttontntnnnonn Map Betacon Protein and Ligand Atams
-15
Ligund peam boce
-20
10
Protein Aram Index
Figure A2: Visualization of CheapNet's applicability in active ligand-SRC complex in DUD- dataset. The most attended pairs of protein and ligand atoms are highlighted, with cyan lines representing interactions. An object connected with yellow lines is ligand, the other with red is protein, This figure demonstrates CheapNet's effectiveness in capturing key binding regions which correspond to cross-attention maps.
A.17 FURTHER VISUALIZZATION OF CHEAPNET'S INTERPRETABILITT
We further explored other cases that show CheapNet's ability interpretability at Figure A3 To fully utilize CheapNet's soft assignment and cross-attention mechanism, summarize the atten- tion scores across both ligand and protein clusters. The attention score between ligand and protein atoms is computed by considering the cross-attention between ligand-to ggaad-to-ppootin (Qr2p- K(2p) and pontein-to-ligant (Qp21- K22t) attention scores, along with the assignment matrices for ligand (S)) and protein (Sp) atoms. The overall attention score can be expressed as:
Q12p Ki 12p vd
(Qraz KT p21
) ST
A = St softmax
softmax
(17)
Vd
The visualization result on 4 samples of PDBbind v2016 core set in Figure A3 further illustrate CheapNet's ability to capture meaningful interactions between ligand and protein atoms. Across the cases, the higher attention CheapNet closely predicts the true binding affinity and performs comparably to GIGN, CheapNet's baseline model. Leveraging the cluster-attention mechanism to identify eritical interactions, Cheap- Net achieves higher accuracy to predict protein-ligann binding affinity. These findings demonstrate CheapNet's strength in providing interpretable insights protein- ligand interactions through its cluster-attention mechanism.
regions of cross-attention map indicate key binding regions.
A.18 SIMULATION ON LACK OF THREE-DIMENSIONAL HIGH-QUALITY DATA
In real-world applications, high-quality data such as three-dimensional crystallized protein struc- tures, as used in this study, may not always be available. In such cases, predicted structures gener- ated by tools like AlphaFold (Abramson et al., 2024) provide viable alternative. However, these predicted structures often contain noise, which negatively impact model performance.
To evaluate the robustness of CheapNet's clustering mechanism handling noisy data, we con- ducted an ablation study by adding Gaussian noise 7 (0, 1), to the initialized atom embeddings in Algorithm [ This experiment aimed to assess how clustering helps group meaningful atoms while filtering irrelevant information, mitigating the effects of noise. To isolate the contribution of clustering, we disabled the cross-attention mechanism in CheapNet for this evaluation, focusing solely hierarchical representations.
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@
h
FSB ID: Say True 5.00 Chepriee 5003 GIGN 5.00
ESB GOCNS 2.00
protann
ligind
Riceeal
Cross-Attention Map Between Protein and Ligand Atoms
Cross-Attention Map Between Protein and Ligand Atoms
0.35
Upand Aoom indox
Ugand Noom index
10
0.3
0.20
15
0.2
0.15
30
40
50
60
Protain Atom Index
Protein Atomi Indix
(c)
(d)
prican
GOGN 6.90
FDB ID 13y
Tree 6:46
Chaghiae
Choppees 5,00
GIEN
Tuae 501
P0U ID: SKOT
protein
ligand
ligand
Cross-Attention Protein and
Cross-Attention Map Ligand
0.6
0.15
0.5
Ugaanic Atom Indox
Liqand mdoo
0.12
10
0.4
0.10
1.5
0.3
0.05
0.04
25-
0.02
60
120
Protein Atom
Figure A3: Visualization of CheapNet's interpretability in various protein-ligand complexes (PDB ID: (a) 3arv, (b) luto, (c) Ir5y, (d) 4agq). The most attended pairs of protein and ligand atoms are highlighted in red boxes, with yellow dashed lines representing interactions. This figure demonstrates CheapNet's effectiveness in capturing key binding regions which correspond cross- attention maps, offering valuable insights into protiin-ligan interactions.
Table A13 summarizes the results of the study. CheapNet, when using hierarchical representations, exhibited performance decline compared other models, demonstrating robustness in noisy environments. While SE(()-equivariant EGNN exhibited even smaller performance declines un- der noisy conditions, CheapNet maintained superior overall performance across datasets. This highlights the value of CheapNet's clustering mechanism for noise reduction and flexible feature extraction, which is especially beneficial for handling noisy predicted structures practical appli- cations.
Furthermore, inspired by GET (Kong et al. 2024). we evaluated CheapNet's performance under varying levels of coordinate noise simulate imperfect real-world conditions. As shown in Ta- ble A14, CheapNet maintains stable performance under low noise levels but experiences a grad- ual decline noise increases, likely due the GIGN encoder (Yang et al. 2023), which is only
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Table A13: Ablation study results for the effect of using hierarchical representations to control additional noise with performance decline (A), parameter counts, and standard deviations on the PDBbind v2013 core set, v2016 core set, and v2019 holdout set.
Model
Noise
Paruma
v2013 core set
v2016 core set
Y2019 boldout set
RMSE.
Pearson
RMSE
Pearson
RMSE
Pearson
GCN Kipl & Welling 2016
0.25M
1,502
1,395
0.039
0.033
0,819 = 0.013
0.773 0,010
1337 0.06
1 + 0.014
0.793 0.014
0,809 = 0.004
1460
1,500
0.009
0.018
0
0.002 0.570 0.004
((5)
-7.600
-5.617
-3.243
-1,978
-3,225
[GN Fing et 2021
1.66M
1.428
0.014 1.474
0,807
0.786
0.003
= 1,269
1.332 1. 0.020
0.795 4. 0.009
1410
1.437 1 0.023
0:015
0.620
0.008
(15))
-3.221
-2,602
-49664
-3.167
-1.15
-1.587
EGNN Satorra al 2021
1.59M
1.498
1,507
0.006
0.025
0,782
0.780
= 0.015
0.009
1,300
1
4: 0.021
0.021
0.812 a 0.015
0.816 a 0.011
1,402
1,399 a 0.013
0.019
0.628
0.629
0.007
0.010
-0,001
40.25
-0,85%
-0,490
-0314
ChoapNot (wio crose-atlention)
0.8IM
1,300
1.352 0.041
0.827
0.013
1,190
0.025
0,842
0.007
1,386
0.014
0.005
0.619 0.008
0.065
(35)
-1,654
-1.548
-2.498
-1.290
-2.19
-1.964
Table A14: Ablation study results for the effect of varying error levels to noise coordinate with standard deviations on the LBA 30% dataset of Diverse Protein Evaluation.
Model
Error Level (Á)
RMSE
Pearson
Spearman
0.0
1.311 + 0.003
0.642 + 0.001
0.639 + 0.010
0.1
1.325 1: 0.011
0.611 0.005
0.625 0.003
CheapNet
0.5
1.340 0.010
0.616 0.005
0.601 +: 0.005
1.0
1.348 0.003
0.608 0.007
0.600 + 0.007
2.0
1.364 1: 0.014
0.603 0.010
0.585 0.009
0.0
1.416 + 0.006
0.548 + 0.007
0.532 0.013
0.1
1.420 0.011
0.545
0.542 + 0.016
CheapNet-EGNN
0.5
1,418 0.019
0.548 =
0.544 + 0.013
1.0
1.418 + 0.011
0.013
0.530 + 0.014
2.0
1.435 + 0.002
0
0.522 + 0.021
translation and rotation invariant. To address this, replaced GIGN with EGNN (Stoorass al., 2021), which is translation-, rotation- and permutation-oquivariann. The resulting model, CheapNet- EGNN, demonstrated more robust performance under higher noise levels. This highlights the mod- ularity of CheapNet's 's architecture, allowing the GNN encoder to be easily replaced to better suit data quality requirements.
A. EXTENDING 3D INFORMATION TO CLUSTER-LEVEL ATTENTION AND AUAL-AWARENESS FRAMEWORK
While CheapNet currently leams interactions during the graph encoding stage through atom em- bedding computation, these interactions could be explicitly incorporated in later stages, such the cross-attention mechanism.
As outlined in Algorithm 2 one potential approach involves pre-computing atom-level edges based on distances between ligand and protein atoms within threshold (c.g.. 5 A). These edges can then be aggregated into cluster-level weights using the soft clustering assignments of atoms clusters. The resulting cluster-level weights, representing interaction likelihoods based on atom-level proxim- ity, could serve as biases in the cross-attention mechanism to guide attention scores. This preserves CheapNet's end-to-end differentiability while embedding biologically meaningful priors into inter- action modeling.
To explore dual-awareness framework that utilizes both atom- and cluster-level representations, we conducted experiments with atom selectors such as TopKPooling (Gao & Ji 2219). which con- siders individual node embeddings, and ASAPooling (Ranjan al., 2020). which aggregates local cluster representations. Additionally, we combined TopKPooing or ASAPooling with CheapNet to implement the dual-awareness framework.
Table A15 shows that integrating TopKPooling or ASAPooling with CheapNet (Dual-) improves performance compared to using atom selectors alone. Notably, CheapNet alone achieves the best
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Published as a conference paper at ICLR 2025
Algorithm 2 Pseudo Code for Distance-Driven Cluster Interaction Weighting
Require: Ligand atoms }.a:}. Protein atoms {pa,}- Atom positions {riag, raa, J. Distance thresh- old detreshold- Soft cluster assignments Mot,ta and Map.pa
Ensure: Cluster-level weights cluster (cl, cp)
Step I: Compute Atom-L.vel Distance Edges
2: for each ligand atom la, and protein atom pa, do
3: Compute dist (la;, pa,):
{
if || rpasll dhreshoold otherwise.
Edist (la;, paj)
0
4: end for
5: Step 2: Aggregate Atom-Level Edges Cluster-Level Weights
6: for each ligand cluster cl and protein cluster cp do
7: Compute clusser (cl, cp):
Ediist eluuster (cl, cp) -ΣΣ Matta, Mep.pp, Eddist (la,, pay)
EEMata
paj
8: end for
9: Step 3: Integrate into Cross-Attention Mechanism
10: Modify cross-attention computation as:
QK" + a Cluster
distt
Attention K, V) = softmax
Vd
Table A15: Results for the dual-awareness framework of CheapNet with parameter counts and stan- dard deviations on the LBA 30% dataset of Diverse Protein Evaluation.
Model
Params #
RMSE
Pearson f
Spearman f
TopKPooling (Gao
2019
1.03M
1.478 = 0.048
0.578 0.013
0.574 + 0.030
ASAPooling (Ranjan et al. 2020
1.16M
1.419 = 0.040
0,592 = 0.017
0.594 + 0.020
Dual- Popollng (Gao & Ji 2019
1.46M
1.417 + 0.007
0.589
0.012
0.587 + 0.010
Dual-ASAPooling (Ranjan al. 2020
1.59M
1.394 + 0.032
0.618 0.013
0.619 + 0.017
CheapNet (ours)
1.39M
1.311 = 0.003
0.642 0.001
0.639 + 0.010
Table A16: Pearson Correlation Results with parameter counts and standard deviations the Protein-Protein Affinity Prediction. The top results are shown in bold, and the second-bes. are underlined, respectively.
Model
Params #
Rigid
Medium 1
Flexible
All
SchNet (Gasteiger al.
2021
0.37M
0.542
0.028
0.507 + 0.020
0.098 + 0.011
0.438 = 0.017
GemNet (Gasterger el al.
2021
2.64M
0OM
TorchMD-NET [Tkkee
Fabritiis
2022
1.00M
0.572
0.498 0.025
0.109
0.093
0.026
MACE (Batatia ef al. 2002
25.7M
0.069 0.616
0.461 =: 0.050
0,275 + 0.032
0.466 = 0.020
Equiformer Liao & Smidi
2022
1.10M
OOM
LEFTNet (Du
3.10M
0.533 0.059
0.494 0.026
0.165 + 0.031
0.445 0.024
GET Kong el it.
2014
2.50M
0.670 0.017
0.512 + 0.010
0,381 + 0.014
0.514 + 0.011
CheapNet (ours)
2.72M
0.680 0.016
0,518 =: 0.008
0.392 + 0.004
0.529 = 0.002
overall results, but the dual-an awarenesss framework demonstrates promising potential for future work.
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Published as a conference paper at ICLR 2025
Table A17: Spearman Correlation Results with parameter counts and standard deviations the Pootiin-Protein Affinity Prediction. The top results are shown in bold, and the second-best are
underlined, respectively.
Model
Params #
Rigid
Medium f
Flexible
All f
SchNet (Gasteiger al.
2021
0.37M
0.476
0.017
0.523 0.014
0.072 + 0.021
0.424 +: 0.016
GemNet (Gasterger el al
2021
2.64M
OOM
TorchMD-NEET hhokke De Fabritiis 2022
0.547
0.516
0.019
0.100 0.111
0.029
MACE (Batatia et a.. 2022
25.7M
0.580
0.075
0.476 + 0.048
0,282 + 0.036
0.470 = 0.016
Equiformer (LBO & Smide 2022
1.10M
OOM
LEFTNet
2014
3.10M
0.476
0.082
0.494
0.037
0.151 + 0.019
0.446 + 0.029
GET (Kong al. 2024
2.50M
0.622 0.030
0.533 + 0.014
0.363 + 0.017
0.533 + 0.011
CheupNet (ours)
2.72M
0.640 0,005
0.535 + 0.008
0.387 + 0.017
0.542 + 0.002
A.20 BROADENING THE SCOPE OF CHEAPNET: APPLICATION TO PROTEIN-PROTER AFFINITY PREDICTION
Protein-Protede affinity (PPA) prediction is essential for understanding the strength of interactions between proteins, which is important in applications such as drug design, signaling pathway analy- sis, and disease mechanism studies. To demonstrate CheapNet's generability and flexibility beyond protein-ligand tasks, we extend it to PPA prediction, highlighting its capability to hand more com- plex interfaces.
Task. PPA prediction involves modeling the binding strength between two proteins, which often requires analyzing large and intricate interfaces. This task presents unique challenges compared to protein-ligand interactions due to the complexity and variability of protein-protein binding sites.
Dataset & Evaluation. For a fair comparison, we follow the protocol from GET (Kong et al. 2024), using 2,500 training complexes from PDBBind (Wang et al. 2004), split by 30% sequence identity. For evaluation, we use the Protein-Protee Protein Affinity Benchmark Version 2 (Vreven et al.] 2015), which categorizes 1 176 protein-protein complexes into three difficulty levels: Rigid, Medium, and Flexible settings. The Flexible category, in particular, involves substantial conformational changes, making it the most challenging. Evaluation metries include Pearson and Spearman relation coefficients, with experiments repeated three times using different random seeds.
We compare CheapNet against state-of -fate-of-the-art models, including TorchMD- NET TTölke & De Fabritiis 2022), LEFTNet (Du al. 2024), and GET (Kong al. 2024). following identical experimental settings for a fair comparison. The results were adopted from GET (Kong et al. 22024), which used the hierarchical methods that integrate atom-level and block- level information.
Baselines.
Performances. Table A16 Table Table A17 demonstrate that CheapNet consistently outperforms all baselines across all difficulty levels, particularly performing exceptionally well in the most challeng- ing Flexible setting. By integrating the cluster-attention mechanism, CheapNet effectively models meaningful interactions between protein clusters, enabling it to handle the complexity of protein- protein interactions. These results demonstrate CheapNet's ability to deliver competitive perfor- mance without extensive hyperparameter tuning, reflecting its robustness and adaptability.
These findings highlight CheapNet's adaptability, demonstrating its ability to address not only protein-ligand tasks but also the more complex challenges of protein-protein affinity prediction. This flexibility suggests that CheapNet can serve as robust framework for a wide range of interaction- related tasks computational biology.
A.21 LIMITATIONS
While CheapNet demonstrates strong performance and efficiency in potein-lligad binding affinity prediction, there some limitations. First, the cluster-level attention mechanism may not capture all nuances of atom-level interactions, especially for complexes where fine-grained atomic interac- tions are crucial. Second, although model achieves lower memory usage, its performance is
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dependent the quality of the differentiable pooling and cross-attention mechanisms, which may require fine-tuning for optimal results across diverse datasets. Lastly, CheapNet's efficiency and scalability have not been extensively tested on extremely large protein-ligand complexes, which could impact its applicability some real-world scenarios. Future work will aim to address these challenges, potentially by integrating more sophisticated clustering techniques exploring multi- scale representations.
34


Reviews:
[{"review_id": "IcX7rG0SzN", "reviewer": "Reviewer_4kHp", "summary": "This paper proposes a new solution to the protein-ligand binding problem, namely modeling molecules and proteins at a higher level than the atom (cluster level). This motivation comes from the fact that modeling only at the atomic level can easily lead to computational burden and reduced accuracy. Experiments on the ligand affinity prediction and ligand efficacy prediction tasks demonstrate the effectiveness of proposed method.", "questions": "1. How to determine the number of clusters for ligand and protein?\n\n2. In fact, the proposed method still needs to learn effective atom-level representation to obtain pooling results and cluster representation. What is the advantage in computational efficiency?\n\n3. The method in this paper does not seem to be limited to processing protein and ligand interactions, but can also handle protein-protein related tasks (please correct me if I am wrong). If the authors can perform additional experiments such as protein-protein interaction, protein-protein docking or protein-protein interface prediction, it will further prove the scope of the proposed method.", "limitations": "", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "1. The motivation is reasonable, and it is possible to enhance the generalization of the model by trying to model at levels other than atoms.\n\n2. The proposed method is simple and easy to understand.\n\n3. Code is provided and is executable.\n\n4. The experimental results are satisfactory in terms of both accuracy and computational efficiency.", "weaknesses": "1. The writing logic of the article is not smooth, making it less readable. Two examples: (1) In the first paragraph in Introduction, a better presentation would be to first introduce the task, then talk about the wet lab approach and limitations, and finally analyze the challenges of deep learning models in solving this problem. Then, the purpose of the sentence describing DTI is also unclear and can be deleted. (2) Why does line 047 begin with \"however\"? Didn't you just talk about the limitations of atom-level modeling?\n\n2. The motivation is reasonable, that is, the entire functional group may interact with a certain protein region. However, the pooling method used does not seem to guarantee this. Can the author consider, at least, adding additional loss to ensure that clusters represent the functional group?\n\n3. The significance of hierarchical representation is usually to allow the model to adaptively learn and select features from different information channels. I also agree that some interaction cases come from the entire functional group rather than the atom, but this is not absolute. Therefore, I prefer dual awareness at the atom-level and cluster-level. Although cluster-level representations are derived from atom encoders, this only complies with the strong assumption that individual atoms do not participate in interactions. The framework I suggest is to use atom selectors (such as attention selection or gating algorithms) to filter important atom representations to merge with cluster representations.\n\n4. Let's analyze the title. This paper's greatest contribution seems to be to propose a specialized adaptive attention mechanism for hierarchical representation learning. However, the proposed cross-attention algorithm seems to be only for the cluster level. In addition, if this is the case, what is the difference between the proposed method and directly adopting the cross attention module in [1]?\n\n5. This is a point I would like to discuss with the author. In this paper, the author allows complex input, but only uses this information in atom embedding computation. Perhaps there is a more explicit way to use this information. Since we already know the rough range of where the interaction occurs, why not use it to guide the coefficient of cross attention. For example, assuming that cl:1 and cp:2 are clusters of ligand and protein at the interface, the correlation coefficient between cl:1 and cp:2 should be much higher than the others.\n\n\n[1] Learning Harmonic Molecular Representations on Riemannian Manifold. ICLR, 2023.", "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": "0HmoxWgrDf", "reviewer": "Reviewer_VFuE", "summary": "Predicting protein-ligand binding affinity is essential for drug discovery. Due to the complexity of protein-ligand interactions, traditional prediction models, which mainly rely on the atom-level interactions, are often computational intensive and unable to capture the complex and higher-order interactions. This paper proposes a deep learning-based model, CheapNet, for protein-ligand binding affinity prediction. CheapNet uses a cross-attention mechanism on hierarchical representations to capture intricate molecular interactions while maintaining computational efficiency.", "questions": "1. Discuss how to deal with the proteins which do not have the experimentally crystallized structures. For instance, combine some AI protein prediction models, or use alternative representations for the proteins without three-dimensional structures\n\n2. Extend the discussion on whether and how CheapNet handle the symmetries of protein-ligand complexes. If CheapNet is not able to address other types of symmetries,  then discuss howthis might impact the model's performance or generalizability, and the further improvement.", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. CheapNet integrates both atom-level and cluster-level representations of protein-ligand complexes, this can significantly enhance the model's ability to predict protein-ligand binding affinity. The idea is novel and meaningful。\n\n2. CheapNet employs the DiffPool method to cluster atoms in both the protein and ligand, reducing complexity while retaining the critical protein-ligand interaction patterns. The use of the cross-attention mechanism between protein and ligand clusters highlights the most relevant inter-molecular interactions, filtering out less impactful interactions and reducing the computational costs.\n\n3. The authors utilized the PDBbind and  CSAR NRC-HiQ datasets to benchmark CheapNet against different types of protein-ligand binding affinity prediction models, They evaluated the model performance on ligand binding affinity and ligand efficacy prediction using different performance metrics. Subsequently, ablation studies were conducted to evaluated the model's effectiveness, focusing on adaptability of cluster-attention, hierarchical representations and attention mechanism, and cluster size. The experiments are comprehensive, and demonstrate CheapNet's superior performance.", "weaknesses": "1. CheapNet relies on high-quality three-dimensional structural data. However, many proteins lack experimentally crystallized structures, which limits CheapNet's ability to make predictions for proteins without available three-dimensional structural data.\n\n2. In the section 'Permutation Invariance of Clusters for Cross Attention', the authors demonstrate that CheapNet’s cross-attention mechanism ensures permutation invariance for protein and ligand cluster-level representations. However, in protein-ligand interactions, three types of symmetries—translation, rotation, and permutation—should be considered. In my opinion, discussing whether and how the model achieves rotation and permutation invariance in local coordinates, as well as translation, rotation, and permutation equivariance in global coordinates, is essential. Only focusing on discussing the permutation invariance is insufficient.", "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": "yOhh46Z2AG", "reviewer": "Reviewer_2uzU", "summary": "The authors developed a novel interaction-based model (called CheapNet) that combines atom-level representations with hierarchical cluster-level interactions using a cross-attention mechanism to predict binding affinity tasks. The authors showed that CheapNet can effectively capture key higher-order molecular representations necessary for accurate binding predictions. They also performed extensive evaluations to show that CheapNet can deliver state-of-the-art performance in various binding affinity prediction tasks while maintaining efficiency in computation.", "questions": "I am curious whether the author can apply the trained models to predict real-world cases involving known disease-causing proteins. Can the models identify compounds from a large library, such as ZINC250K, that are likely to bind to these proteins? Since the authors have emphasized the model's strong interpretability, I would appreciate seeing how the model’s functions are used to interpret the prediction results in this case.", "limitations": "", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "-Used both local and global information to predict the binding affinity. The idea is relatively novel.\n-Compared the performance of the proposed approach to that of many baseline approaches.\n-Demonstrated the model interpretability.", "weaknesses": "-The model performance representation can be further improved, such as using p-values to evaluate whether the proposed approach is significantly better than the baselines? the authors claimed \"significantly outperforming all baselines\", but there are no metrics to support the conclusion.\n-It is not clear whether all the comparisons in the results tables are fair comparisons. For example, all these baselines are based on the same data evaluation strategy as the proposed approach (or the same set of training, validation and test sets) ? If the baseline results are from the original papers, how can we make sure the performance evaluations are fair?", "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": "f9xB75DReV", "reviewer": "Reviewer_vcDV", "summary": "The manuscript proposes a cross-attention method based on atom clustering for protein-ligand affinity prediction. This approach employs a soft-assignment method to separately cluster atoms in the protein and ligand, followed by a cluster-level attention mechanism to facilitate information exchange between the two. The model demonstrates significantly improved performance over baseline methods, and ablation studies indicate that integrating both clustering and cross-attention mechanisms into existing methods enhances prediction accuracy.", "questions": "1. How the numbers of clusters for protein and ligand selected?\n\n2. Is there any experimental evidence explaining why the clustering method enhances model performance?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "The method is innovative. By clustering atoms separately within the protein and ligand, it effectively improves affinity prediction performance.", "weaknesses": "1. The method’s details are not clearly explained. For example, how are the numbers of clusters for protein and ligand selected? Additionally, the process for initializing the representations of the protein and ligand is unclear.\n\n2. While the method is interesting, the reasoning behind the clustering and cross-attention mechanisms' positive impact on model performance is not fully explained. Further analysis would provide valuable insights. For instance, although a soft clustering method is applied, this component is not explicitly supervised in the loss function. Why does such a soft clustering approach improve the model's performance?", "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": "B1vaeJyTbs", "reviewer": "Reviewer_NPNb", "summary": "Summary:  The paper introduces CheapNet, a novel model designed for protein-ligand binding affinity prediction. Focusing on efficiency, CheapNet employs a cross-attention mechanism on hierarchical representations to address limitations of traditional atom-level methods, which often capture noise by treating all atom interactions equally. By integrating differentiable pooling, CheapNet selectively forms clusters of atoms that are relevant to binding interactions, reducing computational complexity and improving accuracy. Experimental results demonstrate CheapNet’s competitive, state-of-the-art performance across multiple datasets.", "questions": "See in weakness.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1.The paper is clearly written, the authors focus on a critical issue in drug discovery for which they proposed a solution and demonstrated by well designed experiments, that their proposed solution works well.\n2.The main idea of using cluster-based, attention-guided binding predictions is well-motivated and aligned with current needs in efficient, scalable drug discovery models.\n3.CheapNet achieves state-of-the-art performance across multiple datasets, showcasing its ability to balance accuracy and computational efficiency effectively.", "weaknesses": "1.The application of clustering and cross-attention is not novel for this field, as clustering is used in models like GemNet, Equiformer, and LEFTNet. Although CheapNet integrates these methods, it does not introduce substantial methodological innovations.\n\n2.The paper lacks a discussion of relevant clustering methods and does not provide sufficient analysis of different clustering approaches. This omission makes it difficult to assess the comparative advantages of CheapNet’s differentiable pooling mechanism.\n\n3.The comparison lacks depth with state-of-the-art methods, including GemNet, Equiformer, and LEFTNet, all of which employ unique strategies for interaction prediction that CheapNet could be benchmarked against more thoroughly.\n\n4.Equation 2’s category count (number of clusters) is unclear. It would be beneficial to specify whether it is a predefined constant or dynamically determined based on molecular size or complexity. This information is crucial for assessing how different molecular structures might impact CheapNet’s clustering performance.\n\n5.The authors should review and discuss the relevance of clustering methods used by existing models like LEFTNet, which employs a layered approach to handle structural hierarchies. Additionally, the work should compare or at least mention methods from “Generalist Equivariant Transformer Towards 3D Molecular Interaction Learning” to position CheapNet’s approach among recent advancements.", "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)