Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Authors: Yingzhao Jian
Yue Zhang
Ying Wei
Hehe Fan
Yi Yang
Venue: ICML 2025 poster (2025)
Keywords: Chemical Reaction Modeling
Reaction Graph
3D Molecular Structure
AI for Chemistry
Primary area: deep_learning->other_representation_learning
TL;DR: In this paper, we introduce Reaction Graph (RG), a unified graph representation that encapsulates the 3D structures within chemical reactions.

Abstract: Accurately modeling chemical reactions using Artificial Intelligence (AI) can accelerate discovery and development, especially in fields like drug design and material science. Although AI has made remarkable advancements in single molecule recognition, such as predicting molecular properties, the study of interactions between molecules, particularly chemical reactions, has been relatively overlooked. In this paper, we introduce Reaction Graph (RG), a unified graph representation that encapsulates the 3D molecular structures within chemical reactions. RG integrates the molecular graphs of reactants and products into a cohesive framework, effectively capturing the interatomic relationships pertinent to the reaction process. Additionally, it incorporates the 3D structure information of molecules in a simple yet effective manner. We conduct experiments on a range of tasks, including chemical reaction classification, condition prediction,  and yield prediction. RG achieves the highest accuracy across six datasets, demonstrating its effectiveness. The code is available at https://github.com/Shadow-Dream/Reaction-Graph.

Reaction Graph:
Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Yingzhao Jian
Yue Zhang'
Ying Wei Hehe Fan
Yi Yang'
Abstract
precise spectral analysis (Young et al., 2024) and quan- tum chemical simulation (Gilmer et al., 2017), improves inverse design of molecular structure (Jin et al., 2018) and retrosynthesis planning (Dong et al., 2022). However, most related methods primarily concentrate on recognizing and understanding single molecules, such as predicting their properties or functions (Yang al., 2019; Zhou al., 2023). The study of interactions between molecules, particularly chemical reactions, has not garnered as much attention.
Accurately modeling chemical reactions using Ar- tificial Intelligence (AI) can accelerate discov- ery and development, especially in fields like drug design and material science. Although Al has made remarkable advancements in single molecule recognition, such as predicting molecu- lar properties, the study of interactions between molecules, particularly chemical reactions, has been relatively overlooked. In this paper, we in- troduce Reaction Graph (RG), unified graph representation that encapsulates the 3D molecular structures within chemical reactions. RG inte- grates the molecular graphs of reactants and prod- ucts into a cohesive framework, effectively captur- ing the interatomic relationships pertinent to the reaction process. Additionally, incorporates the 3D structure information of molecules in simple yet effective manner. We conduct experiments a range of tasks, including chemical reaction classification, condition prediction, and yield pre- diction. RG achieves the highest accuracy across six datasets, demonstrating its effectiveness. The code is available https:/gittub..om/Shheee Dream/Reaction-Graph
Learning accurate representation of chemical reactions is essential for reaction recognition and understanding, ben- efiting various tasks such as predicting reaction condi- tions (Wang et al., 2023b), types (Schwaller et al., 2021a), and yields (Kwon et al., 2022b). As shown in Fig. 1. early works typically employ bit vector representations of reac- tions, i.e. fingerprints, to predict relevant reaction proper- ties (Gao et al., 2018). With the advent of the Transformer in natural language processing, the string-based based Simplified Molecular Input Line Entry System (SMILES) has gained widespread popularity (Wang et al., 2023b; Yin et al., 2024).
Among various representation methods, molecular graphs have proven inherently advantageous for various chemical tasks (Fang et al., 2022; Zhou et al., 2023). However, as shown in Fig. 1, most graph-based methods first employ single-molecule modeling to extract individual molecule- level representations for reactants and products, and then combine these representations to form an ensemble reac- tion representation for the prediction (Kwon et al., 2022a;b; Zhang al., 2022). These methods largely overlook the reaction information itself, relying solely molecule- level representations, which inevitably complicates reaction recognition and understanding. Rxn Hypergraph (Tavakoli et al., 2022) may have potential to mitigate this issue. It first learns a hypernode for reactants and another for products, and then merges these nodes as the reaction representation. However, this method still separates reactions, which also causes loss of reaction information. Moreover, in single- molecule modeling, 3D structures are widely used due to their intrinsic connection to molecular properties. Yet, the utilization of 3D structures has remained largely unexplored in reaction modeling. This oversight prompts the question of whether incorporating 3D molecular structures could enhance reaction prediction.
1. Introduction
In recent years, data-driven Artificial Intelligence (AI) meth- ods have made significant strides in chemistry (De Almeida et al., 2019), bioinformatics (Senior et al., 2020; Jumper et al., 2021; Abramson et al., 2024), pharmaceutical (Wang al., 2023a; Mak et al., 2023), and materials science (Butler al., 2018), considerably enhancing research efficiency and accuracy, reducing costs and accelerating discovery cycles. In the field of chemistry (Cheng et al., 2024), Al enables
'College of Computer Science and Technology, Zhejiang Uni- versity, Hangzhou, China. Correspondence to: Hehe Fan <hehe- fan @ zju.cdu.en>..
Proceedings of the 42nd International Conference Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Molecule Graph
Rxn Hypergraph
Reaction Graph (Ours)
Reaction Graph Pipeline (Ours)
SMILES
Reactant
Product
Reaction
C=O.CC=O>>C=CC-O
RXNMapper
Molocular Graphs
Edge
Mapping
C=0.cC-0
C-CO
Isolated
Unified
Construct Triangles
MMFF94
3D Coord
SMILES String
Graph
Reaction Graph (Ours)
Reaction Graph
Reactant
Product
Ouy.t
C=O. CC= O Formaldehyde
Reactant
Product
Reactant
Product
Acctaléehydlc
Acrelein
Atomm
GNN
Fingerprint
Band
Angular
0110
1110 C=C C-C C=0 0-0
Edge
Appregation
C=C GC C=0 6-0
Unified Reaction Festure
(xistence Plgss Substnuctures
1D
2D
3D
Figure Illustration of Reaction Graph (RG). (1) Existing methods extract isolated representations for reactants and products, then combine them for prediction, which may fail to effectively model reaction relationship. In contrast, RG unifies the modeling for reactants, products and reactions. (2) Existing DD or 2DDbbsedd methods may not adequately capture the complexity of molecular structures. exploits edge length and angular edge to implicitly model the 3D structure information. (3) Our method first constructs molecular graph based on SMILES and predicts atomic mapping for creating reaction edges using RXNMapper (Schwaller et al., 2020). Then, 3D atom coordinates calculated using MMFF94 (Halgren, 1996) and angular edges constructed for each bond angle. Finally, GNN used to extract the unified reaction feature vector based on RG.
In this paper, we propose Reaction Graph (RG) to effectively model chemical reactions. To model the chemical reaction entirety and capture the molecular transformations occurring during reaction, integrate reaction edge into graph. This edge connects nodes representing the same atom in both reactants and products, based on atomic mapping relationships. It discerns molecular independence, while allowing graph neural networks (GNNs) to exchange infor- mation between reactants and products during the message- passing phase, thereby assimilating changes in chemical reactions. Furthermore, we enhance the graph's capability by embedding 3D spatial information through new rota- tionally and tramslationally invariant approach. Specifically, we utilize edge length and introduce an angular edge to implicitly convey bond angle information by forming shape- stable triangles within the molecular graph. We conduct range of reaction-related tasks, including chemical reaction condition prediction, reaction yield prediction and reaction classification. Experimental results indicate that the proposed method is efficient and effective, outperforming existing methods on six datasets. The contributions of this paper are three-fold:
We propose Reaction Graph, a novel unified graph rep- resentation for chemical reactions that allows GNNs extract reaction transformation related features during the message passing stage.
We integrate 3D molecular information into reaction modeling. Additionally, we develop new method to implicitly convey invariant features of bond angles.
We achieved state-of theth-rrrt accuracy in several tasks, demonstrating the effectiveness of our methods.
2. Proposed Method
In this section, first briefly review the Molecular Graph (MG) representation. Then, we discuss the potential limita- tions of MG in reaction modeling and describe the proposed Reaction Graph (RG) in detail. Finally, we incorporate RG into deep neural networks to address multiple chem- istry tasks, including reaction condition prediction, yield prediction, and reaction classification.
extensive experiments
2

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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Reaction Graph
Edge Embedding
Vertex Type(V)
Edge Type
Edge Length
(E)
(L)
RBF Kernel
ldk
Idx
2
4
7
Idx
4
6
EC Reshape
1
2
1
1.2
a(l a((
2
1.2
0.0
4
2.5
1.5
1.2
0.0
0.0
Vertex-Edgs Integration
FC Weight Matrix
S
2
0.0
MPNN
0.0
1.3
1.52..4
Iterativlly Update
0.0
2,4
1.2
(Message
Node Features
Attention-based Aggregation
Output
Set2Set
Reaction Feature
Chemical Reaction Condition
Type
Yield
Update
ESTM
Output
Flant
Jogaz
Safbmoo
Samplnn
Solvent1
Salventz
Reagent
(happett2
Reaction Type
Reaction Piald
Figure 2. Illustration of the proposed Reaction Graph and the associated model architecture. The input contains the type matrix V. the edge type matrix E and the edge length matrix L of Reaction Graph. Model first computes 3D-aware edge embeddings, and then iteratively integrates edge and vertex information into features. Vertex features are aggregated into unified reaction feature using attention-based method. Finally, task-specific output modules generate prediction results based on reaction features.
2.1. Preliminary: Molecular Graph
2.2. Reaction Graph
In computational and mathematical chemistry, molecular graph is representation of a chemical compound's 's struc- tural formula using graph theory. It a labeled graph where the vertices represent the compound's 's atoms and the edges represent chemical bonds. The vertices are labeled with the types of corresponding atoms, while the edges are labeled with the types of bonds.
When using molecular graphs to model chemical reactions, existing methods typically begin by extracting individual representations for each reactant and product, then combine these representations to form an ensemble reaction repre- sentation for prediction. doing so, these approaches often overlook the reaction information itself, relying exclusively molecule-Ieve representations. Moreover, the absence of 3D structural information increases the challenge for deep neural networks to effectively model molecules and reactions.
Specifically, molecular graph can be represented as G (V, E), where V E Nx1 denotes the vertices and E E J denotes the edges. Here, N represents the num- ber of vertices. The edge between the i-th atom and j-th atom is denoted as esy E {0, 1, 2, 3, 4), with each number corresponding to specific type of chemical bond:
To address these issues, we extend the Molecular Graph into Reaction Graph (RG). To incorporate reaction modeling, we introduce reaction edge. This edge links nodes repre- senting the atom in reactants and products based on atomic mapping, enabling deep neural networks to capture changes in chemical reactions. Additionally, to incorporate 3D spatial structure modeling into RG, we develop simple yet effective method that is rotationally and translationally invariant. This method utilizes two chemical bond edges and a proposed angular edge implicitly convey bond angle information by forming stable triangles within molecular
0: edge, 1: single bond, 2: double bond, 3: triple bond, 4 aromatic bond.
Molecular graph provides direct access to the graph under- pinning all molecule objects, allowing seamless integration with existing graph functionality.
3

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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
graphs. The two bond edges serve as adjacent edges, while the angular edge acts the diagonal edge. In summary, we extend Molecular Graph to the following Reaction Graph,
described below:
h +1 1 + n²,c'),
(5)
exp(v) h²)
g = E.).
(1) of
dtt1 Σ
o x x
(6)
Σ 2j=1 exple) h2)
In the Reaction Graph, we introduce a new edge attribute, specifically the edge length L E N to represent the 3D structure. We use las to denote the length be- tween the i-th node and the j-node. Additionally, the edge types are expanded to seven categories, i.c., E E {0, 1, 3, 4, 5, 6) NxN, with each number corresponding to specific type of edge:
where af represents the attention weight of atom at the 1-th iteration. After the T2 iteration, the model outputs the reaction global representation vector r, where r W [q h==11 + b,. with W, and b, being the learnable weight matrix and bias, respectively.
Implementation Details. As shown in Fig. 1, to construct RG, we first use RXNMapper to predict the atomic mapping, and then employ MMFF94 to calculate atom coordinates. Our method traverses all the angles in molecular graphs to construct angular edges and use the atomic mapping to construct reaction edges, resulting in the final RG.
0: no edge, 1 single bond, 2: double bond,
3: triple bond, 4 : aromatic bond,
5: reaction edge, 6: angular edge.
If there is no edge between nodes and j. or if the edge type a reaction edge, the length lig is defined as O.
As shown in Fig. 2, when applying RG to reaction condition prediction, we use an iterative output technique (Gao et al., 2018) to support beam search. Moreover, we employ a two- stage training strategy. Following the joint training in the first stage, the parameters of the neural network are frozen, and the output module's parameters are reinitialized. Then in the second stage, the output module is trained separately.
Edge Embedding. We use the radial basis function (RBF)
kernel to embed the edge length,
bG = exp( Hap(-ori o (l4 1 - )1)))
(2)
where o and μ are learnable parameters that transform the scalar edge length into vector representations.
For reaction yield prediction, due to the high noise in yield data, we follow Kwon et al. (2022b) and simultancously out- put the mean and variance 0² of the predicted yield. When the model encounters noise during training, it can increase the predicted variance to keep the output mean relatively stable, thus enhancing training stability. In implementation, we utilize Multilayer Perceptron (MLP) with Monte Carlo Dropout (Gal & Ghahramani, 2016) technique.
Vertex-Edge Integration. To merge the vertex and edge into a unified representation, we follow MPNN (Gilmer et al., 2017) and convert the edge information, including type and length, into a linear projection, which is then ap- plied to the vertex representation as follows,
Mij Reshape W. eigl); ++1 of +
(3)
Mas.ur of 0/ = Ti
(4) Lastly, the reaction classification module uses a standard three-layer MLP for output.
JEN,
where [::-] denotes concatenation, eij is the one-hot vector of the edge type for edge ij. We is the learnable param- eters for vertex-edge integration, the Reshape(-) function reshapes vector to matrix, N, denotes the set of neigh- bors of the i-th node, Vj represents the representation of the j-th vertex, and Ti denotes the total number of iterations. In this way, the vertex representation oy hecomes edge-related and is able to collect related information from its neighbors.
3. Experiments
3.1. The roles of Reaction and 3D Information
3.1.1. THE EFFECT OF REACTION INFORMATION
Attention Weights Visualization. To illustrate the advan- tages of Reaction Graph (RG) compared to Molecular Graph (MG), we train condition prediction model on USPTO' and visualize the attention weights a; of reactions. At- tention weights can display the model's focus on differrnnt parts of molecules, especially reaction centers, revealing the model's understanding of the reaction mechanism. As shown in Fig. 3, we take (CnH, and its two related reactions examples.
Attention-based Aggregation. To capture the global repre- sentation of a Reaction Graph, inspired by Set2Set ( (Vinyals et al., 2016), we employ attention- based aggregation method with an LSTM. Specifically, at each iteration of the LSTM, we use the hidden state h, initially set to 0 (the same initialization applies to the cell state Co- = 0), to query over all vertices with a softmax-bases attention mechanism and collect the most informative clues from these vertices, as
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Reaction A
Reaction
on Bromo
Curbosyl- hydrasy!
Break
Carbory!
Set2Set Attention
Match
Attention
Mismatch
Mismatch
Weight
0.5
MG
RG (Ours)
MMG
RG (Ours)
0..0
Reaction Center
Reaction Center
Output Head
Output Head
Output Head
Output Head
Error Prediction
Correct Prediction
Error Prediction
Correct Prediction
Figure 3. Visualization of attention weights and prediction results for two reactions involving the hromo and carboxyl-hydroxx groups in C7HgBrNO2. The colors of the atoms in the upper diagrams correspond the types of atoms, while the colors of the in the lower diagrams correspond to the sizes of the atomic attention weights. The model using the Molecular Graph (MG) focuses on atoms that are less relevant the reaction, thus leading prediction errors. contrast, the model equipped with the Reaction Graph (RG) accurately concentrates on the reaction center, and produces the correct prediction results. For more results, please refer to Sec. H.I.
The CrN2BrNO2 features three active functional groups: bromo, amino. and tetboxxl-hydroxy" In reaction A, the bromo group acts the reaction center, while the carboxyl- hydroxyl group serves this role in reaction B.
Table I. Leaving group (LvG) identification results Molecular Graph (MG) and Reaction Graph (RG) representations, with over- LvG atom-specific evaluation.
Overall
LyG Atom-Specific
As depicted in Fig. 3. both reactions, the MG-based model focuses more on the non-reactive amino group and insufficiently on reaction centers, resulting in prediction er- In contrast, the RG-empowered model pays correct at- tention reaction centers and provides reasonable reaction conditions. The experiment results validate our hypothesis: MG, which represents reactants and products independently, struggles to capture atom and bond transformations during reaction process, while RG helps the model accurately locate the reaction center and extract relevant features of reaction changes. More results can be found in Sec. H.1.
Rep.
ACC*
CENJ MCC1 FI1
ACCC CEN; MCC1 FI1
MG
0.950
0.036
0.549
0.365
0.448
0.201
0.519
0.404
RG (ours)
0.997
0.002
0.973
0.904
0.947
0.031
0.945 0.903
class Matthews Correlation Coefficient (MCC), and the Macro Fl Score (FI). CEN assesses the misclassification level, while MCC and Fl measure accuracy accounting for the imbalance of sample categories. We report relevant metrics for all atoms and LvG atoms, separately.
As shown in Tab.1, RG outperforms MG on all metrics. Compared to MG, RG improves the overall ACC, MCC and F1 by 4.7%, 42.4% and 53.9%, respectively. For LvG atoms, RG achieves an ACC of 94.7%, which is twice that of the MG. The advantage of RG on LvG identification demonstrates its ability to understand the reaction mecha- nism. More comparisons and visualizations are in Sec. H.2.
Leaving Group Identification. We design the Leaving Group (LvG) identification task to further validate the ef- fectiveness of RG. LvG refers to the atomic group that is present the reactants and detaches from the products during a reaction, which is closely related to the reaction mechanism (Wang et al., 2023c). LvG identification node-level multi-class classification task, where the node la- bel specifies whether atom belongs LvG and its type. This requires the model to focus not only on the features of the molecule itself but also on reaction-related features.
3.1.2. THE EFFECT OF 3D INFORMATION
Settings. In this section, explore the effects of incorpo- rating various 3D information in RG. Specifically, we inves- tigate: (1) no 3D information, (2) only bond edge length, (3) bond edge length and bond angle, as well as (4) bond edge length and angular edge length. We conduct experiments on the USPTO-Condition dataset evaluate the accuracy.
Both models based on MG and RG are trained on the LvG dataset extracted from USPTO. The evaluation metrics in- clude accuracy (ACC), confusion entropy (CEN), the multi-
5

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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Table Top-k accuracy of reaction condition prediction on the USPTO-Condition and DistaciooCoonduie datasets.
indicates that the
result is sourced from Wang et al. (2023b).
USPTO-Condition
Pistachio-Conditoo
Method
Top-11
Top-3t
Top-5t
Top-10f
Top-15
Top-1f
Top-3t
Top-5t
Top-10"
Top-15t
CRM (Gao et al., 2018)
0.260*
0.377
0.421
0.461
0.472
0.330
0.469
0.510
0.548
0.554
Parrot (Wang al., 2023b)
0.269*
0.404
0.451*
0.491 *
0.503
0.350
0.532
0.588
0.626
0.630
AR-GCN (Maser et al., 2021)
0.146*
0.237
0.273*
0,312
0.326
CIMG (Zhang al., 2022)
0.184*
0.271
0.303*
0.339*
0.353
D-MPNN (Heid & Green, 2021)
0.198
0,300
0.334
0.378
0.392
0,259
0.342
0.378
0,442
0.469
Rxn Hypergraph (Tavakoli et al., 2022)
0.213
0.308
0.345
0.381
0.393
0.288
0.367
0.412
0.464
0.485
Reaction Graph (ours)
0.325
0.434
0.472
0.506
0.518
0.392
0.557
0.604
0.638
0.643
Table 3. Influence of different types of 3D information the USPTO-CCodition dataset. Experimental groups include no 3D information, bond edge length, bond edge length and bond angle, as well as bond edge length and angular edge length.
0.100
Time (s)
0.075
3D Information
Accuracy
0.050
Without 3D Information
0,3133
0.025
Bond Edge Length
0.3165
Bond Edge Length + Bond Angle
0.3179
2000
3000 Num of Atoms
4000
Bond Edge Length Angular Edge Length
0.3246
x Bond Edge Length
No 3D Information x Bond Edge Length + Angular Edge Length
To assess computational efficiency, we further design the following experiments. Inspired by bin-packing (Cormen et al., 2022), we select 16 sets of chemical reactions from USPTO-Condition, ensuring that each set contains the same number of atoms, with quantities ranging from 1500 to 4500. Subsequently, the 16 sets of reactions are input into the condition prediction model, and the average runtime is measured to indicate computational efficiency.
Bond Edge Length Bond Angle
Figure 4. Influence of different methods of 3D structure modeling on running time. Compared to using bond angles, the proposed angular edge method effectively reduces inference time.
3.2. Reaction-related Tasks
3.2.1. REACTION CONDITION PREDICTION
Accuracy Evaluation. According Tab. 3, 3D information effectively improves the model's performance. Specifically, the RG equipped with bond edge length and angular edge length achieves the best performance. Angular edge length is more effective than directly using bond angle. This is because the angular edge length is integrated into the GNN as part of the graph structure. The geometric consistency helps to more accurately maintain the spatial relationship of the molecule. In contrast, the bond angle needs to be treated separately from the bond edge length, which may distort the original geometric continuity and integrity of the molecule.
Dataset. The ESPTO-Conditiin dataset is derived from Parrot (Wang et al., 2023b), comprising over 680K samples, divided into 80% for training, 10% for validation, and 10% for testing. Besides, we construct Pistachio-Condidee from the Pistachio database by thorough cleaning and filtering. includes over 560K samples, with a training, validation, and testing split of 8:1:1.
Evaluation Metries. Following Gao et al. (2018); Wang et al. (2023b), we use the top-k accuracy to evaluate the condition prediction performance.
Efficiency Evaluation. The results in Fig. 4 suggest that incorporating bond length brings almost no extra computa- tional overhead. Besides, compared bond angle, using an- gular edge length can significantly reduce the inference time. Moreover, according to the curve steepness, the time cost associated with using bond angle rises more significantly as the number of atoms increases. Hence, when integrating 3D molecular information into RG, we ultimately employ bond edge length and angular edge length, enhancing accuracy while maintaining efficiency.
Comparison Methods. CRM (Gao et al., 2018) utilizes molecular fingerprints. Parrot (Wang et al., 2023b) employs SMILES. AR-GCN (Maser et al., 2021) and CIMG (Zhang et al., 2022) use MG. D-MPNN (Heid & Green, 2021) lever- ages the condensed graph of reactions (CGR) (Varnek et al., 2005), and Rxn Hypergraph (Tavakoli et al., 2022) employs its own designed graph representation.
Results. The performance comparisons are reported in Tab. 2. Our method outperforms all the comparison meth-
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Table 4. Regression accuracy (R² f) for reaction yield prediction on the Buchwald Huchwald-Hartwig (B-H), Suzuki- -Myaura (S-M), Gram, and Subgram datasets, B-H-1, B-H-2, B-H-3 and B- 4-H are more challenging splits of the B- dataset. (*) indicates the results are reported from the original paper.
Method
Representation
B-H
B-H-1
B-H-2
B-H-3
B-H-4
S-M
Gram
Subgram
DRFP* (Probst et al., 2022)
Fingerprint
0.95
0.81
0.83
0.71
0.49
0.85
0.130
0.197
Beetd-Bert& (Schwaller et al., 2021b)
SMILES
0,95
0.84
0.84
0.75
0.49
0.82
0.117
0,195
Egret* (Yin et al., 2024)
SMILES
0.94
0.84
0.88
0.65
0.54
0.85
0.128
0.206
UGNN (Kwon et al., 20226)
Molecular Graph
0.97*
0.74
0.88
0.72*
0.50
0.89
0.117
0.190
D-MPNN (Heid & Green, 2021)
CGR
0.94
0.80
0.82
0.73
0.55
0.85
0.125
0.202
Rxn Hypergraph (Tavakoli et al., 2022)
Rxn Hypergraph
0.96
0.81
0.83
0.71
0.56
0.85
0.118
0.196
Reaction Graph (ours)
Reaction Graph
0.97
0.80
0.88
0.76
0.68
0.89
0.129
0.216
Table 5. Influence of reaction information (Reaction Edge) and 3D
3.2.2. REACTION YIELD PREDICTION
structure on the prediction of chemical reaction conditions.
Dataset. Buchwald-Hartwip (B-H) (Ahneman et al., 2018) involves six molecules as reactants, with products com- prised of single molecule. B-H is used to create B-H-1 to B-H-4 through different train-test splits, with increasing challenges due to distribution differences. The molecule number involved in each reaction varies in Suzuki- (S-M) (Perera et al., 20.8). USPTO- (Schwaller et al., 2021b) is divided into Gram and Subgram. We also no- tice that in the small-scale B-H and S-M datasets, there are only dozens of different molecular types, some of which are reagents; meanwhile, the USPTO-Yielo dataset contains significant amount of noise. This makes it difficult for the model to capture the relatively complex and variable 3D in- formation, preventing it from learning the correct 3D priors. Therefore, we only test the role of reaction information in the yield prediction task.
Dataset
Reaction Edge
3D Structure
ACC
X
X
0.3050
USPTO
V
0,3090
Condition
X
0,3133
0.3246
X
0.3806
Pistachio
0,3819
Condition
X
0.3852
0.3915
Table Likelihood (y - /02 and log variance log o² metrics on the Gram and Subgram datasets, where likelihood reflects the consistency between predicted variance and regression error, and log variance reflects the size of variance. Within these methods, only UGNN has variance output.
Likelihood
Log Variancel, Subgram
Methods
Gram
Subgram
Gram
UGNN (Kwon et al., 2022b)
1.02
1.20
6.94
7.36
The proposed method simultancously outputs the mean y and variance 0² of the predicted yield. Following Schwaller et al. (2021b); Kwon et al. (2022b), we use the R² score to evaluate the accuracy of the output mean. We additionally introduce likelihood (y - //2 and log variance log 0² from negative tog-likelihooo (Lak- shminarayanan et al., 2017) to evaluate the output variance, where y is the ground truth.
Evaluation Metries.
Reuction Gruph (ours)
1.06
1.18
5.86
6.14
ods both datasets, demonstrating the superiority of RG on reaction feature modeling. On DSSPTO-Condiio com-
pared to domain models with ID and 2D representations, our method improves the top-1 accuracy by 17.2% and 76.6%,
respectively. Compared with graph-based methods, RG improves the top-k accuracy by an average of 39.0%. On Pistachio-Condition RG also demonstrates its advantage by surpassing other methods by 3.4%-18.8%.
Comparison Methods. DRFP (Probst et al., 2022) uti- lizes reaction fingerprint. Yield-Bert (Schwaller et al., 2021b) and Egret (Yin et al., 2024) are based on SMILES. UGNN (Kwon et al., 2022b) employs MG and simultancously predicts yield and uncertainty. D- MPNN (Heid & Green, 2021) employs CGR, while Rxn Hypergraph (Tavakoli al., 2022) uses its uniquely de- signed graph representation.
Ablation Study. The reaction information and 3D structure are key components of RG. We evaluate their respective effects on modeling chemical reactions. Results in Tab. 5 reveal that both the reaction information and 3D structure in RG effectively enhance model performance. Specifically, on USPTO- Conniinnn,,,,,n, the utilization of reaction information and 3D structure brings average performance improvements of 3.9% and 2.5%, respectively; while in Pistachio, the improvements are 1.9% and 1.0%. Moreover, the reaction information and 3D information are complementary, and their combination results in improvements of 6.4% and 2.9% on CSPTO-Condition and Pistachio-Condee Condition, respectively.
Results. As shown in Tab. 4, compared to other advanced methods, RG achieves the highest accuracy on six out of eight yield prediction datasets. Especially on the more chal- lenging B-H-4 and Subgram datasets, RG achieves improve- ments of 21.4% and 4.9%, respectively. Besides, according to Tab. 6, both methods provide uncertainty that accurately
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Results, According to Tab. 7, RG surpasses advanced mod- els on both USPTO-TPL and Pistachio-Typp, demonstrating the effectiveness of the proposed designs. Compared to the state-of-the-ar T5Chem, RG reduces the classification error by 66.6% and achieves nearly 100% accuracy on USPTO- TPL. The superior performance on USPTO-TPL is due to the limited number of reaction templates, which simplifies the classification task. RG's precise identification of the reaction center (detailed in Sec. 3.1.1) enhances template discrimination capability, bringing further performance im- provements. On the complex Pistachio-TType dataset, RG exceeds the best performance by 1.2% on MCC and 1.1% on F1, highlighting its superiority in modeling reactions.
Table 7. Reaction classification results on the USPTO-TPI. and PistachioCoondttion datasets. Evaluation metrics include accuracy (ACC), confusion entropy (CEN), Matthews Correlation Coeffi- cient (MCC) and Macro F1 (F1). (*) indicates that the result is sourced from the original paper.
USPTO-TPL ACC1
Pistachio-Typp
Method
CEN
MCCT
ACC1
CEN
MCC²
DRFP
0,977
0.011
0,977
0.899
0.149
0.890
RXNEP
0,989
0.006*
0,989
0.948
0.078
0.944
TSChem
0,995*
0.003*
0,995*
0.976
0.041
0.974
D-MPNN
0.997
0.001
0.997
0.982
0.033
0.980
Rxn Hypergraph
0.954
0.024
0:953
0.911
0.129
0.903
Reaction Graph (ours)
0.999
0.001
0.999
0.987
0.024
0.986
Ablation Study. We investigate the influence of reaction information and 3D structure in RG on the reaction clas- sification task. As shown in Tab. 8, integrating reaction information reduces classification error by an average of 77% on USPTO-TPL, and 54.1% 1% on Pistachio-TType. On the other hand, 3D structure can also enhance the accuracy across both datasets. The results suggest that reaction in- formation and 3D structures mutually enhance each other, improving the understanding of reaction mechanisms.
Table 8. Influence of the proposed reaction information (Reaction Info) and 3D structure (3D Stru) modeling methods on the USPTO- Condition and PistachioCCondition datasets, using ACC, CEN and MCC as classification metrics.
Reaction Info
3D Stru
USPTO-TPI. CENJ MCCt
Pistachio- Type
ACCI
ACC1
CEN]
MCC1
X
X
0.9921
0,0037
0,9921
0.9658
0.0559 0.9627
0.9955
0.0021
0.9955
0.9669
0.0538 0.9640
V
X
0.9978
0.0010
0.9977
0.9862
0.0262 0.9850
4. Conclusion
0.9991
0.0004
0.9991
0.9873
0.0242 0.9862
In this paper. we propose a unified 3D Reaction Graph (RG) for chemical reaction modeling. Unlike existing methods, the RG is equipped with enhanced capabilities for modeling reaction changes and 3D structures. We conduct extensive experiments across various tasks and datasets, demonstrat- ing RG's effectiveness in understanding chemical reactions. Furthermore, since it is independent of any specific GNN architecture, the RG representation may show increased potential as the underlying network backbone is improved.
reflects the actual error levels, while RG further reduces prediction uncertainty by 12.3% on Gram and 13.3% on Subgram. However, the quality and complexity of the Gram and Subgram datasets restrict further performance improve- ment in existing yield prediction methods.
3.2.3. REACTION CLASSIFICATION
Dataset. The USPTO-TPL. is from Schwaller et al. (2021a), with labels generated by 1000 reaction templates, making relatively simple. We construct the more challenging Pistachio-Type dataset from Pistachio, with labels generated by NameRXN2 based on rules.
Limitations and Future Work. Like most data-driven methods, the quality of data significantly impacts the per- formance of our method. Specifically, inaccuracies in the 3D coordinates of atoms can lead to inferior results. Thus, developing an advanced method for 3D prediction could further enhance our approach, which can be investigated in the future.
Evaluation Metrics. Similar to Schwaller et al. (2021a);
Lu & Zhang (2022), we use accuracy (ACC), confusion en- tropy (CEN), Matthews Correlation Coefficient (MCC) and Macro Fl (Fl) to evaluate the performance. CEN assesses misclassifications to quantify the uncertainty of predictions, while MCC and Fl provide a more comprehensive measure of classification accuracy.
A Acknowledgements
This work was supported by the National Science and Tech- nology Major Project (2023ZD0120803), the National Nat- ural Science Foundation of China (62472381) and the Earth System Big Data Platform of the School of Earth Sciences, Zhejiang University.
Comparison Methods. DRFP (Probst et al., 2022) uses reaction fingerprint. RXNFP (Schwaller et al., 2021a) and T5Chem (Lu & Zhang, 2022) are based on SMILES. D- MPNN (Heid & Green, 2021) employs CGR, while Rxn Hypergraph (Tavakoli et al., 2022) relies on its own graph representations.
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Impact Statement
Chen, L.-Y. and Li, Y.-.. Enhancing chemical synthesis: two-stage deep neural network for predicting feasible reaction conditions. Journal of Cheminformatics, 16(1): 11, 2024.
This paper aims at enhancing deep representation learning in chemistry. The proposed reaction representation has the po- tential accelerate drug design and material development, saving substantial amounts of money and time. Although there may be concerns of misuse, such manufacturing illegal drugs, we strongly believe that the advantages of our method far outweigh the minuscule risk of misuse.
Cheng, A., Tian Ser, C., Skreta, M., Guzmán- Cordero, A.,
Thiede, L.., Burger, A., Aldossary, A., Leong, S. X., Pablo- García, S., Strieth-Kalthoff, F., et al. How to do impactful research in artificial intelligence for chemistry and mate- rials science. arXiv e-prints, pp. 2409, 2024.
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Zhang, Y.. Yu, R., Zeng, K.. Li, D., Zhu, F., Yang, X., Jin, Y., and Xu, Y. Text-augmented multimodal lims for chemical reaction condition recommendation. arXiv preprint arXiv:2407. 15141, 2024.
Zhou, G.. Gao, Z., Ding, Q., Zheng, H., Xu, H., Wei, Z., Zhang, I.,, and Ke, G. Uni-mol: A universal 3d molecu- lar representation learning framework. International Conference on Learning Representations (ICLR), 2023.
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Reaction Graph: Toward Modeling Chemical Reactions with 3D Structures
Appendix
Contents
Introduction
2 Proposed Method
2.1 Preliminary: Molecular Graph
2.2 Reaction Graph
3
3 Experiments
3.1
The roles of Reaction and 3D Information
3.1.1
The Effect of Reaction Information
4
3.1.2
The Effect of 3D Information
3.2
Reaction-related Tasks
3.2.1
Reaction Condition Prediction
3.2.2
Reaction Yield Prediction
3,2.3
Reaction Classification
8
Conclusion
8
Uniqueness of 3D Reaction Modeling
17
Differences between Reaction Graph and Retrosynthesis
17
A.2 Differences between Reaction Graph and Protein Docking/Binding
17
Related Works
17
B.1
Molecular Representation
17
B.2
Reaction Representation
18
B.3 Invariant Neural Network
18
B.4
Reaction Condition Prediction
18
B.5
Reaction Yield Prediction
19
B.6 Reaction Classification
19
Molecule and Reaction Representations
19
C.1
One-Diiensional
19
C.1.1 String
19
C.1.2 Fingerprint
20
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
C.2
Two-Dimensional
22
C33
Three-Dimensional
23
C.4 Comparison of Graph Representations of Reaction
23
Implementation Details
23
D.I
Graph Representations
23
D.1.1 Reaction Graph
23
D.1.2 Rxn Hypergraph
24
D.1.3
CGR
24
D.2
Model Details
25
D.2.1 Ours Model
25
D.2.2
Other Models
26
D.3
Visualization Details
27
D.4 Training Details
27
E Algorithm and Pipeline Details
29
E.1 Reaction Graph Construction
29
E.2 Reaction Condition Prediction
30
E.3 Attention Weights Sample Selection
30
E,4 Leaving Group Extraction
30
E.5
Bin-Packing
30
F
Complexity Analysis
32
F.1
Theoretical Analysis
32
F2
Experimental Analysis
33
F.2.1
Construction Cost
33
F.2.2
Computational Cost
33
Dataset Preprocessing and Analysis
35
G.1 USPTO-Condition
35
G.2 Pistachio-Condition
36
G.3 HTE
37
G.4 USPTO-Yield
37
G.5 USPTO-TPL
39
G.6 Pistachio-Type
39
Supplementary Experiments
42
H.1 Attention Weights Analysis
42
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
H.1.1
Attention Weights Visualization
42
H.1.2
Failure Mode Analysis
42
H.1.3
Statistical Validation
42
H.2
Leaving Group Identification Analysis
46
H.2.1
Error Analysis of Misclassified Cases
46
H.2.2
Additional Baseline Methods
46
H.2.3
Detailed Results
46
H.3
Hyperparameter Selection.
47
H.4
Reaction Condition Prediction
48
H.4.1
Metric Calculation
48
H.4.2
Detailed Results
48
H.4.3
Additional Ablation
53
H.4.4
Merging Dataset
54
H.5
Reaction Yield Prediction
54
H.5.1
Metric Calculation
54
H.5.2
Detailed Results
54
H.6
Reaction Classification
57
H.6.1
Metric Calculation
57
H.6.2
Detailed Results
58
H.7
Architecture Module Selection
H.7.1
Edge Embedding
59
H.7.2
Vertex-Edge Integration
61
H.7.3
Aggregation
61
H.8
Graph Representation
62
H.8.1
3D Information
62
H.8.2 Reaction Information
64
I
Toolkits
65
L1 Calculate/Optimize 3D Conformation
65
1.2 Predict Atom Mapping
65
L.3 Classify Reaction
65
Terminology List
66
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
A. Uniqueness of 3D Reaction Modeling
A.1. Differences between Reaction Graph and Retrosynthesis
Reaction Graph can predict conditions and yields for Retrosynthesis. Retrosynthesis utilizes atom mapping and 3D information, which also inspires the design of Reaction Graph. However, there are key differences between Reaction Graph and Retrosynthesis (Laabid et al., 2024) methods:
1. Reaction Graph uses the entire reaction as input. Retrosynthesis uses only the product as input. Therefore, the task settings are different.
2. Reaction Graph is design to predict transformation invariant reaction properties, so it focuses on being invariant to rotation, translation and even bond torsion. Retrosynthesis methods are designed to generate reactant structure, so they focus on geometric completeness. When geometrically complete, a method will not be invariant to bond torsion. Therefore, the design focuses are different.
3. Reaction Graph takes atom mapping as an input, aiming to enable message passing between reactants and products, and provide reaction change information. Retrosynthesis methods output atom mapping to avoid directly outputting the reactants, thereby reducing diffieulty. Therefore, the roles of atom mapping different.
4. Reaction Graph models the relationship between reaction 3D structure and reaction properties, while the Retrosynthesis methods model the relationship between the product 3D structures and reactant 3D structure. Therefore, the functions of 3D information are different.
A.2. Differences between Reaction Graph and Protein Docking/Binding
The 3D interaction modeling in Protein Docking provides inspiration for Reaction Graph. However, there are key differences between Reaction Graph and Protein Docking (Ganea et al., 202 //Binding (Stärk et al., 2022):
1. Reaction Graph is independent specific 3D scene, thus emphasizes invariance. In contrast, Protein Docking/Binding predicts the transformaaiinn/stuuuuue of the ligand a specific 3D scene, thus it emphasizes equivariance and geometric completeness. Therefore, they have different concerns.
2. Reaction Graph models the interaction between reactants and products. Protein Docking/Binding models the interaction between the ligand and receptor, which is the interaction between reactant and reactant. Therefore, Therefore, their interaction types are different.
3. Reactants and products are the same set of atoms, but exist in differrnnt space and different time. Ligand and receptor are different sets of atoms, but exist in the same space and same time. As result, Reaction Graph models interaction by atomic mapping, while Protein Docking/Binding models interaction by spatial relationship. Therefore, their interaction modelings are different.
B. Related Works
B.1. Molecular Representation
Research interest in molecular representation learning is growing due to its potential various biochemical tasks like virtual screening and inverse design. To enhance the expressive capabilities of molecular representations, efforts are focused on developing network architectures and training strategies suited to different modalities of molecular input. ID molecular fingerprint (Morgan, 1965; Durant et al., 2002; Rogers & Hahn, 2010) and SMILES string (Weininger, 1988; O' O'oyyle & Dalke, 2018; Krenn et al., 2020) are typically processed by language models (Jaeger et al., 2018; Wang et al., 2019; Chithrananda et al., 2020) extract chemical properties. GNN-based methods (Duvenaud et al., 2015; Kearnes et al., 2016; Xiong et al., 2019) are commonly used to model 2D molecular graphs, which intuitively simulate the relationships between atoms (nodes) and bonds (edges). Recently, the integration of high-dimensional geometric information, including molecular point clouds and 3D molecular graphs (Schütt et al., 2017a; Gasteiger et al., 2020; Atz et al., 2021; 1; Fang et al., 2022; Zhou al., 2023; Han et al., 2024), has effectively assisted in understanding complex molecular structures.
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
B.2. Reaction Representation
Representing chemical reactions crucial for scientific discovery. A well-designed reaction representation can facilitate the development of various tasks, such as reaction classification (Ghiandoni et al., 2019; Schwaller et al., 2019; Lu & Zhang, Kwon et al., 2022a; Wang et al., 2023b), and yicld prediction (Schwaller et al., 2021b; Kwon et al., 2022b; Yin et al., 2024). To represent chemical reactions, researchers have developed novel fingerprint (Schneider et al., 2015; Probst et al.. 2022), graph representation (Varnek et al., 2005; Tavakoli et al., 2022), and deep learning- bearning-based methods (Schwaller et al., 2021a; Hou & Dong, 2023). Recently, some studies have introduced strategies such as multi-modal integration (Chen et al., 2024; Zhang et al., 2024) and pre-training (Wen et al., 2022; Shi al., 2024), providing new insights for constructing reaction representations. However, the reaction representation methods do not pay much attention 3D spatial information molecular representation does. Furthermore, current approaches generally represent reactants and products separately, overlooking the modeling of chemical changes during the reaction process.
2022), condition recommendation (Gao et al., 2018; Maser et al., 2021;
B.3. Invariant Neural Network
To enhance model's 's understanding of 3D molecular structure in reaction, integrate 3D information into RG in invariant manner. Invariance ensures that the prediction results remain unaffected by the rotation and translation of molecules. This reduces redundant information, allowing the model to focus on reaction-related features.
Invariant neural network utilizes transformation-invaln invariant features, such as distance and angle (Han et al., 2024). Initially, DTNN (Schütt et al., 201 utilizes distances between atoms with Gaussian basis embedding. Later, SchNet (Schütt et al., 2017a) improves performance by using learnable radial basis function (RBF) kernel embeddings. DimeNet (Gasteiger al., 2020) is the first introduce angle features in quantum chemistry property prediction tasks, and GemNet (Gasteiger et al., 2021) further enhances this by incorporating dihedral (torsion) angles. Subsequently, ComENet (Wang al., 2022) and SphereNet (Liu et al., 2022) introduce new torsion angle representations to reduce computational costs. Additionally, models like ClofNet (Du et al., 2022) and LEFTNet (Du et al., 2024) use a local coordinate system to guarantee invariance.
Difference. While these efforts are dedicated to providing more comprehensive 3D features, we try to take a step back and explore more suitable 3D features. To be detailed, the properties of chemical reactions (e.g. condition, yield, type) are invariant different conformations. Therefore, the 3D features in RG should also be invariant to different conformations. In different conformations, the bond lengths and bond angles exhibit minimal variation, thus they used in RG. However, the torsion angles and pairwise distances may change dramatically, thus they are excluded to further reduce redundant information. We also demonstrate the effectiveness of our design in Sec. 1.8.1.
B.4. Reaction Condition Prediction
Reaction conditions are pivotal for chemical synthesis and drug design. Suitable reaction conditions can significantly accelerate reactions, increase yields, and save raw materials. Condition prediction is an essential step in computer-aided synthesis planning (CASP). Given the representation of a reaction, the model is designed to predict conditions like catalysts, solvents and temperature.
In the early stages, machine learning models used for predicting reaction conditions are primarily based on knowledge graph reasoning (Segler & Waller, 2017), database similarity searches (Lin et al., 2016), and expert systems (Marcou et al., 2015). With (Gao et al., 2018) and others pioneering the use of neural networks trained on large datasets for the prediction of reaction conditions, increasing attention has been given to the potential of deep learning in this task. Researchers attempt to improve upon the inputs to the network. (Afonina et al., 2021) uses ISIDA fingerprints as descriptors for reactions, (Walker et al., 2019) uses MACCS keys as inputs, and (Chen & Li, 2024) uses the difference between the product and reactant Morgan fingerprints as input. Other researchers focus on enhancements in network architecture. (Ryou et al., 2020), (Maser et al., 2021), and (Kwon et al., 2022a) use GNNs for feature extraction, while (Andronov et al., 2023) and (Wang et al., 2023b) attempt to use Transformers extract features of reactions. Additionally, (Kwon et al., 2022a) and (Karpovich et al., 2023), aiming to address the tne-to-many relationship between reactions and reaction conditions, opt to use Variational Autoencoders (VAEs) (Kingma & Welling, 2014) for reaction condition generation.
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
B.5. Reaction Yield Prediction
Yield typically indicates the percentage of reactant molecules converted into the desired product, and is one of the main concern of synthetic route planning. High-yiel synthetic routes can reduce costs and improve product purity. To enhance the yield of the synthetic routes planning result, an accurate yield prediction model is vital.
Similar to condition prediction tasks, early approaches utilize DFT (Ahneman et al., 2018) for yield prediction. These methods are generally applied to specific types of chemical reactions. With the advent of Transformers, efforts to achieve yield prediction using language models like BERT emerge, exemplified by models such as YicldBERT (Schwaller et al., 2021b) and Egret (Yin et al., 2024). Additionally, there are methods employing GNNs (Kwon al., 2022b; Li et al., 2023; Sato al., 2024). Recently, researchers have begun exploring Bayesian Neural Networks (BNNs) (Gal & Ghahramani, 2016; Kendall & Gal, 2017), which output both prediction and confidence (Kwon al., 2022b; Chen et al., 2024). Some studies also attempt to integrate reaction conditions or multimodal information improve practical applicability and model accuracy (Yin et al., 2024; Chen et al., 2024), while the potential of pre-training remains to be explored (Shi et al., 2024).
B.6. Reaction Classification
Reaction type is closely related to the reaction mechanism. Classification of reaction type is beneficial for reaction understanding, and can be used for data augmentation and preprocessing. Additionally, reaction classification task evaluates model's comprehension of reaction mechanisms, contributing to performance analysis.
Earlier, people use rule-based methods to classify chemical reactions (Ghiandoni et al., 2019). These methods are accurate and have strong interpretability, but they require huge amount of labor. In recent years, with the rise of machine learning, data-driven methods begin emerge (Schwaller et al., 2019). RXNFP (Schwaller et al., 2021 a) employs Bert extract implicit vector representations of reactions from SMILES strings, achieving excellent clustering results for reaction types. DREP (Probst et al., 2022) combines circular fingerprints and hash-based fingerprint generation methods to efficiently represent a chemical reaction in an interpretable manner. T5Chem (Lu & Zhang, 2022) utilizes a specially designed multi- task decoder for reaction type classification, enhancing the model's understanding of reaction mechanisms. Furthermore, works like Egret (Yin et al., 2024) use reaction type classifiers trained on the Pistachio dataset for data analysis, aiming to evaluate the model's yield prediction capabilities.
C. Molecule and Reaction Representations
In deep learning tasks, the representations of molecules and reactions are used to describe their chemical features. In terms of modality, these representations can be divided into ID strings and fingerprints, 2D graphs, and 3D point clouds. Tab. 9 lists examples of various representation forms for aspirin, and Tab. 10 lists the representations of chemical reaction for synthesizing aspirin.
C.1. One-Dimensi
C.1.1. STRING
String representations are typically composed of a sequence of characters that express molecular structure. They follow specific grammars that can be parsed by computer programs, and is generally suman-readable, As result, string representations are widely used in chemical databases. Due to their similarity to natural language, Transformers and RNNs often employed extract features from string representations. For these models, the main challenge lies in the many-to-one relationship between strings and molecules. This hinders models from learning molecular structure patterns. To mitigate this problem, canonical algorithms and data augmentation are generally employed.
SMILES. (Weininger, 1988) expression is the most commonly used string representation in deep learning chemistry tasks. It is composed of symbols representing atoms or groups, symbols for bonds, labels for rings, case rules for indicating aromaticity, and symbols for chirality. These symbols work together to represent the atomic composition and topological structure of a molecule.
The SMILES representation of aspirin, as shown in Tab. 9, uses atomic symbols to represent the atoms in the molecule. For example, the symbol for carbon is C, for oxygen is O, and bromine, which does not appear in the example, has the symbol Br. Hydrogen atoms are typically omitted, For chemical bonds, a single bond is represented by a dash (-), which is usually
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Table Example of different types of molecular representations of aspirin, including string-based representations such SMS..S,
SELFIES, DeepSMILES, fingerprint beased representations like ECFP and MACCS, molecular graph and improvements, as well as 3D molecular point cloud (graph).
Type
Representation
SMILES
CC o0ee
ECFP
11101000011001111111000000000010
Molecular
Graph
OH
Point Cloud
omitted, a double bond is represented by an equals sign (=), and a triple bond is represented by a hash sign (#). It's important note the presence of parentheses the structure, which indicate a branch; for instance, the expression C(= O) signifies branch with oxygen where the numbers 1 at both ends indicate that the corresponding carbon atoms connected by bond form ring. The lowercase letter indicates that this is an aromatic ring. Furthermore, SMILES may include functional groups or atoms with valence states enclosed in brackets, such as [O-] and [C'H] Here, [O-] denotes an oxygen atom with negative charge, and the (@) (@) symbol typically indicates a chiral center, with different chiralities distinguished by [C@H] and [C@@H) H). (.) symbol are used to separate the SMILES expressions of different molecules. For chemical reactions, the SMILES notation generally follows the format of reaclants reagents producls, as shown in Tab. 10, which does not include reagents.
connected to the carbon by double bond. Additionally, observe the structure el elecceel
Mainstream Python libraries such as RDKit and OpenBabel* can parse generate SMILES expressions for molecules chemical reactions, and efficiently calculate various chemical properties.
SMARTS. (Daylight Chemical Information Systems, 2007) is an extension of SMILES used to describe patterns or substructures within molecular structures. It allows the use of wildcards and logical operators to represent more complex chemical queries. For chemical reactions, SMARTS strings can include atomic mapping information. For example, in the aspirin synthesis reaction shown in Tab. 10, symbol [C 2] can be found both reactants and products. This indicates that they are the same atom. With atomic mapping information, reaction mechanisms can be easily interpret. Tools like RXNMapper be utilized to predict atomic mapping.
1.2. FINGERPRINT
Another ID representation is fingerprint. They typically manifest as binary vectors, where each bit indicates the presence or absence of substructure or chemical property. These vectors are generally of fixed length, making them easily manageable by most neural network architectures, such as MLPs.
Fingerprints can enhance model's performance on specific tasks by selecting tesk-relevant features; however, this relies on careful manual design and has limited generalization ability. Additionally, fingerprints have mpe-to-many relationship with
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Table 10. Example of different types of reaction representations, including string-based SMILES and SMARTS, fingerprint-hased DRFP and ISIDA, graph representations Molecular Craph, CGR, Rxn Hypergraph and Reaction Graph, well as 3D reaction point cloud.
Type
Representation
SMILES
>> =[[[((00000))ccccc(((((000000000
CC(= 100 :]]j 5]1[cH/ :6]
ccH :|t:::/::::::::10000000000001111
13
SMARTS
>> [CH3 ||]0::[[=00333)0::[:::]]]]] 6]
(elt 8||cH :1::::001:::1||10002000 13]
DRFP
[0
OO
Molecular Graph
+ OF
16
CGR
OO
+
Rxn Hypergraph
Reaction
14
Graph (Omit
Angular
Edges and 3D)
molecules or reactions.
ECFP. (Rogers& & Hahn, 2010) generates fingerprints by traversing the atoms of molecule and their surrounding environ- ments, capturing the topological structure information of the molecule. The ECFP generation algorithm starts by assigning an initial identifier to each atom based on its features. Then, it iteratively combine the feature of each atom with its neighbors. The features of the nith iteration contains the topological information of a radius of r + 1 around the atom. Ultimately, these atomic features are combined into a fixed-length bit vector, as shown Tab. 9.
ECFP is generally designed for molecules, and the ECFP of reaction generally concatenation or difference of the
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
reactant's and product's ECFP.
ECFP can be generated using popular chemical toolkits like RDKit (referred as Morgan Fingerprint), It is efficient to construct and easy to input into various machine learning models. However, the expressive ability of the ECFP is limited and depends on its length (where the ECFP in condition prediction task can reach the length of up to 2 bits).
DRFP. (Probst et al., 2022) shares similarities with ECFP. DRFP first extracts a list of circular molecular n-grams from the reactants and products, then calculates the symmetric difference of the n-gram lists. For each n-gram in the resulting symmetric difference list, a descriptor is computed. Finally, the set of descriptors is converted into a fixed-length vector. This approach is akin to the differentiation method in ECFP, emphasizing the changes that occur before and after the reaction. DRFP can be generated using the Python DRFP library.
C.2. Two-Dimensional
In 2D graph representations, each node corresponds to atom, while edges correspond to bonds. Each node and edge has associated attributes to express its chemical features(e.g. atom type and bond type). Specially designed molecular graphs or reaction graphs may incorporate additional nodes and edges. They can express additional information or enhance message passing. Graph representations are usually processed by GNNs or Graph Transformers.
Due to the similarity between graphs and molecules, graph representations possess advantage in expressing molecular properties. It can correspond one-to-one with molecules, aiding neural network in modeling the correct relationships between them. However, 2D molecular graph may struggle model long-range atomic interaction, and lack 3D structural information. Improving graph representations for more efficient feature extraction is currently a key area of research.
Molecular Graph (MG). (Duvenaud et al., 2015) uses graphs to represent molecules, where nodes correspond to atoms and edges correspond to bonds. Both nodes and edges carries chemical information. Such graphs are typically undirected and stored as an edge matrix of size E x 2, or an adjacency matrix of size V x V. Additionally, there are atom and bond feature matrices of size Vx x Dy and x DE.
As shown in Tab. and 10, the visualization of the aspirin MG reveals that the molccule has 13 nodes and 13 edges, thus V = 13 and E 13. In property prediction tasks, hydrogen atoms typically omitted to reduce complexity. However, in molecular dynamic tasks, hydrogen atoms are generally retained for accurate calculation. Currently, most chemical toolkits support the conversion from SMILES to MGs.
Condense Graph of Reaction (CGR). (Varnek et al., 2005) is a graph specifically designed for chemical reactions, as shown in Tab. 10. CGR can be seen as an analogous approach of DRFP in graph domain. It models the reaction as the superposition of molecules in the reaction. Each node represents the mixed features of the same atom in the reactants and products, while each edge represents the mixed features of the same chemical bond in the reactants and products. The mixing of features is typically done by subtraction or concatenation. If certain atom or edge is absent in either the reactants or products, the feature for the absent side is set to zero.
Compared with MG, CGRs have a smaller size and are computationally efficient, but they may sacrifice the relative independence of the molecules. Algorithms for building CGR are provided in toolkits like CGRTools and Chemprop'.
Rxn Hypergraph. (Tavakoli et al., 2022) is also specifically designed for chemical reactions. As in Tab. 10, all atoms in the molecule are connected to Mol Hypernode that represents the molecule, while all Mol Hypernodes in the reactants or products are connected to a Rxn Hypernode that represents the entirety of the reactants products. Furthermore, the Rxn Hypernodes in the reactants are interconnected, and the Rxn Hypernodes in the products are also interconnected, with no connections between the reactants and products.
The Rxn Hypergraph is designed to adapt the RGAT architecture. The hierarchical structure allows model to focus on features with different granularities within a reaction. However, the reactants remain isolated from the products, and the atomic mapping is absent. As a result, it still has limitations expressing the molecular transformation in reaction.
We couldn't 't find any existing toolkits that can generate Rxn Hypergraphs. The Rxn Hypergraph used in our experiments is implemented based on the formulation in Tavakoli et al. (2022).
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
C.3. I
3D molecules or chemical reactions are typically represented using point cloud or 3D molecular graph (Thomas et al., 2018; Fuchs et al., 2020), shown in Tab. 9 and 10. In point cloud, each node corresponds to atom and contains both chemical properties and structural information(c.gg coordinate). Molecular point clouds are usually processed using Geometric GNNs or Transformers. They use a preset cutoff distance (Schütt et al., 2017a) for graph convolution or attention.
Since molecules can undergo transformations such as translation and rotation in space, there is a many-to-one relationship between point clouds and molccules. This introduces redundant information for chemical property prediction. Therefore, transformation invariance and equivariance are key focus in 3D molecular modeling. Molecular point clouds are generally used in molecular dynamics or quantum chemical property calculations (Jackson et al., 2021; Batzner al., 2022). However, they are relatively rare in predicting yields, reaction conditions, and reaction types.
C.4. Comparison of Graph Representations of Reaction
Table 11. Ability comparison of graph representations of reaction. Itn represents internal message passing within molecule, R to represents message passing between reactants, P to represents message passing between products, R to P represents message passing hetween reactants and products, Mol and Rxn indicate the ability express an independent molecule and an entire chemical reaction during the message passing stage, and 2D and 3D represent the inclusion of 2D and 3D topological structures.
Message Passing
Expression
Representation
Itn
R PtoP
to
Mol
Rxn 2D
3D
MG
Rxn Hypergraph
V
CGR
RG (ours)
Y
As shown in Tab. 11, we compare the message passing and expressive capabilities various reaction representations. All representations allow for message passing between atoms within molecule. Among them, MG lacks edges connecting different molecules. Rxn Hypergraph enables message passing among atoms within the reactants and products; however, it still does not facilitate message passing between reactants and products. CGR models the reaction as superposition of molecules, however, during message passing, the features of the same atom in reactants and products are mixed in one node, which results a loss of relative independence between the molecules.
RG connects the same atom in reactants and products by reaction edges. This improvement achieves reaction-level message passing while preserving molecular-level feature extraction. Moreover, RG incorporates 3D information, which provides richer structural prior compared 2D graphs.
D. Implementation Details
D.I. Graph Representations
D.1.1. REACTION GRAPH
In the implementation, each node and edge of Reaction Graph (RG) contains more information. The attributes of node i can be represented as vector n; E T. (distinguished from v; in the Sec. 2), and the attributes of edge ij can be represented as vector eij E R.P. where v; and eij are the concatenations of all attributes of the node and edge, respectively. Tab. 12 provides an example of all available attribute values (which will have slight difference between datasets). Tab. 13 provides detailed dimensions of node attributes and edge attributes for each dataset. Note that the edge attributes here do not include li,, which is stored in separate matrix L according to our previous definition in Sec. 2.
Torsion Angle Extension. Reaction Graph can be casily extended to model torsion angle by adding torsion angular edges. Specifically, for each edge BC in the molecular graph, the algorithm searches for each edge AB and CD. If # C, D + B, and A + D, torsion angular edge AD is added. In this way, each edge length in tetrahedron ABCD is determined, thereby uniquely defining the tetrahedron. Once the tetrahedron A ABCD D is defined, the dihedral angle between the planes
23

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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Table 12. Example of node and edge attributes in Reaction Graph. Fach attribute is represented by one-hot vector, and the final node attribute edge attribute is the concatenation all relevant attributes.
Table 13. The dimensions node and edge attribute vector for each dataset, where D, denotes node attribute vee- tor dimensions, and D. denotes edge tribute vector dimensions.
Atom Type Charge Type Degree Type
C,O.N, CI, Br,
6,
0, 6,
Dataset
De
Hybridization Type
SP, SP2, SP3D. SP3D2, S
Node
Num of Hydrogens
1,2, 5.0
USPTO-Condition
110
13
Valence Type
0, 3,2,3,,4,5,6,77,
10, 11, 12, 13, 14
Pistachio-Condition
117
13
Ring Size Type
6,7,5,6,7,8
Buchwald-Harde
43
10
Suzuki-Miyaura
49
10
Edge Type
Bond Edge, Reaction Edge, Angular Edge Single, Double, Triple, Aromatic Clockwise, Counterclockwise
Edge
Bond Type
USPTO- Yield
128
14
Chirality Type
USPTO-TPL
135
14
Stereochemistry Type
BondCis, BondTraas
Pistachio-TType
127
17
ABC' and BCD is determined, which corresponds to the torsion angle of BC. One-hot Length Embedding. In our experiments, we also use one-hot length embeddings. We use frequency- discretization, and divide the edge lengths into 16 bins. The specific bond length distribution and the division method are shown Fig.
1e6
Histogram Bond Length
0.1
1.0
12
14
1.6
1.8
2.0
Vellue
Figure 5. Histogram of the bond length distribution of molecular graphs on the USPTO-Condition dataset, along with the division method of the bins.
D.1.2. RXN HYPERGRAPH
Interaction Extension. In Rxn Hypergraph, the interactions between reactants and products can be modeled by adding another hypernode. Specifically, the additional hypernode connects the origin rxn-hypemode of reactants and products.
3D Extension. In supplementary experiments, we add 3D bond length information the Rxn Hypergraph. Different from molecular graph, Rxn Hypergraph contains hypernodes, which do not have actual coordinates. Therefore, the lengths of all edges connected to hypernodes are set to O. This method ensures invariance. We use 4-dimensional RBF kemell to embed the edges, and then concatenate the edge length embeddings to the original edge features.
D.1.3. CGR
3D Extension. In supplementary experiments, we add 3D bond length information to the CGR D-MPNN. Specifically, we implement 3D Featurizer extension of Chemprop library, and calculate the conformation. The conformation is stored
24

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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
as coordinates on the nodes. During inference, we calculate the bond lengths using the atomic coordinates, embedding them with 1 16-dimensional RBF kemel,, and then concatenate the bond length embeddings to the original edge features. Note that in the CGR, edge node corresponds to two atoms, and each edge corresponds to two chemical bonds. Therefore, each node contains two coordinates, and each edge contains two length embeddings.
D.2. Model Details
D.2.1. OURS MODEL
Node Embedding. We simply use fully connected (FC) layer to embed the node vector n,, resulting in v, R
Edge Embedding, We first use the RBF kernel to embed the edge length kúj as lig E PR and concatenate the edge length embedding to the edge attribute vector to obtain e', - [ei; 4iyl- Then, e'y is directly inputted into a FC layer and the output vector is reshaped into matrix May E IR Do DD, Do, This approach is similar to the method of generating weight matrices in
hypernetworks.
Vertex-Edge Integration. We refer to the method in Kwon et al. (2022b), using residual connections to enhance training stability and employing GRU to facilitate node attribute updates. Specifically, the node attributes v, will serve as the memory state of the GRU, while the messages of + EyeN, Mij of aggregated during each MPNN iteration will be treated as the input to the GRU, updating the node attributes instead of directly assignment. The final feature vector of node is calculated by of [0% ".
Attention-based Aggregation. We use 1g* h²] as the input to the LSTM to obtain h The final reaction representation vector r is obtained by mapping [q 1222-1] through FC layer with PReI.U activation.
Output. This module is specifically designed for each downstream task. For the condition prediction task, the output
module is consistent with CRM.
21 = fa; Oc1) z; = (r, 21, 0c,);
(7)
(8)
where fe, linearly map each previously predicted condition 2, to embedding vector h., E RD,, concatenate all 2, with reaction feature r and feed them into a 2-yayer FC classifier with ReLU activation to predict the next probability vector 2; Dec of the i-th condition.
The yield prediction module uses 3-layer MLP. It incorporates PReLU activation and Dropout layers, and simultaneously outputs the predicted mean My and logarithmic variance log o of yield.
Pay log o = fr;
The reaction classification head also uses a 3-layer MI.P with PReI.U activation to output the predicted probability vector of reaction type.
For LvG classification task, we add an FC layer to the last layer of the feature extraction module. It maps the node features into node-level multi-class classification labels.
Hyperparameter Settings. For USPTO-Condition, USPTO-TPL, and Pistachio-Type, we set the edge length embedding dimension D; to 16, with total edge attribute dimension of D + D. = 29. For Pistachio-Condition. D; with D, + D. = 14. For the yield prediction task, since 3D information not used, D, = O.
For condition prediction and reaction classification, we set the embedding dimension D,, of nodes to 200, the number of MPNN iterations Ti 3. the number of Set2Set aggregation iterations T2 to 2, the dimension of the GRU memory state to be the same as D., while the LSTM memory state dimension is set 2 x D.. The final output reaction feature vector has dimension D, of 4096. For yield prediction task, D, is set to 64, D, is set to 1024, and Ti To = 3.
The hidden layer dimension of the reaction condition output head fa is 512, and the dimension of the condition embedding Dg is 256. The hidden layer dimension of the reaction yield output head fr is 512, with a dropout rate of 0. The hidden layer dimension of the reaction classification output head is 4096.
The specific hyperparameter tuning methods can be found in Sec. H.
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
D.2.2. OTHER MODELS
Bond Angle Model. We use the approach of DimeNet (Gasteiger al., 2020) that integrates bond angles, explicitly providing angular information. In the implementation, graph. In the edge graph, nodes represent edges in the molecular graph (MG), and edges represent angles. During each iteration, we first perform message passing in the edge graph to obtain its node features (which is the edge features in MG), and then conduct message passing in MG. Unlike the official implementation targeted at quantum chemistry calculation, we use the method more suitable for property prediction. Following GEM (Fang et al., 2022), we employ 16-dimensional RBF kernel for length and angle embedding".
refer to the official DimeNet code and first construct an edge
CRM. We use the open-source code provided by CRM (Gao al., 2018) to test the results on the Fistachio-Conditie dataset. Since
is similar in scale to USPTO-Condition, refer the hyperparameter settings in the reproduction code of Parrot (Wang et al., 2023b).
Parrot. We use the open-source code" provided by Parrot (Wang et al., 2023b). Specifically, since Parrot employs a SMILES tokenizer, and the Pistachio-Conditio dataset contains vocabulary that is different from the USPTO-Condition dataset, we couldn't use the officially provided pre-trained parameters. Therefore, we first extract the vocabulary from Pistachio-Condition, then apply the RCM pre-training proposed by Parrot, and finally perform supervised fine-tuning on the Pistachio-Condition dataset.
AR-GCN & CIMG. Both methods provide corresponding open-source code 12 but the network structure design of AR-GCN (Maser et al., 2021) only accommodates a specified number of reactants and products, while CIMG (Zhang et al., 2022) does not provide the corresponding training code. Therefore, we only refer to the reproduction results in Parrot (Wang et al., 2023b) for reference and do not train on Pistachio-Condtioon.
D-MPNN. We use the D-MPNN (Heid& Green, 2021) and CGR construction code provided in the Chemprop library. We maintain the default settings for hyperparameters, training strategies, loss functions, and optimizers in all task training.
Rxn Hypergraph. The Rxn Hypergraph (Tavakoli et al., 2022) does not provide related open-source code, but the structure of the Rxn Hypergraph is described in detail in the paper. Therefore, we reproduce the construction of the Rxn Hypergraph using the DGL library!4. 14, Additionally, the Rxn Hypergraph paper conducts experiments using RGAT, but does not specify the exact type of RGAT used. Thus, based on the descriptions in the paper, we employ EGAT provided in DGL, which is a commonly used RGAT.
UGNN. We use the open-source eo provided by UGNN (Kwon et al., 2022b) train on the USPTO- Yield dataset. Since the molecules in the USPTO-Yiee Yield dataset are different from those in the HTE dataset, we adapt the dataset preprocessing script in the open-source code to handle the USPTO-Yice dataset and adjust the input dimension of the fully connected layer in the input layer accordingly to accommodate the reaction data from USPTO-Yien while keeping other hyperparameters unchanged.
DREP. We use the DRFP library 16 to generate DRFP fingerprints. According to the description in the original paper, we select -048-dimensional DRFP and train an MLP with a hidden layer dimension of 1664 and tanh activation function.
RXNFP. We use the RXNFp!7 library to test the performance of Pistachio-Typpe Similar to Parrot, are unable train using the original token settings of RXNFP. Therefore, we construct vocabulary for the FistachioTyype dataset and perform for the reaction classification task. The hyperparameter settings for the model architecture remain at their default values.
MLM pre-training on RXNFP, followed by
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
T5Chem. We use the official open-source code of T5Chem (Lu & Zhang, 2022) train on the USPTO-yield, Pistachio- Type, and Suzuki-Miyaura datasets. The official pre-trained parameters provided by T5Chem based on character tokenization. After checking, we find that TSChem's 's vocabulary includes all characters from our datasets. Therefore, we use the pre-trained parameters provided by T5Chem and train on the downstream tasks for each dataset. The hyperparameters remain at default settings.
UniMol. We use UniMol as a comparison method in our supplementary experiments. We utilize the official code and released pre-trained parameters of UniMol. Specifically, to enable UniMol to handle reaction task, we use the Transformer- based feature extraction module from UniMol, and maintain consistency with our model in subsequent modules. The hyperparameter settings for the feature extraction module align with the default values provided in the UniMol official code, while the hyperparameters for other modules are consistent with our model.
Vector Scalarization Model. We utilize PaiNN to implement vector scalarization. Since PaiNN has not released an official implementation, we refer to a third-party implementation" 20 and develop a DGL version. PaiNN does not support scalar edge attributes. To address this problem, we concatenate the scalar edge attributes with edge length embeddings during message computation. Additionally, since the lengths of reaction edges are to they may lead division-by -y-zzro error. Therefore, we uniformly increase all edge lengths by before embedding, and only compute vector messages for edges other than the reaction edge. These operations does not affect the model's 's equivariance. We set the edge length embedding dimension to 20, with other hyperparameter consistent with our model.
GAT & GIN. We implement GAT and GIN by utilizing the EGAT and GINE modules from DGL, where EGAT employs 8-head attention, and the GINE module adds an additional BatchNormID layer after each iteration to maintain numerical stability. Other hyperparameters, such as iterations, hidden layer dimensions, and subsequent modules, are consistent with our model.
ReaMVP. In the appendix, test the performance of ReaMVP without large-scale yield dataset pre-training. In this way, the yield data used for training is the same as our model and other methods (4k), rather than utilizing much larger dataset (600k) for training. This better reflects the model's 's performance on the benchmark, allowing for fair comparison. Specifically, we obtain the model code and pre-trained parameters from the official repository?!, and keep the default hyperparameter setting. But since the database used by ReaMVP has become proprictary data, we are unable to acquire the dataset and use their pre-training method.
Set Transformer. We attempt to use the Set Transformer as our aggregation module. Specifically, we use the Set Transformer Encoder and Decoder implemented by DGL toolkit for feature aggregation. Since the older version of DGL does not include Set Transformer, we directly used the source code from GitHub. We set the hidden dimension to 200, attention head number to 8, number of layer to 2, for both encoder and decoder.
D.3. Visualization Details
TMAP. We implement TMAP dimensionality reduction by using TMAP22 library in Python.
UMAP. We implement UMAP dimensionality reduction by using UMAP23 library in Python.
I-SNE. We implement I-SNE dimensionality reduction by using Scikit-Leam library in Python.
D.4. Training Details
All the model training is completed on RTX 4090 using CUDA version 11.3, with PyTorch 1.12.1 and DGL 0.9.1. 1.ottl to build the model and training framework. The machine has 512GB RAM and an Intel(R) Xeon(R) Gold 6326 CPU @ 2.90GHz. For the models using Py PyTorch Geometry, we use PyTorch Geometry 2.5.2 for training and reproduction. We
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
use Scikit-Leam and PyCM to compute various evaluation metries. For the replication of other works, we set up the corresponding environments using the official requirements files guidelines provided.
Leaving Group Identification. We use the average of the cross-entropy loss for all atoms and the cross-entropy loss for leaving group atoms. This makes the model focus more on classifying the leaving group type. The training, testing, and validation sets are distinguished according to the USPTO-Condition in an 8:1:1 ratio. A learning rate of 5e-4 is used, along with a ReduceLRROnPltteau training schedule with mode set to min, a factor of 0.1, patience of 5, and a minimum learning rate of 1e-8. Training is conducted with a learning rate of 5e-4, weight decay of le-10, and the Adam optimizer with beta values of [0.9, 0.999]. We use a batch size of 32, and set the accumulation steps 4 (equivalent to a batch size of 128). The training lasts for 50 epochs with early stopping applied. We choose 666 as the random seed and take the best evaluation epoch as the result. The total training time takes approximately 6 hours.
Reaction Condition Prediction. We use an improved cross entropy loss to optimize the condition prediction model:
N1 No. Σ
Waj Cit log emp(zig) Ek= exp(zit)
Lag
(10)
j=1 G Aoo + +11 De)
(11)
where Waj is the weight of class j of i-th type of reaction condition, X; is the label smoothing factor (Szegedy et al., 2016), e; is the predicted result vector for the i-th reaction condition output by the model, while c; is the one-hot encoding of the ground truth for the reaction condition. We use a two-stage training strategy to train our reaction condition model, with learning rate of 5e-4, weight decay of le-10, and the Adam optimizer with beta values of [0.9, 0.999] for each stage. training schedule with mode set min, factor of 0.1, patience of 5, and minimum learning rate of le-8. For Pistachio-Condition we split the dataset into training, validation, and test sets in an 8:1:1 ratio. In the first stage, we train for 50 epochs, using À of 0.9, 0.8, 0.8. 0.7, and 0.7 for catalystl, solventl, solvent2, reagentl, and reagent2, respectively. For the None category of solvent2 and reagent2, we set the learning rate weight w to 0.1. And for USPTO-Condition dataset, we set all and w to 1. After completing the first stage of training, we reset and initialize the weights of the output module using a normal distribution with a mean of 0 and a standard deviation of 0.1, and freeze the feature extraction and aggregation modules for the second stage of training, which lasted for 50 epochs. We use batch size of 32 with 4 accumulation steps (equivalent to batch size of 128). We choose 666 as the random seed and take the best evaluation epoch as the result, with total training duration of approximately 2 days. The training times of other models and representations on USPTO-Condition are roughly the same as the ratio of the training times we presented in Fig. 7.
We employ
Reaction Yield Prediction. We use the training method of BNNs (Gal & Ghahramani, 2016; Kendall & Gal, 2017) combined with L2 regularization to train the yield model:
(y (リ-Mu) (y-1²)² + log o3) +
my)²
ME > M
Co.g = (1-7)+ * (y - 22)² +
M
(12)
oz
where y [0, 1] is the ground truth yield corresponding to G in the dataset, y and À are two regulatory factor, Jyy and Fy are the model output mean and variance, and 0 is the set of model parameters. The first term makes H,y close to the ground truth yield, and the second loss is used to train By to reflect prediction uncertainty. The last term is L2 regularization.
For the HTE dataset, our training framework remains consistent with UGNN, using a learning rate of 1e-3, weight decay of le-5, and the Adam optimizer with beta values of [0.9, 0.999]. For the hyperparameters of the model, we set 7 to le-1 and A to 1e-5. We train for a total of 500 epochs, shuffle the dataset at the beginning of each epoch, and employ the MultiStepLR training strategy with milestones set to [400, 450] and gamma set to 0. The training batch size is 32, with an accumulation step of 4 (equivalent to batch size of 128). Training on each dataset takes approximately 20 minutes.
For the USPTO- Yield dataset, we train for 30 epochs (starts to overfit around the 20th epoch each time), modifying the MultiStepLR milestones to [20, 25). We set to le-1 and A to O. We randomly split off 10% of the training set as a
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
validation set and again choose 10 random seeds to take the best results. Training for Gram takes about 45 minute, while Subgram takes approximately 1.5 hours.
Reaction Classification. For the USPTO-TPL and Pistachio-Type datasets, we use the same training framework, employing cross entropy loss function and the Adam optimizer with learning rate of 5e-5, weight decay of 1c-10, and beta values of [0.9, 0.999]. We utilize Reducel.ROn ROOnllatea Plateau training scheduler with mode set to min, a factor of 0.1, patience of 5, and a minimum learning rate of le-8. We use a batch size of 32 with 4 accumulation steps (equivalent to batch size of 128) and train for 100 epochs. We randomly split off 10% of the training set as validation set and find that the dataset quality is relatively high, allowing us to achieve good performance without careful hyperparameter tuning and early stopping, Therefore, we take the final epoch the result. We choose 123 as the random seed. The training for Pistachio- Type takes 60 hours, while USPTO-TPL takes 40 hours.
E. Algorithm and Pipeline Details
E.1. Reaction Graph Construction
SMILES Formatting. First, given a SMILES expression, the reaction expression takes the form: A>B> D, where and C represent the reactants and products, respectively. Part B typically represents the reagents. In the task of reaction condition prediction, B is one of the prediction targets, so we convert part B into our reagent classification labels. While in the tasks of predicting reaction types and yields, such reagents will be treated as additional prior. Therefore, in these tasks, we concatenate part B with part A using a (-) symbol, treating it as A. D contains additional information about the reaction, which is not require during the construction of RG. At this point, the SMILES of the chemical reaction simplifies to A>>> C.
Reaction Validation. Second, we use the RDKit to parse reactants A and products C. If parsing succeed, A and C are considered valid. Next, we predict the atomic mapping of the reaction by RXNMapper and validate reaction formula by checking if the atoms with mapping in the reactants and products correspond one-to-one. Although this cannot guarantee that all reactions passing the tests are valid, it significantly ensures the quality of our reaction data.
Molecular Graph Construction. For each molecule in the reactants and products, we compute the attributes of each atom and bond by RDKit, as the example in Tab. 12, and use DGL to construct graph-format data. Each atom corresponds to a node while each bond corresponds to an edge in the graph. Note that this is slightly differs from the RG defined earlier in Sec. 2. This simplification of RG is made for the sake of ease of writing and understanding. and the actual nodes and edges in RG contain more information. In addition to the aforementioned attributes of the bond, the edge also has a flag to indicate the type of edge (as there will also be reaction edges and angular edges). After generation, MGs of all molecules will be integrated into single graph for easier manipulation.
Atomic Coordinate Calculation. We first attempt to initialize the conformation using ETKDG, and then optimize the conformation using MMFF94; if it fails, we switch to UFF (Casewit et al., 1992). If it still fails, we use the 2D coordinates of MG as a substitute. This ensures that most molecules contain 3D information, while the remaining has 2D coordinates as an approximation. We use RDKit and OpenBabel in this process to calculate conformations, aiming to cover as many molecules as possible.
Angular Edge Construction. We add angular edges to the graph construct triangles to convey bond angle informations. Specifically, for each MG, we will find all edge pairs of the form a, b and b, c by traversing the adjacency list, and check if there is already an edge connecting a, c. If not, we will construct an angular edge connecting a, to implicitly convey the angle information of the angle Zabc.
Reaction Edges Construction. Finally, we will construct the reaction edges. For all atoms with indices m in the reactants and n in products with the same mapping label, we will construct a reaction edge to connect them.
Torsion Angular Edge Construction. Torsion angular edge is an optional extension of Reaction Graph. In the molecular graph, we traverse all triplets (ab, bc, ed) formed by the edges ab, bc, and ed, where a, b, c, and d are distinct nodes. We then check if there is already bond edge or angular edge ad present. If not, we add a torsional angular edge ad to implicitly convey the torsional angle of bond bc. Additionally, leveraging the advantages of the reaction graph, we can also conduct targeted designs, such as adding the torsional angular edge ad only for edges be that are single bonds, to simplify calculations. This will be explored in future work.
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Algorithm 1 Train Reaction Condition Prediction Model
... ca]. label smoothing coefficients A1..... rate a, model parameters 0, feature extraction and aggregation module f, output modules 91 92:-...
Input:
Reaction Graph 9, ground truth labels Cgt [c1, ........
... As, learning
2: Output: trained model parameters 0'
3: Constant:
dimension of reaction condition labels Di....,D. Ds
4:
5: procedure TrainCConttionMMooee@Onntteeerr Cgt, a, 8 ,I,...,As.
6: let r - [(
7: let é= [21, ....., és] be zero vector like
8: let loss
9:
i from 1 to 5 do
10:
let 8; -- X;c; + (1 (1-x;) X;)
11:
let è; + gr, , C:-1:
12:
loss t loss+ CrossEntropy(s:.cd) 2i)
13: end for
let H <- a Valoss
return 0'
16: end procedure
E.2. Reaction Condition Prediction
Our model autoregressively predict five types of reaction conditions, which are catalyst, solvent1, solvent2, reagentl and reagent2. As shown in Alg. 1, during training, the model predicts next condition based on the reaction representation vector and the ground truth labels of the previous conditions. While during inference, the input the reaction representation vector and all the previous predicted conditions.
We also utilize beam search during inference. As shown in Alg. 2, before inference, we define how many candidate labels to generate for each reaction condition (n1, 122, nay R4, ns). When inferring the i-th reaction condition, we input the reaction representation vector and all combinations of the previously predicted reaction conditions into the current classification head. The classification head produces n X 122 X ... X n4-1 probability vector. For each probability vector, we then select the top-n, as the output labels, forming n1 72 X ... 74-1 X n, combinations of reaction conditions. Then we continue to predict the next condition.
E.3. A Attention Weights Sample Selection
As mentioned in Sec. 3, we use the attention map of representative molecules to observe the model's understanding of reaction mechanism. Specifically, for these molecules, they have different reaction center atoms in different reactions. We identify reaction center by atomic mapping, and extract representative molecules through automated script.
E.4. Leaving Group Extraction
We use a dataset labeled with Leaving Groups (LvGs) in the LvG identification task. To get the LvG label, for each RG in the dataset, we first remove all reaction edges and their connected nodes. This step eliminate all non-LvG atoms, leaving the remaining connected subgraphs the LvGs. We assign temporary labels to these connected subgraphs, and mark the temporary label on the original RG nodes. Next, we perform graph hashing to each LvG by randomization parameter GNN. We count all the hash values and filter in LvGs with frequencies above threshold. This results in 204 LvG labels, while other LyGs are uniformly assigned Other label. Finally, we build a mapping between temporary labels and LvG labels, and update the labels in RG. For atoms that do not belong to LvGs, they are assigned None label.
E.5. Bin-Packing
When testing the model's 's computational efficiency, we first construct a series of reaction bins. Then we test model's 's average runtime on these bins as a measure of efficiency. Each bin contains the same number of (nodes) atoms. To construct these bins, we use greedy algorithm shown in Alg. 3.
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Algorithm 2 Reaction Condition Beam Search Inference
Input: Reaction Graph G, candidate labels (ni, n2, ni, ng, ns), model parameters 6, feature extraction and aggregation
module f. output modules :1 9
2: Output: Predicted reaction condition combinations C' E 11)
3:
4: procedure CondinioonBeamSeerrhhC, (n1, R2,, R2,, R3, 124, 115. 0)
5: let r - -
6: let Ci < (r:
7: let (ei.....,... be top R4 C1
8: let C. be [[cr]]...., [cmnl]]
9: for from 2 to 5 do
10:
let Cnew be empty list for j from 0 to C.length - do
11:
12:
let C c (r 8)
let G1, Can; be top n, c;
for from to n, do
let Cnew & Concatenate [ca]])
16:
append Cnew to Cnew end for end for
17:
18:
19:
C 5- Cuean
20:
end for
let C < Stack(C)
22: return C
23:
end procedure
Algorithm 3 Reaction Bin-Packing
1: Input: Number bins N and capacity of each bin C, number of atoms of reactions .A = [41, 02; a.
2: Output: Indices reactions in each bin B [L,, Cz...., .e....,Cy Ly]
3:
4: procedure ReactionBinaackingCW\ C, A)
5: shuffle AA
6: Initialize B as list of lists of length N
7: Initialize W as zero list of length N
8: for each reaction a; in A do
9: let dmin +-0 0
let +0
N do for j 1 C-WWii a.) if d < dmii and dl > 0 do
13:
14:
dmni x- d k j end end for
15:
16:
17:
l > 0 do
push into B[k]
20:
W[k] + Wik] a;
21:
end if
22:
end for
23:
return B
24:
end procedure
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
F. Complexity Analysis
F1. Theoretical Analysis
Assume that the messages are calculated by passing the atom features through FC layer. We first define:
V: Number of atoms; M: Number of molecules; E: Number of chemical bonds;
D: Maximum degree of atomic nodes; L: Length of the molecular SMILES string;
Hidden feature dimension of atoms; A: Number atoms in a graph node;
N: Number of iterations for the GNN/Transfommer, P: Number of message passing a GNN iteration.
Molecular Grpah. Since each edge needs to calculate the message once each GNN interaction, and the complexity of fully connected layer O(H)), each node in molecular graph represents one atom, the complexity of the original Molecular Graph is O(ENH²)
Reaction Graph (ours). Reaction Graph introduces two types of edges: reaction edges and angular edges.
The number of reaction edges Ereaction cannot exceed the number of product atoms Vproducts and the number of product atoms cannot exceed half of the total atoms, so Ereaction V Vproduct S V/2. Therefore, the computational cost introduced by the reaction edges is O(V/2. N = O(VNH²).
Reaction Edge:
Angular Edge: Since a bond angle is formed between every two neighboring edges of each atom node, and the number of bond angles is equal to the number of angle edges. Therefore, the number of angle edges Fangular VD2 Therefore, the computational cost introduced by the angular edges is O(VD2. NH²).
-
The overall complexity of Reaction Graph is Oi(E V + VD*) N OI(E VD*). NHH). When 3D information is not used, the complexity of the Reaction Graph is Oi(E V) N
Bond Angle Model. Our proposed angular edges are more efficient than explicitly using bond angles. With the angular edge method, there is only one message passing per round of GNN iteration. In contrast, when angle features are explicitly integrated, each GNN iteration requires /' message passing operations. The complexity is Oi(E + VD P.
Rxn Hypergrpah. Rxn Hypergraph adds edges connecting each atom to the corresponding molecule hypernode, introducing computational cost of D(VNH) The molecule nodes between reactants are connected pairwise, all linking to the reactant hypernode. And is similar for the products. The cost for these new edges are O + M)- 2 ( N 2 Finally, the cost for Rxn Hypergrpah is Oi(E + V M²). N
Condense Graph of Reaction. In Condense Graph of Reaction (CGR), each node represents A atoms from the original graph, and each edge represents A edges from the original graph. Therefore, the number of edges in the CGR becomes E/ A, and the dimension of the hidden layer for the nodes becomes AH. Thus, the time complexity of the CGR is O A N. ( = NAH?2..
SMILES-based Methods. SMILES Malsedd methods typically use Transformers as the backbone. In Transformers, the time complexity for each component is:
1. Tokenization: The cost of regex tokenizer is O(L)
2. Embedding: The cost of embedding layer is OLH))
Attention: The size of the attention matrix L so the complexity for attention matrix caleulation is O(L²
4. Feed Forward: Each token's embedding is processed through a fully connected layer, so the time complexity is O(LH²)
And there's N layers of Attention and Feed Forward. The overall time complexity of Transformer O + LH + N.
(LH² L H)] ONN (LH² + L²H)]
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Table 14. Data pre-processing time for different representations. The molccular graph viewed reaction graph without reaction
information and 3D structure information. Time units are milliseconds (ms).
Information
Total Length of Reaction SMILES
Representation
Reac.
3D
60
85
110
135
160
185
210
235
260
285
310
335
360
Reaction Graph
3.2
5.6
10.1
18.1
28.7
24.9
52.5
$4.0
72.4
82.8
100.3
244.4
585.6
923.3
w/o Reaction Edge
X
4
3.6
4.4
7.2
16.8
26.0
28.8
45.9
$7.5
69.3
81.3
91.9
157.8
722.1
945.9
w/o Angular Edge
X
1.2
1.5
2.3
2.7
3.5
3,9
4.8
5.4
6.1
6.8
5.6
5.5
21.7
29.3
Molecular Graph (w/o 3D)
X
x
0.7
1.0
1.3
1.5
2.4
2.2
3.0
3.4
4.7
4.6
4.9
4.1
15.9
19.9
Molecular Graph (w/ 3D)
X
2.9
4.1
7.3
16.5
23.5
26.8
49.5
54.7
69.7
82,4
90.5
156.4
718.7
932.1
Runtime
Disk Space Usage
Number of Edges
1000
100
60000
Space (Byte)
50000
Num of Edges
800
Time (9)
10
40000
600
10-2
30000
400
20000
200
10-3
10000
200
400
200
400
200
400
Length SMILES
Length SMILES
Length of SMILES
Figure Graph construction algorithm metrics different graph representations, including (A) RG, (B) RG with only reaction edges, (C) RG with only 3D information and angular edges, (D) molecular graph (MG), and (E) MG with 3D information. Duc to the overlap between groups (C) and (E) of computation time, and since the number edges in group (D) is equal to that in group (E), group (E) omitted in both figures.
F.2. Experimental Analysis
F.2.1. CONSTRUCTION CoST
We measured the preprocessing cost of the following graph representations, including processing time and disk space:
(A) RG, (B) RG with only reaction edges, (C) RG with only 3D information and angular edges,
(D) molecular graph (MG), (E) MG with 3D information
As shown in Fig. 6, the construction time for graphs exhibits linear increase with the SMILES length. The construction time for RG with angular edges almost the same as that for 3D MG, so the curve is omitted. In RG, the overhead of computing 3D structures is largest, approximately 10a 102 times that of other parts. For hard disk space, the space occupied by angular edges is largest, while reaction edges and conformation storage is relatively small. This is because the number of angular edges is more than other types of edges, and is about 2-3 times the number of edges in the original MG.
Tab. 14 shows the influence of reaction edges, angular edges, and bond edge length on data pre-processing time in RG, as the total length of reaction SMILES increases. During data pre-pu preeppoccssing, the primary time cost comes from 3D conformation calculation. But it an unavoidable cost for any method that utilizes 3D structure information.
F.2.2. COMPUTATIONAL COST
Compared with Graph-based Methods. We test the computational efficiency of graph-based representations and architectures. To ensure fair comparison, we use the same GNN architecture for different graph representations. Note that in CGR, one node is the superposition of two atoms, and one edge in the superposition of two bonds. Results are shown in Fig. 7, 8 and Tab. 15.
Compared with other graph representations. Due to incorporating additional reaction information and 3D structures, our method requires slightly more time than molecular graphs and Rxn Hypergraph representations. However, delivers
33

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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Table 15. Model inference time for different representations the same backbone. Time units milliseconds (ms).
Information
Number of atoms [V in Reaction Graph
Representation
Reaction Infomation
3D Structure
2500
3000
3500
4000
4500
Reaction Graph
37.28
43.77
50.57
58.03
65.45
w/o Reaction Edge
35.36
40.92
48.68
53.30
58.79
w/o Angular Edge
X
22.51
25.96
29.82
34.21
38.77
Molecular Graph
X
18.59
21.93
25.39
28.30
31.48
Rxn Hypergraph
31.18
37.28
43.31
48.53
54.06
Condensed Graph of Reactions
X
44.55
52.48
60.75
66.32
75.34
0.10
3.0
0.08
2.5
Time (s)
0.06
2.0
0.04
1.5
0.02
1.0
2000
3000
4000
2000
3000
4000
Num of Atoms
Num of Atoms
Reaction Graph with Bond Angle
Reaction Graph
Angle
CGR (same atorn dim)
CGR (same atom dim)
Reaction Graph
Reaction Graph
Bond Edge Length Angular Edge Length
Bond Edge Length + Angular Edge Length
Rxn Hypergraph
Rxn Hypergraph
Reaction Graph with Bond Edge Vector
Reaction Graph with Bond Edge Vector
Reaction Edge
Reaction Edge
Molecular Graph
Molecular Graph
CGR (same node dim)
CGR (same node dim)
Figure Computational time of models and graph rep- resentations at different atom counts. Legend order matches line order.
Figure 8. Computational time ratios of models and graph representations in relation to molecular graph at different atom counts.
Table 16. Inference time comparison for Reaction Graph and SMILES-hasce methods. According to the result, Reaction Graph requires smaller computation cost.
Methods
Representation
Time
T5Chem
SMILES
3min 19s
RXNFP
SMILES
23min 43s
Reaction Graph (ours) Reaction Graph
2min 36s
significant performance improvement, justifying the additional time cost. The CGR introduces larger computation overhead because each of its nodes is combination of two atoms, requiring larger hidden layer dimensions in the neural network.
Compared with other 3D informations, angular edge more efficient than explicitly introducing bond angle, concluded in Sec. 3. The computational efficiency slightly lags behind bond vector, which only introduces 50% computational overhead. However, bond vector may introduce redundant information (e.g. torsion angle), resulting in suboptimal performance. In contrast, angular edge significantly enhance performance while maintaining moderate computational overhead.
Compared with Other Methods, We compare the inference time of Reaction Graph and smiles-based methods. The results are shown Tab. 16. Reaction Graph, as a graph-based model, exhibits the shortest inference time.
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
G. Dataset Preprocessing and Analysis
For each dataset, we test various metrics related to dataset distribution and complexity, including the frequency of each label, the frequency of each atom, the total number of atoms and molecules, the total number atoms per molecule and per reaction and on. For clarity, logarithmic scale. Due to the large number of data points, chart, the x-axis represents the data categories, while the y-axis represents the frequency of that category in the dataset.
all data categories by frequency in ascending order except for the yield dataset, and line charts display the data distribution. In each
G.1. USPTO-Condition
Train Catalyst1 Distribution
Train Solvent1 Distribution
Train Solvent2 Distribution
10a
Frequency
Frequency
10*
Frequency
10a
104
10a
10a
10a
10a
10a
10a
10a
Catalyst1 Class
Solvent1 Class
Solvent2 Class
Train Reagent1 Distribution
Train Reagent2 Distribution
Train Atom Distribution
107
Frequency
20
Frequency
10a
Frequency
10a
10a
10
102
10a
Reagent1 Class
Reagent2 Class
Atom Type
Test Catalyst1 Distribution
Test Solvent1 Distribution
Test Solvent2 Distribution
10a
Frequency
10a
Frequency
Frequency
202
10a
102
10a
10a
201
10.
10t
Catalyst1 Class
Solvent1 Class
Solvent2 Class
Test Reagent1 Distribution
Test Reagent2 Distribution
Test Atom Distribution
Frequency
202
Frequency
10a
Frequency
10
10a
10a
10a
101
10
10a
Reagent1 Class
Reagent2 Class
Atom Type
Figure 9. Data distributions of USPTO-Condition, including distribution of the number of data points for each category of reaction conditions, as well as the distribution the occurrence atom types.
The USPTO-Condition dataset is a collection of reaction condition data from USPTO database. We use scripts provided in Parrot (Wang et al., 2023b) to process the raw dataset. First, for each reaction data USPTO, we extract all corresponding reaction condition annotations. Then, we use RXNMapper to predict atomic mapping. Molecules in reactants that do not contain any mapping markers are considered reagents. During this process, all invalid SMILES are discarded. and duplicated data rows are dropped. Afterward, count the frequency of each catalyst, solvent, and reagent, and remove conditions with frequencies below 100. We check reagents with ions and removed non-electrically neutral combinations. Then, to standardize the output format, we delete all data with catalyst > 1, solvent > 2, reagent >> 2, and those without reaction conditions. Finally, the dataset is split into training, validation, and test sets. The various metrics of the dataset are shown in Tab. 17, while the distributions of data are shown in Fig. 9.
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Table 17. Summary of USPTO-Condition, including metrics for measuring the complexity of data points, the overall complexity of the dataset, and the distribution differences between the train/val set and the test set.
Metric
Train/Val
Test
Size
612,666
68,075
Mean Length
96.55
98.44
Mean Atoms
18.20
18.53
Mean Molecules
2.88
2.89
Max Length
868
825
Max Atoms
347
280
Atoms
60
39
Mean Atoms per Molecule
24.22
22.92
Max Atoms per Molecule
176
165
Max Molecules
55
24
Molecules
849,149
135,066
Different Molecules (Train/ Val and Test)
787,898
Num Catalyst
54
Num Solvent I
85
Num Solvent 2
41
Num Reagent
223
Num Reagent
95
Based on the divided CEPTO-Condition. we use the Reaction Graph (RG) construction algorithm in Sec. E to build graph dataset. For molecules that could not generate conformations, we directly discarding them. The number of remaining data samples at each stage is in Tab. 18.
Table 18, Changes the datasct size of USPTO-Condition during the preprocessing process.
Stage
Num of Data Rows
Reaction Data Extraction
3,130,812
Mapping and duplication Dropping
1, 1,117,867
Filter Conditions
680,741
Split Train/Val/Tes
544,591 : 68,075 68,075
Graph Dataset Generation
544,125 : 68,018 68,002
G.2. Pistachio-Condition
For the Pistachio database, we use the same approach as the USPTO-Condition dataset. The difference is that most reactions in Pistachio contains mapping information, and there are also atmosphere labels. To address these problems, during the mapping step, we only predict the missing mapping, during the filtering step, we discard all reaction entries with atmosphere labels. Finally, we also split the dataset into 8:1:1 for training, testing, and validation. The various metrics of the dataset are shown in Tab. 19, while the distributions of data are shown Fig. 10.
Similarly, based on the split dataset, we further generate the RG dataset. And the number of remaining data samples at each stage is as shown in Tab. 20.
The final dataset size is similar to that of USPTO-Condition. However, the reaction conditions in Eastacho-CCodditin are sparse, and the data samples are more complex. The reason the model achieves higher classification accuracy on Pistachio-Condition is also due to the uneven distribution of labels, where the N None class accounts for the majority, which can be observed in the confusion matrix from Sec.
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Train Catalystl Distribution
Train Solvent1 Distribution
Train Solvent2 Distribution
Frequency
100
Frequency
10a
Frequency
10a
10a
10a
10a
10:
Catalvst1 Class
Solvent1
Solvent2
Train Reagentl Distribution
Train Reagent2 Distribution
Train Atom Distribution
Frequency
10a-
Frequency
10a
Frequency
10a
107
10a
101
10a
10t
Reagent1 Class
Reagent2 Class
Atom Type
Test Catalyst1 Distribution
Test Solvent1 Distribution
Test Solvent2 Distribution
Frequency
Frequency
Frequency
1.0
10a
10a
10a
10t
Catalyst1 Class
Solvent1 Class
Solvent2 Class
Test Reagent1 Distribution
Test Reagent2 Distribution
Test Atom Distribution
Frequency
1.0
Frequency
10a
10
10?
10a
10a
10-
100
Reagent1 Class
Reagent2 Class
Atom Type
Figure 10. Data distributions of Pistachio-Condition, including distribution the number of data points for cach category of reaction conditions, as well as the distribution of atom types.
G.3. HTT
use the dataset provided by UGNN (Kwon et al., 2022b), which contains the SMILES expressions reactions and yield data. Due to the small number of molecules included, it is difficult for models learn from the limited conformational data, Therefore, only generate RGs with reaction edges and did not discard any data. Consequently, the final dataset size and metrics shown in Tab. 21 and 22.
The number of data samples in the HTE dataset is nearly thousand times smaller than that in our previous datasets. As all data points belongs to the same reaction, the variety of molecules is relatively limited, and the complexity of the data is relatively low. Previous works also propose using Test datasets to evaluate the model's generalization. Test datasets has greater distribution differences between the training and testing splits. Tab. 23 lists metrics for the Test datasets.
For Test datasets, we can clearly see significant differences between the training and testing sets, which also include different types of molecules. This requires the model to accurately model the relationship between molecules and reaction structures in order to obtain reasonable extrapolation results.
G.4. USPTO-Yield
We use the USPTO- Yield dataset provided in Yield-Bert (Schwaller et al., 2021b), which is extracted from the USPTO database. It is relatively noisy with complex distribution. The dataset is processed similarly as described above, with some specific metrics shown in Tab. 24 and 25, and the distribution of data shown in Fig. 11.
The yield distribution USPTO- Yield is quite uneven, and there is a significant difference in the yield distributions between Gram and Subgram, as noted in (Schwaller et al., 2021b). Additionally, the quality of the yield data is low, and the relationship between yield and molecular structure non-smooth. These factors increases the task difficulty.
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Table 19. Summary of TistachioCoondition dataset, including metrics for measuring the complexity of data points, the overall complexity the dataset, and the distribution differences between the train/val set and test set.
Metric
Train/Val
Test
Size of Dataset
506,224
56,247
Mean Length per Reaction
99.66
99.93
Mean Atoms per Reaction
17.44
17.48
Atom Types
68
50
Mean Atoms per Molecule
24.27
22.73
Max Atoms of Molecule
218
209
Mean Molecules per Reaction
3.04
3.04
Max Length of Reaction
988
878
Max Atoms of Reaction
440
408
Max Molecules of Reaction
18
Molecule Types
761,357
110,771
Different Molecules (Train/Va Val and Test)
718,036
Catalyst Types
69
Solventl Types
134
Solvent2 Types
108
Reagent1 Types
267
Reagent2 Types
198
Pistachio-Condition Table 20, Changes in the dataset size of Pistachio- Condition during the preprocessing process.
Stage
Num of Data Rows
Reaction Data Extraction
145,035,928
Filter Conditions
1,981,122
Mapping and duplication Dropping
562,471
Split Train/Val/Tes
449,977 56,247 56,247
Graph Dataset Generation
449,902 56,240 56,234
Table 21. Summary of Buchwald- Hartwig on metries reflecting dataset complexity.
Table 22, Summary of Suzuki-Miyaura on var-
ious metrics reflecting dataset complexity.
Metric
Value
Metric
Value
Size of Dataset
3,955
Size of Dataset
5,760
Mean Length pre Reaction
216.65
Mean Length pre Reaction
196.925
Mean Atoms pre Reaction
116.15
Mean Atoms pre Reaction
110
Max Length pre Reaction
270
Max Length pre Reaction
300
Max Atoms Reaction
144
Max Atoms of Reaction
146
Mean Molecules pre Reaction
12.14
Molecules pre Reaction
7
Max Molecules pre Reaction
15
Molecule Types
51
Molecule Types
Atom Types
10
Atom Types
16
Mean Atoms per Molecule
13.20
Mean Atoms Molecule
12.14
Max Atoms of Molecule
46
Max Atoms Molecule
42
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Table 23. Summary of Test datasets of Buchwald-Hartwer including metrics for measuring the complexity of data points, the overall complexity of the dataset, and the distribution differences between the train/val set and the test set.
Test1
Test2
Test3
Test4
Metric
train
test
train
test
train
test
train
test
Mean Length per Reaction
213.23
224.62
214.61
221.41
214.53
221.60
214.55
221.54
Mean Atoms per Reaction
16.40
17.05
16.56
16.67
16.53
16.74
16.48
16.85
Max Length of Reaction
289
300
300
300
300
300
300
300
Max Atoms of Reaction
138
146
146
146
146
146
146
146
Molecule Types
45
38
46
38
46
38
46
37
Mean Atoms per Molecule
13.18
14.50
13.61
13.95
13.54
14.03
13.30
14.16
Max Atoms per Molecule
46
46
46
46
46
46
46
46
Different Molecules
13
13
13
14
(Train/Val and Test)
Molecule per Reaction
7
Atom Types
10
Size of Dataset
3955
Table 24. Summary of Gram dataset, including metrics for measuring the complexity of data points, the overall complex- ity of the dataset, and the distribution differences between the train/val set and the test set.
Table 25. Summary of Subgram dataset, including metrics
measuring the complexity of data points, overall com- plexity of the dataset, and the distribution differences be- tween the train/val set and test set.
Metric
Train/Val
Test
Metric
Train/Va
Test
Size Dataset
156,565
39,137
Size of Dataset
240,326
60,075
Mean Length per Reaction
115.97
116.03
Mean Length per Reaction
150.24
150.67
Mean Atoms per Reaction
60.44
60.46
Mean Atoms per Reaction
79.13
79.35
Mean Molecules per Reaction
6.63
6.63
Mean Molecules per Reaction
6.88
6.89
Max Length of Reaction
560
493
Max Length of Reaction
696
641
Max Atoms of Reaction
257
244
Max Atoms of Reaction
352
260)
Mean Atoms per Molecule
20.27
19.33
Mean Atoms per Molecule
25.88
24.91
Max Atoms of Molecule
116
103
Max Atoms of Molecule
166
143
Atom Types Max Molecules of Reaction
67
57
Atom Types
67
57
59
32
Max Molecules of Reaction
38
29
Molecule Types
230,450
74,116
Molecule Types
400,811
123,077
Different Molecules
Different Molecules
197,580
353,890
(Train/Val and Test)
(Train/Val and Test)
G.5. USPTO-TPL
We use the USPTO-TPP -PP dataset from RXNFP (Schwaller al., 2021a). According to Fig. 12 and Tab. 26, the data distribution shares similarity with other datasets extracted from USPTO. However, the labels are extracted based on 1,000 templates. Reaction templates have strong sturctural pattern, which can be easily learnt by the model. Therefore, the difficulty of USPTO-TPL is low.
G.6. Pistachio-Type
Considering the scale of the dataset, we only extract portion of the data in Pistachio. First, we simplify the reaction type labels in Pistachio into 13 major categories. Each category contains multiple reaction templates, making it more complex than USPTO-TPL. Then, we discard the last category with too small quantity. From the remaining 12 categories, we select equal amount of data for each category, and then divide into train/val and test sets.
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Gram Train Yield Distribution
Gram Test Yield Distribution
x 10a
Frequency
Frequency
10
x 10
4 102
10
3 x 102
2 x x0
6 10a
Yield
Yield
Subgram Train Yield Distribution
Subgram Test Yield Distribution
10a
Frequency
Frequency
10a
10a
10a
101
Yield
Yield
Gram Train Atom Distribution
Gram Test Atom Distribution
107
Frequency
10a
Frequency
10a
10a-
10a
10a
10:
Atom Type
Atom Type
Subgram Train Atom Distribution
Subgram Test Atom Distribution
Frequency
10
10a
Frequency
10a_
10a
10a
10a
Atom Type
Atom Type
Figure 11. Data distributions of USPTO-Yield, including distribution of the number of data points in each bin of yield, and the distribution of atom types.
Train Type Distribution
Test Type Distribution
104
Frequency
Frequency
10a
102
10a
Reaction Type
Reaction Type
Train Atom Distribution
Test Atom Distribution
107
Frequency
Frequency
10a
105
10a
10a
10a
10a
Atom Type
Atom Type
Figure 12. Data distributions of USPTO-TPL, including the distribution of the number of data points for various reaction types, well the distribution of atom types.
40

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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Table 26. Summary of USPTO-TPL including metrics measuring the complexity of data points. the overall complex- ity of the dataset, the train/val set and the test set.
Table 27. Summary of Pistachio- Tappe including metrics for suring the complexity of data points, the overall complexity of the dataset, and the distribution differences between the train/val /val set and the test set.
distribution differences between
Metric
Train/Val
Test
Metrie
Train/Val
Test
Size
400,604
44,511
Size
656,640
72,960
Mean Length
124.92
125.15
Mean Length
133.91
133.98
Mcan Atoms
11.29
11.32
Mean Atoms
13.04
13.04
Mean Molecules
5.91
5.91
Mean Molecules
5.36
5.35
Max Length
599
493
Max Length
2706
1118
Max Atoms
332
243
Max Atoms
926
480
Atoms
Mean Atoms per Molecule
25.30
23.61
Mean Atoms per Molocule
24.99
23.31
Max Atoms Molecule
164
99
Max Atoms per Molecule
420
289
Max Molecules
59
31
Max Molecules
64
48
Molecules
581,458
88,219
Molecules
1,007,041
148,239
Different Molecules (Train/Val and Test)
543,559
Different Molecules (Train/ Val and Test)
946,727
Num Types
1000
Num Types
12
Train Type Distribution
Test Type Distribution
5.4825 x 10
Frequency
5.4775 5.475 x
5.48 x 10
10*
Frequency
6.175
6.125 x 10a
6.15 10
5.4725 x 10*
6.1 103
5.47 x 10
6.075
5,4675 10
6.05
5.465 x
6.025 x 10
5.4625 x 10*
6 10a
5.975 10
Reaction Type
Reaction Type
Train Atom Distribution
Test Atom Distribution
Frequency
107
Frequency
10a
10
10a
10a
10
10-
Atom Typc
Atom Type
Figure 13.. Data distributions of Pistachio-Type,, including the distribution of the number of data points for various reaction types, well as the distribution of atom types.
The final Pistachio-Type dataset has a large scale, with data distribution shown in Fig. 13 and dataset metrics shown in Tab. 27. The complexity of Pistachio-Tyee Type is significantly higher than USPTO-TPL, and it is closer to the real-world distribution chemical data.

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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
H. Supplementary Experiments
H.1. Attention Weights Analysis
H.1.1. ATTENTION WEIGHTS VISUALIZATION
We provide the original images the attention weights drawn by RDKit, and additionally selected 4 groups of observation subjects as supplements. Each group contains a molecule with multiple active functional groups and two associated reactions, with each reaction occurring on different functional groups of the molecule. The results are shown in Fig. 14
The results show that for these five molecules and their respective two reactions, the Reaction Graphs help the model accurately identify the reaction centers while reducing attention to irrelevant atoms. In contrast, the model using molecular graphs exhibits a similar distribution of attention weights for the target molecules in both reactions. It frequently focuses on functional groups that are less relevant to the reaction, leading to errors in prediction.
H.1.2. FAILURE MODE ANALYSIS
We analyzed the edge cases and failure modes of the reaction center identification results for molecular graphs and Reaction Graph. As shown in Fig. 14, molecular graphs often mislocate the reaction center when multiple functional groups are present, the model cannot obtain information related to the reaction changes from the molecular graph, making it difficult to determine which functional group is involved in the reaction. In contrast, incorrect localization of the reaction center in Reaction Graph is relatively rare, but still exist. As shown in Fig. 15, the typically reasons are: (1) Errors in the reaction itself; (2) Distraction of attention due to overly complex molecular structures; (3) Encountering rare chemical reactions that do not occur on functional groups
Although the model using Reaction Graph still encounters failures, we observe that even in the failure cases of Reaction Graph, the model still shows higher level of attention the reaction center compared to molecular graphs. This validates the strong udaptability of Reaction Graph to edge cases.
1.1.3. STATISTICAL VALIDATION
We conduct experiments on dataset scale to quantitatively validate that the Reaction Graph aids in identifying reaction centers.
We use USPTO dataset and use the algorithm described in Sec. E.3 to extract a test set of 1000 molecules, as well as 2000 corresponding reactions. We use the condition prediction model trained on USPTO-Condition process these reactions.
Attention weights extracted for reacting atoms and non-reacting atoms from the Set2Set layer for each target molecule. We calculate two metrics to evaluate the model's 's attention on the reacting atoms. First, we consider the proportion of attention weights for reacting atoms relative to the total. Second, we calculate the average attention weights for reacting atoms and non-reacting atoms, denoted as and and computed their ratio a/b. The results are shown in Tab. 28
Table 28, Influence of reaction information on attention weight results on USPTO.
Method
Proportion
Ratio a/b
Molecular Graph
0.4326
1.4542
Reaction Graph
0.5079
2.0390
We further test the relationship between the attention weight results and reaction types, calculating the aforementioned metrics for each reaction type in the dataset. The results are shown in the Tab. 29 and 30. The correspondence between reaction type numbers and specific reaction types can be referenced in the Tab. 39.
Table 29, The proportion of attention weight for the reacting atoms, across various reaction types.
Method
0
1
3
4
5
7
8
9
10
11
Molecular Graph
0.65
0.49
0.50
0.50
0.61
0.35
0.58
0.50
0.38
0.46
0.28
0.04
Reaction Graph
0.70
0.53
0.54
0.54
0.66
0.38
0.65
0.57
0.40
0.52
0.32
0.06
Table 30. The ratio a/b of attention weight between reacting and non-reacting atoms, across various reaction types.
Method
0
1
3
4
5
6
7
8
9
10
11
Molecular Graph
4.65
1.92
2.87
3.07
2.25
0.67
4.56
2.56
0.84
2.84
0.55
0.05
Reaction Graph
6.07
2.35
3.21
3.79
2.86
0.84
6.73
3.39
0.99
3.66
0.64
0.09
42

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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
MG
RG
MG
RG
H.N
C19
MG
RG
MG
RG
Clem
MG
RG
MG
RG
X
14
x
MG
RG
MG
RG
817
R17
F19
X
F19
618
618
220
N10 00
MG
RG
MG
RG
N:1H.
N:1H
C.15
N:14H.
C.15
N.14H,
HN.5
X
HINES
N:12
HNNB
N:19
HN:18
Reaction Center
X
Incorrectly assigned attention weight
Correctly assigned attention weight
Figure 14, Visualization results of attention weights of the reaction condition prediction model molecular graph and Reaction Graph. The depth of red represents the magnitude of attention weights, with deeper shades indicating larger attention weights.
43

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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Failure Case 1: Error Reaction In Database
C:5
N66
C:9
C:10
c:10
N:4
N:8
N
C:7-N:8
N
C:11
C:5
N:12
ERROR HERE
C:3
C.2
N:12
C:11
N:6
MG
C:9
RG
C:9
8
HN:8
N
N
N:12
N:12
C:11
C:11
Failure Case 2: Overly Complex Molecular Structures
0:32
C
cieen
N31
0.30
C28-c23
F22
C24
F26
N7
cieen
NEC
0:30
C28
F27
C24
9:26
F25
11
C9 CD
C20
C22
13 C20
222-
C21
C22
011
01 C15
C:15
MG
RG
F25
224
N
G72
Failure Case 3: Reaction Do Not Occur on Functional Groups
4
C19
C15
C14
13
N10
+
c2=01
C15
N110
C16
C16
C17
MG
C:14
RG
C:14
C:15
C:15
C:2
0:1
C:2
0:1
C:16
C:16
C:17
C:17
Figure Visualization of attention weights for the failure cases. For Reaction Graph, these cases categorized into three types, each being relatively rare. However, even in failure cases, the Reaction Graph (RG) still outperforms the Molecular Graph (MG).
44

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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Success Cases
Molecular Graph
Molecular Graph Ground Truth
I Tin
X
x 2
Reaction Graph Prediction
40 vir
x
x
Reaction Graph Ground
Molecular Graph Failure Cases
Prediction
Molecular Graph Ground Truth
200f
Graph Prediction
Reaction Graph Ground Truth
Reaction Graph Failure Cases
Molecular Graph Prediction
3HO gom
Molecular Graph Ground Truth
D4a
Reaction Prediction
Arttee
3HO
Reaction Graph Ground Truth
DHO
Figure 16. Visualization of the success and failure cases on leaving group identification. Molecular graphs often exhibit eroor in positioning the leaving group when the molecule has multiple functional groups, while emror Reaction Graph relatively rare, typically occurring due to incorrect classification of certain atoms.
45

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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
H.2. Leaving Group Identification Analysis
H.2.1. ERROR ANALYSIS OF MISCLASSIFIED CASES
We conduct a detailed analysis of the failure cases in the leaving group recognition task for molecular graphs and Reaction Graph, and attempt to identify the failure modes.
We visualize the leaving group identification results of molecular graph and Reaction Graph. As shown in Fig. 16, molecular graph often misidentify leaving group positions, hindering accurate classification. In contrast, Reaction Graph position leaving groups correctly at most time, with minor errors mainly in specific type classification. This shows that Reaction Graph effectively helps the model to focus on features related to the reaction.
H.2.2. ADDITIONAL BASELINE METHODS
We conduct extra experiment with D-MPNN and Rxn Hypergraph, and the results are shown in Tab. 31.
Table 32. Results for statistical significance anal- ysis of Reaction Graph on leaving group identi- fication in USPTO, using 1-test method from the mean and standard deviations of multiple trials with different random seeds. The baseline method
Table 31. Performance of different baseline methods on the Leaving Group Identification task.
Overall ACC
LvG ACC
Method
CEN
MCC
CEN
MCC
Molecular Graph.
Molecular Graph
0.950
0.036
0.549
0.448
0.201
0.519
Rxn Hypergraph
0.969
0.026
0.743
0.679
0.150
0.699
Overall
LvG-Speeified
D-MPNN
0.993
0.003
0.949
0.902
0.051
0.899
Metries
ACC
MCC
ACC
MCC
Reaction Graph
0.997
0.002
0.973
0.947
0.031
0.945
-log
13.47
20.19
20.75
20.28
According to the results, Reaction Graph achieved the best performance in leaving group identification compared to other baselines.
H.2.3. DETAILED RESULTS
Standard Deviations. Due to the large size of USPTO, and for the convenience of t-test, we conduct four random tests, which is closest to the square of the t-value (1.96) for a 95% confidence interval. We calculate the results of training under four different random seeds, and then compute the mean and standard deviation. The results are shown in Tab. 33.
Table 33, Results for leaving group identification of Molecular Graph and Reaction Graph on USPTO, including mean and standard deviation from multiple trials with different random seeds.
Overall
LyG--Seecifid
Method
ACC
CEN
MCC
ACC
CEN
MCC
Molecular Graph
0.950+0.001 0.996:0.001
0.03740.001 0.002+0.001
0.538=0.006
0.423=0.004
0,209+0.002
0.497#0.005
Reaction Graph
0.971=0.001
0.944=0.001
0.035+0.001
0.942+0.001
Statistical Significance Tests. Statistical significance testing is essential for determining whether the Reaction Graph demonstrates an improvement over the baseline method. For each task, we selected the optimal baseline and employed the I-test to assess statistical significance. The formula used is v/i z-h where 1 represents the t-statistic, indicating the size of the difference relative to the variation in the sample data; n is the sample size, which in this case 4: x the mean performance of the Reaction Graph; 6 is the baseline performance; and s the standard deviation of the performance measurements. By calculating the t-statistic, statistically significant compared to the baseline method.
evaluate whether the observed improvement in the Reaction Graph is
The significance level P corresponding to the t-value can be found in the lookup 28 and we use log P to make the results easier to observe; the larger the value, the higher the probability that the Reaction Graph shows an improvement over the original methods.
We choose Molecular Graph as the baseline method calculate the t-values, and the results are shown in Tab. 32.
httpp://ww.wwkiiiidd.doo///////e t-distribution
46

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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Cross-validation Results. Cross-validation reduce the bias introduced by the unevenly distributed chemical reaction dataset, ensuring the model's generalization. We test the model's performance using K-fold cross-validation. This means splitting the dataset into K parts, using one part for test and the remaining for train each time. Considering the training cost and the reuse of experiment results, we divide the dataset into 9 folds (excluding the original test set) and conduct three random tests. Including the validation results from the original splits, there are a total of four tests. We take the average as the result K-fold cross-validation. The results are shown in Tab. 34.
Table 34, Cross-vase validation results for leaving group identification Molecular Graph and Reaction Graph on USPTO, including mean and standard deviation from multiple trials with different train/test splits.
Overall
LvG-Specified
Method
ACC
MCC
ACC
CEN
MCC
Molecular Graph
0.948=0.00
0.038=0.003
0.535=0.015
0.418+0.010
0.203+0.001
0.495=000008
Reaction Graph
0.995=0.002
0.004=0.001
0.955=0.012
0.91520.022
0.050=0.011
0.912:0.022
Confidence Intervals. utilize the normal distribution method to calculate the confidence interval (CI) our model using the formula CI + z V where represents the sample mean, 2 is the z-score corresponding to the desired confidence level, s the standard deviation of the sample, and n is the sample size. For a 95% confidence level, the corresponding z-score z = 1.96. We use the results from Tab. 33 to calculate 95% confidence interval. The results are shown in Tab. 35.
Table 35, Confidence interval results [[MinMaxx] for leaving group identification Molecular Graph and Reaction Graph on USPTO. calculated using normal distribution method from mean and standard deviations of multiple trials with different random seeds.
Overall
LvG-Specified
Method
Type
ACC
CEN
MCC
ACC:
CEN
MCC
Molecular Graph
Min
0.949
0.036
0.532
0,419
0.207
0.492
Max
0.951
0.038
0.544
0.427
0.211
0.502
Reaction Graph
Min
0.995
0.001
0.970
0.943
0.034
0,941
Max
0.997
0.003
0.972
0.945
0.036
0,943
H.3. Hyperparameter Selection.
We test several hyperparameters that have the greatest impact on performance, specifically the hidden layer dimension D,- of MPNN and the number of iterations Ti, well the number of iterations T2 for Set2Set. We conduct experiments on the DSPTT-Connition dataset.
Table 36. Top-k accuracies USPTO-Condition under different hyperparameter combinations, including hidden layer dimensions and iterations of GNN and pooling. Each has 3 candidate values.
Hidden Dim D.
MPNN Iters Ti
Pooling Iters 732
Top-11
Top-3t
Top-51
Top-10t
Top-151
200
3
2
0.325
0.434
0.472
0.506
0.518
50
3
2
0.307
0.419
0.456
0.492
0.505
100
3
2
0.315
0.427
0.464
0.500
0.512
200
2
2
0.320
0.433
0.471
0.508
0.520
200
2
0.317
0.428
0.466
0.502
0.514
200
3
0,319
0,430
0.467
0.502
0.514
200
3
3
0.318
0.429
0.465
0.501
0.514
According to Tab. 36, the hyperparameter combination we selected achieves optimal overall performance. Further reducing
the number of iterations for MPNN may enhance the model's top-15 performance, but significantly affects the Top-I performance. We also observe that as the hidden layer dimension increases, the model's performance gradually improves, indicating that our model has scalability. Due to GPU memory limitations, we do not continue to try higher hidden layer dimensions to ensure high training efficiency.
47

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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
H.4. Reaction Condition Prediction
H.4.1. METRIC CALCULATION
In the reaction condition prediction task, the most commonly used metric is the top-k accuracy. Formally speaking, given a ground truth condition
(Ceatalyst: Csolventl: Csalvent2; Creagentl; Creagentt)) calculate top-k aceuracy, allow the model to generate k sets of labels C = {ét c² ..... ... e*), j. Let a represent the correctness of model's prediction on this data sample, and Geategory represent the correctness of model's prediction on this one label category, where category can be one of catalyst, solventl, solvent2, reagentl and reagent2. We have:
{
1, 0,
è (0, otherwise,
a=
(13)
=f 1, 0,
Ccotegory Ceategory: Di E {0, k0, otherwise,
acategory
(14)
And assume the correctness of model data sample i is a², then the overall top-k accuracy on the whole dataset is a = Ene af Na
Σn Na
and the top-k accuracy of a label category is Geategory samples in the test set.
Rentcpory
where N₂ is the number of data Na
important note that the overall accuracy calculation aligns with our intuitive understanding, while the accuracy calculation for each label category is not. This is because it is possible that Coutegory é category where i, {0, 1,..., ......,,), k)) meaning the number of different classification results output by the model is actually less than k. Therefore, this evaluation criterion is stricter than our intuitive understanding. In other words, we do not generate ic labels for each category separately to calculate the top-k accuracy of it.
H.4.2. DETAILED RESULTS
Top-k Accuracy for Each Condition. Following Gao et al. (2018); Wang et al. (2023b), we test the top-k accuracy for the comparison methods in Sec. According Tab. 37 and 38, the model using RG surpasses existing methods on the majority of top-k accuracy, further demonstrating the effectiveness of proposed approach. We also that Parrot shows performance advantages in certain specific condition categories, indicating the effectiveness and potential of large-scale pre-training.
Standard Deviations. We calculated the mean and standard deviation using the results from four different random seeds. The results are shown in Tab, 40.
Statistical Significance Tests. We choose Parrot (Wang et al., 2023b) as the baseline method to calculate the t-values, and the results are shown in Tab. 41.
vols-validation Results. We conduct K-fold cross-validation using the settings in Sec. H.2.3 on the USPTO-Condition and Distachio-Conditton datasets. The results are shown in Tab. 42.
Confidence Intervals. We use the same settings in Sec. H.2.3 on the USPTO-Condition and Pistachio-Condition datasets to calculate confidence intervals. The results are shown in Tab. 43.
Confusion Matrix Analysis. We perform a confusion matrix analysis of the model's classification results in Fig. 18. Due to the uneven data distribution in the dataset, apply row normalization the confusion matrix values, dividing each row's values by the sum of that row. Based on the results, the model can achieve correct classification results for most categories. However, the columns corresponding to the None category and some frequently occurring categories are similarly dark. This is due to the data distribution of the model. From the label distribution of the dataset shown in Sec. G, the number of certain high- high-frequency categories is significantly higher than that of other categories, leading the model to favor predicting the labels of these categories. Although the category weights and label smoothing methods can alleviate these problems, improving performance on these sparse samples still relies on the inclusion of high-quality data.
48

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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Table 37. Detailed results top-k accuracies comparison methods on USPTO-Conditie including performance reaction condition category.
Method
Conditions
Top-1f
Top-31
Top-51
Top-101
Top-151
catalyst
0.9219
0.9219
0,9219
0.9219
0.9219
solvent-1
0.5015
0.6640
0.7055
0.7340
0.7346
solvent-2
0.8130
0.8369
0.8461
0.8525
0.8527
CRM
reagent-1
0.4972
0.6597
0.7402
0.8184
0.8516
reagent-2
0.7622
0.8408
0.8664
0.8876
0.8986
overall
0.2596
0.3771
0.4206
0,4612
0,4717
catalyst
0.9024
0.9024
0,9024
0.9024
0.9024
solvent-1
0.4114
0.5787
0.6295
0.6635
0.6650
solvent-2
0.8093
0.8093
0.8093
0.8093
0.8093
AR-GCN
reagent-1
0.4200
0.5740
0.6667
0,7515
0.7622
reagent-2
0.7486
0.7486
0.7486
0.7486
0.7486
overall
0.1460
0,2374
0,2733
0.3121
0.3261
catalyst
0.9146
0.9146
0,9146
0.9146
0.9146
solvent-1
0.4218
0.6139
0.6542
0.6780
0.6789
solvent-2
0.8110
0.8110
0.8110
0.8110
0.8110
CIMG-Condition
reagent-1
0.4351
0.5685
0.6665
0.7462
0.7598
reagent-2
0.7574
0.7574
0.7574
0.7574
0.7574
overall
0.1839
0,2714
0.3026
0.3391
0.3525
catalyst
0.9250
0.9250
0,9250
0,9250
0,9250
solvent-1
0.5018
0.6858
0.7311
0.7536
0.7543
solvent-2
0.8096
0.8426
0.8521
0,8582
0,8585
Parrot
reagent-1
0.5039
0.6820
0.7629
0.8436
0.8776
reagent-2
0.7648
0.8486
0.8774
0,8998
0.9110
overall
0.2691
0.4035
0.4510
0.4914
0.5031
catalyst
0.9198
0.9198
0,9198
0.9198
0.9198
solvent-1
0.4621
0.6295
0.6583
0.7177
0.7192
solvent-2
0.8120
0.8120
0.8120
0.8120
0.8120
D-MPNN
reagent-1
0.4777
0.6272
0.7449
0.8067
0.8089
reagent-2
0.7702
0.7702
0,7702
0.7702
0.7702
overall
0.1977
0.3000
0.3341
0.3780
0.3924
catalyst
0.9160
0.9160
0.9160
0.9160
0.9160
solvent-1
0.4676
0.6309
0.6767
0.7077
0.7095
solvent-2
0.8089
0.8089
0.8089
0.8089
0.8089
Rxn Hypergraph
reagent-1
0.4761
0.6246
0.7105
0.7844
0.7937
reagent-2
0.7642
0.7642
0.7642
0.7642
0.7642
overall
0.2127
0.3084
0.3447
0.3808
0.3927
catalyst
0.9316
0.9316
0.9316
0.9316
0.9316
solvent-1
0.5429
0.6925
0.7265
0.7475
0.7481
solvent-2
0.8075
0,8564
0.8654
0.8723
0.8725
Reaction Graph
reagent-1
0.5343
0.6982
0.7713
0,8420
0.8729
reagent-2
0.7630
0.8663
0.8928
0.9119
0,9193
overall
0.3246
0.4343
0.4715
0.5061
0,5181
49

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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Table 38. Detailed results of top-k accuracies on Pistachio- Pistachio-Condition, including performance reaction condition calegory.
Method
Conditions
Top-1
Top-3t
Top-51
Top-101
Top-15f
catalyst
0.9943
0.9943
0.9943
0.9943
0.9943
solvent-1
0.5188
0.6954
0.7281
0.7580
0.7584
solvent-2
0.8406
0.9004
0.9077
0.9134
0.9135
CRM
reagent-1
0.4287
0.5990
0.6640
0.7350
0.7643
reagent-2
0.7120
0.8326
0.8603
0.8924
0.9055
overall
0.3300
0.4692
0.5098
0.5476
0.5538
catalyst
0.9951
0.9951
0.9951
0.9951
0.9951
solvent-1
0,5084
0.7667
0.7981
0.8064
0.8065
solvent-2
0.8417
0.9124
0.9160
0.9167
0.9168
Parrot
reagent-1
0.4315
0.6438
0.7236
0.8057
0.8314
reagent-2
0.7341
0.8642
0.8944
0.9225
0.9348
overall
0.3500
0.5323
0.5883
0.6263
0.6301
catalyst
0,9940
0.9940
0.9940
0,9940
0,9940
solvent-1
0.5015
0.6485
0.6871
0.7830
0.7872
solvent-2
0.8614
0.8614
0.8614
0.8614
0.8614
D-MPNN
reagent-1
0.4061
0.5727
0.6844
0.7461
0.7480
reagent-2
0.7491
0.7491
0.7491
0.7491
0.7491
overall
0.2586
0.3422
0.3775
0.4415
0,4693
catalyst
0.9945
0.9945
0.9945
0.9945
0.9945
solvent-1
0.5173
0.6841
0.7466
0.7895
0.7925
solvent-2
0.8619
0.8619
0.8619
0.8619
0.8619
Rxn Hypergraph
reagent-
0,4246
0.5793
0.6608
0.7373
0.7470
reagent-2
0.7520
0.7520
0.7520
0.7520
0.7520
overall
0,2881
0.3671
0,4117
0.4636
0.4851
catalyst
0.9952
0.9952
0.9952
0.9952
0.9952
solvent-1
0.5579
0.7791
0.8032
0.8130
0.8130
solvent-2
0,8539
0,9214
0.9248
0.9261
0.9261
Reaction Graph
reagent-1 0.4884
0.6767
0.7456
0.8123
0.8384
reagent-2 0.7416
0.8733
0.8964
0,9206
0,9319
overall 0.3915
0.5566
0.6039
0.6384
0.6432
Table 39, Correspondence hetween reaction type lahels and reaction types. The class here correspond to the Pistachio-Tyne -ype..
Label
Name
Unrecognized
1
Heteroatom alkylation and arylation
2
Acylation and related processes
3
C-C bond formation
4
Heterocycle formation
5
Protections
6
Deprotections
7
Reductions
8
Oxidations
9
Functional group interconversion (FGI)
10
Functional group addition (FGA)
11
Resolutions
50

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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Table 40. Results for reaction condition prediction of Reaction Graph USPTO-Condition and Pistachio-Conditoon including mean and standard deviation from multiple trials with different random seeds.
Dataset
Top-1
Top-3
Top-5
Top-10
Top-15
USPTO-Condition
0.322+0.002
0.432+0.003
0.469#0.003
0.504=0.003
0.516*000003
Pistachio-Condite
0.391
0.55640.001
0.602+0.001
0.636#0.001
0.641#0.001
Table 41. Results for statistical significance analysis of Reaction Graph reaction condition prediction in Essachio-Conditec using (-test method from the mean and standard deviations of multiple trials with different random seeds. The baseline method is Parrot. The value in the table is logP..
and
Dataset
Top-1
Top-3
Top-5
Top-10
Top-15
USPTO-Condition
11.81
8.69
7.38
6.43
6.43
Pistahio-Conddtae
13.12
11.52
9.90
8.90
9.18
11
11
1
top-1
top-1
top-3
top-3
top-5
10
top-5
top-10
tap-10
top-15
tap-15
3
8
4
5
Figure Radar chart of condition prediction accuracy under various reaction types. The results show that the USPTO-Condition prediction results have stronger correlation with reaction categories than that of Pistachio- -ondiiiin
Catalyst1
Solvent1
Solvent2
Reagent1
Reagent2
Tuo Lobel
Touk
TUE
Catalyst1
Solvent1
Solvent2
Reagent1
Reagent2
Thue Labals
Labres
Thue Labals
Tue
Predicted Labels
Predicted Labels
Predicted Labels
Prudicted Labels
Pradicted Labe's
Figure Normalized confusion matrices of condition prediction results on USPTO Condition dataset, using proposed model architecture with Reaction Graph.
51

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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Table 42. Cross-validation results for reaction condition prediction of Reaction Graph USPTO-Condition and Pistachio-Condition.
including mean and standard deviation from multiple trials with different train/test splits.
Dataset
Top-1
Top-3
Top-5
Top-10
Top-15
USPTO-Condition
0.320=0.003
0.430=0.002
0.467=0.002
0.503+0.002
0.516+0.002
Cettacho-Connditin
0.391=0.002
0.556:0.002
0.603=0.001
0.63640.001
0.641#0.001
Table 43. Confidence interval results ([Min,Max)) for reaction condition prediction of Reaction Graph on USPTO Cenodiooonioo and Pistachio-
Condition dataset, calculated using normal distribution method from mean standard deviations multiple trials with different random seeds.
Dataset
Type
Top-1
Top-3
Top-5
Top-10
Top-15
USPTO-Condition
Min
0.320
0.429
0.466
0.501
0.513
Max
0.324
0.435
0.472
0.507
0.519
Pistachio-Condition
Min
0.390
0.555
0.601
0.635
0.640
Max
0.392
0.557
0.603
0.637
0,642
Table 44. Influence of the output head on model performance. We test the prediction accuracy using different output heads based Molecular Graph on the USPTO-Condition dataset. The results show that CRM output head we use is more effective.
Table 45, Influence the two-stage training on model perfor- mance, using USPTO-Condition. The model based Reaction Graph. The results indicate that the proposed two-stage training strategy significantly improves the top-k accuracy.
Method Cond
Top-11
Top-3t
Top-5t
Top-10t
Top-151
Method Cond
Top-1* 1
Top-31
Top-5t
Top-10f
Top-15
cl
0.922
0.922
0.922
0.922
0.922
cl
0.928
0.928
0.928
0.928
0.928
sl
0.501
0.653
0.712
0.734
0.7347
0.517
0.664
0.702
0.725
0.725
MLP
s2
0.799
0.799
0.799
0.799
0.799
One-
s2 0.799
0.855
0.866
0.873
0.874
Output
rl 0.503
0.638
0.727
0.797
0.811
Stage
rl 0.508
0.685
0.758
0.833
0.869
Head
r2 0.763
0.763
0.763
0.763
0.763
r2 0.7.4
0.866
0.891
0.911
0.920
all
0.249
0.305
0.318
0.387
0,422
all
0,304
0.413
0.449
0.484
0.495
cl 0.926
0.926
0.926
0.926
0.926
0.932
0.932
932
0.932
0.932
sl 0.511
0.656
0.693
0.715
0.716
s1
0.543
0.693
0.727
0.748
0.748
CRM
s2 0,803
0.853
0.863
0.869
0,869
Two-
s2
0.808
0.856
0.865
0.872
0.873
Output
rl 0.500
0.671
0.743
0.821
0.856
Stage
0.534
0.698
0.771
0.842
0.873
Head
r2 0.753
0.861
0.887
0.908
0.917
r2 0.763
0.866
0.893
0.912
0.919
all 0.298
0.400
0.437
0.472
0.484
all
0.325
0.434
0.472
0.506
0.518
Reaction Type Analysis. In addition, we analyze the classification accuracy of different reaction types across the two datasets. The correspondence between the reaction type indices and the names of reaction types is shown in Tab. 39, while results are illustrated Fig. 17. The categories in the USPTO-Condition dataset are classified using the NameRXN tool from (Wang et al., 2023b), while the category labels the Pistachio- Pistachio-Condition dataset are derived from the labels in the Pistachio database.
The accuracy in USPTO-Condition is correlated with the reaction categories, while the correlation is less evident in Pistachio-Condition. This reflects that reaction type distribution has impact model performance. Meanwhile, when increases, the growth of top-k accuracy gradually slows down, suggesting that the choice of top-15 is reasonable. Further increasing the value of does not effectively improve the model's performance and may lead to higher costs for inference.
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Reaction Graph: Towards Reaction-Levd Modeling for Chemical Reactions with 3D Structures
0.50
Top
0.45
Top
0.40
Top
ACC
Top
0.35
Top
0.30
0.25
0.20
0.15
10
20
30
40
50
Epoch
0.50
Top 15
Top 10
0.45
Top 5
0.40
ACC
Top 3
0.35
Top 1
0.30
0.25
0.20
0.15
0
10
20
30
40
50
Epoch
Figure 19. Top-k validation accuracies af two-stage training, where the positions of the optimal results marked with crosses. The upper figure is from the first stage, and the lower figure is from the second stage. The positions where the accuracies change sharply correspond the points where scheduler adjusts learning rate.
H.4.3. ADDITIONAL ABLATION
Output Head. Following Gao et al. (2018), use the CRM output head. It autoregressivelly output conditions, and significantly enhances the performance. In contrast, the MLP outputs all conditions simultaneously. which results in a loss of overall accuracy. To demonstrate the effectiveness of our model architecture design, we eliminate additional influencing factors, and test the model performance the MLP and the CRM output head under the Molecular Graph.
Based on the results shown in Tab. 44, the CRM output head effectively improves the model's 's overall top-k accuracy. However, for each type of reaction condition, the model using the ML. output head achieves accuracy comparable that of the CRM. This indicates that, compared to MLP, CRM can fully consider the previous prediction results when provide the next prediction, allowing it to generate more suitable combinations of reaction conditions.
Training Strategy. We propose a two-stage training strategy, while also incorporating the technique of label smoothing. We test the effects of these two factors on model performance one experiment. Specifically, we use loss function that includes label smoothing and class weight to train the RG model on USPTO-Condition dataset and observe changes in validation top-k accuracy.
According to the results in Tab. 19, the proposed two-stage training strategy effectively enhances the model's performance. Without two-stage training, the timing of the best performance differs for each top-k metric. Especially for the top-15 accuracy, it appears overfitted after reaching its peak. By introducing two-stage training, the timing of the best performance for top-1 to top-15 accuracy is consistent.
Comparing the results in Fig. 19 and Tab. 45 reveals that the inclusion of label smoothing results more imbalance in top-k performance. Therefore, we ultimately do label smoothing on USPTO-Condition.
53

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dataset, indicating a Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
H.4.4. MERGING DATASET
In this paper, we focus on proposing novel chemical reaction representation, which can enhance model performance within fixed data volume. Exploring the effect of training with large-scale data is another interesting research topic, which is not the focus of this paper. Nevertheless, we conduct additional experiments to explore whether combining the USPTO and Pistachio datasets can provide valuable insights. Since the reaction category labels between the two datasets are not completely consistent, we select reactions from Pistachio that match the categories in USPTO. We perform joint training using the merged dataset.
Table 46. Reaction classification results before and after mixing USPTO with Pistachio, on the test set original USPTO-Condition and the OOD test set of Pistachio.
USPTO-Condition Test Set
Pistachio-OOD Test Set
Method
Top-11
Top-31
Top-5t
Top-107
Top-15t
Top-1
Top-3t
Top-5t
Top-10f
Top-151
w/o Pistachio
0.325
0.434
0.472
0.506
0.518
0.177
0.235
0.260
0.284
0.292
W Pistachio
0.323
0.436
0,470
0.500
0.511
0.275
0.455
0.517
0.567
0.578
The results on the USPTO test set are as the left side of Tab. 46. Mixing the two datasets for training does not improve the model's performance on single dataset. This may result from their significant differences in data distribution. Although USPTO and Pistachio are large in scale, their sparse annotations still cannot cover the diverse chemical space.
We further evaluate the effect of mixed data training on model generalization. Specifically, we extract subset of data from Pistachio serve as the test set. This subset is out-of-distribution (OOD), which can reflect the model's generalization performance. The results the Pistachio-OOD test set, while keeping the performance of model on the original benefit for generalization.
the right side of Tab. 46. Training with mixed data significantly improved performance on
H.5. Reaction Yield Prediction
H.5.1. METRIC CALCULATION
In yield prediction task, in addition to the commonly used R2 metric, Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) are also frequently utilized. Assuming the ground truth yield of i-th data sample is the model's output
mean is Ay.. then the MAE of the prediction result Σ B
2. "y RMSE is Na Am.) and R is
Na
N₂
E, "N D)
We also used the Negative Log-Likelihood (NLL) to evaluate the fitting performance of the model that incorporates uncertainty and assess the reasonableness of its output variance. The specific calculation method for NLL as follows:
No
(y) Mgy )2
1
NLL Σ
+ log 1og(2
(15)
20T2 3/ 2
(#) (w:- as Calibration, and the second term log(2To7)) as Tolerance. Additionally, 20
where we call the first term
follow (Schwaller et al., 2021b; Kwon et al., 2022b), we also evaluate the standard deviation of the above metries under ten repetitions of the experiment.
H.5.2. DETAILED RESULTS
Standard Deviations and Cross Validation Results. Following Schwaller et al. (2021b), additionally test the MAE and RMS., as well as the standard deviation of the results. We also introduce more baselines. Specifically, on HTE datasets, we introduce traditional methods such as DFT and MFF. We also compare the performance of the model using one-hot labels of molecules (Onehot). Additionally, we include the performance of T5Chem, as well as the SOTA model RMVP based on large-scale data pre- pre-train On USPTO- -ield, we introduce HRP as our extra baselines. Since we cannot determine whether T5Chem uses average or optimal results, we exclude it from comparison.
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Table 47. Detailed HTE yield prediction results with more comparison methods, using MAE, RMSE and A metries.
Models
B-H
S-M
Test1
Test2
Test3
Test4
DFT
0.92
0.8
0.77
0.64
0.54
Onehot
0.89
0.69
0.67
0.49
0.49
MFF
0.93
0.85
0.71
0.64
0.18
Y-B
3.99+0.15
8.13+0.34
1.35+0.10
7.27=0.72
9.13+0.75
13.67+1.07 .007
6.01
12.07=0.46
11.4440.34
11.14#1.27
14.28+0.82
19.68+1.40
0.95+0.01
0.82+0.01
0.84+0.01
0.84#0.03
0.75+0.04
0.49#0.05
Y-B-A
3.09+0. 12
6.60+0.27
7.02+0.76
6,59+0.33
11.05=0.95
18.4240.62
4.80+0.26
10.52+0.48
11,76+1 .40
9.89+0.74
18. 18.04+1. 1.40
24.28+0049
0.97+0.01
0.86+0.01
0.81
0.87=0.02
0.59+0.07
0.1640.03
DRFP
4.03+0.13
7.00+0.20
8. 8.16+0.07
7.69+0.10
8.92+0.06
12.42+0.07
6.0840.28
11 11.00=0.40
11.9940.10 10
11.26#0.16
15.04+0.06
18.7640.11
0.95+0.01
0.85+0.01
0.81#0.01
0.83+0.00
0.71+0.01
0.49#0.00
T5
0.97
0.86
0.81
0.91
0.79
0.63
Egret
4.47+0.23
7.00+0.20
6.97+0.47
6.31+0.37
10.40+0.71
12.3740.83
6.61+0.30
11,00=0.40
11.0330.64
9.41#0.98
16.58+1.33
17.88+0.99
0.94
0.85+0.01
0.8440.01
0.88#0.03
0.65+0.06
0.54+0.06
UGNN
2.92+0.06
6.12+0.22
8.08+0.83
6.30#0.65
8.99+0.31
13.1910.75
0.43+0.09
9.47+0.46
13.75+1.18
9,48+1.03
14.94+0.62
18.7740.57
0.97+0.01
0.89+0.01
0.7440.04
0.88+0.03
0.72+0.02
0.50+0.03
RMVP
5.13+0.23
7.37+0.21
9.60+0.69
8.02+1.23
10.74+0.72
13.59+1
7.52+0.49
10.79+0.25
13.33+0.63
11.18
15.38+1.20
18. 18.16414 40
0.9240.01
0.85+0.01
0.76+0.02
0.83+0.05
0.70+0.05
0.53+0.08
RMVP (Pretrained)
3.11#0.007
6.59+0.20
1.28+0.12
6.0820.15
8.97+0.49
10.6140.66
4.63+0.11
10.37+0.42
10.77+0.14
8.72+0.18
12.79+0.77
14.62+0.93
0.97+0.01
0.86+0.01
0.84+0.01
0.90+0.01
0.79+0.03
0.69+0.04
D-MPNN
4.72+0.08
7.96+0.21
8.20+0.28
7.81+0.81
9.04+0.26
12.25+0.23
6.41+0.15
10.84+0.44
12,09+1.00 .00
11.21+1.10
14.46+0.60
17.7640.63
0.94+0.01
0.85+0.01
0.80+0.03
0.82+0.03
0.73+0.02
0.55+0.03
Rxn Hypergraph
3.44+0.04
7.83+0.31
8.44+0.30
7.20+0.52
9.01+0.21
11 11.6240.85
5.45+0.08
11.06+0.46
11.6540.49
11.1840.60
14, 14.98+0.48
17.6540.42
0.96+0.01
0.85+0.01
0.81+0.01
0.83+0.02
0.71+0.02
0.56+0.02
RG
3.07+0.06
6.08+0.26
7.84+0.20
6.23+0.45
8.64+0.35
10.8141 11.37
4.64+0.09
9.32+0.47
12.05+0.30
9.20+0.71
13.50+0.61
15.05+1 40
0.9740.01
0.89+0.01
0.80+0.01
0.88+0.02
0.76+0.02
0.68+0.06
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
11
11
RMSE
RMSE
10
2
MAE
MAE
R2
R2
9
9
3
4
6
6
Figure Radar chart of yield prediction metrics under various reaction types. The results show strong correlation between the accuracy of yield prediction and reaction types in the USPTO-Yiee -ield..
Based on the results shown in Tab. 47, RG remains highly competitive. Similarly, as shown in Tab. 48, on USPTO- Yield, RG remains at a leading level. Compared with non-pretrained models and methods, whether based on neural networks or theoretical calculations, most our performance
forefront. Compared to RMVP pre-trained on large-scale datasets, we achieve similar R² scores by using only the original training samples of over two thousand. However, on the more challenging Test4 dataset, our model exhibits significant variance. In ten repeated experiments, RG achieves maximum Ri² score of 0.77, while the minimum R² score is only 0.58. This is due to the small dataset scale and the structure of GNNs. For simpler fingerprint-based models, they have smaller training variance than GNN-based or Transformer- methods.
Table 48, Regression accuracy (R on USPTO-Yies dataset.
Table 49, Results for statistical significance analysis of Reaction Graph on reaction yield prediction task. The bascline method is UGNN.
Model
Gram
Subgram
Metrics
BH
BH1
BH2
BH3
BH4
SM
Gram
Subgram
DRFP
0.130
0.197
-logP
0.69
8.74
0.69
5.52
6.69
0.69
3.27
7.84
Yield-Bert
0.117
0.195
TSChem
0.116
0.202
Table 50. Confidence interval results Max)) for reaction yield prediction Reaction Graph.
Egret
0.128
0.206
UGNN
0.117
0.190
HRP
0.129
0.200
Metrics
Bound
BH
BH1
BH2
BH3
BH4
SM
Gram
Subgram
D-MPNN
0.125
0.202
Rxn Hypergraph
0.118
0.196
R²
Min
0.96
0.79
0.87
0.75
0.64
0.88
0.119
0.208
RG
0.129
0.216
Max
0.98
0.81
0.89
0.77
0.72
0.90
0.131
0.214
Statistical Significance Tests. We use UGNN (Kwon et al., 2022b) as the baseline method in the t-test, and the results are shown in Tab. 49.
Confidence Intervals. We use the settings in Sec. H.2.3 and the result Tab. 47 to calculate confidence intervals. The results are shown in Tab. 50.
Reaction Type Analysis. We analyze the regression performance for different reaction types in the USPTO-YL Yield dataset, shown in Fig. 20. We classify the data samples in USPTO- Yield using classifier trained on Pistachio- -ypee. The results show strong correlation between regression performance and reaction type, with noticeable differences in the Gram and Subgram datasets. For (5) Protections and (10) FGA reactions, the performance of both models is poor. However, when comparing R² metrics with RMSE and MAE, we find that the poor R² for (5) and (10) are due to the complexity of yield distribution. The yield variances of (5) and (10) are significantly greater than that of other reaction types. Similar situations can also be observed for (3) C-C bond formation and (6) Deprotections on the Gram dataset.
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
H.6. Reaction Classification
H.6.1. METRIC CALCULATION
We used ACC, CEN, MCC and FI Score evaluation metrics for reaction classification. In implementation, we used the library functions from PyCM to compute these metrics.
Specifically, we refer to the calculation method in Schwaller et al. (2021a). Let C' be the number of classes, and class labels are from to C. M [0, _jcxe is the confusion matrix where the element M represents the number of instances that belong to the true class but are predicted to be in class j. Mij can be calculated using the following formula:
N
Maj- - Σ 8(y,, 8(E,, j),
k=1
where N is the total number of samples, y/ is the true label of the k-th sample, in. is the predicted label of the k-th sample, and ((a b) is the Kronecker delta function defined as:
[1 i b
{o i
8(a, b)
From the confusion matrix, the following metries can be calculated:
Accuracy (ACC/Micro F1). The accuracy is the ratio of the number of correct predictions to the total number of predictions, It is calculated using the following formula:
Σ M,
Accuracy
N
Macro F1. The macro F1 score is the unweighted average of the F1 scores of each class. It is calculated using the following formula:
Precision = Mi.
Σe Mij
Myj
Recall; Σ M,,
F1,- =2 Precision, Recall
Precision, + Recall,
Confusion Entropy (CEN), The confusion entropy is a measure of the uncertainty in the confusion matrix. calculated using the following formula:
Mij
Mi
pd
Pij DE (Mi, + MR.i)
D (Mi, + Ma.s)
CEN, = Σ
(P),)) + Phi Pog1002( (Pks)) (P/N1082(C-1)
Pj DE (Mix + MR.s)
2 Ma.1
CEN P,CCN,,
j=1
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Matthews Correlation Coefficient (MCC). The Matthews correlation coefficient is usually used in binary classification problems. However, it can be extended to multi-class classification problems using the following formula:
cov(X, E
(Mr,MRR - MM,,Me,,)
idk==
c
cov(X,X) =
Σ
Σ
Mj,
Σ
Mi,
k,i=1,
c
cov(Y, Σ
Σ Mis
Σ
Ma.1
k,E=1,
Cov(X,
MCC
Veov(X, X) Cov(Y,
H.6.2. DETAILED RESULTS
Additional Baselines. additionally introduce HRP, which also tests the performance USPTO-TPL, for comparison. The result is shown in Tab. 51. Reaction Graph demonstrates superior performance all metrics.
Table 51. USPTO-TPL results.
Pistachio
USPTO
Mismatch
Models
ACC
CEN
MCC
Thu Labels
True Labals
DRFP
0.977
0.011
0.977
RXNFP
0.989
0.006
0.989
T5Chem
0.995
0.003
0.995
HRP
0.991
0.005
0.990
Rxn Hypergraph
0.990
0.005
0.990
Labels
Labels
D-MPNN
0.997
0.001
0.997
Reaction Graph
0.999
0.001
0.999
Figure 21. Scaled confusion matrices reaction classification results.
Standard Deviations. We calculated the mean and standard deviation using the results from four different random seeds. The results are shown in Tab. 52.
Table 52, Results reaction classification of Reaction Graph on USPTO-TPL and Pistachio Type dataset, including mean and standard deviation from multiple trials with different random seeds.
USPTO-TPL
Pistachio-Type
Metrics
ACC
CEN
MCC
ACC
CEN
MCC
MtansStd
0.999
0.001
0.001 0.001
0.999 0.001
0.986 0.002
0.026
0.004
0.985 + 0.003
Statistical Significance Tests. We choose D-MPNN (Heid & Green, 2021) as baseline to calculate the t-values. The results are shown Tab. 53.
Table 53. Results for statistical significance analysis of Reaction Graph on reaction classification on USPTO-TP and Pistachio-Tyre Type, using t-test method from the mean and standard deviations multiple trials with different random seeds. The baseline D-MPNN.
USPTO-TPL
Pistachio- Estachio-Type
Metries
ACC
MCC
ACC
MCC
Plog
4.27
4.27
4.27
3.80
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Cross-validation Results. We conduct cross-validation using the settings in Sec. H.2.3 on USPTO-TPL and Pistachio-Type. The results are shown in Tab. 54.
Table 54. Cross-validation results for reaction classification of Reaction Graph on USPTO-TPL and Pistachio- Type dataset, including mean and standard deviation of ACC, MCC and CEN metrics from multiple trials with different train/test splits.
USPTO-IPL
Pistachio-Type
Metrics
ACC
CEN
MCC
ACC
CEN
MCC
StantSid
0,999 0.001
0.001 = 0.001
0,999 1 0.001
0.987 = 0.002
0.025 + 0.003
0.986 # 0.002
Confidence Intervals. We use the same settings in Sec. H.2.3 on the USPTO-TPL and Pistachio- Type to calculate confidence intervals. The results are shown in Tab. 55.
Table 55. Confidence interval results Max]) for reaction classification of Reaction Graph on USPTO-TPL. and Pistachio-Tyre datasct, calculated using normal distribution method from mean and standard deviations multiple trials with different random seeds.
USPTO-TPL
Fistachio-Type
Metries
Type
ACC
CEN
MCC
ACC
CEN
MCC
Sta
Min
0,998
0.000
0.998
0.984
0.022
0.982
Max
1.000
0.002
1.000
0.988
0.030
0,988
Confusion Matrix Analysis. For USPTO-TPL, we map the 1,000 templates into 12 reaction types of Pistachio, making it easier to assess the model's performance. We first use the reaction classification model trained on Pistachio- to predict the types of chemical reactions in USPTO-TPL, Then, we count the frequency of each Pistachio type corresponding to each USPTO-TPL type, selecting the most frequent as the mapped type.
The results are shown in Fig. 21. The reaction type mapping results are shown in the bitmap on the right of the figure, which contains 1,000 points. Each pixel representing a USPTO-TPL template, with values indicating the proportion of predicted types other than the most frequent type. The misclassification rate for all templates does not exceed 0.5, and most of them have misclassification rates close to 0, demonstrating the validity of our mapping and the generalization of RG.
Since both datasets exhibit high classification accuracy, we perform row normalization and amplification in the confusion matrix, with the amplification function V = 1002, According to the result, the misclassification rate of U Unknown type is significantly higher than other types. This is because the boundaries for Unknown are the most ambiguous.
Dimensionality Reduction Visualization. We perform dimensionality reduction visualization on the reaction representation vector r. This experiment aim observe the distribution of chemical reactions, as well as exploring the relationship between and chemical properties. We use three methods for dimensionality reduction visualization: TMAP, UMAP, and t-SNE.
The result is shown in Fig. 22. Based on the results, we can see clear correlation between the dimensionality reduction results and reaction types. Additionally, the results indicate a connection between the reaction representation vectors and the number of H donors. This indicates that the reaction representation vectors extracted by the Reaction Graph implicitly contain high- gigh--imensional features of chemical properties.
H.7. Architecture Module Selection
H.7.1. EDGE EMBEDDING
We use RBF kernel to calculate edge length embedding. RBF can effectively capture the non-linear relationships between distance and molecular property. This method lifts the scalar edge lengths into a high-dimensional vector that can be more easily utilized by machine learning models, focus more on local structural pattern, and produces smooth mappings which help models to capture variations in continuous data. These advantages make RBF kernel suitable for tasks involving local continuous spatial relationships, such in molecular structures where edge lengths indicate bond distances.
To demonstrate the efficiency of RBF kernel embedding, we conduct experiments to compare it with different embedding methods, using USPTO-Condition dataset. We use linear projection and discretization embedding as baselines. Specifically, linear projection directly inputs the edge lengths into a fully connected layer to obtain embeddings. Discretization embedding divides the edge lengths into multiple bins to obtain one-hot embeddings. The embeddings are then concatenated with the edge feature vectors. Detailed bin division method discussed in Sec. D.I.1.
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Reaction Type
Number of H Donors
TMAP
21
10
11
UMAP
14
Gua
0355
Out
Ckas
Came5
Clis-10
Class
t-SNE
03
-75
-100
-25 25
Figure 22, The dimensionality reduction visualization results of the reaction representation vectors extracted from the Reaction Graph. We utilize three unsupervised dimensionality reduction methods: TMAP, UMAP, and t-SNE, The figure shows the relationship between the dimensionality reduction results and reaction types, well as the number of H donors.
60

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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Table 56. Influence of different edge length embedding methods model's performance, using USPTO-CCodiiig dataset.
Method
Top-11
Top-31
Top-51
Top-101
Top-151
Linear Projection Embedding
0.3173
0,4303
0.4684
0.5048
0.5164
Discretization Embedding
0.3101
0,4201
0.4569
0.4926
0.5046
RBF kernel Embedding (ours)
0.3246
0.4343
0.4715
0.5061
0.5181
As shown in the Tab. 56, RBF kernel outperforms other embedding methods, demonstrating its efficiency. Directly using linear mapping may cause the distance feature to lose its non-linearity. Meanwhile, using discrete features easily lead to information loss.
H.7.2. BERTEX-EDGE INTEGRATION
We conduct experiment to tested different vertex-edge integration methods to demonstrate the efficiency of our chosen approach. The baselines include Bond Vector Message Passing Model following PaiNN (Schütt et al., 2021), the Bond Angle Message Passing Model following DimeNet (Gasteiger et al., 2020), the 3D Graph Transformer following UniMol (Zhou al., 2023), EGAT (Monninger al., 2023) and GINE (Hu et al., 2019). Our method follows UGNN (Kwon et al., 2022b) and MPNN (Gilmer et al., 2017)
Table 57. Influence of different vertex-edge integration methods on condition prediction task, using USPTO-Condinne dataset.
Method
Top-1f
Top-31
Top-5t
Top-101
Top-15t
Bond Vector Model
0.290
0.403
0.439
0.475
0.488
Bond Angle Model
0.318
0.429
0.466
0.502
0.514
3D Graph Transformer EGAT GINE
0.300
0.405
0.440
0.469
0.477
0.304
0,417
0.453
0.490
0.502
0.299
0.406
0.441
0.475
0.487
Ours
0.325
0.434
0.472
0.506
0.518
The results in Tab. 57 show that our method is superior other methods, demonstrating its efficiency.
H.7.3. AGGREGATION
Influence of Attention Mechanism and LSTM. Effectively identifying and leveraging the chemical reaction mechanism to understand and reason about reactions is challenging. In our work, we use an attention mechanism to adaptively capture the most important cues for reaction modeling. However, since these cues are not always easy to identify in one time, we employ an LSTM to progressively and interactively discover them. shown in Fig. 3, the attention-based aggregation module with L.STM accurately locates the reaction center on Reaction Graph.
We conduct experiments to demonstrate the roles of attention and LSTM. Specifically, compare the performance of our method with the aggregation module without using attention and LSTM. We USPTO-Condition dataset to evaluate the model's performance. For aggregation module without both attention and LSTM, we use SumPooling. For the attention aggregation module without LSTM, we set the number of iterations for Se12Set to 1, which is equivalent to not using LSTM.
Table 58, Influence of attention mechanism and LSTM on model performance, using USPTO-Condition dataset.
Method
Top-11
Top-3
Top-5t
Top-10
Top-15t
w/o Attention & w/o LSTM
0.3159
0.4276
0.4642
0.4983
0.5110
w/ Attention & w/o LSTM
0.3187
0.4303
0.4670
0.5018
0.5136
w/ Attention & w/ LSTM
0.3246
0.4343
0.4715
0.5061
0.5181
The result in the table above shows that the attention mechanism and LSTM contributes to the performance.

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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Set2Set vs. Set Transformer. We Set2Set capture the global representation of Reaction Graph by aggregating node features. We compare the ability of Set2Set and Set Transformer (lee et al., 2019) for capturing the global representation of a Reaction Graph. The detailed implementation of Set Transformer can be found in Sec. D.
Table 59. Influence of Set Transformer and Set2Set on condition prediction result and inference time, using USPTO-Condition dataset.
Method
Top-1t
Top-3t
Top-5t
Top-107
Top-157
Inference Time
Set Transformer
0.2940
0,4079
0.4471
0.4847
0.4968
6min Is
Set2Sct
0.3246
0.4343
0.4715
0.5061
0.5181
2min 36s
The results indicate that, when used as an aggregation module, Set2Set surpasses the Set Transformer by 5% to 10% in performance and is also more computationally efficient.
We further analyze the reasons for the unsatisfactory performance of the Set Transformer in the reaction property prediction task. We summarize two points:
1. The set message passing in the Set Transformer disrupts the topological constraints of the graph, leading to the loss of structural information.
2. The seed vector in the Set Transformer is fixed, whereas the adaptive seed vector derived from the graph in Set2Set is more advantageous.
We demonstrate these points through experiments. The result is shown in Tab. 60. Specifically, we gradually reduce the number of layers in the Set Transformer Encoder to observe whether the set message passing has negative effect on graph information extraction. Additionally, We compare the performance of the Set Transformer Decoder (without adaptive seed vector) and the Set2Set(with adaptive seed cector) to observe whether the adaptive seed vector contributes to the model's performance. We use subset from OSPTTO-Condtton for training efficiency.
Table 60. The influence of set message passing and adaptive seed vector on model's performance. Using a 1/8 subset of USPTO-Comdition
for training efficiency.
Method
Set Message Passing
Adaptive Seed Vector
ACC1
Set Transformer
2
X
0.1597
Set Transformer
1
0.1634
X
Set Transformer
0
0.1700
Set2Set (ours)
0.1773
According to the results, with the set message passing reduces, the performance gradually improves. This result indicates that set message passing exhibits a negative effect when extracting features from the Reaction Graph. Meanwhile, adaptive seed vector achieves better performance than directly using a fixed seed vector, validating its effectiveness.
H.8. Graph Representation
1. 3D INFORMATION
Different 3D Representations. We demonstrate the efficiency of our 3D representation design through experiments. Reaction Graph includes bond length and bond angle information, where bond angle is implicitly conveyed by angular edge. We compare Reaction Graph with methods that use explicit bond angle, pairwise distance, atomic coordinates, equivariant neural networks, and torsion angles.
The method using explicit bond angle is implemented by directional message passing module from DimeNet (Gasteiger et al., 2020). Pairwise distance is implemented by UniMol (Zhou et al., 2023). The atomic coordinate method is implemented by concatenating the atomic XYZ coordinate with the atomic attributes. The equivariant neural network is implemented by replacing the length information in Reaction Graph with vector, and use PaiNN (Schütt et al., 2021) as our vertex-edge integration module. The torsion angle is implemented by extending the angular edge in Reaction Graph to torsion angular edge, and details can found Sec. D and Sec. E.
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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Table 61. Influence of different 3D representation methods Reaction Graph in the task of predicting reaction conditions, using USPTO-
Condition dataset.
Method
Top-1f
Top-31
Top-51
Top-101
Top-15t
Without 3D Information
0,3133 0.4248 0,4613
0.4961
0,5094
Bond Length
0.3165
0.4251 0.4616
0.4971
0.5090
Bond Length Explicit Bond Angle
0.3179 0.4290
0.4656
0.5018
0.5146
Pairwise Distance
0.2955 0.4054 0.4397
0.4689
0.4766
Atom Coordinate
0.3123 0.4243 0.4628
0.4987
0,5111
Equivariant Neural Networks
0.2899 0,4026 0,4390
0.4749
0,4879
Bond Length Torsion Angular Edge
0.3022 0.4087
0.4467
0.4821
0.4935
Bond Length Angular Edge (ours)
0.3246 0.4343 0.4715
0.5061
0.5181
As shown in the Tab. 61, Bond Length + Angular Edge achieves the best performance. This demonstrates the effectiveness of our approach.
3D Information on Angular Edge. We recognize that the role of the angular edge may not only be to provide angular information but also to serve as shorteut for message passing. Therefore, we conduct an additional ablation experiments.
To analyze the role of the angular edge 3D prior, we set it's length to O. This approach retains the connection of the angular edge to two-hop neighbors, thus also serving shorteut. To analyze the effect of offering a shorteut by angular edge, we remove angular edge from Reaction Graph.
Table 62. Impact of connection and length (for 3D modeling) Angular Edge. Angular Edge is mainly used for providing 3D information. instcad of providing shortcut for message passing.
Method
Top-11
Top-31
Top-51
Top-101
Top-151
w/o connection w/o length for 3D modeling
0.3165
0.4251
0,4616
0.4971
0.5090
w/ connection & w/o length for 3D modeling
0.3150
0.4259
0.4637
0.4991
0.5107
w/ connection & w/ length for 3D modeling (ours)
0.3246
0.4343
0.4715
0.5061
0.5181
The experimental results are shown in the Tab. 62. Based on the results, for angular edge, the role of being shortcut is far less significant than its provision of 3D priors. This also demonstrates that angular edge effectively provides 3D bond angle information.
Adding 3D Information to Other Graphs. To explore whether 3D information can be effective in other methods, we attempt to incorporate bond length information into the D-MPNN and Rxn Hypergraph. The detailed implementation can be found in Sec. 1.1.3 and Sec. D.1.2.
We test the reaction condition prediction performance of D-MPNN and Rxn Hypergraph USPTO-Condition before and after adding 3D information, and the results are shown in Tab. 63.
Table 63. Influence of 3D bond length information on D-MPNN and Rxn Hypergraph's 's performance in reaction condition prediction task, dataset.
using
Method
3D Info.
Top-11
Top-31
Top-5f
Top-101
Top-15f
D-MPNN
w/o 3D
0.1977
0,3000
0.3341
0.3780
0.3924
D-MPNN
w 3D
0.2030
0.3059
0.3410
0.3830
0.3971
Rxn Hypergraph
w/o 3D
0.2127
0.3084
0.3447
0.3808
0.3927
Rxn Hypergraph w/ 3D
0.2149
0.3113
0.3464
0.3825
0.3949
According to the result, the incorporation of 3D information effectively improved the top-k performance of D-MPNN and Rxn Hypergraph. The average top-k performance is increased by 1.8% and 0.7% for D-MPNN and Rxn Hypergraph relatively, and the Top-1 accuracy is increased by 2.7% for D-MPNN, demonstrating the efficiency of 3D structural priors in reaction property prediction tasks.
63

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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
3D Information Accuracy. The accuracy of 3D information affects model performance. To evaluate the impact of 3D accurate method (as computational efficieney of DFT is too low), use alternative
accuracy, instead of using approach. Specifically, we reduce the 3D accuracy by adding normal noise to original MMFF calculation results. The larger the noise, the lower the accuracy. The results are shown in Tab. 64. The results show that the accuracy of 3D information does affect the performance of the model. As the noise level increases, the model's performance gradually declines.
Table 64, The influence 3D accuracy on model performance in condition prediction task. The noise level reflects the accuracy of 3D information. The smaller the noise, the higher the 3D accuracy. We use 1/8 of the USPTO-Condition dataset.
Noise Level
Top-1
Top-3
Top-5
Top-10
Top-15
0.0
0.1773
0.2749
0.3146
0.3534
0.3670
0.05
0.1738
0.2650
0.3044
0.3443
0.3580
0.1
0.1695
0.2633
0.2990
0.3420
0.3570
0.2
0.1635
0.2643
0.2986
0.3397
0.3556
0.4
0.1518
0,2510
0.2940
0.3346
0.3486
Impact of Label Quality on 3D. We investigate the relationship between label quality and 3D model performance. We use the degree of label sparsity as measure of label quality. Specifically, separate Pistachio-Conditio into multiple scaffolds of different sizes. The size of scaffold can reflect the degree of label sparsity. Specifically, the test set is consistent across all scaffolds. From the first to the sixth group, the training set size halves each time, reducing from full size to 1/32 of the original.
Table 65. The influence of label sparsity model performance in condition prediction task. The degree of label sparsity can be reflected by the size of scaffold.
Scaffold Ratio
1/2
1/4
1/8
1/16
1/32
w/o 3D
0.3852 0.3915
0.3503
0.3116
0.2716
0.2210
0.1907
3D
0.3550
0.3146
0.2768
0.2244
0.1857
The result is shown in Tab. 65. The model's performance decreases with the increase of label sparsity. In the smallest scaffold, the effect of 3D information is affected by label sparsity. Combining the results of 3D accuracy and label sparsity, label quality has greater impact on performance than 3D accuracy. The quality of the labels acts as a bottleneck, limiting the 3D information further enhance model performance.
H.8.2. REACTION INFORMATION
Impact of Reaction Edge. We attempt incorporate the proposed reaction edge into other model architectures. Specifically, we test the Bond Vector Model, Bond Angle Model, EGAT and GINE
Table 66. Influence of the proposed reaction information (reaction edge) on the accuracies of different methods, on USPTO-Condition datasct.
Model
Reaction Information
Top-1f
Top-3t
Top-51
Top-10f
Top-15f
Architecture
X
0.282
0.393
0.432
0.468
0.481
Bond Vector Model (Schütt al., 2021)
<
0.290
0.403
0.439
0.475
0.488
X
0.307
0.420
0.456
0.493
0.505
Bond Angle Model (Gasteiger et al., 2020)
<
0.318
0.429
0.466
0.502
0.514
X
0.297
0.406
0.442
0.478
0.489
EGAT (Monninger al., 2023)
0.304
0.417
0.453
0.490
0.502
X
0.289
0.396
0.432
0.468
0.481
GINE (lu al., 2019)
0.299
0.406
0.441
0.475
0.487
The results in Tab. 66 show that reaction information improves the top-k accuracy of all methods. This demonstrates the broad effectiveness of integrating reaction information.
64

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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Rxn Hypergraph with Reaction Hypernode
To further demonstrate the effectiveness of reaction information, we incorporate reaction information into other graph representations. Specifically, we can model the interactions between reactants and products by adding another hypernode in the Rxn Hypergraph. Details can be found in Sec. D.
Table 67. Influence of an additional Reaction Hypernode in Rxn Hypergraph across various tasks.
Cond (T11)
Yield (R21)
Type (ACC1)
Method
U-C
P-C
BH
BH1
BH2
BH3
BH4
SM
Gram
Subgram
U-T
P-T
w/o Hypernode
0.213
0.288
0.96
0.81
0.83
0.71
0.56
0.85
0.118
0.196
0.954
0.911
with Hypemode
0,211
0.289
0.96
0.82
0.81
0.75
0.57
0.86
0.112
0.187
0.984
0.936
Reaction Graph (ours)
0.324
0.392
0.97
0.80
0.88
0.76
0.68
0.89
0.129
0.216
0.999
0.987
To test the performance of this idea, we conduct experiments on various tasks using the hypernode method. The results are presented in Tab. 67.
According to the result, the hypernode method shows improvement in reaction classification by increasing the accuracy on USPTO-TPL. by 3% and that of Pistachio-TTe Type by 2.5%, while it has slight impact on condition and yield prediction. This may be because reaction classification is relatively intuitive, while condition and yield prediction are complex. To improve the performance of condition and yield prediction, more accurate interaction modeling (e.g., Reaction Graph) is needed. Reaction Graph surpasses the performance of the hypernode method, demonstrating its efficiency in interaction modeling.
I. Toolkits
We use a series of tools for chemical property calculations, data analysis, and Reaction Rraph construction. We have conducted a brief comparison and summary of these tools, and the results are in Tab. 68.
I.1. Calculate/Optimize 3D Conformation
ETKDG, UFF, MMFF, and DFT are algorithms for calculating optimizing 3D conformations. ETKDG and MMFF are accurate for small organic molecules but less effective for larger ones and metal complexes. UFF is more suitable for handling metal complexes. DFT, based on quantum chemistry, provides high precision for various compounds but is inefficient. In this paper, we use large real-world chemical databases, USPTO and Pistachio, with total millions of entries and complex molecular distributions. We find that even with the simplest basis sets, DFT is too time-consuming. Hence, we initialize conformations using ETKDG and then optimize them with MMFF94. For molecules that MMFF94 cannot handle (e.g., involving heavy metals), we use UFF for conformation optimization.
Chemical toolkits such as RDKit and OpenBabel provide implementations of the MMFF and UFF algorithms, with RDKit offering an easy way to initialize conformations using ETKDG. As for calculations like DFT, chemical toolkits such as Psi4 and PySCF provide relevant functionalities. These tools all offer interfaces in Python.
1.2. Predict Atom Mapping
RXNMapper and NameRXN are tools for atomic mapping. RXNMapper is open-source and based on an unsupervised language model, capable of providing efficient and accurate predictions. NameRXN is a commercial rule-based tool, offering highly reliable results, though some reactions fall outside its rule coverage. After evaluating the mapping performance on the USPTO dataset, we choose RXNMapper because it demonstrates high stability and most of predictions are accurate.
I.3. Classify Reaction
NameRXN is also a tool for reaction classification. In this paper, the labels of the Pistachio dataset are annotated using NameRXN.
65

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Reaction Graph: Towards Reaction-Level Modeling for Chemical Reactions with 3D Structures
Table 68. Comparison between Data Preprocessing Tools, including functionality, precision, time efficiency, application scope, and
limitations.
Tools
Function
Precision
Efficiency
Application Scope
Limitation
ETKDG
CalculatsOOptimize 3D Conformation
Low
High
Small Organic Molecules
Fail Some Metal-Comples
UFF
Calculate/ptimmzze 3D Conformation
Relatively Low
High
Universal
Low Accuracy
MMFF
CalculatoOOpmmizee 3D Conformation
Medium
High
Small Organic Molecules
Fail on Some Metal Memal-Complex
DFT
CulculateOptimize 3D Conformation
High
Low
Depend Basis Set
Slow
RXNMapper
Predict Atom Mapping
Relatively High
High
Small Molecules
Lack Rule Constraints
NameRXN
Predict Atom Mapping + Clussify Reaction
High
High
Limited by Manual Rule
Manual Rule Based
J. Terminology List
We explain the methods mentioned in the paper in the Sec. B and Sec. and here provide additional explanations for some remaining concepts.
1. Graph Neural Network (GNN). A type of neural network designed to process graph data.
2. Message Passing (MP). A mechanism in GNNs where nodes exchange information to update their representations based on neighboring nodes.
3. Molecule. group of atoms bonded together, representing the smallest fundamental unit of a chemical compound.
4. Edge. A connection between two nodes graph, representing a relationship or interaction.
5. Node/Vertex. A fundamental unit in graph representing an entity, such an atom in a molecular graph.
6. Atom. The basic unit of chemical element, consisting of protons, neutrons, and electrons.
7. Bond. A lasting attraction between atoms that enables the formation of chemical compounds.
8. Bond Length. The distance between the nuclei of two bonded atoms in molecule.
9. Bond Angle. The angle formed between three atoms, where the central atom is bonded to the other two.
10. Torsion Angle. The torsional angle refers to the angle between two adjacent bonds in molecule.
11. Reaction. A process in which one or more substances are transformed into different substances.
12. Retrosynthesis. The process of deconstructing complex molecule into simpler precursors to design synthetic pathways.
13. Catalyst. A substance that accelerates a chemical reaction without being consumed in the process.
14. Solvent. A substance, typically a liquid, in which solutes are dissolved to form a solution.
15. Reagent. A substance used a chemical reaction detect, measure, or produce other substances.
16. Computational Chemistry. The use of computer simulations to solve chemical problems and predict molecular behavior.
17. Atom Mapping. The correspondence of atoms between reactants and products.
18. High-ttrougghput Experiment (HTE). A method that allows rapid testing of multiple conditions or compounds simultaneously to accelerate research.
19. Conformation. The 3D shape of a molecule resulting from the rotation around its single bonds.
20. Bond Edge. Represents edge in the reaction graph that corresponds to chemical bond, distinguished from Reaction Edge and Angular Edge.
21. Transition State (TS). The transition state is a high-energy, unstable arrangement of atoms that occurs during a chemical reaction, representing the point at which reactants are transformed into products.
66


Reviews:
[{"review_id": "FKWGz9JAIp", "reviewer": "Reviewer_DHMj", "summary": "This paper introduces the Reaction Graph to model the chemical reaction as a graph and capture the molecular transformations during reaction. The reaction edge connects nodes representing the same atom in both reactants and products based on atomic mapping relationships.\n\nMain Results:\n\n1. A condition prediction model on USPTO to show the advantages of the Reaction Graph (RG), demonstrating their model could focus on different parts of molecules, especially reaction centers.\n\n2. The proposed model shows superiority on the Leaving Group (LvG) identification, Reaction Condition Prediction, and Reaction Yield Prediction tasks.\n\n\nMain algorithmic ideas:\n\n1. The paper proposed a Reaction Graph based on atomic mapping relationships, whose edge connects nodes representing the same atom in both reactants and products.\n\n2. Integrate 3D molecular information into reaction modeling.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for acknowledging that our method \"**shows superiority on various tasks**.\"\nWe also appreciate your suggestions.\n\n## Ⅰ. Comparison with Recent Studies\nThe performance of our method **outperforms** recent methods ReaKE [2] and UniRXN [3] (see **Tab 1**).\n\n**Tab 1: Comparison with recent baselines. [\\*] are reported in [2-3]**\n|Method|U-C|B-H|S-W|Test|U-T\n|-|-|-|-|-|-|\n|ReaKE [2]|0.23|0.89|0.76|0.76*|0.95|\n|UniRXN [3]|0.20|0.94|0.85|0.58|0.92*|\n|Ours|0.33|0.97|0.89|0.78|0.99|\n\nCHESHIRE [1] may **NOT** be directly related to our paper. It focuses on filling missing edges in a Genome-scale Metabolic Graph, while we focus on predicting chemical reaction properties.\n\n## Ⅱ. Innovation in Using 3D\nPrevious methods typically use bond lengths and bond angles.  \nHowever, their differing physical meanings and numerical distributions may cause feature mismatches.  \nTo address this, we innovatively introduce angular edge, which uses edge length to implicitly represent angle, achieving a unified representation.\n\n## Ⅲ. Why not Equivariant NNs?\n**Equivariant Networks (EqvNs)** are suitable for tasks that depend on specific conformations, such as energy prediction.  \n**Invariant Networks (InvNs)** are suitable for tasks that rely solely on the type of molecule rather than specific conformations, such as predicting reaction conditions and yields.  \nThis paper focuses on predicting reaction properties, which are invariant to specific conformations, requiring an InvN.\n\nResults in **Tab 2** validate the advantage of InvNs in reaction modeling.  \nHence, our RG uses the invariant features.\n\n**Tab 2: Comparision of EqvN and InvN.**\n|Method|T1|T5|T15|\n|-|-|-|-|\n|EqvN|0.29|0.44|0.49|\n|InvN|0.33|0.47|0.52|\n\n## Ⅳ. Calculation of 3D Coords\nThe entire RG is **NOT** directly used as input for calculating 3D coords. \nCoords of each molecule are calculated individually. \nSpecifically, we input each molecule in reaction into RDKit, and then use the ETKDG + MMFF to calculate 3D atomic coords.\n## Ⅴ. Further Ablation Analysis\nWe conduct additional ablations on model components and training strategies.  \nOur backbone, equipped with **CRM-H** and trained with a **two-stage strategy**, achieves a top-1 accuracy of 0.3, surpassing the baseline’s 0.2.  \nIncorporating RG further boosts the accuracy to 0.33. Details are in Appendix Sec. H.4.3.\n\n**Tab 3: Ablation results.**\n|CRM-H|2 Stage|RG|T1|T5|T10|\n|-|-|-|-|-|-|\n||||0.25|0.32|0.39|\n|√|||0.30|0.44|0.47|\n|√|√||0.31|0.45|0.49|\n|√|√|√|0.33|0.47|0.51|\n\n## Ⅵ. Using 3D Info in Other Frameworks\nThe results in **Tab 4** show that introducing 3D info into other frameworks leads to accuracy improvements.\n\n**Tab 4: Using 3D Info on other frameworks.**\n|Method|3D|T1|T5|T15|\n|-|-|-|-|-|\n|D-MPNN| |0.1977 |  0.3341 |  0.3924 |\n||√|0.2030|0.3410|0.3971|\nRHG||0.2127|0.3447|0.3927|\n||√|0.2149|0.3464|0.3949|\n\n## Ⅶ. The Necessity of 3D Info\nSeveral methods have explored incorporating 3D info into molecular modeling.  \nUni-Mol [5] uses large-scale 3D positions, GraphMVP [6] uses bond lengths, and GEM [7] uses bond angles.  \nInspired by these works, we explore 3D in reaction modeling, which improves accuracy (see **Tab 5**).\n\nAlthough generating 3D conformations is currently costly, many studies [8–9] are actively addressing this issue.  \nWe are optimistic about the potential of incorporating 3D into the RG framework.\n\n**Table 5: The impact of 3D info.**\n|3D|T1|T3|T5|T10|T15\n|-|-|-|-|-|-|\n||0.313| 0.425| 0.461| 0.496| 0.509 |\n|√|0.325 |0.434 |0.472 | 0.506 | 0.518 | \n## Ⅷ. Discussion of Transition State (TS) Structures\n\n1. TS methods are inspiring to us. However, as discussed in Ⅲ, TS structures are related to specific 3D conformations, whereas reaction properties like conditions are independent of specific conformations. Therefore, their focus in 3D modeling differs.  \n2. We explore TS generation backbones for predicting reaction properties.  \nOur RG achieves better performance (see **Tab 6**). \n3. Methods for calculating TS, such as DFT, are very time-consuming (~10min for 10 atoms[10] and polynomial growth) and unaffordable in dataset like USPTO, which includes 680k reactions with up to 347 atoms. Hence, we didn't use TS structures as inputs for the network.\n\n    **Tab 6: Comparison with TS generation backbones.**\n    |Method|T1|T5|T15|\n    |-|-|-|-|\n    |OARD [4]|0.13|0.20|0.31|\n    |EquiReact [11]|0.12|0.24|0.30|\n    |Ours|0.18|0.31|0.37|\n\n[1]-[4] correspond to those in the comments.\n\n[5] Uni-Mol: A Universal 3D Molecular Representation Learning Framework\n\n[6] Pre-training Molecular Graph Representation with 3D Geometry\n\n[7] Geometry-enhanced molecular representation learning for property prediction\n\n[8] Predicting molecular conformation via dynamic graph score matching\n\n[9] Torsional diffusion for molecular conformer generation\n\n[10] Fast and Automatic Estimation of Transition State Structures Using Tight Binding Quantum Chemical Calculations\n\n[11] 3DReact: Geometric deep learning for chemical reactions", "claims_and_evidence": "1. The experimental results lack comparison with the results of newer papers,  which makes it difficult to evaluate the contribution. \n\n[1] Teasing out missing reactions in genome-scale metabolic networks through hypergraph learning.\n[2] Self-supervised contrastive molecular representation learning with a chemical synthesis knowledge graph.\n[3] Bridging the gap between chemical reaction pretraining and conditional molecule generation with a unified model", "methods_and_evaluation_criteria": "1. The proposed method, which models relationships between reactants and products, is pertinent to chemical reaction characterization. It achieves significant results across six datasets, including tasks like reaction center prediction. But, the evaluation lacks comparison with recent studies.\n\n2. It mainly focuses on enhancing the learning of edge information in 3D graph representations. However, it does not deeply consider molecular equivariance, which is popular in 3D molecular learning. While this approach works, it is quite common in graph network learning. There is limited innovation in addressing more complex properties of molecular structures.", "theoretical_claims": "The theoretical claims presented in the article are straightforward and do not present any issues.", "experimental_designs_or_analyses": "1. The method's evaluation lacks comparison with recent research, making it difficult to assess its advantages.\n\n\n2. It remains unclear whether the entire reaction graph is used as input for calculating 3D coordinates.\n\n3. While the model outperforms baseline methods significantly (0.30 vs 0.21) even without Reaction Edges and 3D structures, there is insufficient ablation analysis to explain which components contribute to this performance. More detailed ablation studies are needed.\n\n4. The impact of using 3D information in other frameworks, such as D-MPNN on MG graphs, has not been explored. Investigating this could provide additional insights into the utility of 3D information across different model", "relation_to_broader_scientific_literature": "1. This paper innovates by constructing reaction graphs to model chemical reactions, diverging from traditional hypergraph-based approaches validated in extensive experiments.\n\n2. Some studies enhance chemical representations through knowledge graphs, integrating broad chemical information for improved performance, unlike the proposed reaction graph method.\n\n3. Incorporating 3D information into the reaction graph framework is uncommon yet adds potential accuracy; however, it raises questions about the necessity and cost-effectiveness due to high generation costs.", "essential_references_not_discussed": "The experimental results lack comparison with the results of newer papers,  which makes it difficult to evaluate the contribution. \n\n[1] Teasing out missing reactions in genome-scale metabolic networks through hypergraph learning.\n[2] Self-supervised contrastive molecular representation learning with a chemical synthesis knowledge graph.\n[3] Bridging the gap between chemical reaction pretraining and conditional molecule generation with a unified model\n\n\nA paper that considers 3D transition state structures in chemical reactions is  also worth including in the discussion:\n\n[4] Accurate transition state generation with an object-aware equivariant elementary reaction diffusion model", "other_strengths_and_weaknesses": "None", "other_comments_or_suggestions": "None", "questions_for_authors": "1. It mainly focuses on enhancing the learning of edge information in 3D graph representations. However, it does not deeply consider molecular equivariance, which is popular in 3D molecular learning. While this approach works, it is quite common in graph network learning. There is limited innovation in addressing more complex properties of molecular structures\n\n2. The method's evaluation lacks comparison with recent research, making it difficult to assess its advantages.\n\n\n3. It remains unclear whether the entire reaction graph is used as input for calculating 3D coordinates.\n\n4. While the model outperforms baseline methods significantly (0.30 vs 0.21) even without Reaction Edges and 3D structures, there is insufficient ablation analysis to explain which components contribute to this performance. More detailed ablation studies are needed.\n\n5. The impact of using 3D information in other frameworks, such as D-MPNN on MG graphs, has not been explored. Investigating this could provide additional insights into the utility of 3D information across different model.", "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": "xwwQkjNvkF", "reviewer": "Reviewer_S7nT", "summary": "This paper proposes a new graph representation for reaction related tasks, named Reaction Graph (RG). Compared to traditional molecule graph representation, RG introduces a new edge type, ie, reaction edge, which indicates the edges that have been changed during the reaction process. The experimental results show that the proposed RG is effective in various reaction tasks.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for acknowledging that this paper proposes a \"**new graph representation**\" and is \"**effective in various reaction tasks**.\"\nWe also appreciate your suggestions.\n\n## Ⅰ. Clarification on Reaction Separation and Information Loss in RXN Hypergraph  \n**Seperate Reactions**: In the RXN Hypergraph, reactants and products are represented as separate graphs, rather than integrating the entire reaction into a single connected graph.\n\n**Information Loss**: This representation lacks atom mapping between reactants and products, leading to the loss of key information on bond breaking, bond formation, and atomic reorganization.\n\n**Experimental Verification**: We try to convert the standard non-connected RXN Hypergraph (w/o Reac) into a connected graph (w/ Reac). The improved performance confirms our claim (see **Tab 1**).\n\n**Tab 1: Impact of reaction connectivity.**\n| Method | U-T | P-T |\n|-|-|-|\nw/o Reac | 0.954|0.911\nw/ Reac |0.984|0.936\n\n## Ⅱ. Results of MG and RG in Typical Framework\n\nWe use the typical used RGCN implementation from DGL offical repo. As in **Tab 2**, RG outperforms MG on all the tasks. \n\n**Tab 2: Results of RG and MG on RGCN.**\nMethod|1/8 U-C|BH 1-4|1/8 U-T\n|-|-|-|-|\nMG|0.13|0.75|0.92\nRG|0.17|0.78|0.97\n\nWe also test MG on its own SOTA framework UniMol. As in **Tab 3**, our method shows advantage in reaction tasks.\n\n**Tab 3: Results of RG and MG on their own SOTA framework.**\n|Method|U-C|BH 1-4|U-T|\n|-|-|-|-|\n|UniMol|0.30|0.62|0.98\n|RG|0.33|0.78|0.99\n\n## Ⅲ. Details about Ablation \n**Method Overview:** The main contribution of this work is proposing Reaction Graph (RG), a new representation for chemical reactions, characterized by two key features: \n- **Reaction info** are used to model reaction change, which is incorporated through reaction egde;\n- **3D structures** are incorporated through bond lengths and angular edges.\n\n**Ablation Settings:** All ablations are conducted on the **same framework**, with **same hyperparameter setting**. We remove reaction edges for reaction info ablation, and set all edge lengths to 0 for 3D ablation.\n\n## Ⅳ. Design and Effect of Each Module in the Framework\n\nOur main contribution is **proposing a novel reaction graph representation**. Still, we have carefully considered the framework and conducted extensive experiments. For more details, please refer to Appendix Sec.H.7.\n\n### 1. Edge Embedding\nWe employ typical embedding layer for edge type, and RBF for edge length. RBF lifts edge lengths into high-dim vector by smooth mappings, which help in capturing variations in continuous data. It focus more on local structural pattern, which is suitable for tasks involving local continuous spatial relationship (e.g. molecular structures). \n\nAs in **Tab 4**, RBF outperforms linear projection and discretization.\n\n**Tab 4: Comparison of different edge embedding methods.**\n| Method | T1 |T5|T15 |\n|-|-|-|-|\nLinear Projection | 0.317|0.468|0.516|\nDiscretization | 0.310|0.457|0.505\nRBF | 0.325|0.472|0.518\n\n### 2. Vertex-Edge Integration\n\nWe map each edge type to a unique learnable message function $f_e(v,e,l_e)$, which computes messages for node feature update. Through this approach, the network can handle bond, reaction and angular edge in a targeted manner, as their semantics are different.\n\nCompared with other vertex-edge integration methods, our method achieves better accuracy (see **Tab 5**). \n\n**Tab 5: Comparison of different vertex-edge integration methods.**\n| Method | T1 |T15 |\n|-|-|-|\nPaiNN | 0.290|0.488\nDimeNet | 0.318|0.514\nGraph Transformer | 0.300|0.477|\nEGAT | 0.304|0.502\nGINE | 0.299|0.487\nOurs |0.325|0.518\n\n### 3. Aggregation\nTo capture RG's global representation, we use an LSTM with attention aggregation. It helps the network focus on the sites related to the reaction change.\nAblation results validates the effectiveness of each component (See **Tab 6**).\n\n**Tab 6: Ablation results of aggregation module.**\nAttention|LSTM|T1|T5|T15|\n|-|-|-|-|-|\n|||0.3156|0.4642|0.5110\n|√||0.3187|0.4670|0.5136\n|√|√|0.3246|0.4715|0.5181\n\n## Ⅴ. Calculation of Edge Length $l_{ij}$\n\nFirst, we input each molecule into RDKit and calculate 3D atomic coords using ETKDG + MMFF.\nThe 3D coords of atoms $i$ and $j$ are $p_i$ and $p_j$, respectively. \nThe length of edge $e_{ij}$ is calculted as:\n$$\nl_{ij} = \n\\begin{cases} \n0, & \\text{$e_{i,j}$ is reaction edge} \\\\\\\\\n||p_i - p_j||_2, & \\\\text{otherwise}\n\\end{cases}\n$$\n\n## Ⅵ. How 3D Info is Included\n1. We calculte the edge length $l_{ij}$ (refer to Ⅴ). \n2. We input $l_{ij}$ to RBF kernel network to get the edge length embedding $\\boldsymbol{l}_{ij}$.\n3. We concat $\\boldsymbol{l}ij$ with edge type embedding $\\boldsymbol{e}_{ij}$.\n4. Edge length and type features are combined with vertex features through vertex-edge integration, thereby incorporating 3D info into RG.\n\n## Ⅶ. Typo Correction \nThe typo in line 3330 has been corrected, and the text has been re-proofread. Thank you for your reminder.", "claims_and_evidence": "1. Unclear claim: \"However, this method still separates reactions, which also causes loss of reaction information.\" How RXN Hypergraph separates reactions and what information is lost remains unclear;\n\n2. In the experiments sections, what specific prediction model is conducted to compare MG and RG representation is ambiguous. Conducting a framework specifically designed for RG on both MG and RG representations may introduce significant bias, as the results could be influenced by the framework's unsuitability for MG representation. For a fair comparison,  the author should conduct a typical used framework on the two representations.\n\n3. Similar to 2, how the 3D information is excluded for comparison is not stated. Will the results of w/o 3D information introduce any bias due to the change of framework?", "methods_and_evaluation_criteria": "Yes.", "theoretical_claims": "No theoretical claims.", "experimental_designs_or_analyses": "How the ablation experiments are conducted is unclear, which may cause some biased results. Does the framework keep consistency in different settings? Will the framework introduce bias to specific settings? Please also check Claims And Evidence part.", "relation_to_broader_scientific_literature": "The proposed Reaction Graph representation can benefit a broad area in chemical reaction related tasks.", "essential_references_not_discussed": "All essential references are covered.", "other_strengths_and_weaknesses": "### Strengths:\n1. The proposed reaction graph is intuitive, which can naturally benefit the chemical reaction related tasks.\n2. The authors conduct a variety of experiments to show the effectiveness of the proposed framework.\n3. The experimental results can demonstrate the priority of proposed framework.\n\n### Weaknesses:\n1. Some implementation details about ablations are not clear. Please check Claims And Evidence.\n2. The experiments mainly focus on demonstrating the effectiveness of RG, but the modules in the framework lack discussion, eg., Attention-based aggregation, Edge-embedding, and Vertex-edge embedding.\n3. The main focus of this paper is not clear. The authors proposed RG and a framework, but how they benefit each other, why they specifically designed a framework for RG, and how effective both modules are, are not clear. The authors should discuss more on each of them, but not only discuss the effectiveness of RG while employing experiments with the overall framework.\n4. Some contributions lack discussion, eg, the framework design.", "other_comments_or_suggestions": "*  A typo at Line 3330.\n* Details about how $l_{ij}$ is calculated.\n* Details about how 3D information is included.", "questions_for_authors": "Please see above.", "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": "EugPSc2AAk", "reviewer": "Reviewer_vEQY", "summary": "The paper introduces a new representation learning framework for chemical reactions. Specifically, the authors propose a graph neural network architecture that takes into account a) explicit inter-reactant/product interactions, and b) the three-dimensional structures of reactants and products. The framework is applied to several reaction-related tasks including reaction classification, yield prediction, and condition recommendation, and is shown to outperform SOTA methods on several benchmarks.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for acknowledging that our method \"**outperforms SOTA methods**\" and that the \"**results clearly support the claim**\".  \nWe also appreciate your insightful suggestions for improving this paper.\n## Ⅰ. Separate vs. Unified Node\nRG separates atoms in reactant and product into two nodes, which can **preserve the uniqueness of molecular structures** and facilitate structural modeling. CGR unifies atoms into a single node, causing their structural features to become entangled during message passing. This may hinder structural understanding.\n\nResults in **Tab 1** show that RG outperforms CGR in condition and yield prediction, which rely on structural modeling.\n\n**Tab 1: Comparison of RG (separate nodes) and CGR (unified nodes).**\nMethod|UC|PC|BH|SM|Test|Gram|SubGram|UT|PT\n|-|-|-|-|-|-|-|-|-|-\nCGR|0.20|0.26|0.94|0.85|0.74|0.13|0.20|0.99|0.98\nRG|0.33|0.39|0.97|0.89|0.78|0.13|0.22|0.99|0.99\n## Ⅱ. Non-reactant Species\nFor condition prediction, we exclude non-reactant species from graph and take them as prediction target, avoiding data leakage. For yield prediction, we keep them in the graph as they have a significant impact on the yield.\n## Ⅲ. Why not Cartesian Coords or Torsional Angles\nOur work aims to predict reaction properties (e.g. conditions), which are **invariant to the specific conformations** of molecules. RG uses bond lengths and bond angles, which vary slightly across different conformations and suit the task. Cartesian Coords and Torsion Angles vary significantly between conformations, introducing redundant information and hindering model learning. \n\nResults in **Tab 2** support this point.\n\n**Tab 2: Comparison of 3D structure representations.**\nMethod|T1|T5|T15\n|-|-|-|-\nCartesian Coords|0.312|0.463|0.511\nTorsion Angles|0.302|0.447|0.494\nOurs|0.325|0.472|0.518\n\n## Ⅳ. Tradeoffs in 3D Structure Calculation\n\nThe reason for using equilibrium structures is the same as in **Ⅲ**.\n\nETKDG+MMFF provides controllable errors (avg 5%< with DFT) and high efficiency (20ms< for 100 atoms). DFT are unaffordable (>10min for 6 atoms and polynomial growth), as USPTO contains >680k samples and reactions with >300 atoms\n\nResults in **Tab 3** show that controllable errors (5%) in 3D coords have a minor impact (0.003).\n\n**Tab 3: Impact of 3D error on 1/8 USPTO-Condition.**\nError %|0|5|10|20|40\n|-|-|-|-|-|-\nAccuracy|0.177|0.174|0.170|0.164|0.152\n## Ⅴ. Challenges of Datasets\n- The key bottlenecks of **USPTO-Yield** lie in the low label quality and missing condition annotations[1]. Although large in scale, the distribution remains sparse due to the large variety of reaction types, making it hard to learn the non-smooth relation between reaction and yield.\n- **B–H/S–M** are come from HTE, which provide dense, high-quality labels but limited data(<10K samples, <50 molecules). Test sets have additives held out from train set, which places high demands on model's generalization on small data scale.\n\nMore stats and discussions can be found in Appendix Sec G.\n\n## Ⅵ. Writing, Content Arrangement, and Figures\nYour suggestions are very helpful for improving the manuscript's quality.\n\n### Introduction Revision\n\n- **AI4Chem:**\nIn the field of chemistry [2], AI enables precise spectral analysis [...] and quantum chemical simulation [...], improves inverse design of molecular structure [...] and retrosynthesis planning [...].\n\n- **GNN:**\nAmong various representation methods, molecular graphs [3,4] have proven inherently advantageous for various chemical tasks [...].\n### Figure Revision\nhttps://huggingface.co/reactiongraph/Revision.\n### Section Arrangement\nSec 3.2 focuses on exploring suitable 3D features, whereas Sec 3.3 focuses on specific task.\n\nBut you made well-reasoned point that these two Secs are not logically parallel. Therefore we rearrange them as followed:\n- 3.1 The roles of Reaction and 3D Information\n    - 3.1.1 The Effect of Reaction Information\n    - 3.1.2 The Effect of 3D Information\n- 3.2 Reaction-related Tasks\n    - 3.2.1 Reaction Condition Prediction\n    - 3.2.2 Reaction Yield Prediction\n    - 3.2.3 Reaction Classification\n## Ⅶ. Data Requirement\nReac info is effective across different data scales. 3D info requires larger amounts of data.\n\nModels trained from scratch on B–H and S–M shows advantage of reac info (Sec 3.4), and we also conduct experiments on 1/8 of USPTO dataset (see **Tab 4**).\n\n**Tab 4: Results on 1/8 data scale.**\nMethod|U-C|U-T\n|-|-|-|\nMG|0.13|0.92\nRG|0.17|0.97\n\nWe use different scaffolds on Pistachio to further explore the data requirements of 3D info. **Tab 5** shows that limited data scale hinders the model from learning 3D priors. Results in [5] also leads to a similar conclusion.\n\n**Tab 5: Results of different data scale.**\nScale|w 3D|w/o 3D\n|-|-|-\n1|0.392|0.385\n1/2|0.355|0.350\n1/8|0.277|0.272\n1/32|0.186|0.191\n\n[1] Prediction of chemical reaction yields using deep learning\n\n[2-4] correspond to the papers in your comment.\n\n[5] Uni-Mol: A Universal 3D Molecular Representation Learning Framework", "claims_and_evidence": "The main claim of this work is that previous reaction representations suffer from two significant limitations: a) They do not adequately capture inter-reactant/product interactions, since they treat all molecules separately and then concatenate their features. B) They ignore three-dimensional structure information. These issues are addressed by the development of a 3D-aware reaction graph model. Experimental evidence (performance metrics on several benchmark tasks) clearly supports the claim of improved predictivity by including interaction and 3D information.", "methods_and_evaluation_criteria": "From my perspective, a number of model design choices remain unclear: \n* Why does the model employ separate nodes for the atoms in the reactants and products instead of using a unified node, as would be expected given that these atoms are chemically identical? (similar to the idea of condensed reaction graphs)\n* The treatment of non-reactant species (e.g. reagents, catalysts, or solvents) is not explained. Are they included in the graph – which would raise concerns about data leakage in the condition prediction task? Are they excluded from the graph – potentially omitting important information for reaction yield prediction? \n* 3D structures of molecules are represented using internal coordinates (i.e. bond/edge lengths and bond angles) rather than Cartesian coordinates commonly used in other works. However, to fully represent the 3D structure of a molecule, bond length and bond angle information is insufficient; and dihedral angles / torsional angles would be required. While this is mentioned in the Supplementary Materials, it is unclear why these features were omitted from the model architecture.", "theoretical_claims": "not applicable", "experimental_designs_or_analyses": "Experimental evaluations are done on four main tasks: Leaving group identification, reaction classification, reaction condition prediction, and yield prediction. All tasks are well-established in the literature (including datasets and train–test splits). The authors provide systematic benchmarks against SOTA methods for each of these tasks. The experimental design, including the evaluation metrics, is sound. For each task, the authors additionally conduct an ablation study to dissect the contributions of inter-reactant/product interactions and 3D information, respectively.", "relation_to_broader_scientific_literature": "As highlighted in the introduction, compared to molecule representations, reaction representations are somewhat underdeveloped. Therefore, the introduction of the 3D-aware model represents a relevant advancement. As discussed in the `Methods and Evaluation Criteria`, some design choices remain unclear, but the improvments in predictivity are significant and noteworthy.", "essential_references_not_discussed": "The introduction of the paper introduces GNNs for molecular property prediction as a relatively recent development. This is misleading, and some foundational works (Scarselli et al. 2009, Duvenaud et al. 2015) are omitted.", "other_strengths_and_weaknesses": "While the technical discussion appears sound, the discussion of chemical concepts could be improved notably. Examples include: \n* While the proposed architecture requires molecular 3D structures, the challenges associated with obtaining such structures are largely ignored. In reality, molecules do not have a dingle 3D structure, but a distribution of 3D structures which is dynamic and depends on the environment. This is inherently hard to capture – and the authors use only equilibrium structures for their model. These structures are generated using a cheap force field method rather than a more accurate, but computationally expensive quantum chemical approach. A discussion of these simplifications and tradeoffs would be valuable. \n* The introduction on the applications of AI in chemistry could be notably improved (for a starting point see e.g. a recent review by Cheng et al., Faraday Discuss. 2024). As an example, “analysis of retrosynthesis” and “streamlines synthetic pathways” effectively describes the same problem. \n* The datasets used, particularly for reaction yield prediction, could be better described to emphasize the specific challenges associated with them. For example, the B–H and S–M datasets originate from focused combinatorial experimentation efforts (meaning high quality, low quantity, low diversity), whereas the USPTO datasets are derived from the patent literature (meaning lower quality, higher quantities, higher diversity). \nAlong the same lines, some statements are too simplistic in my opinion, and should be more nuanced:\n* “study of interactions between molecules, particularly chemical reactions, has been overlooked”\n* “The advantage of RG on LvG identification demonstrates its ability to understand the reaction mechanism.” From a chemical perspective, identifying leaving groups based on the reaction equation is a relatively simple pattern recognition task, and should not be confounded with mechanistic understanding.", "other_comments_or_suggestions": "Organization and clarity of the manuscript could be improved at certain points: \n* The current presentation of experiments in Section 3 is somewhat confusing, as the discussion shuffles between focusing on model capabilities and specific tasks. As an example, section 3.2 studies the effects of different 3D featurization techniques using the condition prediction task – which is then re-introduced in section 3.3. A more logical organization would enhance readability of this section.\n* Figure 1 would benefit from a clearer structure with better defined divisions and sub-headings. \n* The labeling of functional groups in Figure 3 does not conform to standard chemical conventions. The term “carboxyl group” refers to the full COOH unit, and the used labels “carboxyl-hydroxyl” and “carboxyl” are nonsensical from a chemical standpoint. \n* In Figure 4 and the accompanying discussion, it is necessary to specify what type of timings are discussed (training time? inference time? timing of generating a 3D structure in the first place?)", "questions_for_authors": "* Given that GNNs are usually considered rather “data-hungry”, what are the data requirements for training a predictive 2D / 3D model? Is it possible to train the model from scratch, even on the small (S–M, B–H) datasets?", "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": "yf97bl1rFH", "reviewer": "Reviewer_fygo", "summary": "Main Contributions:\n- Reaction Graph (RG) Representation: The authors introduce Reaction Graph (RG), a novel unified graph representation for chemical reactions that integrates both reactants and products into a cohesive framework. This representation incorporates 3D molecular structures, which are crucial for accurately modeling chemical reactions.\n- Incorporation of Reaction Edges: RG includes reaction edges that connect atoms in reactants to their corresponding atoms in products based on atomic mapping. This allows the model to capture changes in molecular structures during reactions.\n- 3D Structure Integration: The authors propose a method to incorporate 3D information into RG using bond lengths and angular edges, which implicitly convey bond angles. This approach is rotationally and translationally invariant.\n- Empirical Results: The authors demonstrate the effectiveness of RG through extensive experiments on various tasks, including reaction condition prediction, yield prediction, and reaction classification. RG achieves state-of-the-art accuracy across multiple datasets.\n\nMain Findings:\n- The proposed Reaction Graph representation significantly outperforms existing methods in modeling chemical reactions.\n- Incorporating 3D structural information and reaction edges enhances the model's ability to understand and predict reaction outcomes.\n- The model achieves high accuracy in predicting reaction conditions, yields, and types, showcasing its potential for accelerating drug design and material science.\n\nMain Algorithmic/Conceptual Ideas:\n- Unified Graph Representation: RG integrates molecular graphs of reactants and products, capturing interatomic relationships pertinent to the reaction process.\n- Reaction Edges: These edges enable the model to exchange information between reactants and products during the message-passing phase of GNNs.\n- 3D Information: The use of bond lengths and angular edges provides a simple yet effective way to incorporate 3D molecular structures into the graph representation.\n- Attention-based Aggregation: The model uses an attention mechanism combined with an LSTM to aggregate node features into a unified reaction feature vector.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for acknowledging that our method is **novel**, **crucial**, and **effective**.  \nWe also appreciate your valuable suggestions for improving this work.\n\n## Ⅰ. Impact of Reac and 3D Info in RG\n\n### 1. Impact on Reaction Types\n\n**Tab 1: Impact of Reac and 3D info on 12 reaction types.**\nReac|3D|0|1|2|3|4|5|6|7|8|9|10|11\n|-|-|-|-|-|-|-|-|-|-|-|-|-|-\n|||0.292|0.292|0.317|0.323|0.396|0.197|0.347|0.244|0.372|0.312|0.259|0.299\n√||0.292|0.306|0.322|0.33|0.403|0.216|0.359|0.246|0.391|0.327|0.277|0.319\n√|√|0.309|0.318|0.327|0.333|0.424|0.229|0.368|0.264|0.391|0.326|0.298|0.338\n\n3D is more critical for Unknown reactions (type 0), as their mechanisms are diverse and reaction patterns are difficult to capture. For C–C bond formation (type 3) and Oxidation (type 8), the contribution of Reac info is greater.\n\n### 2. Impact on Specific Datasets\n\n**Tab 2: Impact of Reac and 3D info on different datasets.** \n|Reac|3D|U-C|P-C|U-T|P-T\n|-|-|-|-|-|-\n|||0.305|0.381|0.992|0.966\n√||0.313|0.385|0.998|0.986\n√|√|0.325|0.392|0.999|0.987\n\nBoth 3D and Reac info contribute to condition prediction. For reaction classification, which is directly related to the reaction change, Reac info is more effective.\n\n## Ⅱ. Error Analysis\n\n### 1. Condition\nThe overall error pattern is in Appendix Fig 18. **A**: US20110105766A1 and **B**: US20040204386A1 are representative failure cases.\n- **Case A.** Correct: PdCl₂ (0.05%) Pred: Pd(PPh₃)₄ (1.82%)\n\n    Conditions with low frequencies (0.05%) may be misclassified, but the Pred still exhibit similarity to the ground truth. \n\n- **Case B.** Correct: CuBr₂ (0.01%<) Pred: None (86.81%)\n    \n    For extremely rare conditions (0.01%<), model struggles and classifies them as None. Data augmentation or pretraining are promising solutions for future exploration.\n\n### 2. Yield\n\nApart from low label quality, the non-smooth relation between structure and yield is the bottleneck of yield prediction. \n\nWe find the top-5 closest reactions of **C** using RXNFP. They have similar structures, yet the yield variance is large (0.5–0.94). This distinction hinders model from correctly predicting **D** and **F**.\n\n    C: CCC(C)(C)N.CCN(C)C.Cl.[Cl-]>>CCC(C)(C)NCCN(C)C\n\n**Tab 3: Correct and Pred yields of 5 similar reactions.**\n|Reaction|Correct|Pred\n|-|-|-\nC|0.60|0.50\nD|0.50|0.68\nE|0.64|0.58\nF|0.94|0.64\nG|0.91|0.83\n\n### 3. Reaction Classification\n\nThe overall error pattern is in Appendix Fig 21. **H** and **I** are representative failure cases.\n\n- **Case H.** Correct: FGI; Pred: Unrecognized\n\n        C1=C[C@H]2[C@H]3C=C[C@H](C3)[C@H]2C1>>C1C=CCC=1\n    \n    For rare types of reaction changes, the model may misclassify them as Unknown.\n\n- **Case I.** Correct: Oxidations; Pred: FGI\n\n        Cl.N#CC1CCCC=1N.NO>>N#CC1CCCC=1NO\n\n    In this case, the annotated and predicted types are both acceptable, but the Pred seems more reasonable.\n\n### 4. Other Tasks\nDetailed analysis is in Sec H1 and H2.\n\n## Ⅲ. Hyperparameter Selection and Training Strategy\n\n### Hyperparameter Selection\n\nResults show that the current setting is optimal, while the performance may scale with the hidden dim.\n\n**Tab 4: Impact of hyperparameters.**\n|Hid Dim|MPNN Iter|Pool Iter|T1|T15\n|-|-|-|-|-\n200|3|2|0.325|0.518\n50|3|2|0.307|0.505\n100|3|2|0.315|0.512\n200|2|2|0.320|0.520\n200|4|2|0.317|0.514\n200|3|1|0.319|0.514\n200|3|3|0.318|0.514\n\n### Training Strategy\n\nAccording to **Tab 5**  and Appendix Fig. 19, our proposed 2-stage training strategy effectively addresses the negative transfer problem in multi-task learning like condition prediction.\n\n**Tab 5: Impact of two-stage training strategy.**\n|Method|T1|T3|T5|T10|T15\n|-|-|-|-|-|-\nOne-Stage|0.30|0.41|0.45|0.48|0.50\nTwo-Stage|0.33|0.43|0.47|0.51|0.52\n\n## Ⅳ. Data Quality\n### Accuracy of 3D Coords\n\nWe control the 3D accuracy by adding gaussian noise to the bond lengths. Results in **Tab 5** show that when noise level is within a certain margin (5%), the performance decrease is minor (0.03).\n\n**Tab 6: Impact of 3D accuracy on 1/8 USPTO-Condition.**\nNoise|0.0|0.05|0.1|0.2|0.4\n|-|-|-|-|-|-\nAccuracy|0.177|0.174|0.170|0.164|0.152\n\n### Label Quality\n\nLabel density is an important indicator of label quality. We investigate its impact on Pistachio-Condition, where the model suffers from sparse condition annotations. Results in **Tab 6** show that label quality is more critical to model performance than 3D accuracy, and is the primary bottleneck.\n\n**Tab 7: Impact of label density on Pistachio-Condition.**\nLabel density | 1/1 | 1/2 | 1/4 |1/8|1/16|1/32\n|-|-|-|-|-|-|-\nAccuracy|0.39|0.36|0.32|0.28|0.22|0.19\n\n## Ⅴ. Computational Time Analysis\n\nAs shown in Appendix F2, for most of the reactions, the construct and inference time of RG are **<50ms**, meeting the real-time requirement. The inference time of large dataset (USPTO test set) are **<3min**, demonstrating the efficiency of RG. We are optimistic that, with the advancement of the conformer prediction, the speed of RG construction will further improve.", "claims_and_evidence": "Claims:\n- Effectiveness of Reaction Graph: The authors claim that Reaction Graph (RG) is more effective than existing methods in modeling chemical reactions.\n- Incorporation of 3D Information: The authors assert that incorporating 3D structural information improves the model's performance.\n- Reaction Edges: The introduction of reaction edges helps the model capture changes in molecular structures during reactions.\n\nEvidence:\n- The authors provide extensive experimental results on various tasks (reaction condition prediction, yield prediction, and reaction classification) across multiple datasets (USPTO-Condition, Pistachio-Condition, USPTO-Yield, USPTO-TPL, and Pistachio-Type).\n- The results show that RG outperforms existing methods, achieving higher accuracy in predicting reaction conditions, yields, and types.\n- Ablation studies demonstrate the effectiveness of incorporating 3D information and reaction edges.\n\nProblems:\n- The claims are generally well-supported by the experimental results. However, the authors could provide more detailed analysis on the impact of different components (e.g., reaction edges, 3D information) on specific types of reactions or datasets.", "methods_and_evaluation_criteria": "The evaluation criteria are standard and widely accepted in the field, making the results comparable to other studies.\nThe datasets used are large-scale and diverse, providing a comprehensive assessment of the model's performance.", "theoretical_claims": "The paper does not present any theoretical proofs. The contributions are primarily algorithmic and empirical, focusing on the development and evaluation of the Reaction Graph representation.", "experimental_designs_or_analyses": "Validity:\n- The experimental designs are sound and follow standard practices in the field.\n- The authors provide detailed descriptions of their methods and datasets, allowing for reproducibility.\n- The results are consistent across different tasks and datasets, supporting the robustness of the proposed method.\n\nIssues:\n- The authors could provide more detailed error analysis to understand the failure cases and potential limitations of the model.\n- The impact of different hyperparameters and training strategies could be further explored to provide a more comprehensive understanding of the model's behavior.", "relation_to_broader_scientific_literature": "I think that important and relevant chemical reaction prediction works have been discussed.", "essential_references_not_discussed": "To my knowledge, Yes, they are", "other_strengths_and_weaknesses": "### Strengths\n- **Originality:** The paper introduces Reaction Graph (RG), a novel unified graph representation for chemical reactions that integrates reactants, products, and reaction edges, along with 3D molecular structures.\n- **Effectiveness:** RG achieves state-of-the-art performance across multiple tasks and datasets, demonstrating its superior ability to model chemical reactions.\n- **Clarity:** The paper is well-structured, with clear methodology, extensive experiments, and detailed results, making it easy to follow and reproduce.\n\n### Weaknesses\n- **Data Quality:** The accuracy of 3D coordinates and reaction labels in the datasets may limit the model's performance and generalization.\n- **Error Analysis:** A more detailed analysis of failure cases and error patterns could provide deeper insights into the model's limitations.\n- **Computational Efficiency:** The model's inference time and computational requirements could be optimized for real-time applications and larger datasets.", "other_comments_or_suggestions": "None", "questions_for_authors": "None", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This research introduces the Reaction Graph (RG), a novel graph-based representation designed to model chemical reactions more effectively. Also 3d information is represented as well under this framework. Experiments have been done on a set of benchmarks.

I appreciate the authors’ effort in addressing reviewers concerns especially regarding several ablation studies, which makes the paper more comprehensive. I hope the authors to take these feedback and additional experiments into the revision of the paper, to reflect the improvements done on the quality of this manuscript.
Decision: Accept (poster)