Graph Piece: Efficiently Generating High-Quality Molecular Graphs with Substructures
Authors: Xiangzhe Kong
Zhixing Tan
Yang Liu
Venue: ICLR 2022 Submitted (2022)

Abstract: Molecular graph generation is a fundamental but challenging task in various applications such as drug discovery and material science, which requires generating valid molecules with desired properties. Auto-regressive models, which usually construct graphs following sequential actions of adding nodes and edges at the atom-level, have made rapid progress in recent years. However, these atom-level models ignore high-frequency subgraphs that not only capture the regularities of atomic combination in molecules but also are often related to desired chemical properties. In this paper, we propose a method to automatically discover such common substructures, which we call graph pieces, from given molecular graphs. Based on graph pieces, we leverage a variational autoencoder to generate molecules in two phases: piece-level graph generation followed by bond completion. Experiments show that our graph piece variational autoencoder achieves better performance over state-of-the-art baselines on property optimization and constrained property optimization tasks with higher computational efficiency.

Under review as a conference paper at ICLR 2022
GRAPH PIECE: EFFICIENTLY GENERATING HIGH- QUALITY MOLECULAR GRAPHS WITH SUBSTRUC- TURES
Anonymous authors Paper under double-bling review
ABSTRACT
Molecule generation, which requires generating valid molecules with desired properties, is a fundamental but challenging task. Recent years have witnessed the rapid development of atom-level auto-regressive models, which usually con- struct graphs following sequential actions of adding atom-level nodes and edges. However, these atom-level models ignore tigh-frequency substructures, which not only capture the regularities of atomic combination in molecules but are also often related desired chemical properties, and therefore may be sub-optimal for gener- ating high-quality molecules. In this paper, we propose a method to automatically discover such common substructures, which we call graph pieces, from given molecular graphs We also present graph piece variational autoencoder (GP- VAE) for generating molecular graphs based on graph pieces. Experiments show that our GAE models not only achieve better performance than the state-of- the-art baseline for distribution-leariig property optimization, and constrained property optimization tasks but are also computationally efficient.
INTRODUCTION
Molecule generation is task that aims produce chemically valid molecules with optimized prop- erties. It is important for a variety of applications, such as drug discovery and material science. Graph-based molecule generation models, which robust molecule substructures (You al. 2018 K won et al. 2019), have gained increasing attention recently (Jin et al. 2018 Li et al. 201 8a
You al. 2018 won al. 2019
De Cao & Kipi 2018 Shi et 2020
al. 2020b
Graph-based molecule generation models typically decompose molccular graphs into sequential ac- tions of generating atoms and bonds autoregressively (Li et al., [0188] You al.) 2018 Li al. 2018a; Jin et al., 2020b). While this decomposition is natural and straightforward. it inevitably ignores the existence of common substructures molecular graphs, as illustrated Figure I Com- pared with using atoms for generating molecules, using graph substructures for generating molecules have three potential benefits. First, using substructures can capture the regularities of atomic combi- nation in molecules, and therefore is more capable of generating realistic molecules. Second, using substructures can better capture chemical properties, as there is correlation between substructures and chemical properties (Murray & Rees 2009; Jin al. 2020b). Third, using substructures enables efficient training and inference. is evident that using substructures to represent molecular graphs result in much shorter sequences, therefore the training and inference process be accelerated. As a result, we believe that models using substructures to represent molecular graphs can generate more realistic molecules with better-optimized properties efficiently.
83.9%
60.5%
41.3%
32.6%
27.5%
Figure 1: Five high-frequency substructures in the standard ZINC250K dataset (Irwin et al.) 2012 Kusner et al. 2017). The percentage means the ratio of molecules which have the substructure.

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In this paper, present an iterative algorithm to automatically discover common substructures in molecules, which we call graph pieces. Initially, graph pieces correspond to single atoms that appear in graphs of given dataset. Then for each iteration, count the occurrence of neighboring pieces in graphs and merge the most frequent neighboring pieces into a new graph piece. Since substruc- tures can be seen as small molecules, we use SMILES (Weininger 1988), text-based representa- tion for molecules, to efficiently judge whether two graph pieces are identical. To effectively utilize these substructures, we also propose a graph piece variational autoencoder (GP-VAE). Our model consists of graph neural network (GNN,(Scarsell) Scarselli et al. 2008) encoder and two-step decoder. The two-step decoder first generates graph pieces auto-regressively and then predicts atom-level bonds between graph pieces in parallel. As result, our GP-VAI decouples the alternated generation of nodes and edges, achieving significant computational efficiency for both training and generation.
We conduct extensive experiments on ZINC250K (Irwin et al., 2012) and QM9 (Blum & Rey- mond] [209 Rupp et al. 2012) datasets. Results demonstrate that our GP- P-E models outperform property optimization, and constrained property op-
state-of-the-an models on distribution-lerriin timization tasks, and are about six times faster than the fastest baseline.
RELATED WORK
Molecule Generation Based on different representations for molecules, molecule generation models can be divided into two categories: text-based and graph-based. Text-based models (Gómez- Bombarelli et al. 2018 Kusner et al.] 2017 Bjerrum Threifall (017). which usually adopt the Simplified Molecular- Input Line-entry System (SMILES) (Weininger] 1988) representation, simple and efficient methods for generating molccules. However, these models are not robust be- cause single perturbation in the text molecule representation can result in significant changes in molecule structure (You et al.] 2018,] Kwon et al. 2019). Graph-based models (De Cao & Kipf. 2018 Shi al., 2020 Jin et al. 2020b), therefore, have gained increasing attention recently. [i ct al. (018b) proposed a generation model of graphs and demonstrated it performed better than text-based generation models on molecule generation. You al. (2018) used reinforcement learn- ing to fuse rewards of chemical validity and property scores into each step of generating molecule. Popova et al. (2019) proposed an MRNN to autoregressively generate nodes and edges based on the generated graph. [Shi et al. (2020) proposed flow-based autoregressive model and use reinforce- ment learning for the goal- directed molecular graph generation. However, these models use atom- level graph representation, which results in very long sequences, and therefore the training process is typically time-consuming. Our method is graph-based and uses substructure-lews representation for graphs, which not only captures chemical properties but also is computationally efficient.
Substructure-level Graph Representation Jin et al. (2018) proposed to generate molecules in the form of junction trees where each node is ring or edge. Din al. (2220a) decomposed molecules into substructures by breaking all the bridge bonds. It used complex hicrarchical model for poly- mer generation and graph-to-graph translation. Jin et al. (2020b) proposed to extract the smallest substructure which maintains the original chemical property. The extracted substructures usually in- clude most atoms of the original molecules, which are too coarse- -aasee-raiied and exert limitations on the search space. The models proposed by Jin et al. (2020a) and Ii et al. (2020b) are not suitable for the experiments in this paper since they either need graph-to-graph supervised data or are incompatible with continuous properties. There exists various methods to discover frequent subgraphs (Inokuchi ct al., 2000 Yan & Han 2002 Nijssen & Kok| 2004). However, they have difficulty decomposing graphs into frequent subgraphs (Jazayeri & Yang 1021) since they mainly aim to discover frequent subgraphs as additional features for downstream network analysis. Therefore they can hardly be applied to substructure-lewe molecular graph representation. Different from Jin al. (2018) 2020a) which use manual rules to extract substructures, we automatically extract common substructures which better capture the regularities in molecules for substmucture-level decomposition.
APPROACH
We first give the definition of graph pieces and algorithms for graph piece extraction in Section
3.1 Then we describe the encoder of our graph piece variational autoencoder model in Finally, we descibe the two-step decoder of GP-VAE in Section 3.3
Section 3.2 3.2
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Algorithm 1: Graph Piece Extraction
Input:
A set of graphs D and the desired number N of graph pieces to learn.
Result:
A set of graph pieces and the counter J of graph pieces.
begin
S GGrap 0]]}; Inirially, S corresponds all atoms appear in
N¹ max(N, |S]:
while N" do
F < EapttMapO::
D Initialize counter.
foreach 9
forall (P,, Eg) in
p Mergo (P,, E.)));
Merge neighboring graph pieces into grapk piece.
8 Graph SMILLE(P
p. Convert a graph to SMILES representation. Update the counter, default value a new O.
cnd
end
15
8 TopElem
Find the most frequent merged graph piece. Convert the SMILES string graph represeniution.
SMIL Gaipphst
S - SU D'
16
foreach 9 D MergeSubGrapp((..P
Update the graph representation possible.
D' + D' J
end
30
D D D end
22 end
3.1 GRAPH PIECE
A molecule can be represented as a graph G = (V,E), where V set of nodes that correspond atoms and is of edges that correspond to chemical bonds. Instead of using atoms, we use substructures, which we call graph pieces, as building blocks. We define a graph piece P as a subgraph (V, that appears in graph G. where V V and & S It should noted that either a single atom or whole graph is valid graph piece. Given set of graph pieces S. suppose the graph G can be decomposed into n graph pieces S, then G can be alternatively represented as (P.). (. where &gg denotes the set of edges between two neighboring graph pieces P. and P.. The decomposition of a graph G into graph pieces satisfies the following constraints:
Figure 2: Four graph pieces in example molecule. Different graph pieces highlighted in different colors.
(I) the union of all atoms in the graph
pieces equals to all atoms in the molecule, namely U, V4 = V: (2) there is no intersection between any two graph pieces, namely Vi # J.nn = 0. and &, nε, 0: (3) the union of all connections within and between graph pieces equals all bonds in the molecule, namely Ul, U E.j)) E, where i range from to and] range from i + 1 to Figure shows decomposed molecule.
The algorithm for extracting graph pieces from a given set of graphs D is given in Algorithm [ Our algorithm draws inspiration from Byte Pair Encoding (Gage) 1994, BPE). Initially, graph & in D is decomposed into atom-level graph pieces and the vocabulary S of graph pieces is composed of all unique atom-level graph pieces that appear in D. Given the number N of graph pieces to learn, each iteration, our algorithm enumerates all neighboring graph pieces and edges that connect the two graph pieces in G, namely (P:, Pj, E.y). ). As (P., Pjs Eiz) is also valid subgraph, we merge it into graph piece and count its occurrence. We find the most frequent merged graph piece and add it into the vocabulary S. After that, also update graphs in D that contain by merging (P., P,, Egy) into P. The algorithm terminates when the vocabulary size exceeds the predefined number N. Note that we use SMILES (Weininger) 1988) represent a graph piece in our algorithm therefore we ensure the uniqueness of a graph piece. A running example of our graph piece extraction algorithm illustrated in Figure At test time, we first decompose a molecular graph into atom-level graph pieces, then apply the learned operations to merge the graph pieces into larger ones. This process ensures there is a piece-level decomposition for an arbitrary molecule. We provide the pseudo code for the piece-level decomposition in Appendix A for better understanding. We provide the complexity analysis for both algorithms in Appendix B
We use RDKit (www. rókit t .org) perform the conversion hetween molecular graph and SMILEE.
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(a) Initialization
(b) Iteration
(c) Iteration 2
Figure 3: Two iterations of our graph piece extraction algorithm on {C=CC=C, CC=CC, C-CCc). (a) The vocabulary initialized with atoms. (b) Graph piece CC is the most frequent and added to the vocabulary. All CC are merged and highlighted in red. (c) Graph piece C=CC is the most frequent and added to the vocabulary. All C=CC are merged and highlighted in green (molecules and 3). After iterations the vocabulary is {c, CC, C-CCj. Note that due the uniqueness of SMILES, graph piece C=CC will not be translated into CC=C.
3.2 GRAPH ENCODER
As shown in Figure 4 use GNN to encode a molecular graph 9 represented by graph pieces into a latent variable z. Each node has feature vector 2o which indicates its atomic type, the type, and generation order of the graph piece it is in. Each edge has feature vector indicating its bond type. Modern GNNs follow neighborhood aggregation strategy (Xu et al.) 2018). which iteratively update the representations of nodes with AGGREGATE and COMBINE operations. The representation of node v in the k-th iteration is calculated follows:
AGGREGATE" (LA M (NU)),,
(1)
h(4) COMBINE( (n! a ())
(2)
where AGGREGATE and COMBINE vary in different GNNs. N(w) denotes neighboring nodes
of e. We set to Ta and use GIN with edges feature (Hu et al. 2019) the backbone GNN network, which implements AGGREGATE and COMBINE as follows:
a = Σ
Re (k-1) + eav),
(3)
mEN(()
(k-1) 100h = he((1 + +ehh 8)h! (%))
(4)
where he is neural network and 8 is constant. We implement he as a 2-layer multilayer per- ceptron (Gardner& & Dorling 1998 MLP) with ReLU activation and set E = 0. Since the k-th representation captures k- h-hop feature of nodes (Xu et al. 2018). we obtain the final representations of nodes as h, [n_") we compute the representation of the graph G through summation hg Evev h. We use hg to obtain the mean lrg and log variance ag of variational posterior approximation q(2[g) through two separate linear layers and use the reparameterization trick (Kingma & Welling 2013) to sample
! so that contains 1-hop to (-hop contextual information. Then
from the distribution in the training process.
3.3 TWO-STEP DECODER
With a molecule & represented as ((P.), (Ei, H), our model generates (P.} and {Ey } in two con- secutive phases. The two phases move from coarse to fine granularity.
Piece-level Sequence Generation Given a latent variable z, our model first uses an autoregressive sequence generation model P(P,)Pec,,)) to decode sequence of graph pieces [Pıy..., P. Dur- ing training, we insert two special tokens "<bos>" and "<eos>" into the begin and the end of the graph piece sequence to indicate the begin and the end. respectively. During testing, the generation stops when a "<eos>" is generated. The sequence model can be RNNs, such as LSTM (Hochreiter Schmidhuber 1997) and GRU (Cho et al., 2014). In this work, we use a single layer of GRU and project the latent variable to the initial state of GRU. The training objective of this stage is to minimize the log- likeelllooodd Lp of the ground truth graph piece sequence:
Cp
log P(P.(Pei.))
(S)
The ordering of graph pieces not unique. We train with order and leave this problem for future work.
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(9)
(6)
(8)
GRU
GRU
GRU
GRU
GRU
10x
Figure 4: Overview of the graph piece variational auloencoder. (a) Piece-level decomposition.
Atoms and bonds which belong to different graph pieces are highlighted in different colors. (b) Molecular graph. We inject piece-level information into the molecular graph through atom features.
(c) Latent space encoding. We obtain the latent variable & through the graph encoder (Section (d) Piece-level sequence generation. sequence of graph pieces is auto-regressively decoded from the latent variable by GRU (Section 3.3) (e) Incomplete molecular graph. The generated graph pieces form an incomplete molecular graph where inter-piece bonds are absent. (f) Bond completion. Completion of inter-piece bonds is formalized as a link prediction task for GNN (Section 3.3 After training, we can directly sample from the latent space to generate molecules.
3.2
Bond Completion We generate {Eir} non-autoregressivlly For the architecture, we use a GNN with the same structure as the graph encoder in Section 3.2 but with different parameters to obtain the representations h of each atom the graph pieces. Given nodes and u, we predict their connections as follows:
p(euol=)= = Ho(ho hu; zl),
(6)
where He is neural network. In this work we adopt 3-layer MLP with ReLU activation. Apart from the types of chemical bonds, we also add special type "<none>" to the edge vocabulary which indicates there is no connection between two nodes. During training, we predict both P(e.v)
and P(e..) to let Ha learn the undirected nature of chemical bonds. We use negative sampling (Goldberg & Levy 2014) balance the ratio of "<none>" and chemical bonds. Since only about 2% pairs of nodes has inter-pices connections, negative sampling significantly improves the com- putational efficiency and scalability. The training objective of this stage is minimize the log- likelihood Cg of the ground truth inter- sier-ppece connections:
LE
Σ
log P(eun|z).
NEP,.EP,,.44
The reconstruction loss of our GP-VAE model is:
Lree Ls Lgg
(8)
To decode (Eig) inference time, the decoder first assigns possible inter-piece connections with bond type and corresponding confidence level. We try to add bonds that have a confidence level higher than &n = 0.5 to the molecule in order of confidence level from high to low. For each attempt, perform valency check and cycle check to reject the connections that will cause violation of valency or form unstable rings which are too small or too large. Since this procedure may form unconnected graphs, find the maximal connected component the result of the generation. We present the pseudo code for inference in Appendix C
We jointly train 2-layer MI.P from z to predict the scores of target properties using the MSE loss. Denote the loss the predictor as Lappp the loss function of our GP-VAE is:
f = aLac a + BDL.. 3
where a and 3 balance the reconstruction loss, the property loss, and the KL divergence DKI. be- tween the distribution of and the prior distribution (O, I).
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4 EXPERIMENTS
4.1 SETUP
Evaluation Tasks We first report the empirical results for the distribution- -eaauuinninnnnnnnnnngggnn tasks of the GuacaMol benchmark (Brown et al. 2019) to evaluate the ability of the model to generate realistic and diverse molecules. Then we validate our model on two goal-directed tasks. Property Optimiza- tion requires generating molecules with optimized properties. Constrained Property Optimization concentrates on improving the properties given molecules with a restricted degree of modification.
Dataset We use the ZINC250K (Irwin et al., 2012) dataset for training, which contains 250,000 drug-like molecules up to 38 atoms. For GuacaMol benchmark, we also add results on the QM9 (Blum & Reymond 2009 Rupp et al. 2012) dataset, which has 7,165 molecules up to 23 atoms.
Baselines We compare our graph piece variational autoencoder (GP-VAE) with the following state-of-the-art models. JT-VAE (Jin et al.) 2018) is a variational autoencoder that represents molecules as junction trees. It performs Bayesian optimization on the latent variable for property optimization. GCPN (You et al. 2018) combines reinforcement learning and graph representation for goal-directed molecular graph generation. MRNN (Popova et al. 2019) adopts two RNNs to autoregressively generate atoms and bonds respectively. combines policy gradient optimization to generate molecules with desired properties. Graph (Shi et al.) 2020) is flow-based autoregres- sive model which is first pretrained for likelihood modeling and then fine-tuned with reinforcement learning for property optimization.6e GA (Nigam et al.) 2020) adopts genetic algorithms for property optimization and model the selection of the subsequent population with neural network.
Implementation Details We choose N 300 for property optimization and N = 500 for con- strained property optimization. GP-VA EAE is trained for epochs with batch size of 32 and learning rate of 0.001. We set 0.1 and initialize 3 O. We adopt a warm-up method that increases 3 by 0.002 every 1000 steps to a maximum of 0.01. More details can be found in Appendix
4.2 RESULTS
GuacaMol EestriuutionLeeaniig Benchmarks The distribution-learne benchmarks incorpo- rate five metrics 10,000 molecules generated by the models. Validity measures whether the gen- crated molecules are chemically valid. Uniqueness penalizes models when they generate the same molecule multiple times. Novelty assesses the ability of the models to generate molecules that are not present the training set. KL Divergence measures the closeness of the probability distributions of variety of physicochemical descriptors for the training set and the generated molecules. Fréchet ChemNet Distance ( (FCD) calculates the closeness of the two sets of molecules with respect to their hidden representations in the ChemNet trained for predicting biological activities. Each metrie is normalized to 0 to 1, and a higher value indicates better performance. Table shows the results of Destrbutionn-eerning benchmarks on QM9 and ZINC250K. Our model achieves competitive results in all five metrics, which indicates our model can generate realistic molecules and does not overfit the training set. We present some molecules sampled from the prior distribution in Appendix !
Table I: Results of GuacaMol distribution-Leariin benchmarks on QM9 and ZINC250K. KL Div refers to KL Divergence and FCD refers to Fréchet ChemNet Distance.
Model
Validity(1)
Uniqueness(t) Novelty(t)
KL Div(t)
FCD(1)
QM9
GraphAF
1.0
0.500
0.453
0.761
0.326
GA
1.0
0.008
0.008
0.429
0.004
GP-VAE(ours)
0.673
0.523
0.921
0.659
ZINC250K
GraphAF
1.0
0,288
0.287
0.508
0.023
GA
1.0
0.008
0.008
0.705
0.001
GP-VAF(ours)
1.0
0.997
0.997
0.850
0.318

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Property Optimization This task focuses on generating molecules with optimized Penalized logP (Kusner et al. 2017) and QED (Bickerton et al. 2012). Penalized logP is logP penalized by synthesis accessibility and ring size which has unbounded range. QED measures the drug-likeness of molecules with a range of [.. Both properties are calculated by empirical prediction models
(Wildman & Crippen 1999 Bickerton et al.] 2012). and are widely used in previous works (Tin
et al. [2018] You et al. 2018 Shi et al. (020). We adopt the scripts of Shi et al.) (2020) to calculate property scores so that the results are comparable. We directly perform gradient ascending on the
2018). Hyperparameters can be found in Appendix D Following previous works (Jin et al. 2018 You et al.) 2018 Shi al.) 2020), we generate 10,000 optimized molecules from the latent space and report the top-3 scores found by each model. Results in Table 2
latent variable (Jin et al. 2018 Luo et al.
show that our model surpasses the state-of-the-art models consistently.
Table 2: Comparison of the top-3 property scores found by each model
Penalized logP f
QED f
Method
1st
2nd
3rd
Validity
1st
2nd
3rd
Validity
ZINC250K
4.52
4.30
4.23
100.0%
0.948
0.948
0.948
100.0%
JT-VAE
5.30
4.93
4.49
100.0%
0.925
0.911
0.910
100.0%
GCPN
7.98
7.85
7.80
100.0%
0.948
0.947
0.946
100.0%
MRNN
8.63
6.08
4.73
100.0%
0.844
0.796
0.736
100.0%
GraphAF
12.23
11.29
11.05
100.0%
0.948
0.948
0.947
100.0%
GA
12.25
12.22
12.20
100.0%
0.946
0.944
0,932
100.0%
GP-VAE 13.95
13.83
13.65
100.0%
0.948
0.948
0.948
100.0%
Constrained Property Optimization This task concentrates on improving the property scores of given molecules with the constraint that the similarity between the original molecule and the modi- fied molecule is above a threshold d. Following Jin et al. 2018); You et al. (2018); Shi et al. (2020), choose 800 molecules with lowest Penalized logP in the test set of ZINC250K for optimization and Tanimoto similarity with Morgan fingerprint (Rogers & Hahn 2010 as the similarity metric.
Similar the property optimization task, perform gradient ascending the latent variable with a max step of 80. We collect all latent variables which have better-predicted scores than the previous iteration and decode each of them 5 times, namely up to 400 molecules. Following Shhi et al. (2020), we initialize the generation with sub-graphs sampled from the original molecules. Then we choose the one with the highest property score from the molecules that meet the similarity constraint. Table 3 shows our model can generate molecules with a higher Penalized logP score while satisfying the similarity constraint. Since our model uses graph pieces as building blocks, the degree of modification tends to be greater than atom-level models, leading to lower success rate. Nevertheless, our model still manages to achieve high success rates close to atom-level models.
Table 3: Comparison of the mean and standard deviation of improvement of each model on con- strained property optimization.
8 8= 0.2
8 0.4
8 0.6
Model
Improvement
Success
Improvement
Success
Improvement
Success
JT-VAE 1.68+1.85
97.1%
0.84
83.6%
0.21
46.4%
GCPN
4.12+11.19
100%
2.49+11.30
100%
0.79+00.3
100%
GraphAH
4.99
100%
3.24
100%
1.95+0.99
98.4%
GA 3.04
100%
2.34
100%
1.36
95.9%
GP-VAE
6.42+11.8
99.9%
4.19=1.30
98.9%
2.52+1112
90.3%
RRsslls are obtained by running the seripts from the original paper and use the scripts of Shi al. 2020 to evaluate property scores. WWe rerun GraphAF on the same 800 molecules using its script to obtain the results since the original paper chooses different of 800 molecules whose results are not comparable.
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4.3 RUNTIME COST
We train VT-,AE GraphAF and our GP-VAE on machine with 1 NVIDIA GeForee RTX 2080Ti GPU and 32 CPU cores and use them to generate 10,000 molecules to compare their efficiency of training and inference. As shown in Table 4 our model achieves significant improvements the ef- ficiency of training and inference due to graph pieces and the two-step generation. With graph pieces building blocks, the number of steps required compared to the atom-level models like GraphAF. Moreover, since the two-step generation approach separates the generation of graph pieces and the connections between them into two stage and for- malizes the bond completion stage as a link prediction task, it avoids the complex enumeration of possible combinations adopted by JA-. Therefore, our model achieves tremendous improvement in computational efficiency over both atom-level and substructure-level baselines.
generate a molecules is significantly decreased
Table 4: Runtime cost for JT-VAE, GraphAF and our EP-VAE on the ZINC250K dataset. Inference time is measured with the generation of 10,000 molecules. Avg Step denotes the average number of steps each model requires to generate a molecule.
Model
Training
Inference
Avg Step
JA-VAE
24 hours
20 hours
15.50
GraphAF
7 hours
10 hours
56.88
GP-VAE (ours)
1.2 hours
0.3 hour
6.84
4.4 ABLATION STUDY
We conduct an ablation study further validate the effects of graph pieces and the two-step genera- tion approach. We first downgrade the vocabulary to contain only single atoms. Then we replace the two-step decoder with fully auto-regressive decoder. We present the performance on property op- timization and constrained property optimization after the modification in Table S direct introduction of the two-step generation approach leads improvement on property optimiza- constrained property optimization. This is because separating
and Table The
tion but harms the performance the generation of atoms and bonds brings massive loss of bond information for the atom generation process. However, the adoption of graph pieces building blocks alleviates this negative effect since the graph pieces themselves contain abundant bond information. Therefore, while two- step generation approach enhances computational efficiency, the state-of-ther the-arrt performance of our model mainly credited to the use of graph pieces.
Table 5: The top-3 property scores found by GP-VAE without certain modules.
Penalized logP
QED
Method
1st
2nd
3rd
Validity
1st
2nd
3rd
Validity
GP-VAE
13.95
13.83
13.65
100.0%
0.948
0.948
0.948
100.0%
piece
6.91
5.50
100.0%
0.870
0.869
0.869
100.0%
two-step
3.54
3.54
3.22
100.0%
0.737
0.734
0.729
100.0%
Table 6: Comparison of GP-VA VAE without certain modules on constrained property optimization
8 0.2
0.4
5 0.6
Model
Improvement
Success
Improvement
Success
Improvement
Success
GP-VAE
6.82
99.9%
4.19.111.30
98.9%
2.52
90.3%
piece
2.33=1.46
74.8%
2.12-11.36
50.9%
1.87-11.12
27.0%
two-step
3.36=1.58
98.6%
2.72
82.0%
1.88=1100
45.1%
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5 ANALYSIS
5.1 GRAPH PIECE STATISTICS
We compare the statistical characteristics of the vocabulary of JT- that contains 780 substruc- tures and the vocabulary of graph pieces with a size of 100, 300, 500, and 700. Figure shows the proportion of substructures with different numbers of atoms the vocabulary and their frequencies of occurrence in the ZINC250K dataset. The substructures in the vocabulary of JT-VAE mainly concentrate on 5 to 8 atoms with a sharp distribution. However, starting from substructures with atoms, the frequency of occurrence is already close to zero. Therefore, the majority of substructures in the vocabulary of JT-VAE are actually not common substructures. On the contrary, the substruc- tures in the vocabulary of graph pieces have a relatively smooth distribution over 4 to 10 atoms. Moreover, these substructures also have a much higher frequency of occurrence compared to those in the vocabulary of JT VAE. We present samples of graph pieces in Appendix H
0.30
Jtvae
Evas
2 100
1=0
300
Requnny occumenca
N-3
500
K-500
0.20
700
N07
63-
82-
0.10-
0.00
Number
Figure 5: The left and right figures show the proportion of and frequency of occurrence of substruc- tures with different number of atoms in the vocabulary, respectively.
5.2 PROPER GRANULARITY
larger N the graph piece extraction process leads to an increase in the number of atoms in graph pieces and decrease in their frequency of occurrence, illustrated in Figure These factors affect model performance in opposite ways. On the one hand, the entropy of the dataset decreases with more coarse- grained decomposition (Martin & England 201T), which benefits model learning (Bentz& & Alikaniotis 2016). On the other hand, the sparsity problem worsens as the frequency of graph pieces decreases, which hurts model learning (Allison al., 2006). We propose a quantified method to balance entropy and sparsity. The entropy of the dataset given set of graph pieces S is defined by the sum of the entropy of each graph piece normalized by the average number of atoms:
1 Σ log)
Hs
(10)
RS PES
where P(P) is the relative frequency of graph piece P in the dataset and n. is the average number of atoms of graph pieces in S. The sparsity of is defined as the reciprocal of the average frequency of graph pieces normalized by the size of the dataset:
M
Ss
(11)
fs
where M is the number of molecules in the dataset and fs is the average frequency of occurrence of graph pieces in the dataset. Then the entropy sparsity trade-off (T) can be expressed as:
T's Hs + SS
(12)
where y balances the impacts of entropy and sparsity since the impacts vary across different tasks. We assume that Ts negatively correlates with downstream tasks. Given a task, we first sample several values of N to calculate their values of T and then compute the y that minimize the Pearson correlation coefficient between T and the corresponding performance on the task. With the proper y, Pearson correlation coefficients for the three downstream tasks in this paper are -0.987, -0.999, and

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Under review as a conference paper at ICLR 2022
-0.707, indicating strong negative correlations. For example, Figure shows the of entropy sparsity trade-off with maximum of 3,000 iteration steps for the property optimization task. From the curve, choose N 300 for the property optimization task.
PARTOO Number 2h10m
Ennee Spectty
3000
2000
2005
3000
Figure 6: Entropy Sparsity trade-off, average number of atoms in graph pieces and average fre- quency of occurrence of graph pieces with maximum 3,000 iteration steps.
5.3 GRAPH PIECE PROPERTY CORRELATION
To analyze the graph piece-propens correlation and whether our model can discover and utilize the correlation, present the normalized distribution of generated graph pieces and Pearson correlation coefficient between the graph pieces and score of Penalized logP (PlogP) in Figure 7
The curve of the Pearson correlation coeffcient indicates that some graph pieces positively correlate with PlogP and some negatively correlate with it. Compared with the flat distribution under the non- optimization setting, the generated distribution shifts towards the graph pieces positively correlated with PlogP under the Poog-ooptimization setting. The generation of graph pieces negatively corre- lated with PlogP is also suppressed. Therefore, correlations exist between graph pieces and PlogP, and our model can accurately discover and utilize these correlations for PlogP optimization.
Porner Cire ehn Cuetont
Oven Pocce
Figure 7: The distributions of generated graph pieces with and without optimization of PlogP, as well as Pearson correlation coefficient between the graph pieces and the score of PlogP. PlogP refers to Penalized logP. The distributions are normalized by the distribution of the training set, which means the frequency of occurrence of graph piece is divided by its count of occurrence the training set.
CONCLUSION
We propose an algorithm to automatically discover the regularity molecules and extract them as graph pieces. We also propose graph piece variational autoencoder utilizing the graph pieces and generate molecules in two phases. Our model consistently outperforms state-of-the-an models distribution-leamiin property optimization and constrained property optimization with higher computational efficiency.Our work provides insights into the selection of granularity on molecular graph generation and inspire future search in this direction.
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A PIECE-LEVEL DECOMPOSITION ALGORITHM
Algorithm 2 presents the pseudo code for the piece-level decomposition of molecules. The algo- rithm takes the atom-level molecular graph, the vocabulary of graph pieces and their frequencies of occurrence recorded during the graph piece extraction process as input. Then the algorithm it- eratively merge the graph piece pair which has the highest recorded frequency of occurrence in the vocabulary until all graph piece pairs are not in the vocabulary.
Algorithm 2:
Piece-I Level Decomposition
Input: graph G that decomposed into utom-level pieces, the set learned graphs pieces,
and the counter If of learned graph pieces.
Result: A new representation G' of that consists of graph pieces in S.
begin
g' <- G:
while True
freq <
1;P None;
Torall Py.PP,EEs)) in G' do
p' + Mergel (P,, Ey))))
b. Merge neighboring graph pieces into grapk piece. Convert graph SMILES representation.
GraphTTSMIIESSS
if in and Fla] > freg then
freg Fla
p pl;
end
end
13
if freg = then
M
break;
15
G' MergeSubCraphi((I
Update the graph representation.
end
end
end
B COMPLEXITY ANALYSIS
Graph Piece Extraction Since the number of graph piece pairs equals the number of inter-piece connections in the piece-level graph, the complexity is O(NMe). where N is the predefined size of vocabulary, M denotes the number of molecules in the dataset, and denotes the maximal number of inter-piece connections in single molecule. The number of inter-piece connections decreases rapidly in the first few iterations, therefore the time cost for each iteration decreases rapidly. It cost 6 hours to perform 500 iterations on 250,000 molecules in the ZINC250K dataset with 4 CPU cores.
Piece-Leved Decompusition Given an arbitrary molecule, the worst case is that each iteration adds one atom existing subgraph until the molecule is finally merged into single graph piece. In this case the algorithm runs for V iterations. Therefore, the complexity is O(Vi) where V includes all the atoms in the molecule.
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C INFERENCE ALGORITHM FOR BOND COMPLETION
Algorithm 3 shows the pseudo code of our inference algorithm. We first predict the bonds between all possible pairs of atoms in which the two atoms are different graph pieces and sort them by the confidence level given by the model from high to low. Then for each bond with confidence level higher then the predefined threshold dcs, which is 0.5 in our experiments, we add into molecular graph if it passes the valence check and cycle check. The valence check ensures the given bond will not violate valence rules. The cycle check ensures the given bond will not form unstable rings with nodes less than 5 more than 6.
Algorithm 3: Inference Algorithm for Bond Completion
Input:
An incomplete molecular graph & composed of graph pieces where inter- inter-piece bonds are absent, the predicted bond type for all possible inter-piece connections B and the map to their confidence level C, the threshold for confidence level dzh A valid molecular graph G'
Result:
begin
G' 9;
+ Sort.ByConficeeceeB... forall buo in B do if C(buul 6eh then
> Sort the bonds by their confidence level from high low.
continue;
Discard edges with confidence level lower than the threshold.
if valence
check((..)) valence.check(bbr. and cycle.check((bo then G' <- AddEdge(S buv);
b Add edges that pass valence and cycle check to G'
end
11
end
MaxCComectaCCompoenn(())
Find the maximal connected component in g'
13 end
D EXPERIMENT DETAILS
Model and Training Hyperparameters We present the choice model parameters in Table and training parameters in Table 8 We represent atom with three features: atom embedding. piece embedding and position embedding. Atom embedding is a trainable vector of size Catom for each type of atoms. Similarly, piece embedding is trainable vector of size épiece for each type of pieces. Positions indicate the order of generation of pieces. We jointly train 2-layer MLP from the latent variable to predict property scores. The training loss represented as C a Liee + a) Lpopp + 3 DRL where balances the reconstruction loss and prediction loss. For 3, we adopt warm-up method that increase by Bauage every fixed number of steps maximum of 9mm.. We found 33 higher than 0.01 often causes KI. vanishing problem and greatly harm the performance. Our model and the baselines are trained on the ZINC250K dataset with the same train valid test split as in Kusner et al. (2017).
Table 7: Parameters in the graph piece variational autoencoder
Model
Param
Description
Value
atomm
Dimension of embeddings of atoms.
50
Common
Epicoo
Dimension of embeddings of pieces.
100
Dimension of embeddings of postions.
Epos
The max position is set to be 50.
50
Dimension of the node representations h,
300
Encoder
dg
The final representaion of graphs are projected to dg.
400
dz
Dimension of the latent variable.
56
Number of iterations of GIN.
4
Decoder
dGRU dp
Hidden size of GRU.
200
Predictor
Dimension of the hidden layer of MLP.
200
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Table 8: Training hyperparameters
Param
Description
Value
Ir
Learning rate
0.001
Weight for balancing reconstruction loss and predictor loss
0.1
Buii
Initial weight KL Divergence
miax
Max weight of KL Divergence
0.01
kiwaarmu
The number of steps for one stage up in /
1000
Pstage
Increase of B every stage
0.002
use gradient ascending to search in the continuous space of latent variable. For simplicity, we set target score and optimize the mean square error between the score given by the predictor and the target score just as in the training process. The optimization stops if the mean square error does not drop for 3 iterations normalize the Penalized logP in the training set to [0, 1] according to the statistics of ZINC250K. By setting target value higher than the model is supposed to find molecules with better property than the molecules in the training set. To acquire the best performance, we perform a grid search with ir E {0.001, 0.01, 0.1, 2). mazslep (20, 40, 60, 80, 100} and largel {1, 4). For optimization of QED, we choose Ir 0.01, mazstep = 100, target = 2. For optimization of Penalized logP, we choose 0.1, marstep 100, tar
Property Optimization
has been iterated the marstep. We
65483
09422
-10244
23002
2006
D5482
03ste
(a) Penalized logP optimization
(b) QED optimization
(c) Constrained optimization of Pe- nalized logP
Figure 8: Samples of property optimization and constrained property optimization. In (c) the first and the second columns are the original and modified molecules labeled with their Penalized logP.
Constrained Property Optimization We use the same method as property optimization to opti- mize the latent variable. We also perform grid search with Ir E {0.1, 0.01} and target E {2, 3). We select Ir 0.1, maastep 80 and target = For decoding, we first initialize the generation with submol sampled from the original molecule by teacher forcing. We follow Shi et al. (2020) to first sample a BFS order of atoms and then randomly drop out last m atoms with m up to 5. We collect all latent variables which have better predicted scores than the previous iteration and decode each of them 5 times, namely up to 400 molecules. Then we choose the one with the highest property score from the molecules that meet the similarity constraint. For the baseline GA (Ahn et al., 2020). we adjust the number of iterations to and the size of population to 80, namely traversing up 400 molecules, for fair comparison.
E DATA EFFICIENCY
Since the graph pieces are common subgraphs in the molecular graphs, they should be relatively stable with respect to the scale of training set. validate this assumption, we choose subsets of different ratios to the training set for training observe the trend of the coverage of Top 100 graph pieces the vocabularies as well as the model performance on the average score of the distribution- learning benchmarks. As illustrated in Figure 9 with subset above 20% of the training set, the constructed vocabulary covers more than 95% of the top 100 graph pieces in the full training set, as well as the model performance the distribution-leamii benchmarks.
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Distribution Leaming Perforaacee
0.8
0.88
Graph Piaca Coverage
dalasel OMS
dalaset QNO
0.4
0.4
0.0
0.0
(a) Top 100 graph piece coverage
(b) Distribution-leariin benchmarks performance
Figure 9: The coverage of top 100 graph pieces and the relative performance on the distribution- learning benchmarks with respect to subsets of different ratios the full training set.
F FUSED RINGS GENERATION
We conduct an additional experiment to validate the ability of GP-VAE to generate molecules with fused rings (cycles with shared edges), because first thought it seems difficult for GP-VAE to handle these molecules due to the non-overlapping nature of graph pieces. We train atom-level and piece-level GP-VAEs all 4,431 structures consisting of fused rings from ZINC250K. Then we sample 1,000 molecules from the latent space to calculate the proportion of molecules with fused rings. The results are 94.5% and 97.2% for the atom-level model and the piece-level model, respectively. The experiment demonstrates that the introduction of graph pieces as building blocks will hinder the generation of molecules with fused rings.
Figure 10: Decomposition of three molecules with fused rings (cycles that share edges).
G DISCUSSION
Universal Granularity Adaption The concept and extraction algorithm of graph pieces resemble those of subword units (Sennrich et al., (2015) in machine translation. Though subword units de- signed for the out-of-vocabularyy problem of machine translation, they also improve the translation quality (Sennrich al., 2015). In this work, we demonstrate the power of graph pieces and are curi- ous about whether there is universal way adapt atom-level models into picce-level counterparts to improve their generation quality. The key challenge is to find an efficient and expressive way to encode inter-piece connections into feature vectors. We leave this for future work.
Searching in Continuous Space In recent years, reinforcement learning (RL) is becoming dom- inant in the field of optimization of molecular properties You et al.) [2018] Shi et al. 2020). These RL models usually suffer from reward sparsity when applied to multi-objective optimization (Jin) et al. 2020b). However, most scenarios that incorporate molecular property optimization have multi-objective constraints (e.g.,drug discovery). In this work, we show that with graph pieces, simple searching method like gradient ascending surpass RL methods single-objective optimization. It is possible that with better searching methods in continuous space our model can achieve competitive results multi-objective optimization.
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H
GRAPH PIECE SAMPLES
We present 50 graph pieces found by our extraction algorithm in Figure 11
CC
OCHCE
8
0.5
XCO
CCD
CCCCHO
0-5-0
copao
G+OCH-do-db-c
WOH0C-CCHCI
CONC
0000)000-004
W
COC.0
COCCC-O
cagp
CNON
CCUCOC
CONDTE-
CCLCCC-NNCC
Figure 11: 50 Samples of graph pieces from the vocabulary with 100 graph pieces in total. Each graph piece is labeled with its SMILES representation.
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1 MORE MOLECULE SAMPLES
We further present 50 molecules sampled from the prior distribution in Figure 12
8a
expt
awt
olop
Buoo
ano
stoee
9
onpp
Figure 12: 50 molecules sampled from the prior distribution N/ I)
18


Reviews:
[{"review_id": "yhGe-UEumQi", "reviewer": "Reviewer_TrJs", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "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": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "The manuscript is unclear: how exactly is the piece level sequence generation autoregressive model connected to the bond completion? how is the fine structure (ie the nodes and edges) of each piece generated so that the bond-completion model can work only on nodes across different pieces? The summary offered is too high level and crucial information is missing (also Fig 5 is too generic). \n\nThe properties of the proposed way to generate pieces (fragments) are unclear: what is the size distribution of the fragments generated? It seems that very large fragments would be generated, but then those would be very infrequent (?), how is the tradeoff between frequency and size controlled? Why aren't there any experiments to showcase the sensitivity of the approach to the number of fragments?  What is the computational complexity of the fragment generation phase?\nHow often are novel fragments appearing as a function of the training set size? What are the consequences of this, with respect to the generalisation/representational capacity of the approach? i.e. the smaller the training sample the fewer the fragments (and vice versa).\nEfficiency in this case seems to be in trade off with flexibility and capacity to generate novel substructures: can experiments be devised to evaluate this trade-off in a quantitative way?\nWhy is the vast literature of graph mining completely absent in the review section? \n", "summary_of_the_paper": "The author propose a variational auto encoder for graphs based on an autoregressive model for larger fragments and a GNN for edge prediction to connect the fragments. ", "summary_of_the_review": "The justification for this work is that autoregressive models tend to ignore the existence of common substructures and hence a specific mechanism that is aware of larger fragments is needed. This fact is however never demonstrated and possibly incorrect (that is autoregressive models do not encode explicitly substructures but do this in the latent space given the compression constraints they are subject to). It would be of interest if the paper would analyse this statement empirically or theoretically, but the only results available are the usual weakly informative experiments on validity, uniqueness and novelty, and property optimization experiments (without any notion of statistical significance for the comparative results). \nThe presentation is overall unclear and the literature review incomplete. ", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "J1knh56FC9", "reviewer": "Reviewer_sMpt", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "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": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "The graph piece extraction algorithm is not clear. The iteration 1 highlights the most frequent piece CC in Fig4(b). Then how C=CC in Fig4(c) is searched by merging CC and C? Line 12 of the pseudo code in appendix is not clear about how to do  “mol.merge(piece)”. Line 10 finds only the most frequent piece? Or the two most frequent pieces?  What if these two most ferquent pieces are not connectable in molecules? \nAnd how expensive the process will be?  \nFor molecules with rare atoms, their piece-level decomposition will be a set of single atoms?  A pseudo code algorithm will be helpful for understanding.  \n\nIn Fig 5, the GNN was applied on decomposed molecule. However, section 3.3. introduces that GNN is applied on the whole graph G, like what has been done in previous GNN-based molecular graph representation. \n\nAnother concern is about the generated results. The proposed model has lower uniqueness than JT-VAE and GCPN, although very close in uniqueness metric values. \n\nQM9 is another very popularly used dataset for molecule generation evaluation. Evaluation and comparison on this QM9 dataset can strengthen the evaluation results. \n\nAn error to correct:  We try to add bonds which has \n", "summary_of_the_paper": "This is a paper working for molecule generation, especially considering the high-frequency and important subgraphs called graph pieces. ", "summary_of_the_review": "The details of the proposed model were not clearly introduced. The evaluation should be strengthened. ", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "8oWiQgvThpI", "reviewer": "Reviewer_LbDK", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 4, "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": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "## Strength\n\nAlthough each step of the proposed strategy is a straightforward application of existing methods, the overall proposed strategy is novel and interesting. In particular, it is interesting that the proposed method uses graph pieces in its training instead of directly using a given collection of graphs, which is the key idea of this paper.\n\nPresentation of this paper is good. The paper is clearly written overall.\n\n## Weakness \n\n- Empirical evaluation is not thorough. Recently it is widely known that benchmarks such as the penalized logP and QED are not appropriate for evaluation and using Guacamol is highly recommended (see https://pubs.acs.org/doi/abs/10.1021/acs.jcim.8b00839).  So please evaluate the proposal on Guacamol.\n- Ablation study is not convincing. An important evaluation is to compare the proposed method and that without the graph piece generation step, that is, directly using a given graph datasets in the training of GNN without decomposing them into graph pieces. This experiment tells us the effectiveness of the graph piece step.\n- The proposed graph piece extraction is fully based on sequence representations of graphs, hence it does not treat all the possible subgraphs of molecular graphs. Therefore, there should be various subgraphs that cannot be extracted by the proposed method. I wonder how crucial this loss of information is. Some discussion would be desirable.\n\nI am happy to increase my score if my concerns are addressed in the revision.\n", "summary_of_the_paper": "This paper proposes a new molecular graph generation method and empirically shows its effectiveness.\nThe proposed method first decomposes molecular graphs into smaller parts (called graph pieces), followed by training a variational autoencoder so that it can generate the collected graph pieces. The trained model is expected to generate a variety of graphs with desirable properties.\n", "summary_of_the_review": "The idea of the proposed method is technically interesting, while its empirical evaluation is not sufficient.", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "0O-gm_X3IAa", "reviewer": "Reviewer_ogN1", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "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": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "- strengths: \n\n\n1. The idea of using common substructures to generate molecular graphs is novel and original.\n\n\n2. The source code and dataset provided in supplementary material facilitate good reproducibility of this work. \n\n\n3. The authors claim that the proposed method has two benefits: (1) captures correlation; (2) accelerates computation. In my opinion, it seems that the essential benefit is that, using substructure instead of atoms could reduce the search space for this combinatorial problem. Maybe the authors could theoretically analyze this.\n\n\n- weaknesses:\n\n\n1. I would like to know the connection and difference between graph pieces and frequent subgraph discovery. Could the authors discuss this? \n\n\n2. How to obtain ground truth graph piece sequence, and why?\n\n\n3. The authors state that: larger N indicates more coarse-grained decomposition. Then, how to determine proper N for different down-stream tasks?\n\n\n4. The experiment is less convincing. The proposed method is only evaluated on one dataset ZINC250K. In Table 1, JT-VAE achieves perfect results, while the proposed method seems to show limited competitiveness.\n\n\n5. This work misses one very related baseline [ICML 2018] [GraphRNN] Generating Realistic Graphs with Deep Auto-regressive Models, which also generates graphs in an autoregressive fashion. The authors should discuss the differences between them, and compare the performance in the experiment.\n\n\n6. Figure 3 and Figure 6 are not mentioned and explained in the main text.\n\n\n7. The notations are confusing. In Section 3.1, the authors state that: \"$\\tilde \\varepsilon$ contains all the connections between the atoms in different graph pieces\". In Section 3.2, the authors state that: \"$\\tilde \\varepsilon$ contains all bonds connecting two atoms in A and B\".\n\n\n8. Algorithm 1 is not clear. What is the process of MolToSmiles? The authors are expected to clearly explain each line of the proposed algorithm.", "summary_of_the_paper": "This paper proposes to use substructures instead of atoms (nodes) for generating molecular graphs.", "summary_of_the_review": "The idea of this work is reasonable, but some technical details have not been clearly presented.", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}]

Author rebuttal:

Meta-review: While the reviewers appreciated the new methodology and presentation of the paper the reviewers were concerned about the experimental section. Specifically they wanted to see optimization outside of penalized logP and QED, which are now viewed by the community as toy molecule optimization tasks (e.g., Penalized logP can always be improved by just adding a longer chain of carbon atoms). The authors responded that this would have taken too long to run Guacamol tasks in the rebuttal phase as all methods would need to be rerun for all tasks, but this is not true: many methods e.g., Ahn et al., 2020, already have reported these results and could be directly compared against (as this paper is near state of the art this would have been a convincing comparison). Another odd thing about the experimental setup is that the authors compare with Ahn et al., 2020 only for constrained property prediction. However Ahn et al., 2020 achieves a Penalized logP of 31.40 whereas the proposed method only achieves 13.95. It's suspicious that this result is missing in Table 2 of the current paper. If the authors are able to improve their work beyond Ahn et al., 2020 and related recent work on Guacamol and othe real-world tasks, the paper will make a much stronger submission.
Decision: Reject