Molecule Generation by Principal Subgraph Mining and Assembling
Authors: Xiangzhe Kong
Wenbing Huang
Zhixing Tan
Yang Liu
Venue: NeurIPS 2022 Accept (2022)
Keywords: molecule generation
principal subgraph
global assembling

Abstract: Molecule generation is central to a variety of applications. Current attention has been paid to approaching the generation task as subgraph prediction and assembling. Nevertheless, these methods usually rely on hand-crafted or external subgraph construction, and the subgraph assembling depends solely on local arrangement. In this paper, we define a novel notion, principal subgraph that is closely related to the informative pattern within molecules. Interestingly, our proposed merge-and-update subgraph extraction method can automatically discover frequent principal subgraphs from the dataset, while previous methods are incapable of. Moreover, we develop a two-step subgraph assembling strategy, which first predicts a set of subgraphs in a sequence-wise manner and then assembles all generated subgraphs globally as the final output molecule.  Built upon graph variational auto-encoder, our model is demonstrated to be effective in terms of several evaluation metrics and efficiency, compared with state-of-the-art methods on distribution learning and (constrained) property optimization tasks.

Molecule Generation by Principal Subgraph Mining and Assembling
Xiangzhe Kong' Wenbing Huang Zhixing Tan Yang Liu 12,3+
l Dept. of Comp. Sci. & Tech., Institute for AI, BNRist Center, Tsinghua University 2 Institute for AIR, Tsinghua University BBejjngg Academy of Artificial Intelligence GGollin School of Artificial Intelligence, Renmin University China 5 Beijing Key Laboratory of Big Data Management and Analysis Methods, Beijing, China Jackie KXZ@outlook. com, hwenbing@126. com, {zxtan, liuyang2011 @tsinghuttsinnaa edu. cn
Abstract
Molecule generation is central to variety of applications. Current attention has been paid to approaching the generation task as subgraph prediction and assembling. Nevertheless, these methods usually rely on hand-crafted construction, and the subgraph assembling depends solely on local arrangement. In this paper, we define novel notion, principal subgraph that is closely related the informative pattern within molecules. Interestingly. our proposed merge-and- update subgraph extraction method automatically discover frequent principal subgraphs from the dataset, while previous methods are incapable of. Moreover, we develop a two-step subgraph assembling strategy, which first predicts a of subgraphs in sequence-wist manner and then assembles all generated subgraphs globally as the final output molecule. Built upon graph variational auto-encoder, our model is demonstrated to be effective in terms of several evaluation metrics and efficiency, compared with state-of-the-aae methods on distribution learning and (constrained) property optimization tasks.
external subgraph
Introduction
Generating chemically valid molecules with desired properties is central to a variety of applications in drug discovery and material science. In contrast to searching countless potential candidates by expert chemists or pharmacologists, designing generative models that can produce molecules automatically is more efficient and now prevailing topic in machine learning. Recently, there have been various works[18, 26, 47, 24, 9, 39, 20] utilizing graphs to characterize the distribution of molecules.
83.9%
60.5%
41.3%
32.6%
27.5%
Figure 1: Five frequent subgraphs in ZINC250K [16, 23] marked with their frequencies of occurrence.
In general, these craph-based generation methods be clustered into two categories: the atom level [25, 47, 26, 20] and the subgraph level [18, 19, 46], in terms of what the basic generation unit is. Compared with the atom-level methods, exploring subgraphs for generating molecules (as illustrated in Figure 1) exhibits three potential benefits. First, can capture the regularities of atomic combinations and discover repetitive patterns in molecules, thus more capable of generating realistic molecules. Second, it is able to reflect chemical properties, since it has been revealed that the chemical properties closely related certain substructures (i.e., subgraphs) [31, 20]. Finally, leveraging subgraphs as the building blocks enables efficient training and inference, as the searching time is remarkably reduced by representing molecule set of subgraphs other than atoms.
"Wenbing Huang and Yang Liu are corresponding authors.
36th Conference on Neural Information Processing Systems (NcurIPS 2022).

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However, current subgraph- methods [18, 19, 46] are still suboptimal in two senses. For one thing, the vocabulary of the molecular fragments is constructed by simple hand-crafted rules [18. 19] or borrowed straightly from external chemical fragment libraries [46], which is unable (at least uncertain) to reveal the frequent patterns existing in the dataset. For another, the prediction and the assembling of the subgraphs are conducted either autoregressively [19, 46) or according to pre-defined tree structure [18], both of which are inflexible and defective, since each newly predicted subgraph is only allowed to attach a local set of previous subgraphs during the assembling process.
To address the above two pitfalls, this paper proposes novel framework: Principal Subgraph Variational Auto-Encoder (PS- VAE). PS- VAE first creates vocabulary of molecular fragments from any given dataset, which starts from all distinct atoms and then merges the neighboring fragments as a new one to update the vocabulary. Interestingly, the fragments derived by such a merge merge-and- and-update strategy are actually principal subgraphs which, as a novel concept defined by this paper, represent the frequent and largest repetitive patterns of molecules. We also theoretically prove that any principal subgraph can be universally covered by our vocabulary. Moreover, we develop a two-step subgraph assembling strategy, which first sequentially predicts set of fragments and then assembles all generated subgraphs globally. This two-step fashion makes our method less permutation-dependeen and focus more on global connectivity against traditional methods [18, 19, 46].
We conduct extensive experiments on the ZINC250K [16] and QM9 [6, 37] datasets. Results demon- strate that our PS-VAE outperforms state-of-the art models on distribution learning, (constrained) property optimization as well as GuacaMol goal-directed benchmarks [7]. Besides, PS- VS-VAE is efficient and about six times faster than the fastest autoregressive baseline.
2 Related Work
Molecule Generation. Regarding the representation of molecules, existing generation models can be divided into two categories: text-based and graph-based methods. Text-based models [13, 23, 5] usually adopt the Simplified Molecular- Line-entry System ([40]. SMILES) to describe each molecule, which is simple and efficient. However, they are not robust because slight perturbations in SMILES could result in significant changes in molecule structure [47, 24]. The graph- based counterparts [9, 39, 20], therefore, have gained increasing attention recently. Li al. [25] proposed generation model for graphs and demonstrated it performed better than the text-based strategy. You et al. [47] used reinforcement learning to generate molecules sequentially under the guidance of mixed rewards in terms of the chemical validity and other property scores. Popova et al. [34] proposed MRNN to autoregressively generate nodes and edges. Shi et al. [39] designed a flow-based autoregressive model and exploited reinforcement learning for goal-directed generation. However, these models use atoms as the basic generation unit, leading to long sequences and therefore time- consuming training process. On the contrary, method applics subgraph-level representation, which not only captures chemical properties but also is computationally efficient.
Subgraph-Level Molecule Generation Several works have been developed for subgraph-level generation. In particular, Jin et al. [18] suggested generating molecules in the form of junction trees where each node is ring or edge. Jin et al. [19] decomposed molecules into subgraphs by breaking all the bridge bonds. It used a complex hierarchical model for polymer generation and graph-to to-graph translation. Yang et al. [46] integrated reinforcement learning with the subgraph vocabulary created from existing chemical fragment libraries. Different from Jin et al. [18, 19], Yang et al. [46] which use manual rules to extract subgraphs or utilize existing libraries, we automatically extract frequent principal subgraphs to better capture the regularities in molecules for subgraph-level decomposition.
Our work also relates to traditional subgraph mining literature [15, 45, 33]. While seeking generic frequent subgraphs is known to be NP-hard [22, 17], our work focuses on finding frequent principal subgraphs by merging two adjacent fragments, which alleviates time complexity to a large extent. To the best of our knowledge, we are the first to utilize frequent subgraphs in generation tasks.
3 Our Proposed PS-VAE
This section presents the details of the proposed VAE, consisting of the principal subgraph definition and extraction in Section 3.1 and the two-step generation in Section 3.2.
2

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3.1 Principal Subgraph
molecule can be represented as a graph g = (V. E), where iss a set of nodes corresponding to atoms and & is a set of edges corresponding to chemical bonds. We define a subgraph of G as S= E) S G, were V C V and & C E. We say subgraph & spatially intersects with subgraph S' there are certain atoms in a molecule belong to both S and S', denoted as S S * Note that if two subgraphs look the same (with the same topology), but they are constructed by different atom instances, they are not spatial intersected. Similarly, two subgraphs S and S' appear in the same molecule, we call their spatially union subgraph as l = SUS", where the nodes of U are the union set of V and V and its edges the union of & and E" plus all edges connecting S and S'. A decomposition of a molecule 9 is derived as a set of non-overlapped subgraphs {S:}? and the m. edges connecting them {Eg Ji.j if (U, S,) U(U Eiz) and S; SS 0 for any i * j. The frequency of subgraph occurring in all molecules of given dataset measures its repeability and epidemicity, which should be an important property. Formally, we define the frequency S as e(S) E, (())))) where c(S)g) (;) computes the occurrence of S in a molecule Gj. Without loss of generality, we assume all molecules and subgraphs we discuss are connected.
subgraph
With the aforementioned notations, we propose a novel and central concept below.
Definition 3.1 (Principal Subgraph). We call subgraph S a principal subgraph, any other subgraph S' that spatially intersects with S in certain molecule satisfies either S' C S or c(S') S c(S). Amongst all subgraphs of the larger frequency, principal subgraph basically represents the "largest" repetitive pattern in size within the data. It is desirable to leverage patterns of this kind as the building blocks for molecule generation since those subgraphs with larger size than them are less frequent/reusable. We will prove that our designed vocabulary is capable of mining these subgraphs.
Now we introduce the proposed vocabulary construction process. We call each subgraph of the constructed vocabulary as a fragment. We generate fragments via the following stages:
Initialization. The vocabulary V is initialized with all unique atoms (subgraph with one node).
Merge. For every two neighboring fragments F and F' in the current vocabulary, we merge them by deriving the union FUF. Here, the neighboring fragments of a given fragment F a molecule is defined as the ones that contain at least one first-order neighbor nodes of certain node in F..
Update. We count the frequency of each identical merged subgraph in the last stage. We choose the most frequent one as new fragment in the vocabulary V. Then, we go back to the merge stage until the vocabulary size reaches the predefined number N.
Algorithm 1 Principal Subgraph Extraction
1: Input: A set of graphs D and the desired number N of principal 11:
c(s) c(s) + 1; (Update the counter. The initial value 0.]
subgraphs leam.
2: Output: A set of principal subgraphs V and the counter C of
12:
end for
principul subgraphs.
13:
3: y <- (GraphToSMITLFE ((a), d))}; (Initially, V corre-
14:
TopElem(C); [Find the most frequera merged frog-
sponds to atoms a that appear in D.)
m
4: N' 6- max I9)):
15:
F <- CoIppssTorraph(s (Convrr the SMIL string
5: while [V] < N' do
to graph representation.
6: C EmptyMapp:: (Jnitialize counter:
16:
(+). D' O:
7: for G in 27 do
17:
for 9 in D do
8: for F3. Eng) in 5
18:
G' MergoSabCraah((G. FFF (Update graph
9:
F Merge(( ((F,, FF. E.,)),))): (Merge neighboring
representation if possible.
fragments into a new fragmentt
19:
+ (9'):
10:
+ GraphToTSMLLESS [Convert the graph
20:
end for
SMILES representution.)
21:
D + D':
22:
while
(a) Initialization
(b) Iteration
(c) Iteration 2
Figure 2: Fragment extraction on (C=CC=C, CC=CC, C=CCC). (a) Initialize vocabulary with atoms. (b) Fragment CC is the most frequent and added to the vocabulary. All CC are merged and highlighted in red. (c) Fragment C=CC the most frequent and added to the vocabulary. All C=CC are merged and highlighted in green (molecules I and 3). After 2 iterations the vocabulary is (C, CC, C=CC).
Figure illustrates the above processes and Algorithm I gives the flowchart. Notice that Algorithm has exploited the conversion from molecular subgraph to SMILES [40] to not only ensure the
3

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(a)
M
(6)
GRU
GRU
GRU
GRU
GRU
Figure 3: Overview of the principal subgraph variational auto-encoder. (a) Subgraph-level de- composition. Atoms and bonds different principal subgraphs are highlighted in different colors. (b) Molecular graph. We inject subgraph-level information into the molecular graph through atom features. (c) Latent space encoding. We obtain the latent variable 2 through the graph encoder. (d) Subgraph-level sequence generation. A sequence of principal subgraphs is autoregressively decoded from the latent variable by a GRU. (e) Incomplete molecular graph. The generated principal subgraphs form incomplete molecular graph where inter-subgraph bonds are absent. (f) Bond completion. Completion of inter-subgraph bonds is formalized as a link prediction task for GNN. After training, can directly sample from the latent space to generate molecules.
uniqueness but also better calculate the occurrence of each merged subgraph by string comparison. One notable merit is that we always track the decomposition of each molecule at each iteration, which is crucial for the training of the two-step decoder introduced in the next subsection.
More importantly, have the following theorem demonstrate the benefit of Algorithm 1. Theorem 3.2. The vocabulary V constructed by Algorithm exhibits the following advantages.
(i) Monotonicity: The frequency of the non-single-ant attnglle-ttomaee fragments in V decreases monotoni- cally, namely, F,,,FF E V, c.F..) S c(F,), if j.
(ii) Significance: Each frugment in V is a principal subgraph.
(iil) Completeness: For any principal subgraph arising in the dataset, there always exists fragment F in V satisfying S F, c(S) c(F), when V has collected all fragments with frequency no less than c(S)-
The conclusion by Theorem 3.2 is interesting and valuable. states that our algorithm is able to discover frequent principal subgraphs, and any principal subgraph can be represented (at least contained) by our certain extracted fragment if the size of the vocabulary is sufficiently large. This is also meaningful extension to traditional subgraph mining literature [17], in which seeking the most frequent subgraphs is known to be NP-hard. Algorithm can somehow address this problem efficiently by focusing mainly finding the most frequent principal subgraphs.
3.2 Two-step Molecule Generation
The molecule generation is modeled as two-step task: first predicting which fragment should be chosen from the vocabulary created in the last subsection, and then proceeding with how to assemble the predicted fragments. Although in the first step we predict the fragments in sequence manner, we globally investigate if every two predicted fragments should be linked in the second step. This two-step fashion makes our method not only less permutation-dependeee sample-efficient than the generic autoregressive counterparts [25], but also more flexible than the methods [18] that require predefined junction tree or adjacent connections between subgraphs. We will provide experimental evaluations in Table to justify the benefit of our proposed two-step generation strategy. Below, we provide the details of the two steps.
and thus more
What to assemble. This step is of the VAE style [21]. As shown in Figure 3, we use GNN to encode a molecular graph G into a latent variable z. Each node has a feature vector x, which the concatenation of three learnable embeddings: its atomic type, fragment type and the generation order of the fragment. Each edge has feature vector indicating bond type. Specifically, we utilize GIN with edge feature [14] as the backbone GNN network, which computes the Æ-th layer as follows:

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0
ReLU(h + ewv),
(1)
mEN(w)
h he((1 + + (k-1) )
where, h is the hidden activation of node (h (0) ). Cue is the edge feature between node and v, (u)) returns the neighbors u. he a neural network, and E is a constant. We implement he 2-layer Multi-Layer Perceptron ([10), MLP) with ReLU activation and set
We obtain the final representations nodes as h2 = [h. () ..... ) so that it contains the contextual information from 1-hop to t-hop. The graph-level representation is given by summation hg Evey h.. We use hg to obtain the mean Mlg and log variance og of variational posterior approximation g( (G) through two separate linear layers and use the reparameterization trick [21] to sample from the distribution in the training process.
Given latent variable z, our model first uses an autoregressive sequence generation model P(F x) to decode an sequence of graph fragments [Fi...., Fr]. Note that the set of subgraphs into which molecule is decomposed should not be ordered. Here, although we violate this law by using the ordered decoder, this issue is practically relieved by data augmentation of random fragment permutations during training, and it is further mitigated by the second step (presented later) where the assembling of the predicted subgraphs is not order-sensitive During training, we insert two special tokens "<start>" and "<end>" indicating the beginning and the end sequence generation, respectively. We implement the sequence model via single layer of GRU [8] and project the latent variable z to the initial state of GRU. The training objective of this stage to minimize the log- liliikeiihodd Cp of the ground truth fragment sequence:
LF
log P(F((Fes))))
(3)
During testing, the generation stops when "<end>" is outputted.
How assemble. This step estimates all inter-fragment edges {Ei, non-autoregressively and globally. Specifically, we use GNN with the same architecture in the last step but with different parameters obtain the representations h of each atom v in all fragments. Given nodes and in two different fragments, we predict their connections as follows:
P(euol=) = Ho Hhh h,; 2)),
where Ho is 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...) and P(e to let Hg learn the undirected nature of chemical bonds. We use negative sampling [12] to balance the ratio of "<none>" and chemical bonds. Since only about 2% pairs of nodes has inter-fragment connections, negative sampling significantly improves the computational efficiency and scalability. The training objective of this stage is to minimize the log- ligeciklioood::
LE
Σ
log P(ewvlz).
(5)
WER.EEF,
Joining the reconstruction losses of both steps (Eq, 3 and Eq. 5), we arrive at: Lree = Lx + Le- When considering target property, we jointly train 2-layer MLP from to predict the scores of target properties using the MSE loss. By denoting this extra loss as Lpopp the final objective of our PS- VSE becomes:
L= aLac (1 a) Crru + BDKL.
(6)
where the the KL divergence Dxi. aligns the distribution with the prior distribution. A/ I); a and /3 balance the trade-off between different losses.
To decode {E.g) in the inference phase, the decoder first assigns all possible inter-fragment con- nections with bond type and corresponding confidence level. We try to add bonds that have
5

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confidence level higher than én = 0.5 to the molecule in order of confidence level from high to low. For each attempt, we perform valency 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, we find the maximal connected component as the final result. The pseudo code for inference is deferred to Appendix D.?
4 Experiments
We first report the empirical results for the distribution-lerriing tasks in Gua- caMol benchmarks [7] to evaluate if the model can generate realistic and diverse molecules. Then we validate our model on two common problems and the goal-directed tasks of the GuacaMol bench- marks. Property Optimization requires generating molecules with optimized properties. Constrained Property Optimization concentrates on improving the properties of given molecules with a restricted degree of modification. GuacaMol carefully curated by domain-expert expprtss [48, 43, 11].
Evaluation Tasks
Benchmarks consist of 20 molecular design tasks
Baselines We compare our principal subgraph variational auto-encoder (PS-VAE) with the follow- ing state-of-the-art models. JT--VAE [18] is variational auto-encoder that represents molecules as junction trees. It performs Bayesian optimization on the latent variable for property optimization. GCPN [47] combines reinforcement learning and graph representation for goal-directed molecular graph generation. MRNN [34] adopts two RNNs to autoregressively generate atoms and bonds respectively. combines policy gradient optimization to generate molecules with desired properties. GraphAF [39] is a flow-based autoregressive model which is first pretrained for likelihood modeling and then fine-tuned with reinforcement learning for property optimization. GraphDF [28] is another flow-based autoregressive model but leverages discrete latent variables to better capture the discrete distribution of graphs. GA [32] adopts genetic algorithms for property optimization and models the selection of the subsequent population with a neural network. HierVAE [19] extracts fragments by breaking bridge bonds in molecules and uses them as building blocks. FREED [46] is an RL-based model and uses fragments from existing chemical libraries to construct the subgraph vocabulary. MARS [44] adopts Markov chain Monte Carlo sampling for generation and is the state-of sfate-of-thh-att theh-rttt approach on the GuacaMol goal-directed benchmarks. Since our generation model is universally compatible with molecular decomposition of non-overlapping fragments, we also integrate vocab- ularies from VierVAE and FREED into two-step generation model, which are abbreviated as H-VAE" and F-VAE", respectively.
We use the ZINC250K [16] dataset for training, which contains 250,000 drug-like molecules up to 38 atoms. For GuacaMol benchmark, we add extra results on the QM9 [6, 37] dataset, which has 133,014 molecules up to 23 atoms. We choose N 300 for property optimization and N 500 for constrained property optimization. PS- SAE is trained for 6 epochs with a batch size of 32 and learning rate of 0.001. We set 0.1 and initialize 3 = O. We adopt warm-up method that increases 3 by 0.002 every 1000 steps to a maximum of 0.01. More details are in Appendix G.
4.1 Results
GuacaMol Distribution-L cearrbbution-Learnnng Benchmarks These benchmarks evaluate four metrics on 10,000 molecules generated by the models. Since all methods introduce validity check into generation, they can always generate chemically valid molecules. Uniqueness measures the ratio of unique ones in generated molecules. Novelty assesses the ability of the models to generate molecules not contained in the training set. KL Divergence evaluates the closeness between the training set molecules and the generated molecules in terms of the distributions of various physicochemical properties. Frécher ChemNet Distance (FCD) calculates the closeness of the two sets of molecules with respect their hidden representations in the ChemNet [35]. Each metric is normalized to 0 to 1, and a higher value benchmarks on QM9
indicates better performance. Table 1 shows the results of distribution-leammii and ZINC250K. Our model achieves competitive results in all four metrics, which indicates our model can generate realistic molecules and prevent overfitting the training set. addition, with the same vocabulary, H-VAE" surpasses Vie consistently, confirming the advantage of our two-step generation model over the one used in HierVAE. Moreover, even sharing the same two-step
"Codes for our PS- VAE availabel at https http:////gggtttt.co///oo//////// VAE.

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decoder, PS- VSAV is still better than H-V and F- FAVE consistently, which is probably because our constructed vocabulary discovers more meaningful and reusable patterns than H- H-VAE* and F-VAE". We have displayed some molecules sampled from the prior distribution in Appendix I..
Table I: Results of GuacaMol distribution-leann lerabiniinn- benchmarks QM9 and ZINC250K. Uniq, KL Div and FCD refer to Uniqueness, KL Divergence and Fréchet ChemNet Distance, respectively.
QMY
ZINC250K
Model
Uniq(T)
Novelty(")
KL Div(f)
FCD(T)
Umig(t)
Novelly(")
KL Div(t)
FCD(T)
JT-VAE
0.549
0.386
0.891
0,588
0,988
0,988
0.882
0.263
GCPN
0.533
0.320
0.552
0.174
0.982
0,982
0.456
0.003
GruphAF
0,500
0.453
0.761
0.326
0.288
0.287
0.508
0.023
GraphDF
0.672
0.672
0.601
0.137
0.998
0.998
0.459
0.001
GA
0.008
0.008
0.429
0.004
0.008
0.008
0.705
0.001
MARS
0.659
0.612
0.547
0.123
0.737
0.737
0.798
0.271
HierVAE
0.416
0.285
0.802
0.426
0.131
0.131
0.602
0.001
H-VAE*
0.619
0.487
0.869
0.588
0.991
0,991
0.611
0.037
F-VAE*
0.466
0.400
0.889
0.490
0,988
0.988
0.676
0,085
PS- VAE (ours)
0.673
0,523
0.921
0.659
0.997
0.997
0.850
0.318
Property Optimization This task focuses on generating molecules with optimized Penalized logP ([23], PlogP) and QED [4]. PlogP is logP penalized by synthesis accessibility and ring size which has an unbounded range. QED measures the drug-likeness of molecules with a range of [o, 1]. Both properties are calculated by empirical prediction models [42, 4], and are widely used in previous works [18, 47, 39]. We constrain all models to generate molecules under 60 atoms to prevent them from utilizing the flaw of PlogP by keeping extending the carbon chain [39]. We first train predictor on the latent space of previously-trained VAE models to simulate the scoring functions, then perform gradient ascending to search for optimized molecules [18, 27]. Hyperparameters can be found in Appendix G. Following previous works [18, 47, 39], we generate 10,000 optimized molecules and report the top-3 scores found by each model. Results in Table 2 show that model surpasses the baselines consistently. Note that with the same vocabulary, F-VAE achieves much better results than FREED, which indicates the superiority of our two-step generation strategy to the one in FREED.
Table 2: Comparison of the top-3 property scores.
Penalized logP
QED
Method
Ist
2nd
3rd
1st
2nd
3rd
JT-VAF
5.30
4.93
4.49
0.925
0.911
0.910
GCPN
7.98
7.85
7.80
0.948
0.947
0.946
MRNN
8.63
6.08
4.73
0.844
0.796
0.736
GraphAF
12.23
11.29
11.05
0.948
0.948
0.947
GraphDF
13.70
13.18
13.17
0.948
0.948
0,948
GA
12.25
12.22
12,20
0,946
0.944
0,932
MARS
7.24
6.44
6.43
0,944
0.943
0,942
FREED
6.74
6.65
6.42
0.920
0.919
0.908
II-VAE
11.41
9.67
9.31
0,947
0.946
0.946
F-VAE"
13.50
12.62
12.40
0.948
0.948
0.947
PS- VAE (ours)
13.95
13.83
13.65
0.948
0.948
0.948
This task refines molecular properties under the constraint that the Tanimoto similarity with Morgan fingerprint [36] is above a threshold 8. As suggested by previous works [18, 47, 39]. we optimize 800 molecules with the lowest PlogP in the test set of ZINC250K. Similar to the property optimization task, we perform gradient ascending on the latent variable with max step of 80. We collect all latent variables which have better- preterepreditted scores than the previous iteration and decode each of them 5 times, namely up to 400 molecules. Following Shi et al. [39], we initialize the generation with sub-graphs sampled from the original molecules. Then we choose the highest scoring one from the molecules that meet the similarity constraint. Table 3 shows our model can generate molecules with a higher PlogP score under the similarity constraints. Since our model uses subgraphs as building blocks, the degree of modification tends to be greater than atom-level models, leading to a lower success rate. Even so, the success rates by our model are still on par with the atom-level counterparts and are the best among all subgraph-level methods.
Constrained Property Optimization
GuacaMol Goal-Directed Benchmarks To further explore the efficacy of PS- VAE, we provide the results for GuacaMol goal-directed benchmarks [7] in Table All scores are continuous values between O and 1, and the higher, the better. In order to obtain more discernible results between
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Table 3: Mean (standard deviation) on improvement in constrained property optimization.
0.2
0.4
5 0.6
Model
Improvement
Success
Improvement
Success
Improvement
Success
ST-VAE
1.68.1885
97.1%
0.84.11.45
83.6%
0.21110.71
46. 46.4%
GCPN
1.12+1.19
100%
1.49+1130
100%
0.79+40.63
100%
GraphAF
4.99+11.38
100%
3.74+1.25
100%
1.95++0.99
98.4%
GraphDF
5.62.11.65
100%
4.13.1141
100%
1.72.11.15
93.0%
GA
3.04.11660
100%
2.34:1134
100%
1.35:11.06
95.9%
MARS
4.13+1.23
100%
2.41+0.766
99.2%
1.21+00664
69.6%
II-VAE"
3.42.11.65
89.9%
2.68.11.44
74.0%
1,90.1..06
51.5%
F-VAE" 1.57
98.9%
3.6011.39
89.9%
2,40:11.17
68.6%
PS-VAE (ours)
6.442:1.86
99.9%
4.19:11.0
98.95
2.52:11.12
90.3%
different approaches, we conduct experiments on QM9 and ZINC250K which have much less high- scoring molecules than ChEMBL [30] to make the tasks more challenging. Otherwise the majority of the benchmarks are easy to be optimized to the upper bound [1]. We adopt the same optimizing strategy as in the property optimization tasks. Hyperparameters can be found in Appendix G. Table 4 shows that our model remarkably performs better than H- HAVE and F- F-VAE", and thus exhibits the benefit of our subgraph extraction method. The superior of H- VAVE to VierVAE indicates the advantage of our two-step assembling over the sequential sampling strategy.
Table 4: Results for GuacaMol goal-directed benchmarks. H-VAE", F-VAE' and PS- VAE refer to VAE models with vocabularies from Hier VAF, FREED and our principal subgraphs, respectively.
benchmark
JT-VAE
GA
H-VAE"
F-VAB"
HierVAE
MARS
PS-VAE
ZINC250K
Celecosib rediscovery
0.245
0.073
0.252
0.310
0.223
0.137
0,451
Troglitazens rediscovery
0,171
0,080
0.205
0.215
0.181
0.163
0.254
Thiothixene rediscovery
0.225
0.091
0.240
0.236
0.191
0.072
0.286
Aripiprazole similarity
0.351
0.240
0,382
0.300
0,340
0.350
0.432
Albutcrol similarity
0.126
0.137
0.401
0.184
0.130
0.567
0.611
Mestranol similarity
0.278
0.337
0.360
0.377
0,28
0.297
0.515
C11H24
0.014
0.124
0.634
C9H10N202PP2C1
0.200
0.659
0.523
0.567
0.023
0.435
0,782
Median molecules 1
0.161
0.190
0.191
0,204
0.115
0.167
0,263
Madian molecules 2
0.166
0.111
0.178
0.166
0.199
Osimettinib MPO
0.693
0.585
0.758
0.768
0.538
0.745
0,800
Fexofenadine MPO
0.607
0,495
0.555
0.685
0.523
0.682
0.715
Ranelazine MPO
0,350
0.250
0.411
0.532
0.305
0.552
0.688
Perindopmil
0.239
Amlodipine MPO
0.442
0,413
01477
0.463
0.341
0.477
0.544
Sitngliptin MPO
0.160
0,243
0.246
0,350
0.092
0.261
0.439
Zaleplon MPO
0,259
0.394
0.329
0,495
Valsartan SMARTS
0
0
0
5.398
Deco Hop
0.576
0,530
0.577
0,577
0.559
0.572
0.601
Scaffold Hop
0.440
0,375
0,443
0.442
0.486
Colecosib rediscovery
0.023
0.210
Trogliraooee rediscovery
0,070
0.110
0.124
0.131
0.121
0.085
0.152
Thoothsene rediscovery
0.047
0,061
0.115
0. 1000
0.059
0.037
0.146
Aripipaazole similarity
0.095
0.167
0.178
0.104
0.214
Albutcrol similarity
0
0,243
0.305
0.277
0.380
0,305
0.463
Mestranal similarity
0,170
0.134
0.157
0,122
0.234
0,233
0.198
C11H24
9.734
2.148 10
6,800 x 10
2.979 10
0.007
1,969 10
0.015
C9H10N2029F331
0.182
0.066
0.236
0.109
0,250
0.190
0.381
Median molecules 1
0.226
0,185
0.195
0,194
0.229
0.143
0.261
Median molecules 2
0.063
0.062
0.091
0.091
0.08]
0.085
0.112
Osimertinib MPO
0.556
0.541
0.555
0.636
Fexofenadine MPO
0.217
0.403
013007
0.288
0.355
0.443
0.373
Ranelazinc MPO
0.004
0.170
0.007
0,010
0.011
0.032
0.018
Perindoprl MPO
0.104
0,061
0.166
0.165
0.145
0.205
Amlodipine MPO
0.192
0.166
0.258
0.211
0.300
0,284
0.303
Sitagliptin MPO
2.556 x 10-6
1688 x 10-4
2,807
10-5
5.114
10-5
01.511 x 10-1
0.138 x 10
0.319 10-3
Zalopion MPO
10-
0.03
10-5
5.617
10-5
0.771
10
0.033
0.085
Valsartan SMARTS
0
0
0
Deco Hop
0.505
0.525
0.506
0.492
0.512
0.513
0.545
Scaffold Hop
0.341
0.361
0.340
0.354
0.351
0.362
0.393
4.2 Ablation Study
We conduct an ablation study to further validate the effects of principal subgraphs and the two-step generation approach. We first downgrade the vocabulary to contain only single atoms. Then we replace the two-step decoder with fully autoregressive decoder. We present the performance on (constrained) property optimization in Table and Table 6. The direct introduction of the two-step generation approach leads to improvement in property optimization but harms the performance on constrained property optimization. This is reasonable as separating the generation of atoms and bonds brings in information loss of bonds for the atom-level generation process. However, the
8

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adoption of principal subgraphs as building blocks alleviates this negative effect since the principal subgraphs themselves contain rich bond information. Therefore, integrating principal subgraphs with our two-step generation approach leads to the best choice in our model design. Furthermore, we provide the runtime cost baselines and PS- -AE in Appendix to demonstrate the improvement in efficiency brought by the principal subgraphs and the two-step generation approach.
Table 5: Comparison of the top-3 property scores found by PS- VAE without certain modules
Penalized logP
QED
Method
1st
2nd
3rd
1st
2nd
3rd
PS-VAE
13,95
13.83
13.65
0.948
0,948
0,948
PS
6.91
5.50
5.12
0.870
0.869
0.869
two-step
3,54
3,54
3.22
0.737
0.734
0.729
Table 6: Comparison of PS- VAE without certain modules constrained property optimization.
= 0.2
8 0.4
5 0.6
Model
Improvement
Success
Improvemmett
Success
Improverent
Success
VAR PS
6.42++1.86
99.9%
4.19+1130
98.9%
2.52++1.12
90.3%
2.33+
74.8%
2.12++1.36
50.9%
1.87+
27.0%
two-step
3.36
98.6%
2.72+1124
82.0%
1.88+1005
45.1%
5 Analysis
Principal Subgraph Statistics We compare the distributions of the vocabulary of JA-, FREED, HierVAE, and the vocabulary constructed by principal subgraph extraction methods with size of 100, 300, 500, and 700. Figure 4 shows the proportion of fragments with different numbers of atoms in the vocabulary and their frequencies of occurrence in the ZINC250K dataset. The fragments in the vocabulary of VA--VAE mainly contain 5 to 8 atoms with a sharp distribution. However, starting from fragments with 3 atoms, the frequency of occurrence is already close to zero. Therefore, the majority of fragments in the vocabulary of JA-VAE are actually not common fragments. On the contrary, the fragments in the vocabulary of principal subgraphs have a relatively smooth distribution over 4 to 10 atoms. Moreover, these fragments also have much higher frequency of occurrence compared those by JT. VAE. Vocabularies constructed by our method show similar advantages compared to those of HierVAE and FREED. We present samples of principal subgraphs in Appendix K.
Proportion in the vocabulary
FREED
FREED
0.-
HierVAE JT-VAE
frequency of accurence
HierVAE
0.4
JT-VAE
0.3
N 100
N = 100
N 300
0.3
N 300
0.2
500
N 500
N 700
0.2
N 700
0.1
10
14
16
18
10
14
16
Number atoms
Number of atoms
Figure 4: The left and right figures show the proportion of and frequency of occurrence of fragments with different number of atoms in the vocabulary, respectively.
Principal Subgraph Property Correlation To analyze the principal subgraph property corre- lation and whether our model can discover and utilize the correlation, we present the normalized distribution of generated fragments and Pearson correlation coefficient between the fragments and Penalized logP (PlogP) in Figure 5. The curve indicates that some fragments positively correlate with PlogP while some negatively correlate with it. Compared with the flat distribution under the non-optimization setting, the generated distribution shifts towards the fragments positively correlated with PlogP under the PlogP-optimization setting. The generation of fragments negatively correlated with PlogP also suppressed. Therefore, correlations exist between fragments and PlogP; and our model can accurately discover and utilize these correlations.
Proper Granularity A larger N in the principal subgraph extraction process leads to an increase in the number of atoms in extracted fragments and decrease in their frequency of occurrence, as illustrated in Figure 6. These two factors affect model performance in opposite ways. On the one hand, the entropy of the dataset decreases with more coarse -oarsc-rrained decomposition [29], which benefits

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Figure 5: The distributions of generated fragments with and without optimization of PlogP, as well Pearson correlation coefficient between the fragments 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 fragment divided by its count of occurrence in the training set.
model learning [3]. On the other hand, the sparsity problem worsens as the frequency of fragments decreases, which hurts model learning [2]. We propose quantified method balance entropy and sparsity. The entropy of the dataset given set of fragments V is defined by the sum of the entropy
of each fragment normalized by the average number of atoms: Hy ny EFey P(F) log P(F), where P(F) the relative frequency of fragment in the dataset and ny the average number of atoms of fragments in W. The sparsity of V is defined as the reciprocal of the average frequency of fragments fv normalized by the size of the dataset M: Sy = M/ fv. Then the entropy sparsity trade-off (T") can be expressed as: Tv = fly + ySv where balances the impacts of entropy and sparsity since the impacts vary across different tasks. We assume that TV negatively correlates with first sample several values of N to calculate their values of
downstream tasks. Given a task, and then compute the y that minimize the Pearson correlation coefficient between T and the corresponding performance first three downstream tasks in this paper are -0.987, -0.999, and -0.707, indicating strong negative correlations. For example, Figure 6 shows the curve of entropy sparsity trade-off with maximum of 3,000 iteration steps for the property optimization task. From the curve, we choose N = 300 for the property optimization task. Please refer to Appendix B for more experimental details.
the task. With the proper y, Pearson correlation coefficients for the
Stee
Figure 6: Entropy Sparsity trade-off, average number of atoms in principal subgraphs and average frequency occurrence of principal subgraphs with a maximum of 3,000 iteration steps.
6 Conclusion
We propose an algorithm to automatically discover the regularity molecules and extract them as principal subgraphs. With the extracted principle subgraphs at hand, we generate molecules in two phases. Our model consistently outperforms state-of-the-arr models on distribution-leamiig (constrained) property optimization, and GuacaMol goal-directed benchmarks, and exhibits higher computational efficiency than certain widely-used baselines. Our work provides insights into the selection of subgraphs molecular graph generation and can inspire future search in this direction.
Acknowledgments and Disclosure of Funding
This work jointly supported by the National Natural Science Foundation of China (No.61925601, No.620061377 Guoqiang Research Institute General Project, Tsinghua Univer- sity (No. 2021GQG1012); Beijing Academy of Artificial Intelligence; Huawei Noah's 's Ark Lab; Beijing Outstanding Young Scientist Program (No. BUWZZYHO01219900000000
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Checklist
1. For all authors...
(a) Do the main claims made in the abstract and introduction accurately reflect the paper's
contributions and scope? [Yes] See abstract and 1.
(b) Did you describe the limitations of your work? [Yes] See Appendix J.
(c) Did you discuss any potential negative societal impacts of your work? [N/A]
(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes] We have read them and ensured that our paper conforms them.
2. If you are including theoretical results...
(a) Did you state the full set assumptions of all theoretical results? [Yes] They are the Appendix A.I.
(b) Did you include complete proofs of all theoretical results? [Yes] They are in the Appendix A.1.
3. If you experiments...
(a) Did you include the code, data, and instructions needed to reproduce the main experi- mental results (either in the supplemental material or as a URL)? [Yes] They are the supplemental material.
(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes] They are in 4 and Appendix G.
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(c)
Did you report error bars (e.g., with respect to the random seed after running experi- ments multiple times)? [Yes] For guacamol benchmarks, they calculate metries with respect to the global data distribution, making the results insensitive to randomness. For the optimization tasks, they simulate the real scenario where bunch of candidates are produced (about 10,000 candidates) and the high-scoring ones (e.g. top-3) are selected for further development, which means the highest scores achieved by each model are relatively stable. For the constrained optimization tasks (Table 3), we report the error bars to evaluate the robustness of the model, since different input molecules may result in different improvements
(d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [Yes] They are in Appendix F.
4. If you are using existing assets (c.g., code, data, models) or curating/relcasing new assets...
(a) your work uses existing assets, did you eite the creators? [Yes]
(b) Did you mention the license of the assets? [N/A]
(c) Did you include any new assets either in the supplemental material or as a URL? [N/A]
(d) Did you discuss whether and how consent was obtained from people whose data you' rr using/curating? [N/A]
(c) Did you discuss whether the data you using/curating contains personally identifiable information or offensive content? [N/A]
5. If you used crowdsourcing or conducted research with human subjects...
(a) Did you include the full text of instructions given participants and screenshots, if applicable? [N/A]
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14


Reviews:
[{"review_id": "hqlog8ZUmvM", "reviewer": "Reviewer_B6na", "summary": "The paper proposes a new method for molecular consisting of a principle subgraph extraction step, a fragment prediction step, and an assembling step to combine the fragments and obtain the final generated graph. The major novelty is the extraction of the so-called “principle subgraph” from the dataset. The two-step molecule generation process is based on VAE and relies on the vocabulary of fragments (principle subgraphs) that is built in the first step. Experiments on distribution-learning, (constrained) property optimization, and GuacaMol goal-directed benchmarks show the superiority of the proposed PS-VAE method.", "questions": "Please see above.", "limitations": "The authors put N/A as the response to the potential societal impact in the last page of the main paper.", "rating": 7, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n1. The proposed method is relatively novel, considering that it is the first work to use frequent subgraphs in the molecule generation domain. Such use of subgraphs is a promising direction and likely to spark future research in this task and other related tasks. \n2. In the appendix, careful hyperparameter selection for N, the number of fragments in the vocabulary, is performed using a curve of entropy-sparsity trade-off. Complexity analysis, runtime cost, and additional details on the method, the experiments, and the experimental results are shown too in the appendix.\n3. The paper is well-written, with ample examples and illustrations to facilitate the understanding of the various proposed components.\n\nWeaknesses:\n1. Since the proposed method consistently outperforms baseline methods, it is important to know which component provides the most useful information. The authors have done a reasonably good job of ablation studies, e.g. by replacing the built vocabulary with other models’ vocabulary. In Section B, the authors talk about the trade-off with the tuning of N, the number of fragments, but it is still unclear what final performance PS-VAE would achieve if some other choices of N are adopted, e.g. N = 100, N = 800, etc. This requires running the whole model multiple times with different choices of N, and would clearly show the performance trend and experimentally validate the claimed trade-off.\n2. Although the authors answer “Yes” for whether error bars are shown, it seems only Table 6 contains error bars without further explanation why this is the case.\n3. In Section F, the authors compare the running time of proposed method with two baseline models, but it would be better to compare with more baselines or at least show the complexity associated with all the methods that are compared across the three tasks in the main paper. So far the authors claim the proposed method “exhibits higher computational efficiency than certain widely-used baselines”, so this is a technically correct statement, albeit leaving readers wonder about the comparison to other methods adopted in this domain.\n", "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": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "7wzEmAiy91N", "reviewer": "Reviewer_EktL", "summary": "The authors propose a novel approach for molecule generation, introducing principal subgraphs. The method can be divided into two steps: The extraction of principal subgraphs from a training dataset and the molecule generation itself. In the first step, principal subgraphs are extracted from a training set by iteratively merging subgraphs, starting with single vertices. In each iteration, two neighboring subgraphs are merged, if the subgraph corresponding to their union is most frequent in the dataset among the possible merges.  For the molecule generation, first subgraphs and then edges between those subgraphs are predicted.", "questions": "* Q1) Are the generated molecules chemically valid and how is this guaranteed?\n* Q2) Which implementation and parameter selection has been used for the different methods?\n* Q3) Couly you provide additional results of the different reference methods?\n    - FREED and MRNN in Tables 1, 3 and 4\n    - MARS in Tables 1-3\n    - JT-VAE, GCPN, GraphAF, and GA in Table 4", "limitations": "Overall these are addressed adequately. However, the limitations of principle subgraphs (e.g., compared to frequent subgraphs) could be explored in more detail.", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "## Strengths\n  * The paper proposes a new approach to molecule generation, the concept of principal subgraphs is nice. Related approaches are adequately cited.\n  * The paper is well structured and written.\n\n## Weaknesses\n  * The concept of principal subgraphs is not explored in full detail. It would be nice to formalize the relation to frequent subgraphs. The authors state that principal subgraphs can be computed more efficiently than frequent subgraphs. Does this come with any costs/limitations, e.g., in terms of the completeness of the vocabulary? Moreover, a detailed complexity analysis would be very helpful to support this argument. The complexity analysis in the appendix is not sufficient. It appears to assume that functions like GraphToSMILES have constant running time, which needs justification. This function solves the graph canonization problem, for which no polynomial time algorithm is known in general.\n  * The experimental evaluation is not fully convincing, e.g., the used implementation and parameter selection of the competitors are not explained.\n \n## Minor comments\n  * Typos Line 151: neighbos, line 474: exits\n  * There is some mix-up of references, especially when referring to the Appendix, which should be corrected: Figure 6 is in the Appendix and not in the submission, so it should be referenced this way. There is no Figure 5 referenced in the submission (maybe 5 and 6 could be swapped). In Question 3 d) you state that you include the total amount of compute and the type of resources used in Appendix H. They are in Appendix F (maybe they should be moved closer to Appendix H).\n  * The presentation of the results and examples could be improved to make them readable in grayscale.\n  * PS-VAE is called GP-VAE in Table 1", "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": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "6rBoT2NDrAS", "reviewer": "Reviewer_ESyH", "summary": "This paper proposes a molecular generation model based on the vocabulary which consists of frequently observed subgraphs. Unlike existing subgraph-based molecular generation methods using chemical domain knowledge, the vocabulary is constructed in an autoregressive manner based on the dataset. It produces molecular graphs by generating subgraphs that act as building blocks and predicting the edges between them.", "questions": "- Although it is forced not to have a ring structure except for a ring with nodes 5 or 6 by the cycle check of Algorithm 3, actual molecular data may have a ring of a different size. Is there a reason to limit the size of cycles?\n- What is the advantage of HierVae and FREED in line 298?\n- I couldn't find any experimental results supporting the sentence \"Otherwise the majority of the benchmarks are easy to be optimized to the upper bound\"(line 270) in [42]. \n- In the proposed method, the decomposed subgraphs are not overlapped. This is different from JT-VAE and HierVAE, which generate subgraphs that can overlap with others and find overlapped parts to connect edges. Is there any advantage to generating non-overlap subgraphs?\n- Is there any correlation between the extracted substructures and other properties except PlogP?", "limitations": "If there is no significant correlation between the frequently observed subgraph and the desired property, the influence of vocabulary could be diminished.\n", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths\n\n- Unlike using predefined substructures such as rings or functional groups, the proposed approach is possible to adaptively extract subgraphs that frequently appear in datasets. Hence, the proposed model uses a vocabulary that reflects the characteristics of the dataset.\n\n- The properties of extracted subgraphs are well analyzed through the theorem.\n\n- The proposed model has high performance compared to baseline methods.\n\n- Some analysis of extracted vocabulary is shown. The fact that high-correlated fragments to PlogP are generated frequently in the PlogP-optimization task strengthens the proposed method. It would have been better to add experimental results for QED or other properties.\n\nWeaknesses and Questions:\n\n- In the experiment part, HierVAE and H-VAE are used as the baseline method. Is there a reason why these methods are chosen as the baseline? Since HierVAE is a model focused on polymer compound production, it would not be the proper baseline for the ZINC250k or QM9 dataset.\n\n- It is unclear why Theorem 3.2 is useful to model molecules. The connection between the theorem and the experimental results are vague and not clearly explained.\n\n- There is an ambiguity in Algorithm 1. The rightmost molecule in Figure 2 (b) has two C-C subgraphs. If the right C-C bond is merged in iteration 1, all subsequent iterations will be changed. In this case, is there a way to determine which fragments to merge?\n\n- The baseline method used in the experiment is insufficient. MARS or FREED is a recent model, but not used in all experiments. Additional experiments compared with GEGL [1], GraphDF [2], and GraphCNF [3] will help to understand the performance of the presented model.\n\n[1] Ahn, Sungsoo, et al. \"Guiding deep molecular optimization with genetic exploration.\" *Advances in neural information processing systems* 33 (2020): 12008-12021.\n\n[2] Luo, Youzhi, Keqiang Yan, and Shuiwang Ji. \"GraphDF: A discrete flow model for molecular graph generation.\" *International Conference on Machine Learning*. PMLR, 2021.\n\n[3] Lippe, Phillip, and Efstratios Gavves. \"Categorical normalizing flows via continuous transformations.\" *arXiv preprint arXiv:2006.09790* (2020).\n\nMinor Errors\n\n- Typo in line 265 (effacy)\n- In 164 lines, it is written that <bos> and <eos> token are used, but in Figure 3, <start> and <end> token is shown.", "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": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}]

Author rebuttal:

Decision: Accept