Molecule Generation by Principal Subgraph Mining and Assembling
Anonymous Author(s)
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Abstract
Molecule generation is central to a variety of applications.
Current attention hasbeen paid to approaching the generation task as subgraph prediction and assembling.
Nevertheless, these methods usually rely on hand-crafted or external subgraphconstruction, and the subgraph assembling depends solely on local arrangement.
In this paper, we define a novel notion, principal subgraph that is closely related tothe informative pattern within molecules.
Interestingly, our proposed merge-andupdate subgraph extraction method can automatically discover frequent principalsubgraphs from the dataset, while previous methods are incapable of.
Moreover,we develop a two-step subgraph assembling strategy, which first predicts a set ofsubgraphs in a sequence-wise manner and then assembles all generated subgraphsglobally as the final output molecule.
Built upon graph variational auto-encoder,our model is demonstrated to be effective in terms of several evaluation metricsand efficiency, compared with state-of-the-art methods on distribution learning and(constrained) property optimization tasks.
Introduction
Generating chemically valid molecules with desired properties is central to a variety of applications indrug discovery and material science.
In contrast to searching countless potential candidates by expertchemists or pharmacologists, designing generative models that can produce molecules automaticallyis more efficient and now a prevailing topic in machine learning.
Recently, there have been variousworks[18, 26, 45, 24, 9, 38, 20] utilizing graphs to characterize the distribution of atoms and bondswithin each molecule.
[Figure]
In general, these graph-based generation methods can be clustered into two categories: the atomlevel [25, 45, 26, 20] and the subgraph level [18, 19, 44], in terms of what the basic generationunit is.
Compared with the atom-level methods, exploring subgraphs for generating molecules (asillustrated in Figure 1) exhibits three potential benefits.
First, it can capture the regularities of atomiccombinations 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 are closely related to certain substructures (i.e., subgraphs) [30, 20].
Finally, leveraging subgraphs as the building blocks enables efficient training and inference, as the searching time is remarkably reduced by representing a molecule as a set of subgraphs other than atoms
However, current subgraph-level methods [18, 19, 44] are still suboptimal in two senses.
For onething, the vocabulary of the molecular fragments is constructed by simple hand-crafted rules [18, 19]or borrowed straightly from external chemical fragment libraries [44], which is unable (at leastuncertain) to reveal the frequent patterns existing in the dataset.
For another, the prediction andthe assembling of the subgraphs are conducted either autoregressively [19, 44] or according to apre-defined tree structure [18], both of which are inflexible and defective, since each newly predictedsubgraph is only allowed to attach a local set of previous subgraphs during the assembling process.
To address the above two pitfalls, this paper proposes Principal Subgraph Variational Auto-Encoder(PS-VAE), a novel framework for molecule generation.
PS-VAE first creates a vocabulary ofmolecular fragments from any given dataset, which starts from all distinct atoms and then mergesthe neighboring fragments as a new one to update the vocabulary.
Interestingly, the fragmentsderived by such a merge-and-update strategy are actually principal subgraphs which, as a novelconcept defined by this paper, represent the frequent and largest repetitive patterns of molecules.
Wealso theoretically prove that any principal subgraph can be universally covered by our vocabulary.
Moreover, we develop a two-step subgraph assembling strategy, which first predicts a set of fragmentsin a sequence-wise manner and then assembles all generated subgraphs globally as the final outputmolecule.
This two-step fashion makes our method less permutation-dependent and focus more onglobal connectivity against traditional methods [18, 19, 44].
We conduct extensive experiments on the ZINC250K [16] and QM9 [6, 36] datasets.
Results demonstrate 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-VAE isefficient and about six times faster than the fastest autoregressive baseline.
Related Work
Molecule Generation.
Regarding the representation of molecules, existing generation models canbe divided into two categories: text-based and graph-based methods.
Text-based models [13, 23, 5]usually adopt the Simplified Molecular-Input Line-entry System ([39], SMILES) to describe eachmolecular, which is simple and efficient.
However, these models are not robust because certainslight perturbations in SMILES could result in significant changes in molecule structure [45, 24].
The graph-based counterparts [9, 38, 20], therefore, have gained increasing attention recently.
Liet al.
[25] proposed a generation model for graphs and demonstrated it performed better than thetext-based strategy.
You et al.
[45] used reinforcement learning to generate molecules sequentiallyunder the guidance of mixed rewards in terms of the chemical validity and other property scores.
Popova et al.
[33] proposed MRNN to autoregressively generate nodes and edges.
Shi et al.
[38]designed a flow-based autoregressive model and exploited reinforcement learning for goal-directedgeneration.
However, these models use atoms as the basic generation unit, leading to long sequencesand therefore time-consuming training process.
On the contrary, our method applies subgraph-levelrepresentation, which not only captures chemical properties but also is computationally efficient.
Subgraph-Level Molecule Generation Several works have been developed for subgraph-levelgeneration.
In particular, Jin et al.
[18] suggested generating molecules in the form of junction treeswhere each node is a ring or edge.
Jin et al.
[19] decomposed molecules into subgraphs by breakingall the bridge bonds.
It used a complex hierarchical model for polymer generation and graph-to-graphtranslation.
Yang et al.
[44] integrated reinforcement learning with the subgraph vocabulary createdfrom existing chemical fragment libraries.
Different from Jin et al.
[18, 19], Yang et al.
[44] whichuse manual rules to extract subgraphs or utilize existing libraries, we automatically extract frequentprincipal subgraphs to better capture the regularities in molecules for subgraph-level decomposition.
Our work also relates to traditional subgraph mining literature [15, 43, 32].
While seeking genericfrequent subgraphs is known to be NP-hard [22, 17], our work focuses on finding frequent principalsubgraphs by merging two adjacent fragments, which alleviates time complexity to a large extent.
Tothe best of our knowledge, we are the first to utilize frequent subgraphs in generation tasks.
Our Proposed PS-VAE
This section presents the details of the proposed PS-VAE, consisting of the principal subgraphdefinition and extraction in Section 3.1 and the two-step generation in Section 3.2.
3.1 Principal Subgraph
A molecule can be represented as a graph G = ⟨V , E⟩ , where V is a set of nodes correspondingto atoms and E is a set of edges corresponding to chemical bonds.
We define a subgraph of G as
S = ⟨ ˜ V , ˜ E⟩ ⊆ G , were ˜ V ⊆ V and ˜ E ⊆ E .
We say subgraph S spatially intersects with subgraph
S ′ if there are certain atoms in a molecule belong to both S and S ′ , denoted as S ∩ S ′ ̸
= ∅ .
Notethat if two subgraphs look the same (with the same topology), but they are constructed by differentatom instances, they are not spatial intersected.
Similarly, if two subgraphs S and S ′ appear in thesame molecule, we call their spatially union subgraph as U = S (cid:83) S ′ , where the nodes of U are theunion set of ˜ V and ˜ V ′ , and its edges are the union of ˜ E and ˜ E
′ plus all edges connecting S and S ′ .
A decomposition of a molecule G is derived as a set of non-overlapped subgraphs {S i } ni and theedges connecting them {E ij } n,ni,j , if G =
( (cid:83) ni S i ) (cid:83) ( (cid:83) n,ni,j E ij ) and S i ∩ S j = ∅ for any i ̸
= j .
Thefrequency of a subgraph occurring in all molecules of a given dataset measures its repeability andepidemicity, which should be an important property.
Formally, we define the frequency of a subgraph
S as c ( S ) =
(cid:80) i
c ( S|G i ) where c ( S|G i ) computes the occurrence of S in a molecule G i .
Withoutloss of generality, we assume all molecules and subgraphs we discuss are connected.
With the aforementioned notations, we propose a novel and central concept below.
Definition 3.1 (Principal Subgraph) .
We call subgraph S a principal subgraph, if any other subgraph
S ′ that spatially intersects with S in a certain molecule satisfies either S ′ ⊆ S or c ( S ′ )
≤ c ( S ) .
Amongst all subgraphs of the larger frequency, a principal subgraph basically represents the “largest”repetitive pattern in size within the data.
It is desirable to leverage patterns of this kind as thebuilding blocks for molecule generation since those subgraphs with a larger size than them are lessfrequent/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 theconstructed vocabulary as a fragment .
We generate all 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 byderiving the union F (cid:83) F ′ .
Here, the neighboring fragments of a given fragment F in a molecule isdefined as the ones that contain at least one first-order neighbor nodes of a certain node in F .
Update .
We count the frequency of each identical merged subgraph in the last stage.
We choose themost frequent one as a new fragment in the vocabulary V .
Then, we go back to the merge stage untilthe vocabulary size reaches the predefined number N.
1: Input: A set of graphs D and the desired number N of principal subgraphs to learn.
2: Output: A set of principal subgraphs V and the counter C of principal subgraphs.
3: V ← { GraphToSMILES( ⟨{ a } , ∅⟩ ) } ; { Initially, V corre- sponds to all atoms a that appear in D . } 4: N ′ ← max( N, | V | ) ; 5: while | V | < N ′ do 6: C ← EmptyMap() ; { Initialize a counter. } 7: for G in D do 8: for ⟨F i , F j , E ij ⟩ in G do 9: F ← Merge( ⟨F i , F j , E ij ⟩ ) ; { Merge neighboring fragments into a new fragment. } 10: s ← GraphToSMILES( F ) ; { Convert the graph to SMILES representation. }
[Table]
[Equation]
[ s ] =
[Equation]
[ s ]
+ 1 ; { Update the counter.
The initial value is 0. } 12: end for 13: end for 14: s =
TopElem( C ) ; { Find the most frequent merged frag- ment. } 15:
F ← SMILESToGraph(s) ; { ConverttheSMILESstring to graph representation .} 16:
V ← V ∪ { s } ; D ′ ← {} ; 17: for G in D do 18:
G ′ ← MergeSubGraph( G , F ) ; { Update the graph representation if possible. } 19:
D ′ ← D ′ ∪ {G ′ } ; 20: end for 21:
D ← D ′ ; 22: end while
[Figure]
Figure 2 illustrates the above processes and Algorithm 1 gives the flowchart.
Notice that Algorithm 1has exploited the conversion from molecular subgraph to SMILES [39] to not only ensure the
[Figure]
After training, we 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, whichis crucial for the training of the two-step decoder introduced in the next subsection.
More importantly, we have the following theorem to demonstrate the benefit of Algorithm 1.
Theorem 3.2.
The vocabulary V constructed by Algorithm 1 exhibits the following advantages.
(i) Monotonicity :
The frequency of the non-single-atom fragments in V decreases monotoni-
cally, namely, ∀F i , F j ∈ V , c ( F i ) ≤
c ( F j ) , if i ≥ j .
(ii) Significance :
Each fragment F in V is a principal subgraph.
(iii) Completeness :
For any principal subgraph S arising in the dataset, there always exits a
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.
It states that our algorithm is ableto discover frequent principal subgraphs, and any principal subgraph can be represented (at leastcontained) by our certain extracted fragment if the size of the vocabulary is sufficiently large.
Thisis also a meaningful extension to traditional subgraph mining literature [17], in which seeking themost frequent subgraphs is known to be NP-hard.
Algorithm 1 can somehow address this problemefficiently by focusing mainly on finding the most frequent principal subgraphs.
3.2 Two-step Molecule Generation
The molecule generation is modeled as a two-step task: first predicting which fragment should bechosen from the vocabulary created in the last subsection, and then proceeding with how to assemblethe predicted fragments.
Although in the first step we predict the fragments in a sequence-wisemanner, we globally investigate if every two predicted fragments should be linked in the secondstep.
This two-step fashion makes our method not only less permutation-dependent and thus moresample-efficient than the generic autoregressive counterparts [25], but also more flexible than themethods [18] that require predefined junction tree or adjacent connections between subgraphs.
Wewill provide experimental evaluations in Table 4 to justify the benefit of our proposed two-stepgeneration strategy.
Below, we provide the details of the two steps.
What to assemble.
This step is of the VAE style [21].
As shown in Figure 3, we use a GNN toencode a molecular graph G into a latent variable z .
Each node v has a feature vector x v which is theconcatenation of three learnable embeddings: its atomic type, fragment type and the generation orderof the fragment.
Each edge has a feature vector indicating its bond type.
Specifically, we utilize GINwith edge feature [14] as the backbone GNN network, which computes the k -th layer as follows: [Equation]
[Equation]
where, h ( k ) v is the hidden activation of node v ( h (0) v = x v ),
e uv is the edge feature between node uand v , N ( v ) returns the neighbos of u , h Θ is a neural network, and ε is a constant.
We implement h Θas a 2-layer Multi-Layer Perceptron ([10], MLP) with ReLU activation and set ε = 0 .
We obtain thefinal representations of nodes as h v =
[ h (1) v , . .
, h ( t ) v ] so that it contains the contextual informationfrom 1 -hop to t -hop.
The graph-level representation is given by summation h G = (cid:80) v ∈V h v .
We useh G to obtain the mean µ G and log variance σ G of variational posterior approximation q ( z |G ) throughtwo separate linear layers and use the reparameterization trick [21] to sample from the distribution inthe training process.
Given a latent variable z , our model first uses an autoregressive sequence generation model
P ( F i |F <
i , z ) to decode an sequence of graph fragments [ F 1 , . . . , F n ] .
Note that the set of subgraphsinto which a molecule is decomposed should not be ordered.
Here, although we violate this lawby using the ordered decoder, this issue is practically relieved by data augmentation of randomfragment permutations during training, and it is further mitigated by the second step (presentedlater) where the assembling of the predicted subgraphs is not order-sensitive.
During training, weinsert two special tokens “ <bos> ” and “ <eos> ” indicating the beginning and the end of sequencegeneration, respectively.
We implement the sequence model via a single layer of GRU [8] and projectthe latent variable z to the initial state of GRU.
The training objective of this stage is to minimize thelog-likelihood L P of the ground truth fragment sequence:
[Equation]
During testing, the generation stops when a “ <eos> ” is outputted.
How to assemble.
This step estimates all inter-fragment edges {E ij } non-autoregressively andglobally.
Specifically, we use a GNN with the same architecture in the last step but with differentparameters to obtain the representations h v of each atom v in all fragments.
Given nodes v and u intwo different fragments, we predict their connections as follows:
[Equation]
where H θ is a 3-layer MLP with ReLU activation.
Apart from the types of chemical bonds, we alsoadd a special type “ <none> ” to the edge vocabulary which indicates there is no connection betweentwo nodes.
During training, we predict both P ( e uv ) and P ( e vu ) to let H θ learn the undirected natureof chemical bonds.
We use negative sampling [12] to balance the ratio of “ <none> ” and chemicalbonds.
Since only about 2% pairs of nodes has inter-fragment connections, negative samplingsignificantly improves the computational efficiency and scalability.
The training objective of thisstage is to minimize the log-likelihood:
[Equation]
Joining the reconstruction losses of both steps (Eq. 3 and Eq. 5), we arrive at: L rec =
L F + L E .
When considering target property, we jointly train a 2-layer MLP from z to predict the scores oftarget properties using the MSE loss.
By denoting this extra loss as L prop , the final objective of our
PS-VAE becomes:
[Equation]
6) where the the KL divergence D KL aligns the distribution of z with the prior distribution N ( 0 , I ) ; αand β balance the trade-off between different losses.
To decode {E ij } in the inference phase, the decoder first assigns all possible inter-fragment connections with a bond type and a corresponding confidence level.
We try to add bonds that have a confidence level higher than δ th = 0 .
5 to the molecule in order of confidence level from high to low.
For each attempt, we perform a valency and a cycle check to reject the connections that will causeviolation of valency or form unstable rings which are too small or too large.
Since this proceduremay form unconnected graphs, we find the maximal connected component as the final result.
Thepseudo code for inference is deferred to Appendix G.
Experiments
Evaluation Tasks We first report the empirical results for the distribution-learning tasks in GuacaMol benchmarks [7] to evaluate if the model can generate realistic and diverse molecules.
Then wevalidate our model on two common problems and the goal-directed tasks of the GuacaMol benchmarks .
Property Optimization requires generating molecules with optimized properties.
Constrained
Property Optimization concentrates on improving the properties of given molecules with a restricteddegree of modification.
GuacaMol Goal-Directed Benchmarks consist of 20 molecular design taskscarefully curated by domain-experts [46, 41, 11].
Dataset We use the ZINC250K [16] dataset for training, which contains 250,000 drug-likemolecules up to 38 atoms.
For GuacaMol benchmark, we add extra results on the QM9 [6, 36] dataset,which has 133,014 molecules up to 23 atoms.
Baselines We compare our principal subgraph variational auto-encoder ( PS-VAE ) with the following state-of-the-art models.
JT-VAE [18] is a variational auto-encoder that represents molecules asjunction trees.
It performs Bayesian optimization on the latent variable for property optimization.
GCPN [45] combines reinforcement learning and graph representation for goal-directed moleculargraph generation.
MRNN [33] adopts two RNNs to autoregressively generate atoms and bondsrespectively.
It combines policy gradient optimization to generate molecules with desired properties.
GraphAF
[38] is a flow-based autoregressive model which is first pretrained for likelihood modelingand then fine-tuned with reinforcement learning for property optimization.
GA [31] adopts geneticalgorithms for property optimization and models the selection of the subsequent population witha neural network.
HierVAE [19] extracts fragments by breaking bridge bonds in molecules anduses them as building blocks.
FREED [44] is an RL-based model and uses fragments from existingchemical libraries to construct the subgraph vocabulary.
MARS [42] adopts Markov chain Monte
Carlo sampling for generation and is the state-of-the-art approach on the GuacaMol goal-directedbenchmarks.
Since our generation model is universally compatible with molecular decompositionof non-overlapping fragments, we also integrate vocabularies from HierVAE and FREED into ourtwo-step generation model, which are abbreviated as H-VAE ∗ and F-VAE ∗ , respectively.
Implementation Details We choose N = 300 for property optimization and N = 500 forconstrained property optimization.
PS-VAE is trained for 6 epochs with a batch size of 32 and alearning rate of 0.001.
We set α = 0 .
1 and initialize β = 0 .
We adopt a warm-up method thatincreases β by 0 .
every 1000 steps to a maximum of 0 .
More details are in Appendix H.
4.1 Results
GuacaMol Distribution-Learning Benchmarks These benchmarks evaluate four metrics on10,000 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 onesin generated molecules.
Novelty assesses the ability of the models to generate molecules not containedin the training set.
KL Divergence evaluates the closeness between the training set molecules andthe generated molecules in terms of the distributions of various physicochemical properties.
Fréchet
ChemNet Distance (FCD) calculates the closeness of the two sets of molecules with respect to theirhidden representations in the ChemNet [34].
Each metric is normalized to 0 to 1, and a higher valueindicates better performance.
Table 1 shows the results of distribution-learning benchmarks on QM9and ZINC250K.
Our model achieves competitive results in all four metrics, which indicates ourmodel can generate realistic molecules and prevent overfitting the training set.
In addition, withthe same vocabulary, H-VAE ∗ surpasses HierVAE consistently, confirming the advantage of ourtwo-step generation model over the one used in HierVAE.
Moreover, even sharing the same two-stepdecoder, PS-VAE is still better than H-VAE ∗ and F-VAE ∗ consistently, which is probably because our constructed vocabulary discovers more meaningful and reusable patterns than H-VAE ∗ and F-VAE ∗ .
We have displayed some molecules sampled from the prior distribution in Appendix M.
[Table]
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 whichhas an unbounded range.
QED measures the drug-likeness of molecules with a range of [0 , 1] .
Bothproperties are calculated by empirical prediction models [40, 4], and are widely used in previousworks [18, 45, 38].
We constrain all models to generate molecules under 60 atoms to prevent themfrom utilizing the flaw of PlogP by keeping extending the carbon chain [38].
We first train a predictoron the latent space of previously-trained VAE models to simulate the scoring functions, then performgradient ascending to search for optimized molecules [18, 27].
Hyperparameters can be found in
Appendix H.
Following previous works [18, 45, 38]
[Table]
we generate 10,000 optimized molecules andreport the top-3 scores found by each model.
Results in Table 2 show that our model surpasses thebaselines 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]
Constrained Property Optimization This task refines molecular properties under the constraintthat the Tanimoto similarity with Morgan fingerprint [35] is above a threshold δ .
As suggested byprevious works [18, 45, 38], 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 latentvariable with a max step of 80.
We collect all latent variables which have better-predicted scores thanthe previous iteration and decode each of them 5 times, namely up to 400 molecules.
Following Shiet al.
[Table] we initialize the generation with sub-graphs sampled from the original molecules.
Thenwe choose the highest scoring one from the molecules that meet the similarity constraint.
Table 3shows 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 greaterthan atom-level models [Table] leading to a lower success rate.
Even so, the success rates by our model arestill on par with the atom-level counterparts and are the best among all subgraph-level methods.
[Table] GuacaMol Goal-Directed Benchmarks To further explore the effacy of PS-VAE, we provide theresults for GuacaMol goal-directed benchmarks [7] in Table 4.
All scores are continuous valuesbetween 0 and 1, and the higher, the better.
In order to obtain more discernible results betweendifferent approaches, we conduct experiments on QM9 and ZINC250K which have much less highscoring molecules than ChEMBL [29] to make the tasks more challenging.
Otherwise the majority ofthe benchmarks are easy to be optimized to the upper bound [42].
We adopt the same optimizingstrategy as in the property optimization tasks.
Hyperparameters can be found in Appendix H. Table4 shows that our model remarkably performs better than H-VAE ∗ and F-VAE ∗ , and thus exhibitsthe benefit of our subgraph extraction method.
The superior of H-VAE ∗ to HierVAE indicates theadvantage of our two-step assembling over the sequential sampling strategy.
[Table]
Valsartan SMARTS [Table] Celecoxib
[Table]
Troglitazone
[Table] Thiothixene [Table] Aripiprazole similarity
[Table]
4.2 Ablation Study
We conduct an ablation study to further validate the effects of principal subgraphs and the two-stepgeneration approach.
We first downgrade the vocabulary to contain only single atoms.
Then wereplace the two-step decoder with a fully autoregressive decoder.
We present the performance on(constrained) property optimization in Table 5 and Table 6.
The direct introduction of the two-stepgeneration approach leads to improvement in property optimization but harms the performance onconstrained property optimization.
This is reasonable as separating the generation of atoms andbonds brings in information loss of bonds for the atom-level generation process.
However, theadoption of principal subgraphs as building blocks alleviates this negative effect since the principalsubgraphs themselves contain rich bond information.
Therefore, integrating principal subgraphs withour two-step generation approach leads to the best choice in our model design.
Furthermore, weprovide the runtime cost of baselines and PS-VAE in Appendix F to demonstrate the improvement inefficiency brought by the principal subgraphs and the two-step generation approach.
[Table] [Table]
Analysis
Principal Subgraph Statistics
We compare the distributions of the vocabulary of JT-VAE, FREED,
HierVAE
[Table]
and the vocabulary constructed by our principal subgraph extraction methods with a size of100, 300, 500, and 700.
Figure 4 shows the proportion of fragments with different numbers of atomsin the vocabulary and their frequencies of occurrence in the ZINC250K dataset.
The fragments in thevocabulary of JT-VAE mainly contain 5 to 8 atoms with a sharp distribution.
However, starting fromfragments with 3 atoms, the frequency of occurrence is already close to zero.
Therefore, the majorityof fragments in the vocabulary of JT-VAE are actually not common fragments.
On the contrary, thefragments in the vocabulary of principal subgraphs have a relatively smooth distribution over 4 to10 atoms.
Moreover, these fragments also have a much higher frequency of occurrence comparedto those by JT-VAE.
Vocabularies constructed by our method show similar advantages compared tothose of HierVAE and FREED.
We present samples of principal subgraphs in Appendix L.
Principal Subgraph - Property Correlation To analyze the principal subgraph - property correlation and whether our model can discover and utilize the correlation, we present the normalizeddistribution of generated fragments and Pearson correlation coefficient between the fragments and
Penalized logP (PlogP) in Figure 6.
The curve of the Pearson correlation coefficient indicates thatsome fragments positively correlate with PlogP while some negatively correlate with it.
Comparedwith the flat distribution under the non-optimization setting, the generated distribution shifts towardsthe fragments positively correlated with PlogP under the PlogP-optimization setting.
The generationof fragments negatively correlated with PlogP is also suppressed.
Therefore, correlations existbetween fragments and PlogP, and our model can accurately discover and utilize these correlations.
Conclusion
We propose an algorithm to automatically discover the regularity in molecules and extract themas principal subgraphs .
With the extracted principle subgraphs at hand, we generate molecules intwo phases.
Our model consistently outperforms state-of-the-art models on distribution-learning,(constrained) property optimization, and GuacaMol goal-directed benchmarks, and exhibits highercomputational efficiency than certain widely-used baselines.
Our work provides insights into theselection of subgraphs on molecular graph generation and can inspire future search in this direction.
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