Hierarchical Graph-to-Graph Translation for Molecules
Authors: Wengong Jin
Regina Barzilay
Tommi Jaakkola
Venue:  (2020)
Keywords: graph generation
deep learning

Abstract: The problem of accelerating drug discovery relies heavily on automatic tools to optimize precursor molecules to afford them with better biochemical properties. Our work in this paper substantially extends prior state-of-the-art on graph-to-graph translation methods for molecular optimization. In particular, we realize coherent multi-resolution representations by interweaving the encoding of substructure components with the atom-level encoding of the original molecular graph. Moreover, our graph decoder is fully autoregressive, and interleaves each step of adding a new substructure with the process of resolving its attachment to the emerging molecule. We evaluate our model on multiple molecular optimization tasks and show that our model significantly outperforms previous state-of-the-art baselines.

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HIERARCHICAL GRAPH-TO-GRAPH FOR MOLECULES
TRANSLATION
Anonymous authors Paper under double-blind review
ABSTRACT
The problem of accelerating drug discovery relies heavily on automatic tools to optimize precursor molecules to afford them with better biochemical properties. Our work in this paper substantially extends prior state-of-the-art on graph-to-grapp translation methods for molecular optimization. In particular, we realize coherent multi-resolution representations by interweaving the encoding of substructure com- ponents with the atom-level encoding of the original molecular graph. Morcover, our graph decoder is fully autoregressive, and interleaves each step of adding substructure with the process of resolving its attachment to the emerging molecule. We evaluate our model on multiple molecular optimization tasks and show that our model significantly outperforms previous state-of-the-art baselines.
INTRODUCTION
Molecular optimization seeks to modify compounds order to improve their biochemical properties. This task can be formulated Given a corpus of molecular pairs {(X, Y)). where Y is a paraphrase of X with better chemical properties, the model is trained to translate input molecular graph into its better form. The task is difficult since the space of potential candidates is vast, and molecular properties can be complex functions of structural features. Moreover, graph generation is computationally challenging due to complex dependencies involved in the joint distribution over nodes and edges. Similar to machine translation, success in this task predicated on the inductive biases built into the encoder-decoder architecture, in particular the process of generating molecular graphs.
graph-to-graphe translation problem analogous to machine translation.
Prior work (Jin et al. 2019) proposed junction tree encoder-decoder that utilized valid chemical substructures (e.g., aromatic rings) as building blocks to generate graphs. Each molecule was represented as a junction tree over chemical substructures in addition to the original atom-level graph. While successful, the approach remains limited in several ways. The tree and graph encoding were carried out separately, and decoding proceeded in strictly successive steps: first generating the junction tree for the molecule, and then attaching its substructures together. This means the predicted attachments do not impact the subsequent substructure choices (see Figure[[b) Moreover, the attachment prediction process is noneautoregrsssive, thus it can predict inconsistent substructure attachments across different nodes in the junction tree (see Fig
We propose multi-resolutin hierarchically coupled encoder-decoder for graph generation. Our auto-regressive decoder interleaves the prediction of substructure components with their attachments the molecule being generated. In particular, a target graph unraveled sequence of triplet predictions (where to expand the graph, new substructure type, its attachment). This enables us to model strong dependencies between successive attachments and substructure choices. The encoder is designed to represent molecules at different resolutions in order to match the proposed decoding process. Specifically, the encoding of each molecule proceeds across three levels, with each layer capturing essential information for its corresponding decoding step. The graph convolution of atoms at the lowest level supports the prediction of attachments and the convolution over substructures at the highest level supports the prediction of successive substructures. Compared to prior work, our decoding process is much more efficient because it decomposes each generation step into a hierarchy of smaller steps in order to avoid combinatorial explosion. We also extend the method to handle conditional translation where desired criteria are fed as input to the translation process. This enables method to handle different combinations of criteria at test time.

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Junction Tree Decoder
Graph Decoder
attach
Inconsistent
cannot be assembled
attach
Independent
Interioave trap and graph decoding
change
can be assembled
Problem 1: Isolation between tree and graph decoder
Problem 2: Non-autoregressive graph decoder
Key limitations of Jin et al. (2019)'s approach: a) Since their tree and graph decoders are isolated, the model can generate invalid junction trees which cannot be assembled into any molecule. This problem can be solved when we interleave the tree and graph decoding steps, allowing the predicted attachments to guide the substructure prediction; b) Their non-autoregressive graph decoder often predicts inconsistent local substructure attachments during training. To this end, we propose an autoregressive decoder that interleaves the prediction of substructures with their attachments.
Figure 1:
We evaluate our new model on multiple molecular optimization tasks, Our baselines include previous state-of-the- graph generation methods (You et al. 2018a| Liu al. 2018 Jin et al., 2019) and an atom-based translation model we implemented for more comprehensive comparison. Our model significantly outperforms these methods discovering molecules with desired properties, yielding 3.3% and 8. % improvement on QED and DRD2 optimization tasks. During decoding, our model generation methods. We further conduct
runs 6.3 times faster than previous substructure-bant ablation studies to validate the advantage of our hierarchical decoding and multi-resolution encoding. Finally, we show that conditional translation can succeed (generalize) even when trained on molecular pairs with only 1.6% of them having desired target property combination.
RELATED WORK
Molecular Graph Generation Previous work have adopted various approaches for generating
molecular graphs. Methods (Gómez-Bombaree Bombarelli et al.] 2018 Segler et al., 2017: Kusner et al.
2017: Dai al.) 2018: Guimaraes et al. [001] [ Olivecrona et al. 2017 et al. [018]] Kang
& Cho 201 8) generate molecules based on their SMILES strings (Weininger 1988). Simonovsky Kooodakii (2018): De Cao Kipf (2018); 8): Ma et al. (20T8) developed generative models which
output the adjaccncy matrices and node labels of the graphs at once. You et al. (2018b); Li et al. (2018); Samanta et al. (2018); Liu et al. (2018) proposed generative models decoding molecules sequentially node by node. You et al. (2018a): Zhou al. (2018) adopted similar node-by-node approaches in the context of reinforcement learning. based method for molecule generation.
Jearmin..Kajjp Kajino (2018) developed hypergraph grammar
Our work most closely related to Jin et al. 2018 2019) that generate molecules based on substruc- tures. They adopted two-stage procedure for realizing graphs. The first step generates junction tree with substructures as nodes, capturing their coarse relative arrangements. The second step resolves the full graph by specifying how the substructures should be attached to each other. Their major trawbacks are 1) The second step introduced local independence assumptions and therefore the decoder is not autoregressive. 2) These two steps are applied stage-wise wise during decoding first realizing the junction tree and then reconciling attachments without feedback. In contrast, our method jointly predicts the substructures and their attachments with an autoregressive decoder.
Graph Encoders Graph neural networks have been extensively studied for graph encoding (Scarselli
al.
2009
Bruna et al. 2013 Li al. [2013] Niepert et al.] 2016] Kipf Welling 2017 Hamilton
et al.
2017 Lei et al. 2017 Velickovic et al. 2017: Xu et al.) 2018). Our method is related to
graph encoders for molecules (Duvenaud et al. 2015 Kearnes et al. 2016 Dai et al., 2016 Gilmer method represents molecules as trees.
al. 2017 Schütt et al. 2017). Different these approaches,
hierarchical graphs spanning from atom-level graphs to substructure-
Our work is most closely related to (Defferrard al. 2016 Ying et al. 2018 Gao & Ji 2019) that learn to represent graphs in hierarchical manner. In particular, Defterrard et al. (2016) utilized graph coarsening algorithms construct multiple layers of graph hierarchy and Ying et al. (2018);
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Molecular Graph
Encoder
C
Atom Layer
Attachment Layer
Substructure Layer
Substructure Tree
Decoder
Attachment Predictionn
Attachment Prediction
Substructure Prediction
Figure 2: Overview of our approach. Each substructure S; is subgraph of a molecule (e.g.. rings). In each step, our decoder adds a new substructure and predicts attachment to current graph. Our encoder represents each molecule across three levels (atom layer, attachment layer and substructure layer), with each layer capturing relevant information for the corresponding decoding step.
Gao & Ji 2019) proposed to learn the graph hierarchy jointly with the encoding process. Despite some differences, all of these methods seek represent graphs single vector for regression or classification tasks. In contrast, our focus is graph generation and a molecule is encoded into multiple sets of vectors, each representing the input at different resolutions. Those vectors are dynamically aggregated by decoder attention modules in each graph generation step.
3 HIERARCHICAL GENERATION OF MOLECULAR GRAPHS
The graph translation task seeks to learn a function FF that maps a molecule into another molecule with better chemical properties. FF is parameterized Both our encoder and decoder are illustrated in Figure 2] In each generation step, our decoder adds new substructure (substructure prediction) and decides how should be attached the current graph. The attachment prediction proceeds in two steps: predicting attaching points in the new substructure and their corresponding attaching points in the current graph (attachment prediction 1-2).
an encoder-decoder with neural attention.
To support the above hierarchical generation, we need to design a matching encoder representing molecules multiple resolutions order provide necessary information for each decoding step. Therefore, we propose to represent a molecule X by a hierarchical graph Hx with three components: 1) substructure layer representing how substructures are coarsely connected; 2) attachment layer showing the attachment configuration of each substructure; 3) atom layer showing how atoms connected in the graph. Our model encodes nodes Hlx into substructure vectors cx. attachment vectors ex and atom vectors ex which are fed to the decoder for corresponding prediction steps. As encoder is tailored for the decoder, we first deseribe decoder clarify relevant concepts.
3.1 HIERARCHICAL GRAPH DECODER
Notations We denote the sigmoid function as ol-). MLP(a, b) represents multi-layer neural network whose input is the concatenation of and attentiong(h,, cx) stands for bilinear attention over vectors cx with query vector h..
Substructures We define substructure S; (V;, &,) subgraph molecule G induced by atoms in V; and bonds in &, Given molecule, we extract its substructures S S, such that their union covers the entire molecular graph: == U, V; and = U, &,. In this paper, we consider two types of substructures: rings and bonds. We denote the vocabulary of substructures S, which is constructed from the training set. In our experiments, |S| < 500 and has over 99.5% coverage on test sets.
Substructure Tree To characterize how substructures
connected in the molecule G, construct its corresponding substructure tree T. whose nodes are substructures S ,S,- Specifically, we construct the tree by first drawing edges between S, and S, if they share common atoms, and then applying tree decomposition over to ensure it is tree-structured.
Generation Our graph decoder generates molecule & by incrementally expanding its substructure tree in its depth-first first order. Suppose the model is currently visiting substructure node S,. makes the following predictions conditioned encoding of input X (see Fig

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Current state
One Generation Step
Next state
Subsiructure Prediction
Attachment Prediction
Attachment Prodiction
Figure 3: Illustration of hierarchical graph decoding. Suppose the decoder is visiting the substructure
Sg. 1) decides to add new substructure (topological prediction). 2) It predicts that new substructure S₁ should be ring (substructure prediction) 3) It predicts how this new ring should be attached to the graph (attachment prediction). Finally, the decoder moves to St and repeats the process.
1. Topological Prediction: It first predicts whether there will be new substructure attached Sk- If not, the model backtracks to its parent node Sd, in the tree. Let hss the hidden representation of S& learned by decoder (which will be elaborated in 43.2) This probability is predicted by MLP with attention over substructure vectors cx of X:
P = a (MLP(hs,, a()) a attentiona (hs.. cx)
(1)
2. Substructure Prediction: If ps: > 0.5, the model decides to create new substructure S, from S₁ and sets its parent d, = k. It then predicts the substructure type of Se using another MLP that outputs distribution the vocabulary S:
ps, softmax(MLP(hss ax)))
a attention, (hs. cxx
(2)
Attachment Prediction: Now the model needs to decide how S, should be attached to Sg. The attachment between S; and S3 is defined as atom pairs M, = {(u,, ey)) |u E Sc, ey E S where atom u, and 0y are attached together. We predict those atom pairs in two steps:
1) We first predict the atoms {uz} } C& that will be attached to Sk- Since the graph S, is always fixed and the number of attaching atoms between two substructures is usually small, can enumerate all possible configurations {uz} to form a vocabulary A(S,) for each substructure S,- This allows to formulate the prediction of {vy } as classification task predicting the correct configuration A, = (S,, {u,}) from the vocabulary A(S,):
PA. softmax (MLtmax ax))
a attention, (
(3)
2) Given the predicted attaching points {u,), need find the corresponding atoms {uz} in the substructure S₁. As the attaching points are always consecutive, there exist at most Sx] different attachments M {[u,, }. The probability of a candidate attachment M is computed based on the atom representations huy and hog learned by the decoder:
PM = softmax (hM- attention, (hM.c)) hM - E, ML,, Bay))
(4)
The above three predictions together give an autoregressive factorization of the distribution over the next substructure and its attachment. Each of the three decoding steps depends on the outcome of previous step, and predicted attachments will in turn affect the prediction of subsequent substructures. During training, we apply teacher forcing to the above generation process, where the generation order is determined by a depth-first traversal over the ground truth substructure tree. The attachment enumeration is tractable because most of the substructures are small. In our experiments, the average size of attachment vocabulary [A(S)) < 3 and the number of candidate attachments is less than 20.
3.2 HIERARCHICAL GRAPH ENCODER
Our encoder represents a molecule X by a hierarchical graph H.x in order to support the above decoding process. The hierarchical graph has three components (see Figure 4
1. Atom layer: The atom layer is the molecular graph of X representing how its atoms are connected, Each atom node is associated with a label a, indicating its atom type and charge. Each edge (u, v) in the atom layer is labeled with buv indicating its bond type.
2. Attachment layer: This layer is derived from the substructure tree of molecule X. Each node A; in this layer represents a particular attachment configuration of substructure S; in the vocabulary A(S.). Specifically, A, (S,, (oy}) where {ry} the attaching atoms between S, and its parent Sn, in the tree. This layer provides necessary information for the attachment prediction (step 1). Figure illustrates how A, and the vocabulary A(S:) look like.
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Attachment Vocabulary
A
St
Atom Layer
Attachment Layer
Substructure Layer
Figure 4: Left: Hierarchical graph encoder. Solid arrows illustrate message passing in each layer. Dashed arrows connect each atom to the substructures belongs. In the attachment layer, each node A is particular attachment configuration of substructure St. Right: Attachment vocabulary for ring. The attaching points in each configuration (highlighted in red) must be consecutive.
3. Substructure layer: This layer is the same as the substructure tree. This layer provides essential information for the substructure prediction in the decoding process.
We further introduce edges that connect the atoms and substructures between different layers in order to propagate information in between. In particular, we draw a directed edge from atom in the atom layer to node A, in the attachment layer v E S,. We also draw edges from node A, to node S in the substructure layer. This gives us the hierarchical graph Hxx for molecule X, which will be encoded by a hierarchical message passing network (MPN) (see Figure ( The encoder contains three MPNs that encode each of the three layer. We use the MPN architecture from Jin et al. (011 For simplicity, we denote the MPN encoding process as ( with parameter 15.
Atom Layer MPN We first encode the atom layer of Hxx (denoted H The inputs to this MPN are the embedding vectors (e(a.)), {e(b..)} of all the atoms and bonds in X. During encoding, the network propagates the message vectors between different atoms for T iterations and then outputs the atom representation h, for each atom e:
c (h,) MPN da (H&, (e(a.)), {e(b..)))
(5)
Attachment Layer MPN The input feature of each node A, in the attachment layer Hy is an concatenation of the embedding e(A;)) and the sum of its atom vectors (h, v E Si}:
fA MLP (e(A.), E h.d
(6)
The input feature for each edge As) in this layer is embedding vector e(d,)). where d, describes the relative ordering between node A, and A, during decoding. Specifically, we set dıy if node A; is the k-th child of node Aj and dij if Ai is the parent. We then run T iterations of message passing over H to compute the substructure representations:
ox (h..) = MPN (H (fA. (E(dG)))
Substructure Layer MPN Similarly, the input feature node S, in this layer is computed as the concatenation of embedding e(S:) and the node vector hA, from the previous layer. Finally, message passing over the substructure layer Hxx to obtain the substructure representations:
(8) In summary, the output of our hierarchical encoder is a set of vectors Cx & Uc o that represent a molecule X at multiple resolutions. These vectors are input to the decoder attention.
fs. = MLP (e(()))
& = (hs,) MPN (Hxx (fs. (e(d:))))
use the same hierarchical MPN architecture to encode the hierarchical graph Hg at each step t. This gives us the substructure vectors hss, and atom vectors hu, in [..] All future nodes and edges are masked to ensure the prediction current substructure and attachment only depends on previously generated outputs.
Decoder MPN During decoding,
3.3 TRAINING
Our training set contains molecular pairs (X, Y) where each compound can be associated with multiple outputs Y since there many ways modify X to improve its properties. In order to
We slightly modified their architecture by using I.M instead of GRU for message propagation due to its hetter empirical performance. The details are shown in the appendix.
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Multi-resolution Representation ex
Algorithm Variational Translation (uncon- ditional setting, without target criteria g)
Encode
Decode
Y
1: for (X, Y) in the training set do
2: Encode molecule X, Y into vectors CY,
Latent Code (for output diversity)
3: Compute μx,Y, xx, from 5x,y
Modulate
4: Sample latent code Qxz|X,Y)
Target Criteria (Y is bioactive & drug-like
8x.y
ENIMERD
5: Generate molecule Y given Cx and
Modulate
6: end for
Figure Conditional translation.
generate diverse outputs, we follow Jin et al. 2019) and extend our method to a variational translation model F (X, + with an additional input The latent vector indicates the intended mode of translation which is sampled from a Gaussian prior P()) during testing.
We train our model using variational inference (Kingma & Welling 2013). Given training example - (Mxx, xx,Y). To compute Q( X, Y), we first encode and into their representations cx and cy and then compute vector ōx.y that summarizes the structural changes from molecule X to Y at both atom and substructure level:
(X, Y), we sample x from the posterior
x = -
X,Y -
Finally, we compute [uX,Y xx,y MLP
8x x and sample z using reparameterization
trick. The latent code is passed to the decoder along with the input representation Cx reconstruct output Y. The overall training objective follows a standard conditional VAE:
Y(X,Y) = E-zz-pllog P(Y|z, X)] + DKI. [Q Y)II
(10)
Conditional Translation the above formulation, the model does not know what properties are being optimized during translation. During testing, users cannot change the behavior of trained model (i.c., what properties should be changed). This may become limitation of our method in multi-property optimization setting. Therefore, we extend our method handle conditional translation where the desired criteria are also fed as input to the translation process. In particular, let gx.y be a translation criteria indicating what properties should be changed. During variational inference, we compute μx, and ox,y with an additional input gx,Y
WXx.Y,x.YV = MLP xx. 9x.y)
(11)
We then augment the latent code [z, yx,y and pass it to the decoder. During testing, the can specify their criteria in gx,y to control the outcome (e.g.. Y should be drug-like and bioactive).
4 EXPERIMENTS
We follow the experimental design by Jin et al. (2019) and evaluate our translation model on their single-property optimization tasks. As molecular optimization in the real-world often involves different property criteria, we further construct a novel conditional optimization task where the desired criteria is fed as input to the translation process. To prevent the model from ignoring input X and translating it into arbitrary compound, we require the molecular similarity between X and output Y to be above certain threshold sim(X, Y) ö at test time. The molecular similarity is defined as the Tanimoto similarity over Morgan fingerprints (Rogers & Hahn 2010) of two molecules.
Single-property Optimization This dataset consists of four different tasks. For each task, train and evaluate our model on their provided training and test sets. For these tasks, our model trained under an unconditional setting (without gx,y as input).
The penalized logP score (Kusner et al. 2017) measures the solubility and synthetic accessibility of compound. In this task, the model needs translate input into output Y such that lYgP(Y'= > IxgP(X). We experiment with two similarity thresholds 8 = {0.4, 0.6). QED Optimization: The QED score (Bickerton al., 2012) quantifies compound's 's drug- likeness. In this task, the model required to translate molecules with QED scores from the lower range [0.7, 0.8) into the higher range [0.9, 1.0). The similarity constraint is sim (X, Y) > 0.4.
LogP Optimization:

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Table 1: Results on single-property translation tasks. "Div." stands for diversity. "Suce." stands for success rate. "Improve." stands for average property improvement.
logP (sim 2 0.6)
logP (sim 2 0.4)
QED
DRD2
Method
Improve.
Div.
Improve.
Div.
Succ.
Div.
Suce.
Div.
JT-VAE
0.28 + 0.79
1.03 + 1.39
8.8%
3.4%
CG-VAE
0.25 = 0.74
0.61 + 1.09
4.8%
2.3%
GCPN
0.79 0.63
2.49 + 1.30
9.4%
0.216
4.4%
0.152
MMPA
1.65 1.44
0.329
3.29 + 1.12
0.496
32.9%
0.236
46.4%
0.275
Seq2Seq
2.33 + 1.17
0.331
3.37 + 1.75
0.471
58.5%
0.331
75.9%
0.176
JTNN
2.33 1.24
0.333
3.55 + 1.67
0,480
59.9%
0.373
77.8%
0.156
AtomG2G
2.41 + 1.19
0.379
3.98 + 1.54
0.563
73.6%
0.421
75.8%
0.128
HierG2G
2.49 + 1.09
0.381
3.98 + 1.46
0.564
76.9%
0.477
85.9
0.192
This task involves the optimization of a compound's biological activity against dopamine type receptor (DRD2). The model needs translate inactive compounds (p < 0.05) into active compounds (p 2 0.5), where the bioactivity is assessed by a property prediction model from Olivecrona al. 2017). The similarity constraint is sim sim(X, Y) 0.4.
DRD2 Optimization:
Conditional Optimization This new task requires the model translate input X into output Y to satisfy different combination of constraints over its QED and DRD2 scores. We define a molecule Y as drug-like if QED 0.9 and DRD2-active if its predicted bioactivity DRD2(Y) 2 0.5. At test time, our model needs to handle the following two criteria over output molecule Y:
1. Y is both drug-like and DRD2-active. Here both properties need to be improved after translation. Y is drug-like but DRD2-inactive. this case, DRD2 an off-target that may cause side effects. Therefore only the drug-likeness should be improved after translation.
As different users may be interested in different settings, we encode the desired criteria as vector g and train our model under the conditional translation setup in [3.3] Like single-propen tasks, we impose a similarity constraint sim (X, Y) 2 0.4 for both settings.
Our training set contains 120K molecular pairs and the test set has 780 compounds. For each pair (X, Y), we set 9x.y (T drug-like), [[Y is DRD2-active)). During testing, we translate each compound with g 1]. [1, for each setting. We note that the first criteria (g [1, 1)) is the most challenging because there are only 1.6% of the training pairs with target Y being both drug-like and DRD2-active. To achieve good performance, the model must learn to transfer the knowledge from other pairs with gx.y = [1, o], (o, 1) that partially satisfy the criteria.
Evaluation Metries Our evaluation metries include translation accuracy and diversity. Each test molecule X, is translated K = 20 times with different latent codes sampled from the prior distribution. On the logP optimization, we select compound Y, as the final translation of X; that gives the highest property improvement and satisfies sim [X,, Yi) > 8. We then report the average property improvement $ Σ, (Y,) lxgP(XX) over test set D. For other tasks, we report the translation success rate. A compound is successfully translated if one of its K translation candidates satisfies all the similarity and property constraints of the task. To measure the diversity, for each molecule we compute the average pairwise Tanimoto distance between all its successfully translated compounds. Here the Tanimoto distance is defined as dist(X, Y) = simm( X, Y).
Baselines We compare our method (HierG2G) against the baselines including GCPN (You et al. 2018a), MMPA (Dalke et al., 2018) and translation based methods Seq2Seq and JTNN (Jin et al. 2019). Seq2Seq is sequence-tor peuueecc-to-sqquene model that generates molecules by their SMILES strings. JTNN is graph-to-graph architecture that generates molecules structure by structure, but its decoder not fully autoregressive. We also compare with CG- CG-VAE (Liu al. 2018), generative model that decodes molecules atom by atom and optimizes properties in the latent space using gradient ascent.
To make direct comparison possible between method and atom-based generation, further developed an atom-based translation model (AtomG2G) as baseline. It makes three predictions in each generation step. First, it predicts whether the decoding process has completed (no more new
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Table 2: Results on conditional optimization tasks and ablation studies over architecture choices.
(a) Conditional optimization results: g [1, means the
(b) Ablation study: the importance of hierarchi- output Y needs to drug-like and = [. means it cal graph encoding. LSTM MPN architecture and needs to be DRD2-active.
structure-based decoding.
Method
g
[1, 1]
g [1.0]
Method
QED
DRD2
Succ.
Div.
Suce.
Div.
HierG2G
76.9% %
85.9 %
Seq2Seq
5.0%
0.078
67.8%
0.380
atom- decoder
76.1%
75.0%
JTNN
11.1%
0.064
71.4%
0.405
two-layer encoder
75.8%
83.5%
AtomG2G
12.5%
0.031
74.5%
0.443
one-layer encoder
67.8%
74.1%
HierG2G 13.0%
0.094
78.5%
0.480
GRU MPN
72.6%
83.7%
atoms). If not, it creates new atom a, and predicts its atom type. Lastly, it predicts the bond type between a and other atoms autoregressively to fully capture edge dependencies (You et al. (018b).
The encoder of AtomG2G encodes only the atom-layer graph and the decoder attention only sees the atom vectors ex All translation models are trained under the same variational objective (3.3)
Single-property Optimization Results As shown in Table T our model achieves the new state-of- the-art on the four translation tasks. In particular, our model significantly outperforms JTNN in both translation accuracy (e.g.. 76.9% versus 59.9% on the QED task) and output diversity (e.g.. 0.564 versus 0.480 on the logP task). While both methods generate molecules by structures, autoregressive which can learn more expressive mappings. More importantly. our model runs 6.3 times faster than JTNN during decoding. Our model also outperforms AtomG2G on three datasets, with over 10% improvement on the DRD2 task. This shows the advantage of our hierarchical model.
decoder is
Conditional Optimization Results For this task, we compare our method with other translation methods: Seq2Seq. JTNN and AtomG2G. All these models are trained under the conditional trans- lation setup where we feed the desired criteria gx.y as input. As shown in Table 2a our model outperforms other models in both translation accuracy and output diversity. Notably, all models achieved very low success rate on c = [1, 1] because it has the strongest constraints and only 1.6K of the training pairs satisfy this criteria. In fact, training
model on the 1.6K examples only gives 4.2% success rate as compared to 13.0% when trained with other pairs. This shows our conditional translation setup transfer the knowledge from other pairs with gx,y = [1, Oj. [0, 1).
Ablation Study To understand the importance different architecture choices, we report ablation studies over the QED and DRD2 tasks in Table 2b We first replace our hierarchical decoder with atom-based decoder of AtomGGG to see how much the structure-based decoding benefits us. We keep the same hierarchical encoder but modified the input of the decoder attention to include both atom and substructure vectors. Using this setup, the model performance decreases by 0.8% and 10.9% on the two tasks. We suspect the DRD2 task benefits more from structure-basee based decoding because biological target binding often depends on the presence of specific functional groups.
Our second experiment reduces the number of hierarchies our encoder and decoder MPN, while keeping the same hierarchical decoding process. When the top substructure layer is removed, the translation aceuracy drops slightly by 0.8% and 2.4%. When we further remove the attachment layer, the performance degrades significantly on both datasets. This is because all the substructure information is lost and the model needs to infer what substructures are and how substructure layers are constructed for each molecule. Implementation details of those ablations Lastly, we replaced our LSTM MPN with the original GRU MPN used in JTNN. While the translation performance decreased by 4% and 2.2%, method still outperforms JTNN by wide margin. Therefore we use the LSTM MPN architecture for both HierG2G and AtomG2G baseline.
shown in the appendix.
5 CONCLUSION
In this paper, we developed a hierarchical taahh-to-grapl translation model that generates molecular graphs using chemical substructures building blocks. In contrast to previous work, our model is fully autoregressive and learns coherent multi- resluiiiosoltiinn representations. The experimental results show that our method outperforms previous models under various settings.
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Under review as a conference paper at ICLR 2020
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Under review as a conference paper at ICLR 2020
Zhitao Ying, Jiaxuan You, Christopher Morris, Xiang Ren, Will Hamilton, and Jure Leskovec. Hierarchical graph representation learning with differentiable pooling. In Advances in Neural Information Processing Systems, pp. 4800-4810, 2018.
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Zhenpeng Zhou, Steven Kearnes, Li Li, Richard Zare, and Patrick Riley. Optimization of molecules via deep reinforcement learning. arXiv preprint arXiv: arXiv: 1810.88000 2018.

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Under review as a conference paper at ICLR 2020
A
ADDITIONAL FIGURES
CI
C
C
g [1,1]
[1,0]
(0E1=0.841, DRD2=2e-4)
(QED=0.911, DRD2=0.964)
(QED=0.914, DRD2=6e-4)
Figure 6: Illustration of conditional translation. Our model generates different molecules when the translation criteria changes. When ! [1, 1]. the model indeed generates compound with high
QED and DRD2 scores. When g = [1, 0). the model predicts another compound inactive DRD2.
B NETWORK ARCHITECTURE
LSTM MPN Architecture
The LSTM MPN a slight modification from the MPN architecture used in Jin et al. 2019). Let N (v) be the neighbors of node 2. the node feature of and Tu be the feature of edge (u, v). During encoding, each edge (u, v) is associated with two messages May and Pou. representing the message from to and vice versa. The messages updated by an LSTM cell with parameters v = ( W W w defined as follows:
Algorithm 2 LSTM Message Passing
function LSTMs
Lu Duvs (vras Cwr (EEN(())
W
Fuy Buns Σ,
(t)
b²
Ouv
W
Tu: Burr
Σ
(1)
wi
bo
fan
W
Fuy Buns
(1)
+ b"
Cyo inv + tanh Ww
Dus Tues Σ un
(t) wr
+b) + Σ
fun O Cur
v (t+1) 00
One tanh c(++1))
(++1) (++1)
Return
end function
The message passing network MPN,, (H, (x.): {w...) over graph H is defined as:
Algorithm 3 LSTM MPN with 7' message passing iterations
function MPN,, (H. {ær}, ) (avv)) Initialize messages: 2 O, c for t = 0 to T do
Compute messages (++1) (t+1)
LSTM, (Zus Buvs {v (6) FweN(w)r)) for all edges
Cuv
(u, v) E H simultaneously.
end for
Return node representations h. MLP Tv EvEN(O) (TT end function
Attention Layer Our attention layer is a bilinear attention function with parameter {Ag):
exp(o" Aghh))
attentiong (v, (h:1) Σ Bih
B, = exp(( Agh,)
(12)
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Under review as a conference paper at ICLR 2020
C
Current
Prediction
Prediction
Next
Figure 7: Illustration of AtomG2G decoding process. Atoms marked with red circles are frontier nodes in the queue Q. In each step, the model picks the first node 0; from Q and predict whether there will be new atoms attached to 14 If so, it predicts the atom type of new node de (atom prediction). Then the model predicts the bond type between and other nodes in Q sequentially for [ steps (bond prediction,
Ω = 2). Finally, it adds the new atom to the queue Q.
AtomG2G Architecture AtomG2G is an atom-based translation method that is directly comparable HierG2G. Here molecules are represented solely as molecular graphs rather than hierarchical graph with substructures. The encoder of AtomG2G is the same LSTM MPN over molecular graph. This gives us a set of atom vectors ex representing molecule X only at the atom level.
The decoder of AtomG2G is illustrated in Figure 7 Following You et al.
201 Liu al. (2018), the model generates molecule G atom by atom following their breath-first order. During generation, maintains a FIFO queue that contains the frontier nodes in the graph (i.e., nodes who still have neighbors to be generated). Let U2 be the first node in Q and Ge be the current graph at step t. In each step, the model makes three predictions expand the graph Gr:
1. It predicts whether there will be new atoms attached to et. If not, the model discards v and move on to the next node in Q. The generation stops if empty.
2. Otherwise, it creates a new atom de and predicts its atom type.
3. Lastly, it predicts the bond type between My and other frontier nodes in Q autoregressively fully capture edge dependencies (You et al., 2018b). Since nodes are generated in breath-first order, there will be no edges between u, and nodes outside of Q.
To make those predictions, we use the same LSTM MPN to encode the current graph G.- Let h be the atom representation of Vt We represent Gt as the sum of all its atom vectors hgg Eveg, hy. In the first step, we model the probability of expanding a new node from Ut as:
Pt (M.P heg a())
attentions (lhv, hgg xxx
(13)
In the second step, the atom type of the new node is predicted using another MLP:
q = softmax MaatinaxxMMP(..... hG. of))
of = allention, ((here ha.), ex
(14)
In the last step, we predict the bonds between u, and nodes in Q = 01, .-. an sequentially starting with ai v.. Specifically, for each atom pair (ue, ag), we predict their bond type (single, double, triple none) as the following:
Dagas softmax (MLP t hog a.))
(15)
at = attention, (lhg, h har, og
(16)
where ha, is the atom representation of node as and h is the representation of node ue at the E.th bond prediction. Let N&(u)) be node u, 's current neighbor predicted in the first k steps. h is computed as follows to reflect its local graph structure after 1-th bond prediction:
MLP
Bus E Par,e
Vioaa MLP (h Bowy F..
(17)
where Fu, is the atom feature of u, (i.c., predicted atom type) and Tw,,, is the bond feature between and We (i.c., predicted bond type). Intuitively, this can be viewed as running one-step message passing at each bond prediction step (i.e., passing the message Vw,u, from w to 4z).
AtomG2G trained under the same variational objective as HierG2G, with the latent code z sampled from the posterior Q(21X, Y) A(xx,, xxx,) and [ux,Y, x MLP of Σ Eg
13

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Under review as a conference paper at ICLR 2020
logP 0.6)
logP (ò 0.4)
QED
DRD2
Training set size
75K
99K
88K
34K
Test set size
800
800
800
1000
Substructure vocabulary |S|
478
462
307
307
Average attachment vocabulary IA(S))
3.68
3.50
3.62
3.30
Table 3: Training set size and substructure vocabulary size for each dataset.
C EXPERIMENTAL DETAILS
Data The perppeeyropetty optimization datasets are directly downloaded from the link provided in Jin et al. (211)) The training set and substructure vocabulary size for each dataset is listed in Table 3 We constructed the multi-property optimization by combining the training set QED and DRD2 optimization task. The test set contains 780 compounds that are not ftrug-like and DRD2-inactivn The training and test set is attached as part of the supplementary material.
Hyperparameters For HierG2G, set the hidden layer dimension to be 270 and the embedding layer dimension 200. We set the latent code dimension | = 8 and KI. regularization weight ÅKL. 0.3. We T = 20 iterations of message passing in each layer of the encoder. For AtomG2G, we set the hidden layer and embedding layer dimension to be 400 so that both models have roughly the same number of parameters. We also set ÅKL 0.3 and number of message passing iterations to be T = 20. We train both models with Adam optimizer with default parameters.
For CG-VAE (Liu al. 2018), we used their official implementation for experiments. Specifically, for each dataset, we trained a CG-VAL to generate molecules and predict property from the latent space. This gives us three CG- VAE models for logP. QED and DRD2 optimization tasks, respectively, At test time, each compound X is translated following the same procedure in Jin et al. (20 8). First, we embed X into its latent representation and perform gradient ascent over to maximize the predicted property score. This gives us ... =K Vectors for K gradient steps. Then we decode K molecules from , ... zK and select the one with the best property improvement within similarity constraint. We found that it is necessary to keep the KL regularization weight low (ΔKL 0.005) to achieve meaningful results. When ÀKL = 1.0, the above gradient ascent procedure always generate molecules very dissimilar the input X.
Ablation Study Our ablation studies are illustrated in Figure our first experiment, we changed decoder the atom dase- decoder of AtomG2G. As the encoder is still hierarchical, modified the input of the decoder attention to include both atom and substructure vectors. We set the hidden layer and embedding layer dimension to be 300 match the original model size.
Our next two experiments reduces the number of hierarchies in both our encoder and decoder MPN. In the two-layer model, molecules are represented by cx = cg U cτ. We make topological and substructure predictions based on hidden vector h., instead of hs, because the substructure layer is removed. In the one-layer model, molecules and substructure predictions based on atom vectors Eves, hp. The hidden layer dimension is adjusted accordingly match the original model size.
represented by cx = cg and make topological
ALDIT- Decader
DOO
One-iayer Encoder
Atacciman
Figure 8: Model Ablations: 1) Atom-based decoder; 2) Two-layer encoder; 3) One-layer encoder.
14


Reviews:
[{"review_id": "r1l4ndZq5r", "reviewer": "AnonReviewer4", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "This paper proposed a hierarchical graph-to-graph translation method to modify compounds to improve the biochemical properties. The authors proposed to generate the new molecular in a autoregressive manner. To improve the performance of the model, the input molecular is encoded into different resolutions including atom, attachment, and substructure layer. The paper is well written and the figures in the paper also enable the paper easy to read. In the experiments, the authors compare the proposed method with serval state-of-the-art methods. The results well analyzed and the ablation study is provided. Overall, this is a good paper considering its technical contribution and writing.\n\nHowever, there are some small issues should be addressed:\n\n1. There are some typos in the paper. For example, in the topological prediction section in page 3,  \"the hidden representation of $S_k$ learned be the decoder \" -> learned be encoder.\n\n2. In the training, the authors apply teacher forcing to the generation process with depth-first order. Why do you use depth-first order not any other orders?  \n", "extra_scores": {"experience_assessment": "I do not know much about this area.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I assessed the sensibility of the derivations and theory.", "review_assessment:_checking_correctness_of_experiments": "I carefully checked the experiments.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper thoroughly."}, "extra_text": {}}, {"review_id": "Bkep99YXqr", "reviewer": "AnonReviewer1", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "This paper developed a hierarchical graph-to-graph translation model to generate molecular graphs using chemical substructures as building blocks. In contrast to previous work, the proposed model is fully autoregressive and learns coherent multi-resolution representations. The experimental results show that the proposed method outperforms previous models.\n\nA few comments: \n\n1.The novelty\n- The method seems to be almost the same as the previous junction tree based formulation.  The paper includes a straightforward hierarchical extension and provides limited novelty with respect to deep learning.  \n- Can the method be used for other types of graph generation? \n\n2. Some minor wording issues\n- For instance, in the abstract, \" In particular, we realize coherent multi-resolution representations ..\" What does this mean? \n\n3. The main claim : \" ... our graph decoder is fully autoregressive..\"  why is this a merit? \n\n4.  The paper provided results from multiple molecular optimization tasks. The results and analysis seem comprehensive. The model was shown to significantly outperform baseline methods in discovering molecules with desired properties. The model runs faster during decoding and can perform conditional translation. \n ", "extra_scores": {"experience_assessment": "I have read many papers in this area.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper at least twice and used my best judgement in assessing the paper.", "review_assessment:_checking_correctness_of_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I assessed the sensibility of the derivations and theory."}, "extra_text": {}}, {"review_id": "B1lPC22v5H", "reviewer": "AnonReviewer3", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "The authors present a heirarchical graph-to-graph translation method for generating novel organic molecules.\nWorking from the model of Jin et al. (2019), the authors introduce a three step heirarchy - the model first determines where a substructure should be generated, what is the substructure, then the attachments to the existing molecule.\nAll steps of this uses embeddings generated from a message passing network - these embeddings are input into a few bilinear attention layers to obtain the heirarchical generation scheme.\nThe model is trained with molecular pairs (X, Y), and a VAE loss - a hidden z vector controls the way to modify X to improve its properties.\nThe encoder is just a MLP over the difference between sum of embeddings at a atom level and at the substructure level.\nThe model is evaluated on accuracy and diversity, in both conditional and unconditional settings.\nThe experiments show a small improvement over previous SOTA algorithms.\n\nThis is a borderline paper, and I'm leaning towards a weak reject, because I don't believe the model is well motivated enough:\n- Sec 3.1 it's unclear how the substructures are generated - they provide a lot of inductive bias for the algorithm. \n  Are they automatically generated or built from a database of substructures?\n- Variational decoding does not seem well motivated enough - would a stochastic decoding procedure not work as well as having a latent vector that essentially adds noise to the training?\n- The experiments seem interesting and comprehensive - it seems that the model learns to exploit the biases and increase logP, as well as showing the ability to conditionally turn off DRD2-active properties of the molecules.\n\nSome questions:\n- Why not use a Transformer instead of an LSTM or GRU? The cell naturally acts over sets of neighbors and transformers are a natural model to tackle this problem.\n- Sec 3.1 Topological Prediction, the attention is over c_{X}^{S} but the text claims it should be over c_{X}^{G}? Is ^G the attention substructure?\n- Sec 3.1 Attachment Layer MPN: the A_i seem to be a tuple (S_i, {v_j}). The set of attaching atoms is limited to 2 right? It might be more clear to simply enumerate them here if so.\n- Sec 3.1 Substructure Tree: Since tree decompositions are not unique, does this work use the different tree decompositions and DFS traversals as data augmentations?\n- Table 2b: What is a \"two-layer\" and \"one layer\" encoder? Is it the size of the MLP or the removal of the attachment MPNs?\n- Ablation study: Since the Attachment Layer has all the substructure information, this ablation should ideally make sure the models all have a similar number of parameters, and the decrease in performance isn't due to the decrease in parameters.\n\nNits:\n- Sec 3.1 \"bi-linear\" should not have a dash, bilinear is one word.\n", "extra_scores": {"experience_assessment": "I have read many papers in this area.", "review_assessment:_checking_correctness_of_derivations_and_theory": "N/A", "review_assessment:_checking_correctness_of_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_thoroughness_in_paper_reading": "I made a quick assessment of this paper."}, "extra_text": {}}]

Author rebuttal:

Meta-review: Two reviewers are negative on this paper while the other reviewer is slightly positive. Overall, the paper does not make the bar of ICLR. A reject is recommended.
Decision: Reject