ChemSpacE: Interpretable and Interactive Chemical Space Exploration
Authors: Yuanqi Du
Xian Liu
Nilay Mahesh Shah
Shengchao Liu
Jieyu Zhang
Bolei Zhou
Venue: Accepted by TMLR ()

Abstract: Discovering meaningful molecules in the vast combinatorial chemical space has been a long-standing challenge in many fields, from materials science to drug design. Recent progress in machine learning, especially with generative models, shows great promise for automated molecule synthesis. Nevertheless, most molecule generative models remain black-boxes, whose utilities are limited by a lack of interpretability and human participation in the generation process. In this work, we propose \textbf{Chem}ical \textbf{Spac}e \textbf{E}xplorer (ChemSpacE), a simple yet effective method for exploring the chemical space with pre-trained deep generative models. Our method enables users to interact with existing generative models and steer the molecule generation process. We demonstrate the efficacy of ChemSpacE on the molecule optimization task and the latent molecule manipulation task in single-property and multi-property settings. On the molecule optimization task, the performance of ChemSpacE is on par with previous black-box optimization methods yet is considerably faster and more sample efficient. Furthermore, the interface from ChemSpacE facilitates human-in-the-loop chemical space exploration and interactive molecule design. Code and demo are available at \url{https://github.com/yuanqidu/ChemSpacE}.

Published in Transactions on Machine Learning Research (03/2023)
ChemSpacE: Interpretable and Interactive Chemical Space Exploration
Yuanqi Du Cornell University
yd392@cornell.edu
Xian Liu The Chinese University of Hong Kong
abrinliu@@ie.cuhhk.ce edw.kk
Nilay Shah
nshah7660..clee edu
University of California Los Angeles
Shengchao Liu
liusheng@mäll. quebec
Mila, Université Montréal
Jieyu Zhang University of Washington
Bolei Zhou
boleißes. ucla edu
University of California Los Angeles
Reviewed on OpenReview: https: //
// wpw.:/vee...e.eee.ommee net/ forum? C1X18dCCc
Abstract
Discovering meaningful molecules in the vast combinatorial chemical space has been long- standing challenge in many fields, from materials science to drug design. Recent progress in machine learning, especially with generative models, shows great promise for automated molecule synthesis. Nevertheless, most molecule generative models remain black-boxes, whose utilitics are limited by a lack interpretability and human participation in the generation process. In this work, we propose Chemical Space Explorer (ChemSpacE)), simple yet effective method for exploring the chemical space with pre-trained deep generative models. Our method enables users to interact with existing generative models and steer the molecule generation process. We demonstrate the efficacy of ChemSpacE optimization task and the latent molecule manipulation task in single-property and multi- property settings. On the molecule optimization task, the performance of ChemSpacE is on par with previous black-box optimization methods yet is considerably faster and more sample efficient. Furthermore, the interface from ChemSpacE facilitates human- in- to-thh-loop chemical space exploration and intoractive molecule design. Code and demo are available hhtta://giithbl wttp:/hhwb..cmmuuuniii.uuuuu Chapsspaeeeeemee
the molecule
1 Introduction
Designing molecules with desired properties is crucial for wide range of tasks in drug discovery and materials science (Chen et al. 2018). Traditional pipelines for molecule design require exhaustive human effort and domain knowledge to explore the vast combinatorial chemical space, making them exceedingly difficult to scale. Recent studies exploit deep generative models to tackle this problem by encoding molecules into a meaningful latent space, from which random samples can be drawn and then decoded into new molecules. Such deep molecule generative models can facilitate the design and development of new drugs and materials (Lopez et al. 2020 (Sanchez-Lnggeing & Aspuru-Guzik 2018).

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Despite the promising results of deep generative models for molecule generation, much less effort has been made in understanding the internal representation of molecules and the underlying working mechanisms of these models, which are key to interpretable and interactive Al-empowered molecule design. Most existing models are based on deep noural networks or black-box optimization methods, which lack transparency and interpretability (Samek et al. 2019). Outside of the molecule generation domain; many allempts have been made to improve the interpretability of deep learning models from various aspects, e.g., representation space (Zhou al.) 2016), model space (Guo et al., 2021), and latent space (Shen et al. 2020: Shen & Zhou, 2021). In molecule generation, interpretability can be studied from two perspectives: (1) the interpretation of the learned latent. space where traversing the value of latent vectors could lead to smooth molecular property change, and (2) the interpretation of the chemical space where adjusting molecular properties could further provide insight to smooth and consistent struclure change of molecules (i.e. structure-activity relationships).
Furthermore, it remains difficult to generate molecules with desired properties. Previous works tackle the problem with reinforcement barning-basod. latent space optimization-based and searching-based methods to achieve property control of the generated molecules (Shi et al., 2020 Jin el al. 2018a). Specifically, rein- forcement learning-bast based algorithms (You et al., 2018a) equip the model with rewards designed to encourage the models to generate molecules with specific molccular properties. Latent space optimization-based algo- rithms take advantage of the learned latent space of molecule generative models and optimize the molecular properties via Bayesian Optimization (Liu et al. 2018). Searching-based algorithms, on the other hand. directly search the discrete, high-dimensional chemical space for molecules with optimal properties (Kwon et al. 2021). However, these works often have three major issues. (1) They require many expensive oracle calls to provide feedback (f.e., property scores) on the intermediate molecules generated during the searching optimization process (Huang al. 2021 (2) They often only focus on the outcome of the process while ignoring its intermediate steps which can provide crucial insights into the rules that govern the process to chemists and pharmacologists.
(3) They focus on local gradients and put less emphasis on exploring global directions in the Ahemical/latenn space.
To lackle the above challenges, we propose a simple yet effective method to explore the chemical space for molecule generation by interpreting the latent space of pre-trained deep generative models. The motivation for our approach is based on the emergent properties of the latent space learned by molecule generative mod- els (Gómez-Bombaree
et al. 2018 Zang & Wang 2020): (1) molecules sharing similar structures pproperresp tend to cluster in the latent space, (2) interpolating two molecules in the latent space leads to smooth changes in molecular structures/ structures/properties propertiis. Thus, we develop ChemSpace Explorer, a aonnss-agoottcc method to ma- nipulate molccules in the latent space of molecule generative models. It has broad applications ranging from molecule optimization to chemical space interpretation. Specifically, ChemSpuce Explorer first identifies the property separation hyperplane which defines the binary boundary for some molecular property (e.g., drug-like or drug-unlike) in the learned latent space of a generative model. Based on the identified property separation hyperplane, it then estimates the latent directions that govern molecular properties, navigating which can enable smooth change of molecular structures and properties without model re-training. This manipulation process improves the interpretability of deep generative models by navigating their latent spaces and enables human-in-the-loop exploration of the chemical space and molecule design. It allows users to manipulate the properties of generated molecules by leveraging the steerability and interpretability of molecule generative models. To the best of our knowledge, this work is the first attempt to achieve interactive molecule discovery by steering pre-trained molecule generative models.
Our experiments demonstrate that our method can effectively steer state-of-the-art molecule generative models for latent molecule manipulation with a small amount of siniinngiiffeencee time, data, and oracle calls. To quantitatively measure the performance of latent molecule manipulation, we design two new evaluation metries, strict success rate and relor success rate, which explain the percentage of successful manipulation paths with smooth property-changing molecules. In addition, we compare ChemSpacE with a gradient- based optimization method that traverses the latent space of molecule generative models on the molecule optimization task. To facilitate interactive molecule design and discovery for practitioners, we further develop interface for real-time interactive latent molccule manipulation and smooth molccular structure/ property change. We sunmarize the main contributions as follows:
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Identify Scparation Boundary
drug-unlike mols
Brkg-like mols
drug-unlike mols
n
Generate
Predict
drug-like mols
separationtboundary
MOO, !) Latent Space
x= Structure/Molecularr Space
f-
Property Space
Figure 1: ChemSpacE framework: (1) pre-trained molecule generative model generates many molecules from random vectors sampled from the latent space, (2) an off-the-shelf oracle function is used to predict molecular propertics of the generated samples in the chemical space, (3) ChemSpacE identifies directions in the latent space which govern molecular properties via the property separation hyperplane.
We explore task called latent molecule manipulation, which aims to steer the latent space of molecule generative models to manipulate the chemical propertics of the output molecule and facilitate lummn-in--he--lopp molecule design.
We develop efficient model-agnostic method named ChemSpacE for latent molecule manipulation, which can be incorporated in various pre-trained hate-of-theeart molecule generative models without needing to re-train modify them.
We demonstrate the effectiveness and efficiency our method in molecule optimization and achieving ceetann-i-tth-loe molecule design through comprehensive experiments. We further develop an interface to exhibit interactive molecule discovery and design.
2 Problem Formulation of Latent Molecule Manipulation
Molecule Generative Models. In molecule generation, a generative model M encodes the molecular graph X as latent vector Z R' where is the latent space dimension, and then decodes the latent vector back to the molecular graph. Variational auto-encoders (VAE) (Kingma & Welling) 2013) and flow-based models (Flow) (Rezende & Mohamed 2015 are the two most commonly used models for molecule generation, which typically encode the data from the molecular space to latent space of Gaussian distribution. The encoding and decoding process can be formulated as:
2 = f(),
x' g'=)
(1)
where x and s' the ground-truth and reconstructeel/samplee data respectively, and Z represents latent vector in the latent space, f()) and g(-) are the encoder and generator gencrator/decooee /ccoderr of the generative model. Note that simplify the expression here to represent the general latent space that seek to navigate in both VAEs and Flows. In practice, VAEs resort to reparametrization trick such that 2 = a where C c~~(0, T).
Latent Molecule Manipulation Formulation. To leverage the steerability and interpretability of molecule generative models, we explore new task, latent molecule manipulation, which interprets and steers the latent space of generative models in order manipulate the properties of the output molecules. To be specific, deep generative model contains generator g: Z X, where Z E RR stands for the
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I-dimensional latent space, which is commonly assumed to be a Gaussian distribution (Kingma & Welling 2013 Rezende & Mohamed, 2015). There exist property functions fr which define the property space P via P- = fp(X). The input to latent molecule manipulation is a list of n molecules X = {=1, 22, Ind and a list of m molecular properties P = {PI.P2. Pmm)- We aim to manipulate one or more molce- ular properties p of a given molecule in consecutive steps and output the manipulated molecules with properties p' = (p(4),)) p()),.... ,... ..(k)))))))))) By manipulating the given molecule, we can observe the alignment of - X + P, where the relationship between 2 and X explains the latent space of molecule generative models and the relationship between X' and P reveals the correlations between molecular structures and changes.
properties. By traversing the latent space, we can generate molecules with continuous structure/ property
Evaluation Criteria. We need to evaluate the latent molecule manipulation task with respect to both smooth structure change and the smooth property change. Thus, we design two now evaluation metrics, strict success rule (SSR) and relazed success rale (RSR), that measure the quality of the identified latent direction in controlling the molecular property. For calculating the strict success rate, consider manipulation path to be successful only if we generate molecules with monotonically-changin properties and structures in consecutive & steps of manipulation. The constraints are formulated as follows:
Φspc(x,k,f) 1 [k],s.t., f(x(1) (000))f((((())))) f(x((-1)) =0,
(2)
@ssc(2,k, 1[ [k].s.t., (1+ ,0(1) - 6(x(") ())) S.),
(3)
ΦDIV (2, 1[3 i [k],s.t., x00 + x011
(4)
where is property function which calculates certain molecular property, 8 denotes structure similarity between molecules 20(), x(++1) generated two adjacent manipulation steps. ΦsPC defines the strict property constraint; Øssc defines the strict structure constraint; @DIV defines the diversity constraint. The strict
success rale is defined as:
SSR - X(P. = X Σ PEPEEX
[ k. ossc(ap, k) A ΦnIv (nIv(Ep.)))
(5)
As monotonicity is rather strict, we propose a more relaxed definition of success rate, namely relaxed success rate, constructed via. relaxed constraints, as follows:
(RPc(s,k, = 1[ i E s.t, (1x - ((a S c). @2sc(2,k, = 1 i [k), 6(x(11) 1)) - -0) (1) S 7/.
(6)
(7)
(2Iv(z,k) 1 E [k), s.t., s # 111),,
(8)
where e is a predefined tolerance threshold that weakens the monotonicity requirement. We also provide two implementations of relaxed success rate, which define different tolerance variables e, one with a local relaxed constraint (RSR-L) and the other with a global relaxed constraint (RSR--). For the global constraint, we obtain by caleulating the possible values (ranges) of the molecular properties in the training dataset, while for the local constraint, we obtain by calculating the possible values (ranges) of the molecular properties only in the specific manipulation paths. The formulation of RSR-L and RSR-G is as follows:
1 RSR - L(P,X, = x
Ep
[[ORPO(T,, k, fp, @Rsccap, A (DIv(Ep,
(9)
RSR G(P, P
1
Σ PEPAEX
[0RPo k, fps Eg) A @RSO k; ΦDIv (xp;
(10)
While is more challenging for the model to pass RSR-L with a local constraint (smaller range) when ovaluating a successful path, it has an added benefit in that takes into account the ability of the model manipulate one molecular property (i.e., the larger the range, the higher the tolerance score, thus the better chance to achieve successful manipulation).
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& y n do
n 60
on
1
10
20
80
10
8
00
en
100
641
60
A brat e
A
7 60
8 & & A
1
-00
52
-50
100
(c) Latent Molecule Cluster
(b) Interpolation
(c) Latent Property Boundary
Figure 2: (a) Molecule clusters in the latent space, where the number represents structure similarity (Bajusz et al. 2015). The red box denotes the base molecule and the and y axes represent two random orthogonal directions to manipulate.
(b) Linear interpolation of two (top and bottom) molecules. (c) The latent property boundary for QED is visualized for MoFlow trained on ZINC by reducing the dimension of the latent vectors by PCA.
3 ChemSpacE for Latent Molecule Manipulation
3.1 Latent Cluster Assumption
We examine the properties of the latent space learned by generative models and have the following obser- vations: (1) molecules with similar structures tend to cluster together in the latent space, (2) interpolating two molecules æ1 and 22, represented by latent vectors 21 and z2; can lead to list of intermediate molecules whose structures/prope prrpeertie gradually change from ø1 to Z2. As molecular structures determine molecular propertics (Seybold et al. 1987), the observations imply that molccules with similar values of a certain molecular property would cluster logether, and interpolating between two molecules with different values of the molecular property could lead to gradual changes in their molecular structure. As shown in Fig, []] there may exist two groups of molecules, drug-like and lincarly interpolating between two latent vectors with one molocule from each group could lead to a direction that crosses the property separation boundary. These observations also match the analysis from the prior work
where each group cluster together and
et al., 2018 Zang & Wang 2020). To verify our assumption, we visualize the latent space of the pre-trained MoFlow model in Fig. 2 The left figure shows that molecules close together in the latent space are similar in structure, the middle figure shows that interpolating between two molecules in the latent space could lead to smooth structure changes, and the right figure shows that a latent boundary is present for the QED property in the pre-trained MoFlow model.
3.2 Identifying Latent Directions
Latent Separation Boundary. With the verifications shown above and the previous work of analyzing the latent space of generative models (Shen al.] 2020 [au et al.) [2017 Jahanian et al., 2019 Plumerault et al. 2020), we assume that there exists separation boundary which separates groups of molecules for each molecular property (e.g., drug-like like and drug- and the normal vector of the separation boundary defines latent direction which controls the degree of the property value (Fig. [ When moves toward and crosses the boundary, the molecular properties change accordingly (e.g., from drug-unlike to brug-like). A perfect separation boundary would have molecules with different properties well separated on different sides. From that, we can find a scparation boundary for cach molccular property with a unit normal vector n R', such that the distance from any sample z the separation boundary as:
d(z, n) nf Tzz
(11)
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Latent Direction. In the latent space, the molecular structure and property change smoothly towards the new property class when moves towards the separation boundary and vice versa, where we assume linear dependency between and p: fr(g(z)) = a n(z,n).
(12)
where fr an oracle function and a is a degree scalar that scales the changes along that corresponding direction. Extending the method to multiple molecular property manipulation, we have:
[p(a(=)) AN
(13)
where A Diag(ai,... (mm) is the diagonal matrix with linear coelficients for each of the molecular properties and N [.1.-.. Am] represents normal vectors for the separation boundaries of m molecular propertios. We have the molccular properties P following multivariate normal distribution via:
μp E(AN" AN = O,
(14)
Σp E(ANT= 22 NAT) ANTE(Z=))NAL ANT
(15)
We have all disentangled molecular properties in P if and only if Ep diagonal matrix and all directions in N are orthogonal with each other. Nevertheless, not all molecular properties purely disentangled with each other. In that case, molecular properties correlate with each other and nł n2 is used to denote the entanglement between the i-th and j-th molecular properties in P.
3.3 Latent Molecule Manipulation
After we find the separation boundary and identify the latent direction, to manipulate the generated molecules towards desired properties, we first move from the latent vector z along the direction n with a degree scalar a, giving the new latent vector
===+om
(16)
The expected property value of the new manipulated molecule is (with i as a scale factor):
fr(g(z + am) = fr(g(=)) + ko.
(17)
For singlo-property manipulation, we can simply take the identified direction, but when multiple propertics correlate with each other, we need to determine whether the two directions are entangled or disentangled. We can then take the disentangled and positively correlated attributes of the directions the new direction:
n n4 + (1 [m 2n220)) n2.
(18)
4 Experiments
4.1 Setup
Datasets. We use three molecule datasets, QM9 Raaaakishhaa et al. 2014), ZINC250 (Irwin & Shoichet 2005), and ChEMBL. (Mendez al. 2019). QM9 contains 134k small organic molecules with up to 9 heavy atoms (C, O, N, F). ZINC250K (Gômez-Bombarell et al., 2018) ZINC, & free database of commerciilly--vvillbbe compounds for drug discovery with an average of ~23 heavy atoms. ChEMBL is manually curated database of bioactive molecules with drug-like properties and contains 1.8 million molecules.
sampled set of 250K molecules from
Baselines. We include two baseline methods of identifying the latent direction that governs the molecular property and one gradient-based method, which optimizes the molecular property of the generated molecules via gradient ascent/descue for comparison. Random manipulation randomly samples latent directions for molecular properties. Largest range manipulation draws latent vectors from the training set and defines the directions via calculating the direction between one molecule with the largest. property score

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Table 1: Quantitative Evaluation of latent molecule manipulation over a variety of molecular properties (numbers reported are strict success rate in %. The best performances bold.)
Dataset
Model
Avg.
QED
pLogP
SA
DRD2
JNK3
GSK3B
MolWt
Random
1.65
1.50
0.00
0.50
0.00
0.00
0.00
0.50
MoFlow
Largest
3.43
1.50
1.00
0.50
0.00
1.50
0.00
0.50
Gradient-based
N/A
3.50
6.00
6.50
2.00
8.00
8.50
7.50
QM9
ChemSpacB
37.52
12.50
9.00
10.00
11.00
45.50
16.50
10.50
Hie
Random
29.29
1.00
1.50
0.50
0.50
1.00
1.00
0.50
Largest
30.69
0.50
0.00
0.00
0.50
2.00
0.00
0.50
ChemSSacc
66.23
27.00
32.00
35.00
41.50
51.50
30.00
39.50
Random
4.25
1.50
1.50
2.50
3.00
3.50
1.50
2.00
MoFlow
Largest
5.61
1.50
6.50
2.00
6.00
2.50
4.00
1.50
ZINC
Gradient-based
N/A
1,50
9.50
0.50
2.00
15.50
23.00
0.00
ChenSpacE
58.08
52.00
53.50
51.50
55.00
56.50
55.50
53.50
HierVAE
Random
25.59
0.00
0.00
0.00
0.00
0.00
0.00
0.00
CHEMBL.
Largest
22.98
0.00
0.00
0.00
0.00
0.00
0.00
0.00
ChemSpacE 47.70
0.50
3.00
3.00
6.00
7.50
5.50
4.50
and another molecule with the smallest property score for each molecular property. The gradient-based method optimizes the molecular property of the generated molecules by searching for a latent vector with More specifically, it requires pre-training a
the optimized molecular property via gradient ascent/ property predictor on the latent space that first initializes a latent vector and then optimizes the latent minimize vector to maximize/ minimmiieemiiiiieeee the output of the predicted property value.
Molecular Properties. QED is quantitative estimate of drug-likeness. PLogP refers to the partition cocfficient logarithm of octanol-water which measures the lipophilicity and water solubility. SA denotes the synthesis accessibility score. MolWt denoles the molecular weight. DRD2, JNK3 and GSK3B are three binding affinity scores.
Implementation Details. We take publicly available pro-trained models from their respective GitHub repositories for HierVAE (Jin et al. 2020) and MoFlow (Zang & Wang 2020 All the molecular properties are calculated by RDKit (Landrum al. 2013)) and TDC (Huang al. (021).. We utilize the implementation
of linear models (linear SVM) from Scikit-learn (Pedregosa et al. 2011 More details are available in Appendix A
Intoractive Demo. An interactive demo for latent molccule manipulation is provided at https:// and one exam-
urive.google wwt.cooo//iv/eee ple is shown in Fig. (right).
4.2 Quantitative Evaluation of latent molecule manipulation
In Tables and 2 we report the quantitative evaluation results for both single property and multi-property latent molecule manipulation. Table shows the strict success rate and relaxed success rate-L/G while Table 2 reports the training and inference times, data requirements, and number of oracle calls from evaluations on 212 molecular properties over 200 randomly generated molecules. From the tables, we obtain the following insights:
(1) Our proposed method, ChemSpacE, as the first attempt for latent molecule manipulation, achieves excellent performance in both single and multi-property manipulation of molecules with two state-of-the taate-of-the-art molecule generative models (VAF-based and Flow-based). For some important molecular properties (e.g..

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Table 2: Efficiency in terms of training/inferent time, data, and number of oracle calls of ChemSpacE compared to the gradient-basee based method.
Model
Dataset Training(s)
Inference/Pathie
Data
# Oracle calls
QM9
137.03
0.02
120k
120k
Cradient-based
ZINC
1027.26
0.04
200k
200k
QM9
0.05
0
300
300
ChemSpacE
ZINC
0.95
0
400
400
QM9
2740x
0.02 t
400x
400x
Speedup
ZINC
1080
0.04 f
500x
500x
Table 3: Single property constrained molecule optimization for Penalized-logP the ZINC dataset with four comparison methods (ò is the threshold for similarity between the optimized and base molecules).
MoFlow
ChemSpacE
6
Improvement
Similarity
Success
Improvvment
Similarity
Success
0.0
8.61 :: 5.14
0.30 0.20
98.88%
9.91
(.18 = 0.14
100%
0.2
7.06 5.04
0.43
96.75%
7.17 6.50
0.42 0.21
96.00%
pLogl
0.4
4.71 1. 4.55
0.61 0.18
65.75%
4.16 1 4.43
0.65 1: 0.20
84.38%
0.6
2.10 2.86
0.79 0.14
58.25%
1.76 2.40
(181 + 0.15
39.63%
0.0
9.99
10 $ 2.282
10
0.29 0.17
100%
2.12
21188 x
0.05 1 0.06
107%
0.2
7.66
10 2.66
10
0.36 0.13
100%
5.49 x
10 1.46
10-2
0.31 0.14
99%1
DRD2
10-3 10-3
0.12
98.60%
1.04
10-3 1.83
0.57
95.75%
0.6
1.67 10 4.10
0.78
0.14
65.20%
1.79
4.14.15 x
0.80 1 0.15
83.00%
0.39
90.40%
1.79 10-"0""""20 =2.15
0.19 0.15
100%
0.2
10-4x10-222200 10-2
0.44 0.19
98.80%
3.24 x 10-2
10-2
0.39 + 0.17
90.38%
JNK3
0.4
1.33 x 2.54
0.16
95.60%
1.94 x 2.188888 x
0.58 0.15
97.13%
6,27x00"=1100x
0.19
77.80%
10 10
10
0.76
85.00%
0.0
x.09x1100 x
10
0.20
98.60%
1.21 10 1182
10-2
0.15
100%
GSK33
4.21 x - 10
0.17
97.40%
7.06 x 10 +5.01
10-2
0.35 0.15
99.50%
0.4
2.87 x 10 3.02
0,58
0.15
95.20%
3.87 x 10 136.4
10
0.57
1 0.16
97.63%
0.6
1.1
10
2
0.78
85.60%
1.54 x 2.28
10
0.78 1 0.15
86.633
QED), we (with MoFlow) achieve a 52% manipulation strict success rate on the ZINC dataset, outperforming the baseline methods 6x on average.
(2) The bascline (random manipulation) method sometimes "finds" directions that control molecular prop- erties. As shown in Fig. [ the molecules are well-clustered in the latent space with respect structures that determine molecular properties (Scybold et al. 1987). However, the largest range manipulation method performs worse possibly due to its strong assumption in determining the direction via the molecules with extreme property values (largest property and smallest property values) in the dataset.
(3) The ChemSpacE mothod outperforms the popular gradient-based method in generating smooth manip- ulation paths, time, and data efficiency. As shown in Table 2 ChemSpacE speeds up the training time by at least 1000x, and reduces data requirements and the number of oracle calls necessary by at least 400x.
More results can be found in Appendix Tables
5 and 6
4.3 Quantitative Evaluation of Molecule Optimization
We further compare our methods under the common molccule optimization sctting through two tasks: single properly constrained oplimization and malli--ropperly constrained oplimization. Beginning with a set of candidate molecules, we aim to optimize their molecular properties while maintaining the structural similarity of the optimized molecules to the base molccules. This sctting is relevant to many drug discovery tasks where one needs to optimize the properties of a given molecule while keeping the structure similar.
Single Property Constrained Optimization. We evaluate our method against four previous works (Jin ct
2018a You al. 2018a Zang & Waang 2020 Eckmann et al. 2022) with the exact same of molccules
In practice, we the Tanimoto similarity the Morgan fingerprint Rogers Hahn 2010
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the penalized logP property and test four different similarity constraint thresholds. We report the property improvement. and similarity compared to the base molecule as well as the percentage of successfully optimized molecules within the threshold in Table 3 In addition, we evaluate on three more real-world properties, activitics at the targets DRD2, JNK3, and GSK33, under the same constrained optimization setting. our reported results, ChemSpacE. manipulating over the latent space learned by MoFlow, as MoFlow leverages a gradient-based method that traces the local gradient leading to property improvements in every step while we take on more efficient way by learning the global improvement direction and following it for all steps. We perform surprisingly well and even better than the craeed method used in MoFlow, thus empirically supporting our assumption about latent space exploration.
plogp: -5 200 QED: 0.360
plogp: -1.671 QED: 0.645
plogp: -6.366
plogp: -2.726
QED: 0.449
QED: 0.809
Figure 3: Illustrations of multi-property constrained optimization. The Tanimoto similarity between base and optimized molccules is 0.709 (top row) and 0.647 (bottom row) respectivcly.
Multi-Property Constrained Optimization. As no previous work reports on multoi-property con- strained optimization, we propose to optimize QED and penalized logP as multi-property constrained optimization task. We also propose two simple baselines: (1) we add up the two properties (QED and penal- ized logP) be optimized as new objective and run single-property constrained optimization on it, (2) we take into account the two gradient directions of the propertics and in each step of gradient ascent, we move in both directions. As shown in Appendix (Table S) demonstrate the capability of ChemSpacE) for effi- cient multi-objectiven constrained optimization. Our method improves both QED and penalized logP more than the two gradient-based methods. We showcase two examples in Fig. 3 that demonstrate ChemSpacE's ability to optimize molecules and achieve desired property improvements while maintaining high structure perseverance.
Options
MolSpace Explorer
Sestes
0.447 -1293
QED LogP0.339 0.339
Log!
L.555
QED 0.484
L33
0.75 0.475
QED
TogP0.585
LogP
QED
Figure 4: Manipulating QED and LogP properties of sampled molecules simultaneously with the MoFlow model trained the QM9 dataset (the repeated molecules are removed for better visualization) (left). A Real-time Interactive System Interface. Please refer to the Appendix D video for a demo of interactive molecule discovery (right).

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Published in Transactions on Machine Learning Research (03/2023)
4.4 Qualitative Evaluation of Latent Molecule Manipulation and Interpretation
In Fig. we visualize the property distributions of QED, MolWt and LogP along a 7-step manipulation path. For each step, draw property distribution. The candidate molecules are place and we attempt to manipulate the molecular property to the left (lower) and the right (higher). From the figure, we clearly observe that the property distribution shifts to the left and right accordingly when we manipulate the molecule to the left and right. For example, when we manipulate the molecules three steps to the left, the range of QED shifts from [0, 0.7] to [0,0.5]; when the molecules are manipulated three steps to the right, there are far more molecules that have QED > 0.5 than the base distribution. Similar trends can also be seen for MolWt and LogP.
0.8
8
0.35
0.30
Demsity
6-
0.25
gemsity
0.5
0.20
4
0.3
2-
0.10
0
0.00
0.0
0.0
0.3
115
125
135
-3
-2
2
QED
MolWE
MollogP
Figure 5: Visualization of molecular properly distribution shifts while manipulating molecules with MoFlow on the QM9 dataset (0 denotes the randomly sampled base molecule and +r and -r denote manipulation directions and steps).
Single Property Manipulation. To qualitatively evaluate the performance our method for latent molecule manipulation, we randomly select the successful manipulation paths from three generative models Fig. 6 The figures show that our method successfully learns interpretable and stcerable directions. For example, for HierVAE in Fig. G we can find that gradually increasing LogP of a molecule may lead to the removal of the heavy atoms O and N from the structure. With respect to QED, the molecule drops double bonds, as well as heavy N and O atoms, when increasing QED for the HierVAE model. A similar trend can be observed in the MoFlow model that increasing QED drops double bonds and O atoms on the left of Fig.
Multi- Multi-Property Manipulation. When comes multi-property manipulation, the goal control multiple molccular propertics of a given molecule the same time. In Fig. (left), we show how our method manipulates multiple molecular properties. For simplicity, we remove the duplicate molecules and only leave the distinct molecules during the manipulation. From the figure, LogP and QED since when we increase QED, LogP also increases accordingly.
observe some correlations between
QED
0.39
0.41
0:45
0.88
0.48
0.50
0.50
0.41
0.46
0.48
0.50
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0.53
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D
MolWi
126.0
127.19
122.19
13012
13012
$7.06
9808
9K.05
107.07
11909
211:11
247.13
LogP
MoFlow
HierVAE
Figure 6: Manipulating QED, MolWt and LogP properties of sampled molecules. The backbone model is MoFlow and VAE trained on QM9 dataset.
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Published in Transactions on Machine Learning Research (03/2023)
5
Related Work
Molecule Generation. Recent studies have explored a variety of deep generative models for molecule
generation (Du et al. 2022), including variational autoencoders (VAEs) [Jin et al. 2018a), generative ad-
versarial networks
(GANs) (De Cao & Kipf 2018), reinforcement learning models Oliveeroona et al. 2017
Zhou et al.
2019
Yang et al., 2021), etc Yang et al.) 2020 Xie et al., 2021). normalizing flows
Mad-
hawa et al.;
2019
Shi et al. 2020; Luo et al. 2021), and energy-based models (EBMs) (Liu et al.,
2021
For instance, JT- VAE (Jin et al. 2018a) proposes a VAE-based architecture to encode both atomic graphs
and structural graphs for efficient molecule generation. MolGAN (De Cao & Kipl] 2018) exploits GANs
for molecule generation, where discriminators are used to encourage the model to generate realistic and
chemically-valid molccules. MRNN (Popova ct al. 2019 extends the idea of GraphRNN (You ct al. 2018b)
to formulate molecule generalion as an aulo-regressive process. GCPN (You et al. 2018a) formulates the molecule generation process as a reinforcement learning problem where it connects atoms in a step- by-peb fashion to obtain a molecule and uses reward for steerable generation. GraphNVP (Madhawa et al. 2019)
introduces normalizing flows for molecule generation, where the generation process is invertible. Later works improve nomralizing flow-based molecule generative models by introducing auto-regressive generation Shi
et al. 2020), valency correction (Zang & Wang) 2020), and discrete latent representation (Luo et al.) 2021]
GraphEBM (Liu et al.) 2021) introduces energy-based model for molecule generation. More recently,
diffusion models have been applied to molecule generation (Niu et al. 2020 Jo et al. 2022 Vignac et al. 2022).
Controllable Molecule Generation. One practical application of molecule generation is to generate new molecular samples with specific properties. Early work (Segler et al. 2018) involved biasing the distribution of the data and training generative models with known desired propertics to generate molecules with those properties. In contrast, recent works have focused on leveraging latent space gradient-bes baseentt-baedd (Jin et al. 2018a:
You et al. 2018a Hoffman al.] 2020 Winter et al. 2019), reinforcement learning- based (Shi et al.
2020
Zang & Wang 2020 Blaschke et al. 2020); and searching-baser (Brown et al. 2019 Yang et al.
2020
Kwon et al.) 2021] approaches to generate molecules with desired properties. Latent space gradient-
based methods are flexible and can work directly on both molecules (Fu et al. 2022) and the learned latent
vectors (GómezzBBobareel) et al. [2188] Jin et al.) 2018b Winter et al. 2019 Griffiths & Srrrnández-Lobatee
2020
Notin et al. 2021). Reinforcement lcarning- based methods usually formulate controllable generation
as a sequential decision-mmaking problem and require a score-function to reward the agent. Searching- based
approaches (Brown et al.] 2019: Vang et al., 2020 Kwon et al., 2021 Renz et al. 2019 Fu et al. 2020 Xie
let al.) 2021 Maziarz et al. (021)) can search over the chemical space for molecules with desired properties
by defining set of discrete actions. Additionally, some works (Chethhmmarakshan et al. 2020 Das et al.,
b leverage the learned latent space and achieve controllable generation by accepting/ rejecctnggjj sampled molecules based on molecular property predictor.
6 Conclusion, Limitations and Future Work
In this work, we propose simple yet effective method called ChemSpacE. to generate molecules with desired properties by leveraging the steerability and interpretability of pre-trained generative models. Furthermore, our interface demonstrates promising applications of interactive molecule design and discovery. Nevertheless, we acknowledge two limitations of this work, (1) it cannot yet study the activity cliff phenomenon, (2) it lacks theoretical analyses explaining why the latent space of deep generative models can be learned with property boundaries. Studying the activity cliff, a phenomenon in which structurally similar molecules may have very different potencies against the same target (Stumpfe et al.) 2014) is very challenging task that requires specific benchmark datasets, and reliable oracle functions for molecule generation, making it beyond the scope of this study. We expect that an enhanced understanding of the chemical space will lcad to promising directions of study in understanding such challenging phenomena. Furthermore, alt although it has been widely observed that semantic directions can be found in the latent space of generative models and exploited for data editing, we believe that the thcoretical underpinnings of these observations are not well understood and merit further study. Finally, we hope ChemSpacE opens up a new research avenue to study the interpretability and steerability of molecule generative models for achieveing interactive design.
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Published in Transactions on Machine Learning Research (03/2023)
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Appendix for "ChemSpacE: Interpretable and Interactive Chemical Space Exploration"
A Experiment Protocols
Pre-trained Models. We apply ChemSpacE,, as well as baselines, on two state-of-the-art molecule gen- erative models with publicly available pre-trained models. Vie (Jin et al. 2020) embeds molecular structure motifs into a hicrarchical VAE-based generative model; MoFlow (Zang & Wang 2020 designs a normalizing flow-based model which learns an invertible mapping between imput molecules and latent vec- tors. Molecular Properties. We study molccular properties identified in the chemistry community through open-source cheminformatics software, RDKit (Landrum al. 2013) and protein binding affinity, synthesis accessibility oracles in TDC (Huang et al. 2021 h. In total, we analyze 212 molecular properties from multiple dimensions, including distributions, cotter-correationss, etc. Details can be found in Appendix G Due to the page limit, we mainly report results for 7 molecular properties, including 4 very common yet important ones, drug-likeness (QED), molecular weight (MolWt), partition coefficient (LogP), synthesis accessibility (SA), and 3 binding affinity scores. For continuous molecular properties, we take the molecules with largest and smallest propertics for training the lincar models.
Quantitatively, evaluate the ability of the model to manipulate the given molecular property of molecules with the proposed strict success rate and relaxed success rate-L/G metries (see Sec. 2 We evaluate the model's efficiency by comparing the training process of the linear models with neural network- predictor for a commonly used optimization- based method in terms of training/inferent /inference time, data, and number of oracle calls. Qualitatively, we visualize latent molecule manipulation including property distribu- tion shift during manipulation, single and multiple property manipulations.
Hyperparameters. ChemSpacE does not entail many hyperparameters, the only important one is the manipulation range which is critical to the exploration degree of the latent space. For latent molecule manipulation experiments, we set the range as [-,, While for molecule optimization lask, it requires more aggressive exploration strategies to reach the expected latent area which poses optimal property values. We utilize [-100, 100] and [-30, 30] for single property optimization and multi-property optimization experiments respectively. Wo report the results for single property optimization with ranges from [1,5, 10, 15, 20, 30, 50, 100] Table
we would like a gradual change over the molecular structure and property,
Extended Latent Molecule Manipulation Experiments
B.1 Molecule Generation Evaluation
We evaluate the Validity, Novelty and Uniqueness of the generated molecules as proposed in Kusner et (2017) in Table g We can observe that ChemSpacE not only improves the success rate from the baseline methods, but also in general improves the novelty and uniqueness during manipulation.
B.2 Multi-property Latent Molecule Manipulation Evaluation
We evaluate molecules on ZINC dataset in Table
(penalized logp, QED) latent molecule manipulation over 200 randomly sampled
C Extended Molecule Optimization Experiments
We report more experiments about single property and multi-property optimization in this section. In Table g pushing further across the property separation boundary increases the improvement for molecule optimization but lowers the similarity scores.
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Table 4: Single property constrained molecule optimization for Penalized-logP on ZINC dataset with differ- ent manipulation ranges of ChemSpacE (6 is the threshold for similarity between the optimized and base molecules).
ChemSpacE-1
ChemSpacE-5
Improvement
Similarity
Success
Improvement
Similarity
Success
0.0
2.61 + 2.55
0.71 0.23
83.25%
3.33 3.74
0.67 0.26
84.25%
0.2
2.56 + 2.51
0.72 = 0.22
97.1%
3.60
0.69 0.23
84.13%
0.4
2.26
+ 2.28
0.75 + 0.20
77.25%
2.62 3.08
0.73 + 0.20
78.13%
0.6
1.34 + 1.54
0.84 + 0.14
57.0%
1.43 + 1.54
0.84 = 0.14
57.38%
ChemSpacE-10
ChemSpacE-15
6
Improvement
Similarity
Success
Improvement
Similarity
Success
0.0
4.97 + 4.86
0.57 = 0.27
90.75%
5.92 + 5.11
0.51 + 0.26
93.75%
0.2
4.70 + 4.71
0.60 + 0.24
90.13%
5.62 + 5.05
0.55 + 0.23
93.25%
0.4
3.43 + 3.96
0.69 = 0.20
82.38%
3.96 + 4.28
0.73 + 0.20
84.25%
0.6
1.67
2.32
0.82 = 0.15
59.00%
1.73 2.35
0.81 = 0.15
59.63%
ChemSpacF-200
ChemSpacF-30
8
Improvement
Similarity
Success
Improvement
Similarity
Success
0.0
6.62 + 5.57
0.46 + 0.25
94.40%
7.77 + 6.34
0.39 + 0.24
96.38%
0.2
6.11 + 5.14
0.51 = 0.22
93.75%
6.50 - 5.40
0.48 = 0.22
94.50%
0.4
4.22 4.50
0.65 = 0.19
85.13%
4.47 4.73
0.64 = 0.19
85.88%
0.6
1.79
2.36
0.81 = 0.15
59.88%
1.78 2.37
0.81 + 0.15
60.25%
ChemSpacE-50
ChemSpacE-100
8
Improvement
Similarity
Success
Improvement
Similarity
Success
0.0
8.80 6.35
0.30 = 0.21
98.38%
9.94 6.09
0.18 + 0.14
100%
0.2
6.99
5.53
0.44 = 0.21
95.00%
7.17 5.59
0.42 + 0.21
96.00%
0.4
4.45 + 4.65
0.63 + 0.19
85.38%
4.16 + 4.43
0.65 + 0.20
84.38%
0.6
1.87 + 2.56
0.80 = 0.15
60.13%
1.76 + 2.40
0.81 0.15
59.63%
17

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Published in Transactions on Machine Learning Research (03/2023)
Table Quantitative Evaluation of latent molecule manipulation for Multiple Properties. (-R denotes model with random manipulation, MoFlow-1 and MoFlow-2 denote two variants of gradient-basod bascline methods, RSR(L) denoles reluzed success rale-I, L, RSR(G) denoles relazed success rale- G).
Metric
MoPlow-1
MoFlow-2
ChemSpacE
SSR-both 28.00
27.00
62.00
RSR(L))-oth 29.50
28.00
63.00
RSR(G)-bool 41.00
38.50
76.00
Table 6: Quantitative Evaluation of latent molecule manipulation over a variety of molccular properties (numbers reported are reluzed success rale-L / relazed success rale- %. The best performances are bold.)
Dataset
Model
LogP
SA
DRD2
JNK3
GSK3R
Razaooa
27.21 / /32.11
1.50 2.00
0.00 3.00
1.00 3.00
0.00
46.00
4.00 / 4.00
0.00 / 15.50
1.50 / 55.00
HorYAE Motlow
Largest:
29.28 35.20
3.00 8.00
1.00
7,00
1.00 / 2,00
0.50
42.50
6,00
6,00
0.50
7.50
1,00 / 58.00
4.50/6.50
6.50/8.50
8,50/13.00
3.00/15.0
10.50/10.50
10.50/17.50
8.50/22.00
QM9
ChemSqueR
63.97
G1.56
16.00
28.00
13.50 / 28.00
17.50 / 39.50
17.50 / 72.50
58.50 / 68.50
21.50
49.00
15,00 / 72.00
Razalota
2.62 / 26.06
1.00
1.00
1,50
1.30
0.50 / 0.50
0.50 / 1.50
1:00
5.50
1.00 3300
0.50 2.50
Largest
3.25
0.50
0.00
0.00 /
0.50 /
8.50
CheenSgock
46.72
61.49
27.00
35.00
32.00
44.00
35.00 / 42.00
41.50 / 48.50
51.50 / 60.00
30.00
/3355
39.50
45.50
Randonn
35.85 41.70
9.50
6.00
2.50
7.50
3.50 / 6.50
5.50
79.00
4.00
56.50
1.50
27.50
4.50
HERVAE MoF.ow
Largese
37.46
43.12
3,00
4.50
9.00
15.00
2.00 / 6.00
8.00
81.50
4.00)
67.50
4.00
33.00
3,00 / 14.50
Cradicur-baodd
1.50/2.00
15.50
1.00/2.50
2.50/5.50
18.00/21.08
23..0/288.00
0.50/1.50
ChetnSpacE
60.54
63.23
53.50
57.00
S7.00 / 73.50
54.00 / 61.50
55.50 / 65.50
57.50 / 63.50
56.00
68.00
56.00 71.00
Racdlon
2:00
0.00
CLEMBL
Largest
0.25 / 17.88
0.00
0.00
0.00
2.50
0.00 / 0.00
0.00 / 0.50
0.00 / 1.00
0.00 / 0.00
0.00
2.00
ChenSqoeR
13.76
36.26
0.50
2.50
3.00
3.50
3.00 / 5.00
6.00
11.00
7.50
15.00
5.50
9,00
4.50 9.00
D ChemSpacE Demo
As shown in Fig. rright), we design an interactive real-time system for latent molecule manipulation, where the user can click random to randomly sample a molccule and freely select which model to inter- pret, which property to interpret, and luning the slide bar manipulates the molecule accordingly in real- time. The demo video is anonymously provided https://drive wwt.://w..oooooe.eooooooieeeieee htt.a///o../////t/////////////// Xtw.://gg.J.....O0OX////ssuuuuu
35
5M
DM
38
43
382
CRC
Figure 7: Optimizing molecular properties with optimization-besee method.
18

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Published in Transactions on Machine Learning Research (03/2023)
Table 7: Single property molecule optimization for Penalized-logP and QED on the ZINC dataset
Method
N
QED
pLogP
Top
0.948 #1.47e
4.287
10.138
ZINC
Top 10
0.948
#1.44e
4
4.180 10.154
Top 25
0.948 #2.18e
3.998 10.181
Top
0.948 +1.26e
3.972 +0.075
MoFlow
Top 10
0.948
#1.38e - 4
3.879 =0.110
Top 25
0.948 +2.37e
3.766 10.118
Top
0.948 +1.41e
3.933 +0.020
ChemSpacE
Top 10
0.948 #1.7le -
3.879 =0.068
Top 25
0.948 +2.43e 4
3.777 #0.101
Table Constrained multi-property molecule optimization for Penalized-logP and QED on the ZINC dataset with two variants gradient-basse methods (5 the threshold for similarity between the optimized and base molecules).
MoFlow-1
8
QED Improvement
QED % Improvement
pLogP Improvement
pLogP % Improvement
Similarity
Success
0.0
0.17::0.11
42.06 +: 35.69%
4.49 3.87
51.00 29.299300 29.36%
0.44 = 0.24
91.50%
0.2
0.16 0.11
37.84 4 32.16%
4.42 3.78
51.26 96%
0.48 0.21
90.75%
0.4
0.12 + 0.10
29.53 + 27.45%
3.64 3.43
44.61 29.34%
0.61 0.17
73.25%
0.6
0.07 0.08
17.44 + 20.36%
1.85 2.18
26.38 25.59%
0.78 0.15
41.13%
MoFlow-2
QED Improvement
QED % Improvement
pLogP Improvement pLogP Improvement
Similarity
Success
0.0
0.18 0.12
45.09 +: 39.71%
4.67 4.23
50.74 +: 28.79%
0.41 = 0.23
92.88%
0.2
0.16 0.11
40.12 + 35.36%
1.48 3.78
51.32 1: 29 11%
0.47 = 0.20
91.50%
0.4
0.13 + 0.10
31.25 + 29.87%
3.70 3.37
45.16 29.27%
0.60 0.17
74.88%
0.6
0.07 +: 0.08
17.61 4: 20.88%
1.97 2.51
26.74 4: 26.30%
0.78 + 0.15
41.88%
ChemSpacE
8
QED Improvement
QED % Improvement
pLogP Improvement
pLogP % Improvement
Similarity
Success
0.0
0.20 + 0.12
50.75 41.77%
1.66 4.34
50.01 24.36%
0.34 = 0.23
76.38%
0.2
0.1810.11
42.70 4: 37.
1.36 3.50
51.57 27%
0.45 - 0.19
76.75%
0.4
0.14 0.10
33.59 + 27.92%
3.78 3.49
46.07 28.09%
0.58 0.16
63.13%
0.6
0.08 0.08
20.12 4: 22.33%
1.80 1.81
26.77 24.75%
0.77 0.15
32.13%
19

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Published in Transactions on Machine Learning Research (03/2023)
Table 9: Quantitative Evaluation of Latent Manipulation.
Datasets
Models
Validity (%)
Novelty (%)
Uniqueness (%)
MoFlow
100.00
98.23
98.27
Random
91.60
91.60
8.06
QM9
Largest
40.75
40.75
9.32
ChemSpacE
91.63
88.71
24.23
Hie
100.00
79.39
95.14
Random
100.00
84.53
28.91
QM9
Largest
100.00
84.05
27.26
ChemSpacE
100.00
79.66
34.81
MoFlow
100.00
100.00
100.00
Random
69.98
69.98
29.04
ZINC
Largest
43.36
43.36
24.87
ChemSpacE
71.26
71.26
15.82
HicrVAE 100.00
94.03
99.45
Random
100.00
84.53
28.91
ChEMBL
Largest
100.00
93.00
55.09
ChemSpacE
100.00
94.24
56.58
E Molecule Representations
Molecule Graph. A molecule can be presented as graph X = (V,E,E,)) where V denoles set of N vertices (f.e., atoms), & S V x V denotes a set of edges (i.e., bonds), F {0, NxD denotes the node features (i.e., atom types) and E' E {0, NxxNx denotes the edge features (i.e., bond types). The number of atom types and bond types are denoted by and K, respectively.
F Molecule Generative Models
In Table we summarize list representative molccule generative models, which span various types of deep generative models, including the type of generative models, the type of generation process and whether latent space is learned. We also provide the formulation for two types of deep generative models (VAE and Flow) in Section F that are very popular for molecule generation task.
Table 10: A summary of mainstroam molecule generative models.
Prior Work
Generative Model
Sequential
Latent Space
JT-VAE (Jin al.
2018a
VAE
CGVAE Liu et al.
2018
VAE
MRNN PPpova al.
2019
RNN
GraphNVP
Madhawa et al.
2019
Flow
GCPN You
20
RL
GraphAF Shi et a.. 2020
Flow
MoFlow
Zang Wang
2020)
Flow
HierVAE
Jin et al. 2020)
VAE
GraphEBM
Liu et al.
2021
EBM
GraphDF
Luo et all
2021
Flow
20

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Published in Transactions on Machine Learning Research (03/2023)
F.1 Molecule Generative Model Formulation
VAE. gets a lower bound (ELBO) for the data log probability by introducing proposal distribution.
log)(z) = log J. p(zlz)p(z)dz
(19)
2 log ([( + {L(q(\|=)llp(2)
Flow. The key of Flow model is design invertible function with the following nice property:
20 Po(2
= fi(21-1)
1 Si (z:)
(20)
di; dz,
det di² dzg
p=(z)) = Pi- 12-1(2i11)
Pi-1(J
where fo is invertible function. To be more concrete, like Gaussian distribution, and repeating this for K steps will lead to the data distribution, i.c.;
take some tractable noise distribution,
r zk = fK o fk-1 ... fi(z)).
Thus, the log likelihood of the data is as follows:
log p(x) = logpx(=k)
logpk- - llog det dfk
džk
loggK-2(ZK-2) llog det df 1
dfk d2x -1
log
det
d2k -2
(21)
dft dz;-1
log (o(o)
Σ
log
det
1=1
G Study of Molecular Properties
List of Molecular Properties. In total, study 208 molecular properties from the open chemistry library RDKin and important molccular propertics including synthesis accessibility and bind- ing affinity scores from TDC They MaxESlatelndex, MinEStatelndex, MaxAlsESSaaelnddex MinADssSStattendex,, qed, MolWt, Heavy AtomMolw, ExactMolWt, NunValenceFlectrron, NumRad- fealBlectrons, MaxPartialChaage, MinPartialCharge, MaxAbssPartialChargge MinAlssPartialChaaage MoDensityMorganl, FpDensityMorgan2,, FpDensityMorgans, BCUT2D _WHH, BCUT2D SCUT2D_MWLOW MWLOW.
BCUT2D CHGHT, BCUT2D CHGLO, BCUT2D LOGPHT, BCUT2D LOGPLOW, BCUT2D MRHT, BCUT2D BCUT2D_MRLOW, BalabanJ, BertzCT, Chi0, ChiOn, ChiOv, Chil, Chiln, Chilv, Chi2n, Chi2v, Chi3n, Chi3v, Chi4n, Chi4v, HallKierAlpha, Ipc, Kappal, Kappa2, Kappa3, LabuteASA, PEOE VSAL, PEOE_VSA10, VSA10, PEOE VSA11, PEOE VSA12, PEOE VSA13, PEOE VSA14, PEOE VSA2, PEOE VSA3, PEOE VSA4, PEOF VSA5, PEOE VSA6, PEOE VSA7, PEOE VSA8, PEOE VSA9. SMR VSAI, SMR VSA10, SMR VSA2, SMR VSA3, SMR VSA4, SMR VSA5, SMR VSA6, SMR VSA7, SMR VSA8, SMR VSA9, SlogP VSA1, SlogP VSAI0, SlogP VSA11, SlogP VSA12, SlogP VSA2, SlogP VSA3, SlogP VSA4, SlogP VSA5, SlogP VSA6, SlogP VSA7, SlogP VSAS, SlogP VSA9, TPSA, EState VSA1, EState VSA10, EState VSAI1, EState VSA2, EState VSA3, ES-
PEOE
tale VSA4, EState VSA5, EState VSA6, EState VSA7, EState VSAS, EState VSA9, VSA EStatel,
https://www. http:/twwwrrkkt...oeee..ee. wtt../dcc//dde...cc.....mmmm
https://tdcommone.
21

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Published in Transactions on Machine Learning Research (03/2023)
VSA EState10, VSA EState2, VSA EState3, VSA EState4, VSA EStateS VSA EState6,
VSA FSState7, VSA EState8, VSA EState9, FractionCSP3, Heavy AtomCount, NHOHCount, NOCouni, Num.AiphatieCattocrees,, Mum.Aiphaaticleteroyclle NumAliphatickingg Num.AromatiCCarbocylee N Sum.AtomaticHectrrcyyydss NumAromaticRings, NumHAcceptorss, NumHDonors, NumHeteroatooms, NunsSturaalellHaeeoccyeees RingCount, MolLogP, MolMR, A1 AI_COO Al AHOH fr Al ALAAOOF OH noTert, fr __ArN, fr Ar Ar _r_CCO,, fr Ar N, fr Ar NH, Ir Ar OH, fr COO, fr COO2, ft C O, fr C O noCOO, C. S, fr HOCCN, fr Imine, fr NHO, fr NHH, fr NH2, fr I_No O, fr Adealkylation,, fr Ndeelkylation2, fr Nhpyrrole, fr SH, fr_ -__alchyde, fr_ r_alkyl carbamate, fr alaakyl halide, fr *_allylic oxid, fr -_aiide, fr amidine, fr aniline, fr aryl methyl, fr azide, fr azo, fr barbitur, fr benzene, fr benzodiazepine, fr bicyelic, fr diazo, fr dihydropyridine, fr epoxide, Ir ester, Ir ether, fr furan, guanido, fr halogen, fr hdrzine, isothiocyan, fr ketone, fr ketone Topliss, fr _acaamm
N Bunno,,,ablBBonds NunsSurraleeCarbboydes.
NumSaturateddings
fr hdrzone, fr imidazole, fr imide, fr iissocynn, fr lactone, fr_ m__mcohoxy, fr morpholine, fr nitrile, fr nitro, fr nitro nitro_arom, fr nitro aitro__rrmm arom nonortho, Ir nitroso, fr oxazole, fr oxime, fr para hydroxylation, fr phenol, fr phenol noOrthofbond, fr phos acid, fr phls__hsteee fr piperdine, fr "i_perrze,ne, fr priamide, fr prisulfonamd, fr pyrriiiiee, fr quatN, fr sulfide, fr sulfonamd, fr sulfone, fr term acetylene, fr tetrazole, fr thiazole, fr thiocyan, fr thiophene, fr_ unbrch mubrch_alkann, fr urea, sa, drd2, jnk3, gsk3b.
However, not all of the molecular properties are varied in the three datasets. Specifically, QM9 contains 29 frozen molecular properties, NumRadicalElletrons, VSA7, SlogP_VSAS VSA9, EState _VS11, VSA EStatel0, fr C S, fr fr_N_,,,,_____ fr SH, fr azide, fr azo, fr barbitur, fr benzodiazepine, fr diazo, fr hdrzine, fr hdrzone, fr isocyan, fr isothiocyan, fr nitroso, fr ___hho____ __idd fr "__ohos__ phos__sterr, fr prisulfonamd, fr sulfieee fr sulfonamd, fr sulfone, fr thiazole, fr thiocyan, fr thiophene, ZINC contains 4 frozen molecular properties, NunRadicalElectroow SMR VSAS, SlogP_VS VSA9, fr "=_priuuffooadd and ChEMBL contains only 3 frozen molecular properties, SMR SMR_VSAS VSA9, fr_ fr_prisulfoamdd
SMR VSA8, SlogP VSA12,
fr_____
Inter-correlations of molecular properties. Fig. we visualize the linear correlations bet ween each pair of molecular properties across three datasets. From the heatmaps, we can observe that there are no lincar correlations between half of the molccular properties, and similar patterns observed in ZICC and ChEMBL datasets.
3.5
0.5
C35
400
0.50
300
51
4025
191
25
20
775
330
200
Figure 8: Inter-correlation heatmaps for studied molecular properties in QM9, ZINC and CLEMBL datasets.
Molecular Property Distributions. We visualize 7 molecular property distributions reported in section 4 in Fig. 9 From there, we can observe that the property distribution may vary a lot in terms of different datasets. Notably, the distributions of some properties, e.g., QED, are very similar in ZINC and ChEMBL, datasets, while some are quite different, e.g., MolWt.
Latent Space Evaluation
To evaluate the quality of the learned latent space, we utilize three disentanglement evaluation metries, disen- tanglement, completeness and informativeness (Eastwood & Williams 2018).. To be specific, disentanglement measures the degree to which each latent dimension controls most molecular property, completeness
22

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Published in Transactions on Machine Learning Research (03/2023)
Figure 9: Property distributions of randomly selected molecular properties on QM9, ZINC and ChEMBL datasets. QED
MolWt
LogP
BalabanJ
BertzCT
CHGHT
CHGLO
100
800
QM9
ZINC
13
5000
ChEMBL
measures the degree to which each molecular property is governed by at most one latent dimension, and informativeness measures the prediction accuracy of molecular properties given the latent representation. From Table II we find MoFlow learns a better and more disentangled latent space than HierVAE. One possible reason is that MoFlow (369) has larger latent space than HierVAE (32) since Flow restricts the latent size to be equal to the input size.
Table 11: Quantitative Evaluation of Disentanglement on Latent Space.
Datasets
Models
Disentanglement Completeness Informativenesss
MoFlow
0.24
0.57
0.83
QM9
ViEr
0.13
0.27
0.75
ZINC
MoFlow
0.40
0.62
0.87
ChEMBL
HierVAE
0.14
0.41
0.81
23


Reviews:
[{"review_id": "SXU72ZiyuA", "reviewer": "Reviewer_fKVq", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "*Strengths:* The method addresses a specialized task designed by the authors; i.e. manipulating a starting molecule step by step towards a certain property in an interpretable way. An underlying assumption is the linear separability of the generator's latent space to target property classes. This assumption makes the methodology more suitable for human-in-the-loop exploration but still leads to a competitive optimization strategy. Authors provide means for users to try the manipulation method interactively.\n\n*Weaknesses:* There is an emphasis on how ChemSpacE outperforms two simple baselines (random manipulation and largest range manipulation) and gradient descent/ascend in terms of success rate, speed up, data efficiency and so on. The first two baselines would be lower bounds for any working method for the task as defined by the authors. However, it is unclear what the “gradient descent” based method entails in the manuscript, and if it is fair to compare a local minima finding strategy based on gradients to the author's traversing of the entire latent space in linear strides. Performance is measured  using a continuous metric (success rate as defined by authors) that penalizes the former and favors the latter. Gradient descent would get stuck when initialized in local minima hence perform poorly on the defined metric, whereas authors’ method isn’t constrained by that; in other words, the objectives of the algorithms are different. I think the author's method is still useful, but baselines are not as informative as presented. ", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "Authors describe a simple methodology called ChemSpacE to generate plausible molecules that demonstrate a target property by moving towards a decision boundary explicitly computed for that property, in an already existing latent space of a pre-trained deep generative model. As one can keep track of the molecular changes along this path, the method provides outcomes interpretable by humans. In effect, the model is analogous to training a linear support vector machine for the target property in the latent space of the generative model, after which one can move along the hyperplane normal towards the desired property. Authors design evaluation criteria and benchmark the performance of ChemSpacE in manipulating molecules using various public datasets and models.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "[Critical]:\n- Please describe the gradient descent method used and discuss its suitability for serving as a fair baseline.\n- Given that one of the main contributions is \"demonstrate effectiveness and efficiency of the authors' method in molecule optimization ...\" please, provide or at least comment on an alternative global or Bayesian optimization approach that would be more fair to compare with the presented method.\n\n[Not critical]:\n- Please provide a brief description of target properties QED, logP etc.\n- Figure and Table numbers appear out of order. Please check.\n- What does k denote in Eq.8?\n- What are the functions L and G in Eqs. (13) to (18)?\n- Please leave more space between subfigures in Figure 2 so the readers can more clearly see what visual elements belong to which subfigure, and also explain how Fig2(c) is generated.\n- Please elaborate how Eq.9 helps find direction in multiple property scenarios.\n- Please clarify how ChemSpacE “can be incorporated in various pre-trained state-of-the-art molecule generative models without retraining”. Would the method not require finding the decision boundary for a property in each new generative model’s latent space?\n- What do the “manipulation ranges” mean as listed in the Hyperparameters section? Please explain how these should be interpreted.\n", "broader_impact_concerns": "The reviewer could not identify any concerns on ethical implications of the work.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "jvqzEIXCor", "reviewer": "Reviewer_4w7v", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n - The paper is well written, and easy to follow\n - The work addresses an important application domain\n - It proposes a new task, new metrics, as well as a new method\n - The interactive demo is well designed\n\nWeaknesses:\n - Molecule manipulation baselines are rather weak, especially \"Random manipulation\" and \"Largest range manipulation\"\n - \"Gradient-based method\" as a baseline was not given enough details \n - a few formatting mistakes for citations", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The work presents an interactive tool to navigate the latent space of a pre-trained generative model, in the applied domain of molecule design and discovery. The particular technique of traversing a pre-trained latent space is not particularly novel, but the application to  molecule manipulation (a new task defined by this work) is useful and interesting. The tool can be used to understand and explore the design space, and when combined with human-in-the-loop, optimize molecule design. Experiment results are compelling. Some technical details are missing or buried in Appendix. The paper could be strengthened by adding those details back.\n\n\n\n", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "The two proposed metrics, strict success rate (SSR) and relaxed success rate (RSR), are rather important concepts, but their equations are buried in appendix. The authors should consider moving them to the main paper, especially when they are used to evaluate the proposed method in multiple tables later on.\n\nA few citations are wrongly formatted. For example, \"...during the searching or optimization process Huang et al. (2021).\" should be \"...during the searching or optimization process (Huang et al., 2021).\" Also: \"...emergent properties of the latent space learned by molecule generative models Gómez-Bombarelli et al. (2018); Zang & Wang (2020)\"\n\nGradient-based method is an important baseline, but is given no explanation how it works. \n\nIn Table 1, it is confusing to see new combined names like \"MoFlow-R\" and \"HierVAE-C\". Consider using two separate columns to indicate the generative model and the latent exploration method.", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "GOcc8yw0BY", "reviewer": "Reviewer_JCR3", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Overall, I don't think this paper is a good fit for TMLR.  I don't think it's a great fit for the audience.\n\nI don't mean to sound harsh but I don't believe there is a lot of machine learning research content in this work.  The proposed method is a linear latent space interpolation. Latent space interpolations are well known and linear latent interpolations are usually a first sort of sanity check done to ensure a latent variable model is doing something interesting.  In fact, one of the models used in this work, MoFlow, had in their Figure 4 (with essentially the same visual styling as Figure 2 here) a visualization of a linear latent space interpolation.\n\nPerhaps it is news to the chemical modelling community just how effective linear latent space interpolations can be for manipulating chemical properties, but then the proper audience should be more focused group of chemical modelers.\n\nIf you were looking to expand the research, into something more appropriate for a TMLR audience, I'd consider exploring a wider class of semi-supervised or conditional generative models of molecules that take into account property information.  That is, in this work, first a latent variable model is built, which we can view a a joint model over both chemicals and some latent: $p(z,x)$ and then after the fact, some model is learned to try to associate or align chemical properties with the learned latent, $p(p|z)$, which for this work a simple linear model was used.  First you could consider much richer models for $p(p|z)$ beyond simpler linear ones.  But more generally, I think its much more interesting to ask whether chemical properties can lead to better, more structured generative models.  Instead of bolting the property identification on at the end and hoping that the learned latent variable model has distentangled the desired chemical properties, why not model them as well?  Learn a joint $p(z,x,p)$ model directly.  There are lots of interesting directions to consider along this path, including many standard approaches like semi-supervised VAEs (arxiv/1406.5298).", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper proposes using existing latent variable generative models of chemicals along with linear latent space interpolations to manipulate chemicals for particular properties.\n\nIt then evaluates how well this performs compared to some simple baselines.", "claims_and_evidence_yn": "No", "claims_explanation": "", "audience_yn": "No", "audience_explanation": "", "requested_changes": "The discussion in section \"Molecular Generative Models\" is incorrect. I don't think its fair to say that the encoding and decoding process for a VAE are described by deterministic maps as shown in Equation 1.  I feel as though that sort of misses the point that a VAE is a probabilistic model with a stochastic encoder / decoder.  The encoding process maps an input $x$ to a distribution in the latent space $p(z|x)$.  Granted, for the simplest of VAEs which use mean field gaussian encoders, potentially with fixed variance this map is characterized by the map for the means alone which I think is what is meant to be invoked here.\n\nIn Table 3, e-notation floating point values were dumped into the LaTeX table, i.e. \"2.75e-2\" which turns into $2.75e-2$ and looks terrible.  Please use $2.75\\times 10^{-2}$ instead, as is standard.\n\nThe discussion in Section 3.2 isn't the most clear.  I'd suggest reframing the discussion of your method in the context of a probabilistic model to better align with the audience.", "broader_impact_concerns": "None", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: The reviewers were concerned about the level of machine learning innovation in the paper, however agreed after the rebuttal period that claims were supported by evidence. Authors successfully argued that while linear interpolations in feature space are common, their approach to identifying interesting directions in the feature space was novel and of interest to the community. 
Decision: Accept (poster)