An efficient graph generative model for navigating ultra-large combinatorial synthesis libraries
Authors: Aryan Pedawi
Pawel Gniewek
Chaoyi Chang
Brandon M Anderson
Henry van den Bedem
Venue: NeurIPS 2022 Accept (2022)

Abstract: Virtual, make-on-demand chemical libraries have transformed early-stage drug discovery by unlocking vast, synthetically accessible regions of chemical space. Recent years have witnessed rapid growth in these libraries from millions to trillions of compounds, hiding undiscovered, potent hits for a variety of therapeutic targets. However, they are quickly approaching a size beyond that which permits explicit enumeration, presenting new challenges for virtual screening. To overcome these challenges, we propose the Combinatorial Synthesis Library Variational Auto-Encoder (CSLVAE). The proposed generative model represents such libraries as a differentiable, hierarchically-organized database. Given a compound from the library, the molecular encoder constructs a query for retrieval, which is utilized by the molecular decoder to reconstruct the compound by first decoding its chemical reaction and subsequently decoding its reactants. Our design minimizes autoregression in the decoder, facilitating the generation of large, valid molecular graphs. Our method performs fast and parallel batch inference for ultra-large synthesis libraries, enabling a number of important applications in early-stage drug discovery. Compounds proposed by our method are guaranteed to be in the library, and thus synthetically and cost-effectively accessible. Importantly, CSLVAE can encode out-of-library compounds and search for in-library analogues. In experiments, we demonstrate the capabilities of the proposed method in the navigation of massive combinatorial synthesis libraries.

An efficient graph generative model for navigating ultra-large combinatorial synthesis libraries
Aryan Pedawi Atomwise Inc. aryan@atomvise. com
Pawel Gniewek Atomwise Inc.
Chaoyi Chang
Atomwise Inc.
pawel@atomvise.com com
cchang373@atomwiise. com
Brandon M. Anderson"
Henry van den Bedem
Atomwise Inc.
Atomwise Inc.
branderson@gmail.cmm com
UCSF, Dept. of Bioengineering & Therapeutic Sciences
vdbedem@atomvise com
Abstract
Virtual, make-on-demand chemical libraries have transformed early-stage drug discovery by unlocking vast, synthetically accessible regions of chemical space. Re- cent years have witnessed rapid growth in these libraries from millions to trillions of compounds, hiding undiscovered, potent hits for variety of therapeutic targets. However, they are quickly approaching size beyond that which permits explicit enumeration, presenting new challenges for virtual screening. To overcome these challenges, we propose the Combinatorial Synthesis Library Variational Auto- Encoder (CSLVAE). The proposed generative model represents such libraries as a differentiable, hierarchically- saarrhiiclll-orgniizeedd database. Given a compound from the library, the molecular encoder constructs query for retrieval, which utilized by the molecular decoder to reconstruct the compound by first decoding its chemical reaction and subsequently decoding its reactants. Our design minimizes autore- gression in the decoder, facilitating the generation of large, valid molecular graphs. Our method performs fast and parallel batch inference for ultra-large synthesis libraries, enabling number of important applications in early-stage drug discovery. Compounds proposed by our method are guaranteed to in the library, and thus synthetically and cost-effectively accessible. Importantly, CSLVAE can encode out-of-library compounds and search for in-library analogues. In experiments, we demonstrate the capabilities of the proposed method in the navigation of massive combinatorial synthesis libraries.
Introduction
Virtual high throughput screening (vHTS) has gained significant traction in early-stage drug discovery, owing in no small part to make-on-demane chemical libraries utilizing combinatorial synthesis construction. These combinatorial synthesis libraries (CSLs) enable access to ultra-large swaths of chemical space from a considerably smaller set of chemically accessible building blocks that can be combined according known synthesis routines. recent years, these libraries have
grown from millions, to billions, and now to trillions of compounds [1 32 42 55). For example, the Enamine REaily Accessible (REAL) libraries [19 leverage off-the-shelf molecular building blocks and parallel synthesis, permitting lead times the order of few weeks and ushering in an era ever-decra latency between silico and in vitro high throughput screening.
WWrk performed while at Atomwise Inc. Current affiliation is with Atomic AI.
1 EEuaal senior contributions.
36th Conference on Neural Information Processing Systems (NcurIPS 2022).

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As result of the combinatorial explosion these constructions enable, early-stage drug discovery has now "crossed the Rubicon" into the non-enumerative regime, This presents new challenges for in silico hit discovery and optimization, which rely on screening explicitly enumerated compounds. These methods are ill suited to the non-enumerative setting, scaling linearly with the number of compounds, which motivates our interest in designing scalable approaches for navigating such libraries.
In this paper, we propose the Combinatorial Synthesis Library Variational Auto-Encoder, or CSLVAE for short (pronounced like c' d'est la vie). CSLVAE a graph-based generative model that exploits the structure of CSLs towards efficient navigation of the relevant chemical space. Our model learns hierarchy of keys over the components of the library, and uses these keys to process queries for retrieval. The encoder processes a molecular graph and returns as output a query vector, which the decoder uses to retrieve the molecule through an efficient sequence of query-key comparisons that utilizes the hierarchical construction of CSLs, requiring minimal autoregression and admitting efficient parallelization.
The main contributions of this paper are as follows:
We present a novel graph generative model which acts as a "neural database," providing random access to ultra-large, non-enumerable compound libraries. As such, our model is guaranteed to generate valid and cost-effectively accessible molecules.
Our model overcomes challenges with long autoregressive chains in compound generation, improving scalability large molecular graphs.
Our model reduces the number of parameters ten-fold relative to comparable methods, and offers considerable improvements in computational complexity for searching through CSLs.
2
Related Work
Virtual high throughput screening and enumeration Often, the first step in vHTS campaign is preparing a compound library for subsequent use [1] [6]. While highly optimized compound
sampling and scoring techniques have been developed (17), these approaches nevertheless rely on
an exhaustively accessible library. An exception is the virtual synthon hierarchical enumeration screening (V-SYNTHES) approach [42). which leverages the modular nature of parallel synthesis libraries. However, by design, V-SYNTHES does not permit query-based random access. On the other hand, SpaceMACS 43 and SpaceLight [4] can provide query-based access to modular libraries by decomposing the query into fragments, and matching those by similarity search to synthons in the library. In parallel to these efforts, machine learning has received significant attention in vHTS: for predicting activity scores given docked conformations [14]4]] (54), predicting activity scores given ligand and protein separately (undocked) (3), and in improving or altogether replacing classical molecular docking with machine learning approaches
38 48 49
Deep learning approaches to molecular generation De novo drug design has assumed an increas- ingly prominent role in identifying novel chemical matter drug discovery campaigns 9 35
The two dominant neural nowork--bssed paradigms for molecular generation are text-based and graph-based generative models. Early work in text-based generative models (also called chemical language models) applied recurrent neural networks to SMILES strings [15] 44]. Although these methods have shown a great deal of promise and spurred interest molecular generation within the MI. community, they are not guaranteed to produce valid SMILES strings. Approaches utilizing grammar constraints of SMILES notation have been proposed to improve validity 28]; separately the recently proposed SELFIES notation (27 (36 guarantees validity and has seen increased adoption as such. In both cases, however, there remain known drawbacks to modeling with such text-based representations of chemical matter (e.g., surjectivity, similar molecular structures having possibly large edit distances).
For some applications, it is of interest to utilize generative models which can fit molecular databases, permitting the navigation of these databases via the fitted model. The ability of language models to fit molecular databases was investigated in a prior study (2 that applied deep language models to GDB-13 ( database of 10" compounds formed by fully enumerating molecules up to 13 atoms of clement types C, N, O, S, and Cl, subject to simple chemical stability and synthetic feasibility
2

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rules. The authors trained on 0.1% 1% of the total library and find that the model was capable of covering roughly 70% of compounds in the GDB-13 library. Furthermore, the language model they trained generates compounds not satisfying the GDBB13 construction in approximately 15% of cases.
Graph generative models have received significant attention in recent years as alternative their text-based counterparts. The earliest of these models focused on generating graphs of constant size in single shot 446] or generating graphs of arbitrary size autoregressively. one atom or bond at
time [31 40 57 34 These approaches also struggle to reliably produce chemically valid molecules
and encounter difficulties with large molecular graphs.
In an effort to address both points, fragment based graph generative models have been proposed and are growing in popularity [2 23 24 26]. These models have the advantage of guaranteeing chemical validity by decomposing molecules into valid sub-components and explicitly disallowing actions which yield invalid combinations of fragments. Such explicit validity checks can be performed on every action, at the cost of additional computation. While other text- and graph-based generative models tend to struggle with large molecular graphs due the long autoregression chains needed to produce them, fragment-ben based graph generative models require autoregression lengths on the order of the number of fragments that comprise molecule. This can be significant when the fragments themselves contain many atoms.
However, some issues persist due to general difficulties with autoregressive graph generation. Unlike text-based models, in which there is less ambiguity in the autoregression order (c.g., tokens are typically decoded in left-to-right order), graphs have no such canonical node order, which presents challenges for graph-based autoencoders [31 [6]. Furthermore, although they require shorter autoregression chains than their counterparts, existing Tragment-based graph generative models nevertheless require autoregression lengths that grow in the overall size of the molecule since autoregressive decoding cannot be effectively parallelized.
While fragment-base graph generative models and SELFIES-bar basee language models each address the issue of chemical validity, there is the separate challenge of synthetic accessibility. Prior work has cast doubt on the synthetic feasibility of compounds proposed by many existing generative models [1].. which can limit the practical utility of these models in drug discovery applications if not appropriately addressed. Subsequent work has attempted to improve on these shortcomings by (i) including explicit penalties for synthetic inaccessibility via scoring function [8], (ii) limiting the model to fragments from known compounds [33 39 50 or (iii) inducing bias towards simple and
known synthetic pathways (7 8 20
3
Methodology
This section formalizes combinatorial synthesis libraries and the proposed model, CSLVAE. Figure provides an illustration of the approach. Details the architectures used for the various modules which comprise CSLVAF can be found in the Appendix.
3.1 Preliminaries
CSLs are composed of set of multi multi-dimmenional synthesis tables (Figure Panel A). Each synthesis table describes a multi-component chemical reaction, which we denote by an index T (c.g..
a natural number). Following 42], we use the term R-group to refer to a singular component in a reaction, and denote by an index r E R. A multi-component reaction takes several reactants (components) as input to produce single molecule via chemical synthesis. We let 1/: T - P (R) be the funetion which returns the set of R-groups vt()) C. R associated with a reaction t, where P(-) denotes the power set function.
Each R-group is spanned by possibly large number of molecular building blocks, called synthons, which can be utilized in the corresponding reaction. We denote a synthon by an index & & 5 and represent with a molecular graph, G2 E $5. We note that synthon can belong to multiple R-groups. For convenience, we use a R + P(S) to represent the function which returns the set of synthons (r) S belonging
particular R R-group
A product x E X is a molecule that is synthesized according to a ke-component reaction with (1)
R- grouups (t) (r .....T (kk)) and corresponding synthon tuple = (s ..... ( where
3

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tbno
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tTo.
0
0
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Figure 1: Overview of CSLVAE. Panel A: Illustration of combinatorial synthesis table, which form the basis of combinatorial synthesis libraries (CSLs). Panel B: CSLVAE an autoencoder whose encoder takes molecular graphs as input and returns query vectors as output, which the decoder then utilizes to retrieve the corresponding products from the library. Panels C-E: The CSLVAE library encoder represents CSLs via a hierarchy of learned representations, It proceeds by encoding individual symthons, represented as molecular graphs, with a graph neural network. It subsequently encodes R-groups with set neural network over their constituent synthon representations. Finally, encodes reactions with a set neural network over their constituent R-group representations. Panel F: The molecular encoder returns query from an input molecular graph (in this case, a product from the library). Panels G-H: The molecular decoder processes the query to retrieve a product from the CSL, by first decoding the reaction type and subsequently decoding one synthon per R- R-group via query-key lookups.
" E (r(")) for all i =;=1.... kr We define to be the synthesis rule which generates a compound from a reaction and synthon tuple pair (4, u). i.e., = [tt, u). In short, as a simple analogy, one can think of a synthesis rule t as specifying an equation of &ę terms, where each term an R- R-group, and their associated synthons correspond to the allowed values for the corresponding term.
Hence, a combinatorial synthesis library (T, R, S. f. th, σ)) is fully characterized by its reactions T, R-groups R, and synthons S, together with the synthesis rule f. reaction to R-groups mapping vA, and R-group to synthons mapping a.
Using the language of probability, one can describe a distribution over products induced by D via the following factorization:
D
Σ Σ p(t(D) p()). LET WEU
(I)
where U, 1 a(r(")) x... x (r( is the set of all eligible synthon tuples for reaction t. This U,=
factorization describes the generative process in which one first samples a reaction t ~ p(t(D) x [ then samples a valid synthon tuple u ~ puult D) = IU, -1 comprised of synthons from the respective R-groups in f, and joins these together via synthesis to form product x (via the deterministic rule f))
As written, all valid (t, u) pairs in D are equally probable under p. Note that if every product in D can be reached according to just single synthesis route, then p(x(D) is uniform distribution over the part of chemical space X accessible by D.
3.2 Combinatorial Synthesis Library Variational Auto-Encoder (CSLVAE)
We consider the task of looking up a product x from a library D, which amounts to finding the reaction and synthon tuple u satisfying f(t, u). This can be cast inference problem

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seeking p(t, u/x, D). A latent variable model for gives rise to variational formulation:
ul,,
p(l, ul2, D) g(z(x)) dz,
with p(z) denoting the prior distribution of the latent variable. One can further simplify the joint conditional distribution of ł and by first selecting the reaction and then selecting the synthons
(1) (Ax) independently conditional on t: p(l, u/z, D) - p(12, D) p(ul,,,,,,)
Su Su
(3)
= p(1zz D)
II p( 12,
(2) (D).
12, 4
(4)
This gives rise to strategy in which one encodes a molecule x into the latent space, z ((z(2).
and proceeds by first decoding the reaction type ~ p(t|z, D) and then, conditional the sampled
reaction, decoding one synthon per R-group ( pl 8u 2 L, rr DD for =I.... to form the synthon tuple U..
The resulting latent variable model is the proposed CSLVAE. Panels B-H in Figure D give a step-by- step depiction of the method. In the forthcoming subsections, we will describe and formalize the three primary modules that comprise CSLVAE in detail: (i) the library encoder, (ii) the molecular encoder, and (iii) the molecular decoder. Module (ii) forms the basis for (z](r), while modules (i) and (iii) form the basis for p(t, u/z, D).
3.2.1 Library encoder
CSL = R. 1b o) is organized hierarchically, with synthons at the bottom of the hierarchy, R-groups R in the middle, and reactions T at the top. We propose strategy for learning an associated hierarchy of representations that describe the library at these three levels of resolution then be used in retrieving results from queries
in end-to-end fashion. These representations into the library. The library encoder is illustrated in panels C-E of Figure [
We start from the bottom of the hierarchy with the synthons S. To learn representation for each synthon in a manner that is fully inductive, we use a graph neural network to parameterize the SynthonEncoder Lg + Rdd, which applies sequence of message passing steps followed by readout to arrive at a dg- digeeeenniooall representation for each synthon.
Moving up the hierarchy, we use deep set neural network to represent the R-groups R by sum- marizing the representations for the synthons belonging to a particular R-group. Formally, the RCroupEncoder RR43 ... x Rds + Rd learns dyzddimensional representation for given R- group from the set of ds-dimensional representations of the constituent synthons. Following (58), the
R-group encoder has the form RGroupEnccoder ((h Vs ar)))) =p (()sar))) ((h))) where s and p are parameterized by multi-layer perceptrons (MLPs) and + is permutation-invarit aggregation operator. While other potentially more performant set-to-vector neural networks could be considered here, c.g., set transformers (30). advantage of this simple construction is that it permits fast querying over library subsets at test time since @(h)) can be cached for all s E S, thereby reducing the required computations for making queries into partitions of the library. We utilize mean pooling as the aggregation operator to focus on characteristics of the distribution synthons in an R-group (as opposed to sum pooling which generally expresses characteristics of the multiset), which improves performance when dealing with R R-groups of varying cardinality.
Finally, to represent reactions, we use yet another deep set neural network as the React onnniodern Rdn .... TR - Rdr This module takes as input variable-sized set of R-group representations corresponding to the reactants in f. and produces dd-dimensional representation for the reaction. We utilize sum as the aggregation operator to learn multiset properties of the R-groups in a reaction.
Putting these together, the representations cascade as follows:
h SyathonEncoder((.)
(5)
h RGroupEncoder (h Vs E o(r)))
(6)
h ReactionEncoder/ (h Vr E v())))
(7)
5

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In 4., we considered factorization of the likelihood such that, given a molecular representation the molecular decoder proceeds by first decoding the reaction type and then decoding one synthon for each R-group separately conditional on the reaction type. Hence, we require key vector for each reaction as well as for each synthon to compare with the associated query vectors (to described). As such, we introduce a Reacti ReactiioneeGGnerratoo reaction representation, and similarly introduce a SynthonkeyGGneratorr Rds + R to produce a key for each synthon. Each of these key generators can be parameterized by MLPs:
Rd - RR which returns key vector given
k Reac.:onnkeyGeeeratttr(h)))) k Syplhonkeydemeratto((1]))
(8)
(9)
3.2.2 Molecular encoder
The MolecularEhcoder 9x + Rd takes input molecular graph Ix Ix and returns
dx-dimensional feature representation,
2 MolecullarFnccoee(((...
(10)
In our implementation, the Molecul arEncoder is graph neural network with variational linear layer stacked on top of the readout, which produces a sample z ~ g(z(z) for a given input graph G.. query induced z into the library D.
As depicted in Figure we interpret the representation
Note that the MolecularEncoder can in principle take any valid molecular graph as input therefore capable of producing queries for compounds that are not in the library D. This can be useful for finding analogues by catalog that is, compounds which can be purchased from a catalog and are chemical analogues of query molecule. This use case will be investigated in later section.
3.2.3 Molecular decoder
Given query MolecullarEacoder((, and a library D, the decoder is tasked with retrieving the molecule from the library, i.e., identifying the reaction and synthon tuple which yield the molecule as a product. We proceed by generating the reaction first. A Reaction deactionnuuryyeneraan generates query from the molecular representation compare against the reaction keys:
Rdx - R²
T ReactionnhheryGnerratttooaa
(11)
T
q"
TT
(ltt)lz.21 D)
softmax
(12)
j=1
This defines a probability distribution over reaction types in T. We can sample according to this distribution to arrive at reaction p(/2,, D).
Given the sampled reaction I, we know the required R-groups (via wh) and further know which synthons eligible for each R-group (via r)) To decode the synthon tuple, introduce
SynthonQueryGenerator [gxx +dr + gess which can be used to query synthons for each
R-group r (i) (t) follows:
L SynthonQuerrGGeerrtttr(llll//// hT
(13)
(o()()) (2 (( DD) 1=1
q tr
SS "
lo(r
softmax
(14)
Vks
In our implementation, both the reaction and synthon query generators are parameterized by MLPs.
3.3 Training algorithm
For large CSL. Dr, encoding the entire library on each iteration of the training loop could require an excessive amount of GPU memory. To overcome this, we utilize minibatch strategy in which

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random subset D C DD is drawn from the full library according to distribution pDD(D*). From D, we form the synthon, R-group, and reaction representations and keys. In particular, we use sub-sampler p(D D") which (i) samples subset of the reactions contained in the full library uniformly at random, keeping only the R-groups contained in the sampled reactions, and (ii) for each reaction, samples a random number of products, retaining only the synthons that are contained in the sampled products. We also utilize teacher forcing, feeding in the ground truth reaction when generating the synthon queries for the respective R-groups. Algorithm I in the Appendix describes the training procedure.
Ex-post density estimation Given a trained generative model po (z)zz) we wish to sample products via (a. z) ~ Po (z) (2) p(z) (discarding z) However, this in general will not correspond well a uniform distribution over the products in DD due to the bias introduced by the batch sampling strategy outlined above (which first uniformly samples reactions and then uniformly samples products given the reaction).
Although this can be corrected with importance weighting during the training phase, we opt for more practical approach by using an ex-post density estimation strategy [13]. We sample a large number of products from the target distribution æ p(z D) and encode these products via the molecular encoder Z ~ qui [z]z). We then fit a density estimator to the aggregated samples, written (2()). In our experiments, we utilize multivariate normal distribution for simplicity, but one could imagine using more expressive density estimators here (e.g.. mixture of multivariate normals).
Now, we can sample products via (ar, z) po(a) z) ga (z), which will more closely align with sampling from p(a: 'D). This helps to correct for bias in the distribution over product space that is induced by the choice of batch sampling strategy.
3.4 Computational complexity, scalability, and efficiency
We now examine the computational complexity, scalability, and efficiency of the proposed method.
First, note that the CSL D can be encoded with O(IS + | (T)) complexity the constant depends on the complexity of the synthon, R-group, and reaction encoders. Nonetheless, this is logarithmic in comparison naively encoding each product in D, which has O(IP)) complexity.
More noteworthy is the computational complexity of the molecular decoder. For clarity, let us consider simplified D comprised of single k-component reaction. Let M, denote the number of synthons for R-group i 1, .,..., k. Naively, a nearest neighbor lookup in D requires O M,) complexity. CSLVAE, on the other hand, performs the lookup over synthons in each R-group independently, which attains O M,) complexity: logarithmic improvement. Hence, the proposed molecular decoder highly suitable for ultra-large CSLs that are of interest in early-stage drug discovery.
Another advantage of CSLVAE's decoding strategy is that it relies only minimally on autoregression. In fact, we only ever need to do a single step of autoregression, irrespective of the size of the graph being generated (autoregression length of exactly two). As such, CSLVAE gracefully scales to large and variable-see sized molecular graphs that follow a combinatorial synthesis construction.
Lastly, we point out that our method is guaranteed to generate chemically valid- and perhaps more importantly, synthetically This compares favorably with prior work, in which the validity of each candidate action verified at each step of the autoregression, with invalid actions excluded from the choice set. Although cheminformatics libraries like RDKit (29) have efficient C++ implementations for these checks, they nonetheless increase runtime rather significantly. Further, in the absence of explicit validity checks, these models have been shown to generate invalid molecular graphs at a markedly higher rate (22).
graphs without performing explicit validity checks.
Experiments
This section covers some of our attempts to validate CSLVAE's performance and highlight its capabilities. We include additional supplementary experiments in the Appendix.
'The parameter 0 represents the parameters for the modules written in typewriter font.
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Data We demonstrate the capabilities of CSLVAE on the Enamine REAL library, which is com- prised of 340K synthons and over one thousand reactions. The reactions in REAL range from two to four components and the number of synthons per R-group range from the single digits to tens of thousands. In total, the REAL library describes chemical space of over 16 billion commercially available compounds{" f Note that this 16 billion compound library is relatively small compared to over-trillion compound libraries that are commercially available today; we use this more modest library size as it makes comparisons to other approaches tractable.
Training During training, we sample subsets of the library as follows. Of the roughly 1300 reaction types in the REAL database, we first uniformly sample 20 reactions at random, and subsequently sample 100 products per reaction, including the associated synthons in the library subset. These library subsets therefore deseribe roughly 300K-1.5M compounds each, which is significantly smaller than the complete library of 16 billion compounds. See Algorithm in the Appendix for details.
Testing For test-time inference, we decode with respect to the full library of 16 billion compounds. This constitutes a test-time distribution shift relative to training, but we observed that CSLVAE generalizes remarkably well to the full library without modifications. For completeness, we include an analysis of the test-time distribution shift in the Appendix (Supplementary Figure 2). In the forthcoming analyses, we share results when performing inference on the full library, as this is our primary objective.
4.1 Molecular reconstruction and generation
Table 1: Comparison of RationaleRL, VAE, and CSLVAE (ours) synthon-basee generative
modeling.
JT. VAV
RationaleRL
CSLVAE (ours)
# Parameters
4.7M
3.4M
380K
Validity
100.0%
100.0%
100.0%
Uniqueness
80.1%
96.3%
98.8%
Average likelihood
18.7%
62.3%
72.4%
In-library proportion
2.9%
50.9%
100.0%
We compare CSLVAE against two state-of-the molecular graph generative models: JT-VAE 22 and RationaleRL (24). All three models were trained from scratch on the Enamine REAL library. Details on the experimental setup and architecture can found the Appendix.
In VAE molecular graphs are represented by junction trees over chemical fragments. Decoding proceeds by first generating the junction tree depth-firs manner, placing fragment in each node, and then subsequently orienting the fragments to match attachment points. RationaleRL, on the other hand, takes as imput a starting chemical fragment or rationale. The decoder's objective to complete the molecule in autoregressive fashion (one graph edit per step). In our setting, we take product from the library and remove all but one synthon, treating the resulting graph as the starting rationale. Thus, RationaleRL. is tasked with generating the missing synthon.
Table I summarizes the key findings. First, we note that our implementation of CSLVAE has roughly 10x fewer parameters than the two alternatives considered, owing to the inductive nature of the library encoder. All three methods achieve 100% chemical validity, but CSLVAE achieves this result without explicit validity checks. The average likelihood is computed by taking the average of per-compound reconstruction likelihoods across large number of products sampled from the library. This is a measure of how well the model is capable of reconstructing the full molecular graph (i.e., on average, interpreted how likely are we to reproduce the query molecule via the decoder) and can also loosely as measure of coverageereachability (i.e., what proportion of the library are we able to faithfully cover). Finally, we highlight the challenges existing graph generative models face when applied to ultra-large CSLs, namely that they struggle to reliably generate in-library compounds. For JT-VAE,
*e release subset of the library alongside our code for reproducing these experiments and to foster further research in the machine learning community applied to combinatorial synthesis libraries: httpp://giis trub. com/ wtt.wwssennc/saaee.e.ee.sessesee Data provided with permission from and attribution to Enam- ine Ltd.
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022055 02000
44
LAMOS
JUOH2 GaSSi
2000
Figure 2: Latent space visualizations. Panel A: Moving left to right in raster order, we linearly interpolate from the starting compound to the target compound. The immediately adjacent molecules reconstructions. Below each molecule are its Tanimoto similarities with the starting and target compound, respectively. Panel B: We sample two random directions the latent space around a query compound and visualize the decoded molecules spaced evenly on the resulting 2D plane.
fewer than in 34 compounds were found in REAL. RationaleRL, on the other hand, generates in-library completions in only about half of the cases (see Supplementary Figure 1 in the Appendix), but has the advantage that it is provided a starting rationale in the form of a compound from REAL stripped of all but one synthon. In contrast, CSLVAE is guaranteed stay the library by design.
4.2 Latent space visualizations
Next, we qualitatively inspect the latent space learned by CSLVAE. In particular, are interested in verifying whether the proposed model has learned a latent space which varies relatively smoothly the covered chemical space (i.e., that small perturbations the query induce only minor edits in the resulting molecular graph). We perform two kinds of checks: latent space interpolations and local neighborhood visualizations.
Panel A of Figure 2 contains an example of interpolations in the latent space. In particular, we interpolate the molecular queries for the starting compound (top left) and target compound (bottom right), in raster order. The molecules immediately adjacent to the starting and target compounds are the associated reconstructions. Products decoded with respect to the full REAL library of 16 billion compounds. Below each molecule are its Tanimoto similarity with the starting and target molecule, respectively. We observe that the interpolations traverse through regions of chemical space that gradually decrease (cf. increase) in similarity with respect to the starting (cf. target) compound.
Panel B of Figure 2 visualizes the latent space around randomly sampled product from the REAL library. Following prior work (28), we form a random 2D plane the high-dimensional latent space by sampling two random directions around the molecular query (center compound) and decoding the resulting products using the argmax decision rule. We observe that the latent space is smooth the sense that molecules morph gradually, with only minor edits when the movement in latent space is small (c.g., one synthon at a time, modifications to smaller functional groups), and that the molecular scaffold is generally conserved locally.
4.3 Analogue retrieval via autoencoding
Lastly, we utilize CSLVAE to find analogues of query compound in a large CSL. In Figure 3 we present the model with two molecules: one which is in the library (left) and one which is not the library (right). Given the molecular query, generate conditionally random completions from the
'The Tanimoto similarity 3 is calculated by taking the intersection-owee over---vvooooon between a pair of bit vectors describing each molecule using hash called molecular fingerprint [5]

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aoour
di
giiones
3480
07900
0800
26017
0881
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0 Goy
14903
1800
6400
8734
Figure 3: Analogue retrieval via autoencoding. Each query molecule (top left) is encoded and stochastically decoded fifteen times. Below each molecule is its Tanimoto similarity with the query molecule. Left: Autoencoding molecule contained in the library. Right: Autoencoding molecule not contained in the library.
decoder. In both cases, autoencoding retrieved highly similar compounds as measured by Tanimoto similarity. For the in-library example, we note that the model is able to successfully retrieve the query compound (third row, second column). Moreover, we find many instances in which autoencoding returns compounds that have the same reaction type as the query molecule, but vary in one or two synthons. For the out-of-library example, we note that CSLVAE finds skeletally relevant compounds with high Tanimoto similarity, indicating the promise of this approach for fast analogue search in large non-ennmerable) libraries.
Closing remarks
We proposed the combinatorial synthesis library variational auto-encoder, or CSLVAE, a new graph- based generative model for the navigation of combinatorial synthesis libraries. CSLVAE utilizes minimal autoregression, permitting efficient generation of large molecular graphs and improving scalability. Compounds generated by CSLVAE are chemically valid and cost-effectively accessible. CSLVAE is a neural database providing random access to non-enumerable libraries. In experiments, demonstrate the capabilities of CSLVAE in modeling ultra-large and realistic make-on-demand libraries, paving a path towards more scalable strategies in the exploration non-enumerable chemical libraries for early-stage drug discovery. Our method can be combined with established techniques for molecular optimization as future direction.
Our approach has some limitations; here, we highlight three. First, the synthon lookup in the decoder scales linearly with the number of synthons in an R-group, which can present challenges as libraries continue to add many synthons per R- E-group. This could be mitigated with more scalable query-kst designs [0 25), but is not considered here. Furthermore, CSLVAE may face difficulties in the pres- of prominent R g-group symmetry (c.g., as in polymers). The decoder would require modifications to break parity, but may not admit the same convenient parallelization. Lastly, softmax has limitations in mapping from realevalued potentials choice probabilities due to its rigid substitution patterns [52]: sparse or alternative-awar softmax variants may be preferable, but are not considered this paper. In future work, we intend to address these shortcomings and look applications in virtual high throughput screening.
Acknowledgments and Disclosure of Funding
This work is sponsored by Atomwise Inc. The authors would like to give special acknowledgement to Christian Laggner, Ho Leung Ng, Srimukh Prasad, Adrian Stecula, and Brad Worley for discussions and helpful suggestions.
10

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Checklist
1. For all authors...
(a) Do the main claims made in the abstract and introduction accurately reflect the paper's
contributions and scope? [Yes]
(b) Did you describe the limitations of your work? [Yes]
(c) Did you discuss any potential negative societal impacts of your work? [No]
(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes]
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(c) Did you report error bars (e.g., with respect to the random seed after running experi- ments multiple times)? [No]
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15


Reviews:
[{"review_id": "Wu4NfgP8Oyd", "reviewer": "Reviewer_UvPu", "summary": "The present paper is concerned about learning a neural representation of a combinatorial synthesis library, whose size is now exploding and which is difficult to use for virtual screening due to its massive size.\n\nThe idea is to construct a generative model of a molecule that receives a continuous vector and outputs a molecule that is constructed by using the combinatorial synthesis library.\nIn particular, the proposed model named CSLVAE consists of a library encoder, a molecular encoder, and a molecular decoder.\nThe library encoder is used to encode the combinatorial synthesis library into keys of reactions and synthons, which are used to retrieve them during generation. The molecular encoder receives a molecular graph and outputs a continuous feature representation of it. The molecular decoder receives a continuous feature vector and constructs a molecule by first retrieving a reaction using the query constructed from the feature vector and the keys defined by the library encoder, and then, retrieving synthons in a similar way.\n\nThe authors empirically compare CSLVAE with baseline methods to show that CSLVAE can generate molecules in the library, whereas the baseline methods cannot. The authors also conduct qualitative analyses to discuss the benefit of CSLVAE.", "questions": "1. I would appreciate it if the authors could provide more detailed explanations in the preliminaries section.", "limitations": "The authors discussed several limitations of the proposed method in terms of computational efficiency, which are reasonable.", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "# Strengths\n- Originality: The problem setting to construct a neural database is interesting. While most of the researchers in the community would consider their generative model of molecules as a neural database for virtual screening, the idea of approximating the existing database is not very common.\n- Quality: The model proposed is sound.\n\n# Weaknesses\n- Clarity: One weakness is the presentation issue. I had trouble reading the preliminaries section (Section 3.1), because i) many of the objects ($T$, $R$, $S$, $X$, $\\mathcal{P}(\\cdot)$, etc.) are not explicitly defined, and ii) technical concepts such as R-group, group, _multi-component_ reaction, and synthon chain are not defined in the paper (and I could not find \"R-group\" in reference [42]). Since the main audience of the NeurIPS conference is not fully aware of the terminology in drug discovery, it would be very helpful (at least to me!) to explain these concepts with some examples.\n- Quality: The empirical studies are limited. Since CSLVAE will be used as a substitute for the original CSL, it is necessary to demonstrate its capability by applying CSLVAE to some realistic tasks to see the computational efficiency and potential performance degradation as compared to the baseline method using the original CSL. Without such an application, the neural database concept suggested in the paper cannot be appreciated.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "5y280IFUvh", "reviewer": "Reviewer_16PZ", "summary": "This paper describes a method called CLSVAE that generates combinatorial libraries of small molecules using a continuous underlying representation. The authors demonstrate the forward and reverse query in such a library.\n", "questions": "\nCan the authors please make a compelling case for this model by demonstrating a usecase that would be onerous with a different toolchain and now becomes accessible?  In the absence of such a demonstration I don't know how to judge the significance of this work and thus feel compelled to reject it from the current conference.  \n\nHow does the reverse search for synthons work when there are degenerate ways to synthesize the same molecule?  Could the authors provide a subset of statistical results for only such molecules?\n\n[Edit: I've updated my score in part due to the additional effort by the authors.  The degeneracies can be significantly more common in large libraries than what the authors suggest.  Also, there are additional ways to find analogues rapidly, and even faster than the current speed the authors demonstrate.  However, the overall ideas are useful and might be worthy of publication.]", "limitations": "The authors address some of the possible technical limitations of this work.  There are no negative societal implications of this work.", "rating": 5, "confidence": 2, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "\nThis work is original, is of reasonable quality, of mixed clarity, and of unclear significance.  \nThe high level idea behind the paper appears reasonable, although the code is currently not provided so it is hard to judge the reproducibility or generalizability of this work in practice (the authors say that they would provide code if this work was accepted).  The description of the method is clear and the math makes sense to me.  The main weakness of this work, however, is that it does not appropriately motivate the rationale behind it so I cannot judge if this is actually significant in practice or not.\n\nIn the presence of the chemical reactions, the forward problem of generating a molecule from the given synthons is actually trivially accomplished with the current methods. The inverse problem of finding the synthons from the molecule is somewhat interesting, though it does not appear a priori difficult to solve with existing methods (though there might be more trial and error involved than with a differentiable code). Perhaps the main point of this work then is that there is some simplification in the search for similar molecules, e.g. during the phase of SAR by catalogue, though it is hard to imagine that such the exhaustive search would be difficult if one limited the library to only those with common disynthons to the full molecule and it is not clear how accurate the search in this latent space actually is. Although it is good to see comparisons with prior generic generators, obviously the main contribution of such molecular generators is that they can in principle access a space much richer than the limited space of enumerable combinatorial libraries (even if the latter soon will exceed 10^12 molecules in size).  \n", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "0KPblJOrcZ", "reviewer": "Reviewer_JV4f", "summary": "Generative modelling of chemicals relies on generated molecules being valid and synthesizable. Often however, due to the size of combinatorial synthesis libraries, it is enough to look for hits in a library (also to forgo synthesizing a molecule oneself). Such libraries can often be (relatively) compactly described as the products of a set of starting reagents and reactions. The authors of this paper build a generative model of molecules in a large combinatorial synthesis library that embeds all molecules in a latent space.\n\nThe authors demonstrate that examples of graph generative models cannot fit the distribution of synthesizable sequences, with much of their support landing on molecules outside of the library. They show their method has a large support, generating many unique molecules, and supports a large part of the library, having a large likelihood on much of the molecules, all of this compared to examples of graph generative models.\n\nThe authors conclude by demonstrating that the latent space is continuous with respect to Tanimoto similarity, presumably making it good for semi-supervised learning.", "questions": "See weaknesses above.", "limitations": "The main limitation of the method is that it relies on a compact description of the library in terms of reactions and reagents. Expanding this method to the set of all commercially available reagents may be a challenge.\nAs well, should a group of reagents appear multiple steps in a reaction, the architecture of the model makes it likely that the same reagent will be selected for both steps. This hinders the ability of the model to fit some sets of molecules, such as polymers.\nThe authors acknowledge the above limitations in their work.", "rating": 7, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 4, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n1) The authors introduce a generative model that is guaranteed to output molecules in a given library.\n2) The authors demonstrate that embeddings of molecules in the library are continuous and so the generative model can be used for optimization or semi-supervised molecular design.\n3) The authors demonstrate that state of the art methods cannot be used to reliably generate within a library, motivating their model.\nThe method points to a novel approach to molecular design that is likely to be very useful to practitioners.\n\nWeaknesses:\n1) It is not checked that deep language models, which now are able to reach >90% synthesizability, can fit combinatorial libraries.\n2) The primary weakness of the paper is the limited check that the latent space may be used for learning chemical features: comparing the performance of classifiers or optimization methods in the latent space of this models and the example graph-generative, and some language models would greatly strengthen the paper.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}]

Author rebuttal:

Decision: Accept