Systems and methods for query-based random access to virtual chemical combinatorial synthesis libraries

Abstract

The present disclosure relates to systems and methods for querying a combinatorial synthesis library comprising a plurality of compounds and representing a plurality of reaction types, wherein each reaction type maps to a plurality of reactants, and each reactant maps to a plurality of synthon, accepting a query to a molecular encoder model in the form of a single graph, thereby obtaining a query vector. The query vector is input into a reaction query generator model, thereby obtaining a first reaction type and a first plurality of reactants. Synthons for each reactant are determined by inputting the reactants into a synthon query generator model. A set of synthons is thus determined, each corresponding to a reactant in the first plurality of reactants. A molecular structure in a combinatorial synthesis library is identified, the combinatorial synthesis library comprising the set of synthons arranged according to synthesis rules related to the first reaction type.

Description

[0001] Cross Reference to Related Patent Applications

[0002] This application claims priority to U.S. Provisional Patent Application No. 63 / 342,574, filed May 16, 2022, entitled “GRAPH GENERATIVE MODEL FOR COMBINATORIAL SYNTHESIS LIBRARIES,” which is hereby incorporated by reference. TECHNICAL FIELD

[0003] The present disclosure relates generally to screening combinatorial synthesis libraries of analogs of interest. BACKGROUND

[0004] Virtual high-throughput screening (vHTS)

[47] has gained tremendous interest in early drug discovery, largely due to the on-demand manufacturing of chemical libraries constructed with combinatorial synthesis. These combinatorial synthesis libraries (CSLs) enable access to an ultra-large chemical space from a relatively small set of chemically accessible building blocks that can be combined according to known synthetic routines. In recent years, these libraries have grown from millions to billions, and now to tens of trillions of compounds [22, 33, 44, 58]. As a result, the size of virtual chemical libraries is rapidly approaching the limits of explicit enumeration, presenting new challenges for virtual screening. For example, the Enamine REadily AccessibLe (REAL) library

[20] leverages off-the-shelf molecular building blocks and parallel synthesis, allowing for a few weeks of turnaround time, and ushering in an era of ever-decreasing latency between in silico simulation and in vitro high-throughput screening.

[0005] Due to the combinatorial explosion of these construction implementations, early drug discovery has now “crossed the Rubicon” into the non-enumerated realm. This presents new challenges for in silico hit discovery and optimization, which rely on screening explicitly enumerated compounds. These methods are not well-suited for non-enumerated settings, which scale linearly with the number of compounds.

[0006] Virtual high-throughput screening and enumeration. Typically, the first step of a vHTS campaign is the preparation of a library of compounds for subsequent use [1, 17]. While composite sampling and scoring techniques have been developed

[18] , these approaches still rely on an exhaustive accessible library. An exception is the Virtual Synthetic Sublayer Enumeration Screening (V-SYNTHES) approach

[44] , which exploits the modular nature of parallel synthetic libraries. However, by design, V-SYNTHES does not allow for query-based random access. On the other hand, SpaceMACS

[45] and SpaceLight [4] can provide query-based access to modular libraries by decomposing queries into fragments and matching them to synthetic sublayers in the library through similarity search. In parallel to these efforts, machine learning has also received significant attention in vHTS: for predicting activity scores for a given docked conformation [15, 43, 57], for predicting activity scores for given ligands and proteins (undocked), respectively [38, 56], and for improving or completely replacing classical molecular docking with machine learning methods [39, 51, 52].

[0007] Deep learning approaches for molecule generation. De novo drug design plays an increasingly important role in identifying novel chemical substances in drug discovery campaigns [10, 36, 50, 54]. Two main neural network-based paradigms for molecule generation are text-based generative models and graph-based generative models. Early work on text-based generative models, also known as chemical language models, applied recurrent neural networks to SMILES strings [16, 46]. While these approaches have shown great promise and inspired interest in molecule generation within the ML community, they do not guarantee the production of valid SMILES strings. Methods have been proposed to exploit the grammatical constraints of the SMILES notation to improve validity [12, 29]; additionally, the recently introduced SELFIES notation [28, 37] guarantees validity and has been increasingly adopted. However, in both cases, there are known drawbacks to modeling with such text-based chemical substance representations (e.g., subjectivity, similar molecular structures can have large edit distances).

[0008] For some applications, it is meaningful to utilize generative models that can fit a database of molecules, allowing navigation of these databases by fitting the model. Previous work [2] investigated the ability of language models to adapt to a database of molecules, applying a deep language model to GDB-13 [7], a database of 975,000,000 compounds formed by exhaustively enumerating molecules of up to 13 atoms of the element types C, N, O, S, and CI, subject to simple rules of chemical stability and synthetic feasibility. The authors trained on 0.1% of the entire library and found that the model was able to cover approximately 70% of the compounds in the GDB-13 library. Furthermore, the language model they trained generated compounds that did not satisfy the GDB-13 construction in approximately 15% of cases.

[0009] In recent years, generative models of graphs have received a great deal of attention as an alternative to their text-based counterparts. The earliest of these models focused on generating a single graph of constant size

[48] or generating graphs of arbitrary size autoregressively one atom or bond at a time [32, 42, 60, 35]. These approaches also struggle to reliably produce chemically valid molecules and have difficulty with large molecular graphs.

[0010] To address both of these points, fragment-based generative models of graphs have been proposed and are gaining popularity [23, 24, 25, 27]. These models have the advantage of guaranteeing chemical validity by decomposing molecules into valid subcomponents and explicitly prohibiting the production of invalid combinations of fragments. Such explicit validity checks can be performed on every action, but at the cost of additional computation. While other generative models of text and graphs tend to struggle with large molecular graphs due to the long autoregressive chains needed to generate them, fragment-based generative models of graphs require autoregressive lengths comparable to the number of fragments comprising the molecule. This can be significant when the fragments themselves contain many atoms.

[0011] However, due to the general difficulty of autoregressive graph generation, some problems remain. Unlike language-based models, where the order of autoregressive sequences is less ambiguous (e.g., tokens are typically decoded in left-to-right order), graphs do not have such a canonical node order, which presents a challenge for graph-based autoregressive models [32, 59]. Furthermore, while they require shorter autoregressive chains than their counterparts, existing fragment-based generative models of graphs still require autoregressive lengths that grow with the overall size of the molecule, as autoregressive decoding cannot be effectively parallelized.

[0012] While fragment-based graph generative models and SELFIES-based language models each address the chemical validity problem, synthetic accessibility presents separate challenges. Previous work has raised questions about the synthetic feasibility of compounds proposed by many existing generative models

[13] , which, if not addressed appropriately, can limit the practical utility of these models in drug discovery applications. Subsequent work has attempted to improve these shortcomings by: (i) including explicit penalties for synthetic inaccessibility through a scoring function

[19] , (ii) limiting the model to fragments of known compounds [34, 40, 53], or (iii) inducing bias towards simple and known synthetic routes [8, 9, 21].

[0013] In view of the foregoing background, there is a need in the art for scalable methods for navigating CSLs with query-based random access. SUMMARY

[0014] The present disclosure addresses the aforementioned needs in the art. Systems and methods for a combined synthesis library of compounds and representing reaction types, where each reaction type maps to a plurality of reactants, and each reactant maps to a plurality of synthon. The system takes a query in the form of a single graph into a molecule encoder model, resulting in a query vector. The query vector is input into a reaction query generator model, resulting in a first reaction type and a first plurality of reactants. Synthons for each reactant are determined by inputting the reactants into a synthon query generator model. A set of synthons is thus determined, each corresponding to a reactant in the first plurality of reactants. Molecular structures in a combined synthesis library are identified, the combined synthesis library comprising a set of synthons arranged according to synthesis rules related to the first reaction type.

[0015] In one embodiment, the molecule encoder model is a graph-based generative model that leverages the structure of the CSL to provide efficient navigation of the relevant chemical space. The model learns the key hierarchy on the library components and uses these keys to process queries for retrieval. The encoder processes a molecular graph and returns a query vector as output, which the decoder uses to retrieve molecules from the CSL through a sequence of efficient query-key comparisons that leverage the hierarchical structure of the CSL, require minimal autoregression, and allow efficient parallelization. In such embodiments, the graph-based generative model acts as a “neural database” that provides random access to an ultra-large, non-enumerable library of compounds. As a result, the model provides efficiently and cost-effectively accessible molecules. Furthermore, the model overcomes the challenge of long autoregressive chains in compound generation, improving the scalability of large molecular graphs. Moreover, relative to comparable approaches, the model reduces the number of parameters by a factor of ten and provides a substantial improvement in the computational complexity of searching through the CSL.

[0016] Systems and methods for querying a combinatorial synthesis library are provided. The combinatorial synthesis library includes a plurality of compounds and represents a plurality of reaction types. Each respective reaction type of the plurality of reaction types has a corresponding mapping to a corresponding plurality of reactants. Each respective reactant of each corresponding plurality of reactants has a corresponding mapping to a corresponding plurality of syntheses.

[0017] In some such embodiments, the plurality of reaction types includes one or more reaction types, and the combinatorial synthesis library includes one or more compounds for each reaction type of the plurality of reaction types.

[0018] A molecular query is input into a molecular encoder model. The query is graph-based. The molecular encoder model includes a message passing neural network that includes a plurality of message passing layers that collectively include a first plurality of parameters. Inputting the graph-based query into the molecular encoder model produces a query vector as an output of the molecular encoder model by applying the first plurality of parameters to the graph-based query

[0019] In some such embodiments, the graph-based query is a single graph that includes a plurality of nodes and a plurality of edges, where each node of the plurality of nodes is connected to another node of the plurality of nodes by at least one edge of the plurality of edges.

[0020] In some such embodiments, each respective node of the plurality of nodes is associated with: (i) a corresponding element type of a plurality of element types, (ii) a node degree of a plurality of node degrees, (iii) a hybridization of a plurality of hybridizations, (iv) a plurality of bonded hydrogens, (v) a formal charge of a set of formal charges, and (vi) a binary indication of aromaticity.

[0021] In some such embodiments, each respective bond of the plurality of bonds is associated with: (i) a bond type, (ii) a binary indication of conjugation, (iii) a binary indication of whether the respective bond is within a ring, and (iv) an indication of stereochemistry.

[0022] In some such embodiments, the graph can be an arbitrary graph representing a single molecular compound, where such single molecular compound is present in the combinatorial synthesis library.

[0023] In some such embodiments, the graph represents a weighted composition of a first graph of a first molecular compound and a second graph of a second molecular compound.

[0024] In some such embodiments, the single graph represents a weighted composition of a plurality of graphs of a second plurality of compounds, where the second plurality of compounds have a common property.

[0025] In some such embodiments, the common property is a valley distance to each other compound of the second plurality of compounds that is less than a threshold value.

[0026] In some such embodiments, the common property is a binding coefficient to the macromolecular target that is less than a threshold value.

[0027] The query vector is input into a reaction query generator model that includes a second plurality of parameters. This results in an output from the reaction query generator model 116 from a first reaction type of a plurality of reaction types by applying the second plurality of parameters to the query vector.

[0028] In some such embodiments, the reaction query generator model is a two-layer perceptron with intermediate ReLU activations.

[0029] In some such embodiments, the output from the reaction query generator model is used to identify, by a first query key lookup, a first reaction key type of a plurality of reaction key types, where each reaction key type of the plurality of reaction key types represents a synthesis reaction that can be used to synthesize one or more compounds in a combinatorial synthesis library.

[0030] A corresponding synthesis sub is determined for each respective reactant of the first plurality of reactants corresponding to the first reaction type from a corresponding plurality of synthesis subs mapped to the respective reactant by inputting the respective reactant 86 into a synthesis sub query generator model that includes a third plurality of parameters, thereby obtaining the corresponding synthesis sub as an output of the synthesis sub query generator model by applying the third plurality of parameters to the respective reactant. This results in a set of synthesis subs, each synthesis sub in the set of synthesis subs corresponding to a reactant of the first plurality of reactants.

[0031] In some such embodiments, the synthesis sub query generator model is a two-layer perceptron with intermediate ReLU activations.

[0032] In some such embodiments, the output from the synthesis sub query generator model is used to identify, by a second query key lookup, a synthesis sub key for the corresponding synthesis sub.

[0033] In some such embodiments, the first plurality of parameters includes 100,000 parameters, the second plurality of parameters includes 5,000 parameters, and the third plurality of parameters includes 5,000 parameters.

[0034] In some such embodiments, the first plurality of reactants includes three or more reactants, and the corresponding mapping of the corresponding plurality of synthesis subs for a reactant of the three or more reactants includes ten or more synthesis subs.

[0035] A molecular structure (compound) is identified in a combinatorial synthesis library, e.g., the combinatorial synthesis library includes a set of synthesis subs arranged according to synthesis rules related to the first reaction type.

[0036] In some such embodiments, the plurality of compounds in the combinatorial synthetic library comprises one billion or more compounds, and the identified molecular structure is any one of the one billion or more compounds that satisfy the query.

[0037] In some such embodiments, the plurality of compounds in the combinatorial synthetic library comprises one trillion or more compounds, and the identified molecular structure is any one of the one trillion or more compounds that satisfy the query. BRIEF DESCRIPTION OF DRAWINGS

[0038] In the drawings, embodiments of the systems and methods of the present disclosure are shown by way of example. It is to be expressly understood that the description and drawings are for purposes of illustration only and as an aid to understanding, and are not intended as a definition of the limits of the systems and methods of the present disclosure.

[0039] Figure 1A and 1B A computer system according to some embodiments of the present disclosure is shown.

[0040] Figure 2A , 2B , 2C, and 2D show methods for querying a combinatorial synthetic library according to some embodiments of the present disclosure, where dashed boxes represent optional elements

[0041] Figure 3A , 3B , 3C, 3D, 3E, 3F, 3G, and 3H collectively show an overview of systems and methods for screening a library of compounds according to some embodiments of the present disclosure. Figure 3A : A combinatorial synthetic library consists of a potentially large number of tables describing multi-component reactions. An example two-component reaction is illustrated with four synthons per group, resulting in sixteen product chemical spaces. Such a constructed library can describe a large accessible chemical space through combinatorial explosion, greatly accelerating early drug discovery. Figure 3B : An example efficient graph generation model was developed and used for navigation of a hyper-large combinatorial synthetic library. At a high level, the example model first encodes a molecule (represented as a graph) through a GNN encoder. Given the molecule representation, a decoder generates a query to the synthetic-based library for retrieval. The decoder is constructed in such a way that retrieval is fast and efficient. Figure 3C : The library encoder starts with learning a representation of each synthon (e.g., 88-1, 88-2, 88-3, 88-4) through a synthon encoder (GNN), represented as a molecular graph. The synthon representation is used to generate a key for each synthon through a multi-layer perceptron (MLP). Figure 3D : Moving up the hierarchy, a group representation is learned through a set of neural networks that operate on the representations of the synthons belonging to each group. Figure 3ESimilarly, the reaction representation is learned by a set of neural networks operating on representations of constituent groups. The reaction key is also generated from the reaction representation by an MLP. Figure 3F The molecule encoder is a graph neural network that takes a molecule graph as input and produces a molecule key as output, which is used to query the library of synthon-based. Figure 3G To reconstruct an input molecule, first a reaction query is generated from the molecule key, which is then compared to the reaction keys to sample a reaction type. Figure 3H Next, a synthon query is independently generated for each group using the molecule key, reaction representation, and group representation (e.g., without self-attention), which is compared to the synthon keys to sample a synthon (e.g., 98-1, 98-2, 98-3, 98-4, 98-5, 98-6, 98-7, and 98-8).

[0042] Figure 4A and 4B Together show interpolation in latent space according to embodiments of the present disclosure. Figure 4A Linear interpolation from start molecule to target molecule moving left to right in raster order. Below each molecule is its valley base similarity to the start and target molecules, respectively. Figure 4B Sampling two random directions in latent space around a queried compound and visualizing the decoded molecules as uniformly spaced on the resulting two-dimensional plane.

[0043] Figure 5A and 5B Together show analog autoencoding according to embodiments of the present disclosure. Each query molecule (indicated by a box in the upper left corner) is autoencoded and randomly decoded fifteen times according to the systems and methods of the present disclosure. Below each molecule is its valley base similarity to the query molecule. Figure 5A Molecules contained in the autoencoding library. Figure 5B Molecules not contained in the autoencoding library.

[0044] Figure 6 shows synthon according to the prior art.

[0045] Figure 7 Show how the in-library ratio of generated samples from RationaleRL decreases rapidly as the number of different reactions present in the training increases, falling below 50% after including only 50 reactions.

[0046] Figure 8 Show how the test time distribution shifts according to library size according to some embodiments of the present disclosure.

[0047] Figure 9 Show the post-hoc density estimation process according to some embodiments of the present disclosure.

[0048] Figure 10 A list of 2021 US Federal Drug Administration new drug approvals used in the simulated comparison is shown in accordance with some embodiments of the present disclosure.

[0049] Figure 11 A comparison of CSLVAE to Arthor in a prior 1 simulated search is shown in accordance with some embodiments of the present disclosure.

[0050] In the several views of the drawings, like reference numerals designate corresponding parts throughout the several views. DETAILED DESCRIPTION

[0051] Reference will now be made in detail to embodiments, examples of which are illustrated in the accompanying drawings. In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the present disclosure. However, it will be apparent to one of ordinary skill in the art that the present disclosure can be practiced without these specific details. In other instances, well-known methods, procedures, components, circuits, and networks have not been described in detail so as not to unnecessarily obscure aspects of the embodiments.

[0052] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs. All patents and publications referred to herein are incorporated by reference in their entirety.

[0053] Definitions.

[0054] As used herein, the terms "administer," "administration," and "administering" mean (1) to provide, give, dose, and / or prescribe, by a health practitioner or his or her authorized agent or under his or her direction, in accordance with the present disclosure; and / or (2) to be taken, ingested, or consumed by a mammal, in accordance with the present disclosure.

[0055] As used herein, the terms "co-administration," "co-administering," "administered in combination with," "administering in combination with," "simultaneous," and "concurrent" encompass administration of two or more active pharmaceutical ingredients to a subject such that the active pharmaceutical ingredients and / or their metabolites are present in the subject at the same time. Co-administration includes administration in separate compositions at the same time, administration in separate compositions at different times, or administration in a composition in which two or more active pharmaceutical ingredients are present. Simultaneous administration in separate compositions and administration in a composition in which both drugs are present are preferred.

[0056] The terms "active pharmaceutical ingredient" and "drug" include the compounds described herein and any pharmaceutically acceptable analog, derivative, salt, solvate, hydrate, co-crystal, or prodrug thereof. The terms "active pharmaceutical ingredient" and "drug" can also include those compounds described herein and any pharmaceutically acceptable analog, derivative, salt, solvate, hydrate, co-crystal, or prodrug thereof that binds to a molecule of interest.

[0057] The term "in vivo" refers to an event occurring in the body of a subject.

[0058] The term "in vitro" refers to an event occurring outside the body of a subject. In vitro assays encompass cell-based assays in which live or dead cells are used, and can also encompass cell-free assays in which intact cells are not used.

[0059] As used herein, the term "if' can be interpreted to mean "when" or "upon" or "in response to a determination" or "in response to a detection," depending on the context. Similarly, the phrase "if determined" or "if [stated condition or event] is detected" can be interpreted to mean "upon a determination that" or "in response to a determination that" or "upon a detection that" or "in response to a detection that," depending on the context.

[0060] The term "effective amount" or "therapeutically effective amount" refers to the amount of a compound or combination of compounds described herein that is sufficient to achieve the intended application, including but not limited to the treatment of a disease. The therapeutically effective amount can vary depending on the intended application (in vitro or in vivo) or the subject and condition being treated (e.g., the subject's weight, age, and sex), the severity of the condition, the manner of administration, and the like, as can be readily determined by one of ordinary skill in the art. The term also applies to a dose that will induce a specific response in target cells. The specific dose will vary depending on the particular compound chosen, the dosing regimen being followed, whether the compound is being administered in combination with other compounds, the timing of administration, the tissue to which it is being administered, and the physical delivery system with which the compound is carried.

[0061] The term "therapeutic effect" as used herein encompasses therapeutic benefit and / or prophylactic benefit. Prophylactic benefit includes delaying or eliminating the appearance of a disease or condition, delaying or eliminating the onset of symptoms of a disease or condition, ameliorating, arresting or reversing the progression of a disease or condition, or any combination thereof.

[0062] The term "pharmaceutically acceptable salt" refers to salts derived from a variety of organic and inorganic counter ions well known in the art. Pharmaceutically acceptable acid addition salts can be formed with inorganic acids and organic acids. Preferred inorganic acids which can be employed to form salts include, for example, hydrochloric acid, hydrobromic acid, sulfuric acid, nitric acid, and phosphoric acid. Preferred organic acids which can be employed to form salts include, for example, acetic acid, propionic acid, glycolic acid, pyruvic acid, oxalic acid, maleic acid, malonic acid, succinic acid, fumaric acid, tartaric acid, citric acid, benzoic acid, cinnamic acid, mandelic acid, methanesulfonic acid, ethanesulfonic acid, p-toluenesulfonic acid, and salicylic acid. Pharmaceutically acceptable base addition salts can be formed with inorganic and organic bases. Inorganic bases which can be employed to form salts include, for example, sodium, potassium, lithium, ammonium, calcium, magnesium, iron, zinc, copper, manganese, and aluminum. Organic bases which can be employed to form salts include, for example, primary, secondary, and tertiary amines, substituted amines, including naturally occurring substituted amines, cyclic amines, and basic ion-exchange resins. Particular examples include isopropylamine, trimethylamine, diethylamine, triethylamine, tripropylamine, and ethanolamine. In some embodiments, the pharmaceutically acceptable base addition salt is selected from the group consisting of an ammonium salt, a potassium salt, a sodium salt, a calcium salt, and a magnesium salt. The term "co-crystal" refers to a molecular complex derived from a variety of co-crystal formers known in the art. Unlike a salt, a co-crystal typically does not involve a hydrogen transfer between the co-crystal former and the drug, but rather involves intermolecular interactions between the co-crystal former and the drug in the crystal structure, such as hydrogen bonding, aromatic ring stacking, or dispersion forces.

[0063] "Pharmaceutically acceptable carrier" or "pharmaceutically acceptable excipient" is intended to include any and all solvents, dispersion media, coatings, antibacterial and antifungal agents, isotonic and absorption delaying agents, and inert ingredients. The use of such pharmaceutically acceptable carriers or pharmaceutically acceptable excipients in active pharmaceutical ingredients is well known in the art. Except insofar as any conventional pharmaceutically acceptable carrier or pharmaceutically acceptable excipient is incompatible with the active pharmaceutical ingredient, its use in the therapeutic compositions of the present disclosure is contemplated. Additional active pharmaceutical ingredients, such as other drugs disclosed herein, can also be incorporated into the described compositions and methods.

[0064] When a range is used to describe, for example, a physical or chemical property, such as a molecular weight or chemical formula, all combinations and subcombinations of ranges, and specific embodiments therein, are intended to be included. When referring to a numerical or numerical range, the use of the term "about" means that the numerical or numerical range referred to is an approximation within experimental variability (or statistical experimental error), and thus the numerical or numerical range can vary. The variation is typically 0% to 15%, or 0% to 10%, or 0% to 5% of the quantity or numerical range described. The term "comprising" (and related terms such as "comprise" or "comprises" or "including" or "includes") encompasses those embodiments, such as "consisting of" or "consisting essentially of" the features recited in any combination of the compositions of matter, methods, or processes.

[0065] As used interchangeably herein, the term“classifier” or“model” refers to a machine learning model or algorithm.

[0066] In some embodiments, the“model” is a supervised machine learning. Non-limiting examples of supervised learning algorithms include, but are not limited to, logistic regression, neural networks, support vector machines, naive Bayes algorithms, nearest neighbor algorithms, random forest algorithms, decision tree algorithms, boosting tree algorithms, multinomial logistic regression algorithms, linear models, linear regression, gradient boosting, mixture models, hidden Markov models, Gaussian NB algorithms, linear discriminant analysis, or any combination thereof. In some embodiments, the classifier is a multinomial classifier algorithm. In some embodiments, the model is a 2-stage stochastic gradient descent (SGD) model. In some embodiments, the model is a deep neural network (e.g., a deep and wide sample-level classifier).

[0067] Neural networks. In some embodiments, the model is a neural network (e.g., a convolutional neural network and / or a residual neural network). Neural network algorithms, also known as artificial neural networks (ANN), include convolutional and / or residual neural network algorithms (deep learning algorithms). Neural networks can be machine learning algorithms that can be trained to map an input dataset to an output dataset, where the neural network includes an interconnected group of nodes organized into multiple layers. For example, a neural network architecture can include at least an input layer, one or more hidden layers, and an output layer. Neural networks can include any total number of layers and any number of hidden layers, where the hidden layers serve as trainable feature extractors that allow a set of input data to be mapped to one or a set of output values. As used herein, a deep learning algorithm (DNN) can be a neural network that includes multiple hidden layers, e.g., two or more hidden layers. Each layer of a neural network can contain multiple nodes (or“neurons”). Nodes can receive inputs directly from input data or from the output of a previous layer of nodes and perform a particular operation, e.g., a summation operation. In some embodiments, connections from inputs to nodes are associated with parameters (e.g., weights and / or weighting factors). In some embodiments, a node can apply an activation function to all inputs x iand a product sum of associated parameters. In some embodiments, the weighted sum is offset by a bias b. In some embodiments, an output of a node or neuron can be gated using a threshold or activation function f, which can be a linear or non-linear function. The activation function can be, for example, a rectified linear unit (ReLU) activation function, a leaky ReLU activation function, or other functions such as a hyperbolic tangent function, an identity function, a binary step function, a logistic function, an arcTan function, a softsign function, a parametric rectified linear unit function, an exponential linear unit function, a softPlus function, a bent identity function, a softExponential function, a Sinusoid function, a Sine function, a Gaussian function, or a sigmoid function, or any combination thereof.

[0068] The weight factors, bias values, and threshold values or other computational parameters of the neural network can be“taught” or“learned” using one or more sets of training data during a training phase. For example, the parameters can be trained using input data from a training data set and a gradient descent or backpropagation method such that the output values of the ANN computation are consistent with instances included in the training data set. The parameters can be obtained from a backpropagation neural network training process.

[0069] According to the present disclosure, any of a variety of neural networks can be applicable. Examples can include, but are not limited to, feedforward neural networks, radial basis function networks, recurrent neural networks, residual neural networks, convolutional neural networks, residual convolutional neural networks, etc., or any combination thereof. In some embodiments, the machine learning utilizes a pre-trained and / or transfer learning ANN or deep learning architecture. Convolutional and / or residual neural networks can be used according to the present disclosure.

[0070] For example, a deep neural network classifier includes an input layer, a plurality of individually parameterized (e.g., weighted) convolutional layers, and an output scorer. The parameters (e.g., weights) of each convolutional layer, as well as the input layer, contribute to the plurality of parameters (e.g., weights) associated with the deep neural network classifier. In some embodiments, at least 100 parameters, at least 1000 parameters, at least 2000 parameters, or at least 5000 parameters are associated with the deep neural network classifier. As a result, deep neural network classifiers require the use of a computer, as they cannot be solved by the mind. In other words, in such embodiments, the output of the classifier given the input to the classifier needs to be determined using a computer, rather than by thought. See, e.g., Krizhevsky et al., 2012, “Imagenet classification with deep convolutional neural networks”, in Advances in Neural Information Processing Systems 2, edited by Pereira, Burges, Bottou, Weinberger, pp. 1097-1105, Curran Associates, Inc.; Zeiler, 2012 “ADADELTA: an adaptive learning rate method”, CoRR, vol. abs / 1212.5701; and Rumelhart et al., 1988, “Neurocomputing: Foundations of research”, Chapter Learning Representations by Back-propagating Errors, pp. 696-699, Cambridge, MA, USA: MIT Press, each of which is hereby incorporated by reference.

[0071] For example, Vincent et al., 2010, "Stacked denoising autoencoders: Learning useful representations in a deep network with a local denoising criterion", J Mach Learn Res 11, pp. 3371-3408, disclose neural network algorithms, including convolutional neural network algorithms, suitable for use as classifiers; Larochelle et al., 2009, "Exploring strategies for training deep neural networks", J Mach Learn Res 10, pp. 1-40; and Hassoun, 1995, Fundamentals of Artificial Neural Networks, Massachusetts Institute of Technology, each of which is hereby incorporated by reference. Additional example neural networks suitable for use as classifiers are disclosed in Duda et al., 2001, Pattern Classification, 2nd Edition, John Wiley & Sons, Inc., New York; and Hastie et al., 2001, The Elements of Statistical Learning, Springer-Verlag, New York, each of which is hereby incorporated by reference. Additional example neural networks suitable for use as classifiers are also described in Draghici, 2003, Data Analysis Tools for DNA Microarrays, Chapman & Hall / CRC; and Mount, 2001, Bioinformatics: sequence and genome analysis, Cold Spring Harbor Laboratory Press, Cold Spring Harbor, New York, each of which is hereby incorporated by reference.

[0072] As used herein, the term "parameter" refers to any coefficient or similar value of an internal or external element (e.g., weights and / or hyperparameters) in an algorithm, model, regressor, and / or classifier that can affect (e.g., modify, customize, and / or adjust) one or more inputs, outputs, and / or functions in the algorithm, model, regressor, and / or classifier. For example, in some embodiments, a parameter refers to any coefficient, weight, and / or hyperparameter that can be used to control, modify, customize, and / or adjust the behavior, learning, and / or performance of an algorithm, model, regressor, and / or classifier. In some cases, parameters are used to increase or decrease the influence of inputs (e.g., features) on an algorithm, model, regressor, and / or classifier. As a non-limiting example, in some embodiments, parameters are used to increase or decrease the influence of nodes (e.g., in a neural network), where nodes include one or more activation functions. The assignment of parameters to a particular input, output, and / or function is not limited to any particular paradigm of a given algorithm, model, regressor, and / or classifier, but can be used for any suitable algorithm, model, regressor, and / or classifier architecture to achieve the desired performance. In some embodiments, parameters have fixed values. In some embodiments, the values ​​of the parameters are adjusted manually and / or automatically. In some embodiments, the values ​​of the parameters are modified through validation and / or training processes of the algorithm, model, regressor, and / or classifier (e.g., through error minimization and / or backpropagation methods). In some embodiments, the algorithms, models, regressors, and / or classifiers of this disclosure include multiple parameters. In some embodiments, the plurality of parameters is n parameters, wherein: n≥2; n≥5; n≥10; n≥25; n≥40; n≥50; n≥75; n≥100; n≥125; n≥150; n≥200; n≥225; n≥250; n≥350; n≥500; n≥600; n≥750; n≥1,000; n≥2,000; n≥4,000; n≥5,000; n≥7,500; n≥10,000; n≥20,000; n≥40,000; n≥75,000; n≥100,000; n≥200,000; n≥500,000; n≥1 x 10⁶; n≥5 x 10⁶ 6 , or n≥1x 10 7 Therefore, the algorithms, models, regressors, and / or classifiers of this disclosure cannot be mentally executed. In some embodiments, n is between 10,000 and 1 x 10⁷, between 100,000 and 5 x 10⁶, or between 500,000 and 1 x 10⁶. In some embodiments, the algorithms, models, regressors, and / or classifiers of this disclosure operate in a k-dimensional space, where k is a positive integer of 5 or greater (e.g., 5, 6, 7, 8, 9, 10, etc.). Therefore, the algorithms, models, regressors, and / or classifiers of this disclosure cannot be mentally executed.

[0073] For the avoidance of doubt, particular features described in connection with a particular aspect, embodiment or example of the disclosure (for example integers, features, values, uses, diseases, formulations, compounds or groups) are to be understood to be applicable to any other aspect, embodiment or example described herein unless incompatible therewith. Such features can therefore be used in any combination with any definition, claim or embodiment defined herein, where appropriate. All features and / or steps disclosed in the specification (including any accompanying claims, abstract and drawings) can be combined in any combination, except combinations where at least some of such features and / or steps are mutually exclusive. The disclosure is not limited to any particular detail of any disclosed embodiment. The disclosure extends to any novel one, or any novel combination, of the features disclosed in the specification (including any accompanying claims, abstract and drawings), or to any novel one, or any novel combination, of the steps of any method or process so disclosed.

[0074] Furthermore, as used herein the term "about" means that dimensions, sizes, formulations, parameters, shapes and other quantities and characteristics are not and need not be exact, but can be approximated and / or larger or smaller, as desired, reflecting tolerances, conversion factors, rounding off, measurement error and other factors and the like known to those of skill in the art. Amounts, sizes, formulations, parameters, shapes and other quantities and characteristics are thus not and need not be exact, but can be approximated and / or larger or smaller, as desired, reflecting tolerances, conversion factors, rounding off, measurement error and other factors and the like known to those of skill in the art. Typically a dimension, size, formulation, parameter, shape or other quantity or characteristic is "about" or "approximate" whether explicitly stated or not. Note that embodiments utilizing very different dimensions, shapes and sizes can employ the arrangements described.

[0075] Furthermore, the transitional terms "comprising", "consisting essentially of, and "consisting of, when used in the appended claims in either the open-ended or the closed- ended sense, shall not be construed to exclude additional claim elements or steps not specified as such in the claims, if any. The term "comprising" is intended to be descriptive and not to exclude any additional, unrecited elements, methods, steps or materials. The term "consisting of" excludes any element, step or material not specified in the claims, and in the latter case, excludes impurities normally associated with the specified material. The term "consisting essentially of" limits the scope of a claim to the specified elements, steps or materials, and those that do not materially affect the basic and novel characteristic(s) of the claimed application. Alternatively, all embodiments of the application can be more specifically defined by any of the transitional terms "comprising", "consisting essentially of, and "consisting of".

[0076] Figure 1A and 1BA computer system 100 for querying a combinatorial synthesis library is shown. See Figure 1A and 1B In typical embodiments, the computer system 100 comprises one or more computers. For purposes of explanation described in Figure 1A and 1B The computer system 100 is represented for purposes of explanation described in this disclosure as comprising a single computer that includes all of the functionality of the disclosed computer system 100. However, the present disclosure is not limited thereto. The functionality of the computer system 100 can be distributed across any number of networked computers and / or reside on each of several networked computers and / or virtual machines. Those skilled in the art will appreciate that various different computer topologies are possible for the computer system 100 and all such topologies are within the scope of the present disclosure.

[0077] With the foregoing in mind, turn to Figure 1A and 1B The computer system 100 includes one or more central processing units (CPUs) 64, one or more graphics processing units (GPUs) 74, a network or other communication interface 76, a user interface 68 (e.g., including an optional display 70 and optional keyboard 72 or other form of input device), a memory 58 (e.g., random access memory, persistent memory, or a combination thereof), one or more magnetic storage disk storage and / or persistent devices 60 optionally accessed by one or more controllers 62, one or more communication buses 12 for interconnecting the aforementioned components, and a power supply 66 for powering the aforementioned components. To the extent that the components of the memory 58 are not persistent, data in the memory 58 can be seamlessly shared with the non-volatile memory 60 using known computing techniques such as caching. The memory 60 can include mass storage that is located remotely with respect to the central processing unit 64. In other words, some data stored in the memory 58 and / or the memory 60 can actually be hosted on a computer external to the computer system 100, but can be electronically accessed by the computer system 100 over the Internet, an intranet, or other form of network or electronic cable using the network interface 76. In some embodiments, the computer system 100 utilizes models that run from memory associated with the one or more graphics processing units 74 to improve the speed and performance of the system. In some alternative embodiments, the computer system 100 utilizes models that run from the memory 58 rather than memory associated with the graphics processing units.

[0078] The memory 58 of the computer system 100 stores:

[0079] • an optional operating system 78 including procedures for handling various basic system services;

[0080] • a combinatorial synthesis library query model 80 for querying a combinatorial synthesis library;

[0081] • the combinatorial synthesis library 82 comprises a plurality of compounds 92, the combinatorial synthesis library representing a plurality of reaction types 82, each such reaction type indexed by a reaction type key 84 and having a corresponding mapping to a corresponding plurality of reactants, each respective reactant 86 in each such corresponding plurality of reactants having a corresponding mapping to a corresponding plurality of synthon 88, each such synthon indexed by a synthon key 90, such that each respective compound 92 is indexed by a reaction type key 94, which in turn can be used to determine a reactant 96 and a synthon key 98 of the respective compound;

[0082] • a molecular query 101 for querying the combinatorial synthesis library 82, wherein the molecular query is in the form of a graph 102 comprising a plurality of nodes 102 and a plurality of edges 104, wherein each node in the plurality of nodes represents an atom, and each node is connected to another node in the plurality of nodes by at least one edge in the plurality of edges, the edge representing a covalent bond between the two nodes;

[0083] • the molecular encoder model 110 optionally comprises a message passing neural network comprising a plurality of message passing layers 112, the message passing layers collectively comprising a first plurality of parameters 114, the molecular encoder model, in response to receiving the molecular query 101 in the form of the graph 102, outputting a query vector by applying the plurality of parameters 114 to the graph 102;

[0084] • the reaction query generator model 116 comprises a second plurality of parameters 118, the reaction query generator model 116, in response to receiving the query vector, providing a first reaction type 82-1 in the plurality of reaction types 82 as output from the reaction query generator model 116 by applying the second plurality of parameters 118 to the query vector; and

[0085] • the synthon query generator model 120 comprises a third plurality of parameters 122, the synthon query generator model 120, in response to receiving an identification of a reactant, providing a corresponding synthon 88 as output from the synthon query generator model 120 by applying the third plurality of parameters 122 to the respective reactant.

[0086] In some embodiments, one or more of the above-identified data elements or modules of the computer system 100 are stored in one or more of the previously mentioned memory devices, and corresponds to a set of instructions for performing the above-identified function. The above-identified data, modules or programs (e.g., sets of instructions) need not be implemented as separate software programs, procedures or modules, and thus various subsets of these modules can be combined or otherwise rearranged in various implementations. In some embodiments, the memory 60 (and optionally the memory 58) optionally stores a subset of the modules and data structures identified above. Furthermore, in some embodiments, the memory 60 (and optionally the memory 58) stores additional modules and data structures not described above.

[0087] Having now disclosed the system for querying a combinatorial synthesis library, the method for performing such a query is described in detail with reference to FIG. 2, and discussed below.

[0088] Referring to block 200, in some embodiments, a system and method for querying a combinatorial synthesis library 82 is provided. The combinatorial synthesis library 82 includes a plurality of compounds 92 and represents a plurality of reaction types 82. Each respective reaction type 82 of the plurality of reaction types has a corresponding mapping to a corresponding plurality of reactants 86. Each respective reactant 86 of each corresponding plurality of reactants has a corresponding mapping to a corresponding plurality of synthon 88.

[0089] One aspect of the present disclosure focuses on a combinatorial synthesis library (CSL) that can be used to represent a large amount of available chemical space (e.g., more than 10 8 , 10 9 , 10 10 , or 10 11 compounds) through the combination of a smaller set of readily available building blocks and a set of pre-described and generally successful multi-component synthesis rules. Figure 3A An illustration of such a construction is provided in FIG. 1. In some embodiments, the CSL consists of a set of multi-dimensional synthesis tables. In some such embodiments, each synthesis table describes a multi-component chemical reaction, which can be indexed by t e T (e.g., a natural number).

[0090] Following

[44] , the term “R-group” or simply group, is used to refer to a placeholder group in a chemical reaction, and is indexed by r e R. Multiple groups can be combined together in one (chemically valid) reaction, indexed by t e T. We let ψ : T → P(R) be a function that returns the set of R-groups required for reaction t.

[0091] Each R-group is spanned by a large number of molecular building blocks, referred to as synthon, that can be used in the corresponding reaction. Synthon is indexed by s e S, and can be represented by a molecular graph​ It is noted that a synthon can belong to multiple R-groups. A target molecule is represented by R-groups, which represent potential starting reagents in the synthesis of the target molecule. For example, in FIG. 6, compound 602 includes two R-groups, the electrophilic “PhCH 2+ ” R-group 604 and the nucleophilic “COOH - ” R-group 606. The two R-groups do not exist in and of themselves; a synthetic equivalent (synthon) corresponding to each R-group reacts to produce the desired R-group, and thus the entire compound. For example, in the illustration provided in FIG. 6, cyanide anion 610 is one possible synthon for the “COOH - ” R-group 606, while benzyl bromide 608 is one possible synthon for the “PhCH 2+ ” R-group 604.

[0092] For convenience, in some embodiments, the notation is used to represent a function that returns a set of synthons belonging to a particular R-group r.

[0093] A product x e X is a molecule synthesized according to a multi-component reaction, where R-groups and corresponding synthon tuples where for all i = 1,..., k t , (k t is between 2 and 4 in some embodiments). Let f be defined as the synthesis rule that generates compound x from a reaction and synthon tuple pair (t, u), e.g., x := f(t, u). In short, as a simple analogy, the synthesis rule t can be viewed as an equation that specifies k t terms, where each term is an R-group and their associated synthons correspond to the allowed values for the corresponding term.

[0094] Thus, a library based on synthons is fully characterized by its reactions T, R-groups R, and synthons S, as well as the synthesis rule f, the reaction mapping ψ on R-groups, and the mapping σ of R-groups to synthons. Due to the combinatorial nature of such constructs, they can be used to construct libraries that span large areas of easily accessible chemical space from which compounds can be obtained (i) with high probability, (ii) at reasonable cost, and (iii) with short turnaround times.

[0095] Using probabilistic language, the distribution on X induced by D can be described by the following factorization:

[0096]

[0097] where​ is the set of all eligible synth chain of reaction t. This factorization describes the generation process, where first a sample is taken from reaction and then the synth tuple that is sampled valid includes synth from the corresponding group in t and combines these synths together by synthesis to form the product x (by deterministic rule f).

[0098] As written, all valid (t, u) pairs in p have the same probability under p. Note that if each product in p can be obtained according to only a single synthesis route, then is a uniform distribution over a part of X that is reachable by

[0099] Referring to block 202, in some embodiments, the plurality of reaction types 82 includes 20 or more reaction types, and the combinatorial synthesis library 82 includes 100 or more compounds 92 for each reaction type 82 of the plurality of reaction types. In some embodiments, the plurality of reaction types 82 includes 20, 30, 40, 50, 60, 70, 80, 90, 100, 500, 1000, 2000, 3000, 5000, 10,000 or more reaction types, and the combinatorial synthesis library 82 includes 100, 200, 300, 400, 500, 1000, or 10,000 or more compounds 92 for each reaction type 82 of the plurality of reaction types.

[0100] Referring to block 204, the molecular query 101 is input into the molecular encoder model 110. The query is graph-based. In some embodiments, the molecular encoder model 101 includes a message passing neural network that includes a plurality of message passing layers 112 that collectively include a first plurality of parameters 114. Inputting the graph-based query into the molecular encoder model 110 produces a query vector as an output of the molecular encoder model by applying the first plurality of parameters 114 to the graph-based query.

[0101] In some embodiments, the molecular encoder model 101 (MolecularEncoder) takes as input a molecular graph and returns a d X dimensional feature representation:

[0102]

[0103] In some implementations, the MolecularEncoder (molecular encoder model 101) is a graph neural network with a variational linear layer stacked on top of a graph reader that takes as input a molecular graph​ A sample z ~ q(z | x) is produced. In Figure 3A -H, z is interpreted as a query introduced by x into the library of queries.

[0104] Note that in some embodiments, the molecular encoder model 110 takes as input a molecular graph and is thus able to produce queries for compounds not in the library of queries. In some embodiments, this is useful for finding analogs through catalogs— i.e., compounds that can be purchased from a catalog and are chemical analogs of the query molecule.

[0105] Referring to block 206, in some embodiments, the graph-based query is a single graph 102 comprising a plurality of nodes 102 and a plurality of edges 104, where each node 102 of the plurality of nodes is connected to another node of the plurality of nodes by at least one edge 104 of the plurality of edges. In some embodiments, the single graph 102 represents a single molecular compound, and each node of the plurality of nodes represents an atom of the single molecular compound, and each edge of the plurality of edges represents a covalent bond between two atoms in the single molecular compound. In some embodiments, the plurality of nodes represents each non-hydrogen atom of the molecular compound. In some embodiments, the plurality of nodes represents each atom of the molecular compound. In some embodiments, the plurality of edges represents each covalent bond of the molecular compound.

[0106] In some such embodiments, each respective node of the plurality of nodes is associated with any 1, 2, 3, 4, or more of the following features: (i) a corresponding element type of a plurality of element types, (ii) a node degree of a plurality of node degrees, (iii) a hybridization of a plurality of hybridizations, (iv) a plurality of bonded hydrogens, (v) a formal charge of a set of formal charges, and (vi) a binary indication of aromaticity.

[0107] Referring to block 208, in some embodiments, each respective node 102 of the plurality of nodes 102 is associated with: (i) a corresponding element type of a plurality of element types, (ii) a node degree of a plurality of node degrees, (iii) a hybridization of a plurality of hybridizations, (iv) a plurality of bonded hydrogens, (v) a formal charge of a set of formal charges, and (vi) a binary indication of aromaticity.

[0108] Referring to block 210, in some embodiments, each respective bond 104 of the plurality of bonds is associated with: (i) a bond type, (ii) a binary indication of conjugation, (iii) a binary indication of whether the respective bond is within a ring, and (iv) an indication of stereochemistry.

[0109] In some embodiments, the atoms and bonds of a molecular compound are represented in the graph as a set of binary features. In some embodiments, these binary features are described in Tables 1 and 2, respectively. In an example implementation, the dimensions of the nodes and edges are each set to 64. Thus, in the example, the atom embedding consists of 50 x 64 = 3,200 parameters, and the bond embedding consists of 12 x 64 = 768 parameters.

[0110] Table 1: Atom feature types.

[0111]

[0112] Table 2: Bond feature types.

[0113]

[0114] In some embodiments, a single graph represents a query molecular compound as a set of atom features and a set of bond features. For example, in some embodiments, a single graph represents a query molecular compound as a set of atom features and a set of bond features of Tables 1 and 2, respectively. In some such embodiments, the set of atom features includes element type, node degree, hybridization, chirality, bonded hydrogen, formal charge, aromaticity, and the set of bond features includes bond order, conjugation, in-ring, and stereochemistry, as set forth in Tables 1 and 2. In some such embodiments, each non-hydrogen atom in the query molecular compound is represented by 500, 1000, 1500, 2000, 2500, 3000, or more than 3000 parameters in the set of atom features, and each covalent bond in the molecular compound is represented by 100, 200, 300, 400, 500, 600, 700, or more than 700 parameters in the set of bond features.

[0115] Referring to block 212, in some embodiments, the single graph 102 represents a single molecular compound present in the combinatorial synthesis library. In some embodiments, the single graph 102 represents a single molecular compound not present in the combinatorial synthesis library.

[0116] Referring to block 214, in some embodiments, the single graph 102 represents a weighted composition of a first graph of a first molecular compound and a second graph of a second molecular compound. In some embodiments, the single graph 102 represents a composition of two or more molecular compounds.

[0117] Referring to block 216, in some embodiments, the single graph 102 represents a weighted composition of a plurality of graphs of a second plurality of compounds, wherein the second plurality of compounds have a common property. Referring to block 218, in some embodiments, the common property is a valley distance to each other compound in the second plurality of compounds that is less than a threshold value. Referring to block 220, in some embodiments, the common property is a binding coefficient to a large molecule target that is less than a threshold value.

[0118] Referring to block 220, the query vector z (e.g., represented by the equation above) is input into the reaction query generator model 116 comprising the second plurality of parameters 118. This results in an output from the reaction query generator model 116 of a first reaction type from a plurality of reaction types by applying the second plurality of parameters 118 to the query vector.

[0119] In some embodiments according to block 220, the query MolecularEncoder and library The task of the decoder is to retrieve the molecule that responds to the query from the library In other words, to identify the reaction and synthesis subtuple that will yield the molecule as a product. In some embodiments, the decoding proceeds by first generating reactions, in accordance with the factorization discussed previously.

[0120] In some embodiments, the reaction query generator model 116 is utilized. In some embodiments, the reaction query generator model 116 can be instructed by an operation

[0121] q T = ReactionQueryGenerator(z). (11)

[0122] In some such embodiments, the ReactionQueryGenerator(z) samples from a probability distribution over reactions according to the query z T for comparison to the reaction key of the CSL In some embodiments, the operation q T = ReactionQueryGenerator(z) performed by some embodiments of the reaction query generator model 116 is mathematically equivalent to:

[0123]

[0124] to define a probability distribution over reaction types in T. From this probability distribution, a reaction

[0125] Accordingly, with reference to block 224, in some embodiments, the output from the reaction query generator model 116 is used to identify, by a first query key lookup, a first reaction key type 84 of a plurality of reaction key types, where each reaction key type of the plurality of reaction key types represents a synthetic reaction that can be used to synthesize one or more compounds 92 in the combinatorial synthesis library 82. In some such embodiments, the output from the reaction query generator model 116 is a reaction key type t. In other embodiments, the output from the reaction query generator model 116 is a probability distribution of reaction key types t, such as the probability distribution derived from equation (12), from which a particular reaction key type t is obtained by sampling the probability distribution.

[0126] With reference to block 222, in some embodiments, the reaction query generator model 116 is a two-layer perceptron with intermediate ReLU activations (e.g., the input layer and the output layer are not computed). In some embodiments, the reaction query generator model 116 is an N-layer perceptron (MLP), where N is a positive integer of 2 or greater (e.g., 2, 3, 4, 5, 6, 7, 8, 9, or 10) and represents the number of hidden layers in the model. In some embodiments, an MLP is a class of feed-forward artificial neural networks (ANN) that includes at least three layers of nodes: an input layer, one or more hidden layers, and an output layer. In such embodiments, each node, except the input nodes, is a neuron that uses a non-linear activation function. In some embodiments, the activation function is a rectified linear unit ReLU activation. In some embodiments, the activation function is a rectified linear unit (ReLU) activation function, a leaky ReLU activation function, or other function, such as a hyperbolic tangent function, an identity function, a binary step function, a logistic function, an arcTan function, a softsign function, a parametric rectified linear unit function, an exponential linear unit function, a softPlus function, a bent identity function, a softExponential function, a Sinusoid function, a Sine function, a Gaussian function, or a sigmoid function, or any combination thereof. Further disclosure regarding suitable MLPs for use as the reaction query generator model 116 in some embodiments of the present disclosure can be found in Vang-mata, ed., 2020, Multilayer Perceptrons: Theory and Applications, Nova Science Publishers, Hauppauge, New York, which is hereby incorporated by reference herein. In some embodiments, the reaction query generator model 116 has the architecture of any of the models disclosed in the above-defined section.

[0127] ​Given a sampled reaction t from the box 220, the R-group (by ψ) required is known, and in addition the synthon (by σ) appropriate for each group is known. Thus, referring to the box 226, in some embodiments, the corresponding synthon for each respective reactant t of the first plurality of reactants is determined from the corresponding plurality of synths mapped to the respective reactant 86 by inputting the respective reactant 86 into the synthon query generator model 120 comprising a third plurality of parameters 122, thereby obtaining the corresponding synthon as an output of the synthon query generator model 120 by applying the third plurality of parameters 122 to the respective reactant. This results in a set of synths, each synth of the set of synths corresponding to a reactant of the first plurality of reactants. In other words, to decode the synthon tuple of reaction t, the synthon query generator model 120 is implemented. In some embodiments, the synthon query generator model 120 implements the operation SynthonQueryGenerator: which in some embodiments of the present disclosure is used to query the synthon for each R-group

[0128]

[0129]

[0130] ​Referring to block 228, in some embodiments, the synthetic subquery generator model 120 is a two-layer perceptron with intermediate ReLU activations. In some embodiments, the synthetic subquery generator model 120 is an N-layer perceptron (MLP), where N is a positive integer of 2 or greater (e.g., 2, 3, 4, 5, 6, 7, 8, 9, or 10) and represents the number of hidden layers in the model. In some embodiments, an MLP is a class of feed-forward artificial neural networks (ANN) that includes at least three layers of nodes: an input layer, one or more hidden layers, and an output layer. In such embodiments, each node, except the input nodes, is a neuron that uses a non-linear activation function. In some embodiments, the activation function is a rectified linear unit ReLU activation. In some embodiments, the activation function is a rectified linear unit (ReLU) activation function, a leaky ReLU activation function, or other functions such as a hyperbolic tangent function, an identity function, a binary step function, a logistic function, an arcTan function, a softsign function, a parametric rectified linear unit function, an exponential linear unit function, a softPlus function, a bent identity function, a softExponential function, a Sinusoid function, a Sine function, a Gaussian function, or a sigmoid function, or any combination thereof. Further disclosure regarding suitable MLPs for use as the synthetic subquery generator model 120 in some embodiments of the present disclosure can be found in Vang-mata, ed. 2020, Multilayer Perceptrons: Theory and Applications, Nova Science Publishers, Hauppauge, New York, which is hereby incorporated by reference herein. In some embodiments, the synthetic subquery generator model 120 has the architecture of any of the models disclosed in the above-defined section.

[0131] Referring to block 230, in some embodiments, the output of the synthetic subquery generator model 120 is used to identify the synthetic subkey 80 of the corresponding synthetic via a second query key lookup.

[0132] Referring to block 232, in some embodiments, the first plurality of parameters 114 (of the molecule encoder model 110) includes 100,000 parameters, the second plurality of parameters 118 (of the reaction query generator model 116) includes 5,000 parameters, and the third plurality of parameters 122 (of the synthetic subquery generator model 120) includes 5,000 parameters. In some embodiments, the first plurality of parameters 114 (of the molecule encoder model 110) includes 10,000, 50,000, 100,000, or 1 x 10 6The second plurality of parameters 118 (of the reaction query generator model 116) include 1,000, 2,000, 3,000, 4,000, 5,000, or 10,000 parameters, and the third plurality of parameters 122 (of the synthetic subquery generator model 120) include 1,000, 2,000, 3,000, 4,000, 5,000, or 10,000 parameters.

[0133] Referring to box 234, in some embodiments, the first plurality of reactants 86 comprises three or more reactants, and the corresponding mappings for the plurality of synthons of the reactants in the three or more reactants comprise ten or more synthons. In some embodiments, the first plurality of reactants 86 comprises 2, 3, 4, 5, 6, 7, 8, 9, or 10 or more reactants. In some embodiments, the corresponding mappings for the plurality of synthons of the reactants in the first plurality of reactants 86 comprise 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 25, 30, 35, 40, 45, 50, or 100 or more synthons.

[0134] Referring to box 236, molecular structures (compounds) 92 are identified in a combinatorial synthesis library 82, which comprises a set of synthons 88 arranged according to a synthesis rule f associated with a first reaction type 82. As used herein, synthesis rule f generates compound x from a reaction and synthon pair (t; u), for example, x := f(t; u).

[0135] Referring to box 238, in some embodiments, the combinatorial synthesis library 82 contains a plurality of compounds comprising billions or more, and the identified molecular structure is any one of the billion or more compounds that satisfy the query. Referring to box 240, in some embodiments, the combinatorial synthesis library 82 contains a plurality of compounds comprising trillions or more, and the identified molecular structure is any one of the trillions or more compounds that satisfy the query. In some embodiments, the combinatorial synthesis library 82 comprises 1 x 10 8 1x10 9 1x10 10 1x10 11 1x10 12 Or 1x 10 13 A compound.

[0136] Combinatorial synthesis library variational autoencoder.

[0137] Next, consider using the library The task of finding the product x is equivalent to finding the reaction t and the synthesized subunit u that satisfy x = f(t, u). This can be viewed as a reasoning problem, searching for... The latent variable model for x yields a variational formula:

[0138]

[0139] where p(z) denotes the prior distribution of the latent variable. By first selecting the reaction t, and then selecting a synthon The joint conditional distribution of t and u can be further simplified independently conditioned on t:

[0140]

[0141]

[0142] This yields a strategy in which molecule x is encoded into latent space z ~ q(z\ x) and first the reaction type is decoded, and then according to the sampled reaction, one synthon for each group is decoded i = 1,..., k t (where t is a positive integer of 2 or more) to form a tuple of synthon

[0143] The resulting latent variable model can be referred to as a combinatorial synthon library variational autoencoder. Figure 3B -H gives a step-by-step description of the method. The three main modules that make up the autoencoder are (i) the library encoder, (ii) the molecule encoder and (iii) the molecule decoder. Module (ii) forms the basis of q(z\ x), while modules (ii) and (iii) form the basis of .

[0144] Library encoder.

[0145] In some embodiments, the combinatorial synthon library is hierarchically organized, with synthon S at the bottom of the hierarchy, R-group R in the middle, and reaction T at the top. Here a strategy is described for learning to describe the associated hierarchy of the library in an end-to-end fashion at these three levels of resolution. These representations can then be used to retrieve query results into the library. The library encoder is shown in Figure 3C -E.

[0146] Starting from the bottom of the hierarchy with synthon S, to learn a representation of each synthon in a fully inductive fashion, a graph neural network is used to parameterize the SynthonEncoder (synthon encoder): which applies a series of message passing steps, followed by a readout to arrive at d S - the dimensional representation of each synthon. In some embodiments, dS The dimensionality in is 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, or more than 20 dimensions.

[0147] Moving up the hierarchy, the R-group R is represented using a deep neural network by aggregating the representations of the synthons belonging to a particular group. Formally, the RGroupEncoder(R-group encoder) is: from the d S dimensional representation of the given R-group in the set R dimensional representation. Following

[61] , the R-group encoder has the form RGroupEncoder In some embodiments, φ and ρ are parameterized as multi-layer perceptrons, and is a permutation-invariant aggregation operator.

[0148] In some embodiments, φ and ρ are parameterized as models other than multi-layer perceptrons. For example, in some embodiments, φ and ρ are parameterized as any of the models disclosed in the definition section of the “Models” disclosed above. In some embodiments, a higher-performing set-to-vector neural network such as, for example, the set transformer

[31] is used. However, the use of multi-layer perceptrons has the advantage that it allows for fast querying of library subsets at test time, since All s ∈ S can be cached, reducing the computation required for querying the partition of the library. In some embodiments, mean-pooling is used as the aggregation operator to focus on features of the synthon distribution in the group (as opposed to sum-pool, which typically expresses multiple-set features). This improves performance when dealing with R-groups of varying cardinality.

[0149] In some embodiments, to represent reactions, another deep set neural network is used as the ReactionEncoder(reaction encoder): This model takes as input a variable-sized set of groups corresponding to the reactants in t, and produces a d T dimensional representation of the reaction. In some embodiments, summing is used as the aggregation operator to learn multiple-set properties of the R-groups in the reaction.

[0150] Putting these together, the representation cascades as follows:

[0151]

[0152] In some embodiments, a factorization of the likelihood is considered, such that given a molecular representation z, the molecular decoder first decodes the reaction type, and then decodes one synthon for each group separately depending on the reaction type. Thus, in some implementations, a key vector is used for each reaction as well as for each synthon to compare against the associated query vector. Thus, in some embodiments, a ReactionKeyGenerator is used to generate a key vector for a given reaction representation with the function and similarly, a SynthonKeyGenerator is used to generate a key vector for each synthon with the function In some embodiments, each of these key generators is parameterized as a multi-layer perceptron:

[0153]

[0154] In some embodiments, each of these key generators is parameterized as some other form of model. For example, in some embodiments, each of these key generators is parameterized as any of the models disclosed under the heading “Models” in the definition of part above.

[0155] Example training.

[0156] For large CSL Encoding the entire library at each iteration of the training loop can require excessive GPU memory. To overcome this problem, in some embodiments, a mini-batch strategy is used, in which a random subset of the library is drawn according to a distribution drawn from the complete library From the synthon, R-group, and reaction representations and keys are formed. In some embodiments, a sub-sampler that (i) uniformly randomly samples a subset of the reactions contained in the entire library, retains only the R-groups contained in the sampled reactions, and (ii) for each reaction, samples a random number of products, retains only the synths contained in the sampled products. In some embodiments, a teacher forcing is further used, feeding in the ground truth reactions when generating the synthon queries for the corresponding R-groups. Algorithm 1 below describes one embodiment of this training procedure used in some embodiments of the present disclosure.

[0157] Algorithm 1 - Training procedure:

[0158] Input complete library library sub-sampler batch size N, model parameters 0, KL divergence weight b > 0, optimization choice

[0159] However, not the highest standard performance

[0160] # Prepare mini-batches

[0161] On the library Take samples

[0162] For each reaction-synthon pair n = 1...N, sample a mini-batch of corresponding products by synthesis, for n = 1...N, x n = f(t n , u n )

[0163] # Encode the library

[0164] For each s e S, obtain a synthon representation as per equation (5)

[0165] For each r e R, obtain a group representation as per equation (6)

[0166] For each t e T, obtain a reaction representation as per equation (7)

[0167] For each t e T, obtain a reaction key as per equation (8)

[0168] For each s e S, obtain a synthon key as per equation (9)

[0169] # Encode the products

[0170] For each n = 1...N, sample a product query z as per equation (10) n

[0171] For each n = 1...N, retain the KL divergence contribution KLD n = D KL (q(z | x n )) || P(z))

[0172] # Decode products related to the library

[0173] For n = 1...N, obtain a reaction query [q T ] n

[0174] For each t e T and n = 1...N, obtain a reaction probability as per equation (12)

[0175] For each n = 1...N and r e σ(t n ), obtain a synthon query as per equation (13)

[0176] For each n = 1...N, and Obtain the synthetic probabilities

[0177] For each n = 1...N Compute the LL contribution

[0178] # Compute the loss and update the parameters

[0179] Compute the loss as the negative of the weighted ELBO,

[0180] Compute the gradient using the optimizer’s choice and update θ, e.g., θ ← optimizer

[0181] End time

[0182] Return the fitted model parameters θ * ← θ

[0183] Posterior density estimation.

[0184] Given a trained generative model p θ (x|z), one can also sample the product (discard z) from (x,z) ~ p θ (x|z)p(z) (Ref. 3). However, due to the batch sampling strategy outlined herein, this typically does not correspond well to a uniform distribution of products in due to the bias introduced by the batch sampling strategy outlined above (first uniformly sample reactions, then uniformly sample products from a given reaction).

[0185] While this can be corrected for during the training phase by importance weighting, in some embodiments, another approach is performed by utilizing the following posterior density estimation strategy

[14] . A large number of products are sampled from the target distribution and encoded by the molecular encoder z ~ q φ (z|x). A density estimator is then fitted to the aggregated samples in some embodiments, written as q λ (z). In some embodiments, a multivariate normal distribution is used for simplicity, but in some embodiments, more expressive density estimators are used (e.g., mixtures of multivariate normals) herein.

[0186] In some embodiments, the products can then be sampled from (x,z) ~ p θ (x|z)q λ (z), which will more closely correspond to a uniform distribution of products from sample alignment. This helps to correct for biases in the product space distribution due to choosing a batch sampling strategy.

[0187] Computational complexity, scalability, and efficiency.

[0188] In this section, the computational complexity, scalability, and efficiency of some embodiments of the presently disclosed systems and methods are described.

[0189] First, note that the library can be encoded in O(|S| + |R| + |T|) complexity, where the constant depends on the complexity of the synthesis sub, R-group, and reaction encoders. Nonetheless, this is logarithmic compared to naively encoding each product in , which has complexity.

[0190] More notably, the computational complexity of the molecule decoder. For clarity, consider a simplified Let M i denote the number of synthesis subs indicating groups i = 1,..., k. Naively, the nearest neighbor lookup in would have complexity. On the other hand, in some embodiments, the presently disclosed systems and methods perform the lookup independently with the synthesis subs in each R-group, which achieves complexity— logarithmic growth. Thus, the structure of the presently disclosed molecule decoder is well suited for the ultra-large combinatorial libraries of interest in early drug discovery.

[0191] Another advantage of the disclosed decoding strategy is that it relies only minimally on autoregression. In fact, in some embodiments, only a single autoregressive step is required, regardless of the size of the generated graph (the autoregressive length is exactly two). Thus, the presently disclosed systems and methods are scalable to large and variable-sized molecular graphs following combinatorial synthesis construction.

[0192] Furthermore, the presently disclosed systems and methods guarantee the generation of chemically valid, synthetically accessible molecular graphs without the need to perform explicit validity checks. This is advantageous compared to previous work, in which the validity of each candidate action is verified at each step of the autoregression, and invalid actions are excluded from the selection set. While chemoinformatics libraries like RDKit

[30] have highly efficient C++ implementations for these checks, they still add a significant overhead to the runtime. Further, in the absence of explicit validity checks, these models have been shown to generate invalid molecular graphs at significantly higher rates

[23] .

[0193] Conclusion.

[0194] The disclosed combinatorial synthetic library variational autoencoder is a new graph-based generative model for combinatorial synthetic library navigation. The disclosed model leverages minimal autoregression, allowing efficient generation of large molecule graphs and improved scalability. Compounds generated by the disclosed model are chemically valid and can be obtained cost-effectively. In some embodiments, the disclosed model is a neural database that provides random access to unenumerable libraries. In the following experiments, the ability of the disclosed model to model ultra-large and realistic on-demand manufacturing libraries is demonstrated, paving the way for more scalable strategies to explore unenumerable chemical libraries for early drug discovery.

[0195] In some embodiments, the synthon lookup in the disclosed decoder scales linearly with the number of synths in the R-group, which can pose a challenge as the library continues to add many synths per R-group. In some embodiments, this can be mitigated by a more scalable query key design [11, 26]. Furthermore, in some embodiments, due to the presence of significant R-group symmetries (e.g., as in polymers), some embodiments of the decoder include parity-breaking modifications, and some such modifications can not allow equally convenient parallelization. Finally, due to its strict replacement pattern, softmax has limitations in mapping from real-valued potentials to selected probabilities

[55] . Thus, in some embodiments, instead of using softmax, a sparse or alternative perception-aware softmax variant is used.

[0196] Synthon Encoder. In some embodiments, the Synthon Encoder is a message passing graph neural network that takes node, edge, and graph features as input and produces updates to these features in a residual fashion after each round of message passing. The following single message passing layer.

[0197] Qualification. Figure By a set of node features Edge features and graph features g 0 Indicate that these are initial or input features; the following indicates the result after the first round of message passing.

[0198] Edge Model. The edge model updates edge features as follows. For edge (i,j) e e, the edge features for the current iteration , the graph features, and the two corresponding node features are concatenated. Then, the concatenated features are layer normalized and processed through a two-layer MLP, resulting in The output dimension of the final linear layer is set equal to the dimension of the edge features, which allows for a residual update of the edge features, e.g., Note that for an edge (i,j) e e, the edge features are maintained separately for i→j and i←j updates; these features are the same for but typically different for subsequent layers.

[0199] Node model. Given a node forms a message from all its neighboring nodes by summing the associated incoming edge features, Similar to the edge model, the node features, messages, and graph features are concatenated, layer normalized, and passed through two layers of MLP, with the output dimension of the final linear layer equal to the dimension of the node features. This results in a residual update of the node features from given. Thus, the node features are updated according to .

[0200] Graph model. The graph features are updated by accumulating the messages from each node in the graph, as follows. Using the now familiar layer norm + MLP design, the node messages of the graph are formed, with the final linear layer having an output dimension equal to the dimension of the graph features. These messages,

[0201] are then aggregated by sum-pooling to form a residual for the graph features, and thus the graph features are updated accordingly, In an embodiment, the node and graph models use a shared MLP with an output dimension equal to the sum of the node and graph feature dimensions, which is then split into two parts: one part is routed to the node update, and the other part is routed to the graph update.

[0202] Putting it all together. The message passing neural network applies a series of message passing layers as described above. In one embodiment according to the present disclosure, the node, edge, and graph feature dimensions are set to 64 and four message passing layers are utilized. For the input graph features, a zero vector is used in some embodiments. The final graph features are used as the synthetic sub- representation for generating synthetic sub-key as well as the concatenated representation of R-groups and reactions. In total, one embodiment of a SynthonEncoder according to the present disclosure is described by 152,832 parameters.

[0203] R-Group Encoder. In some embodiments according to the present disclosure, the R-Group Encoder (RGroupEncoder) follows the design outlined in DeepSets, where the synthon each represents is individually processed by an MLP, merged together (here, mean-pooling is used to allow the network to focus on the distributional features of the synthon belonging to the R-Group), and the result is processed by yet another MLP. In some embodiments according to the present disclosure, the two MLPs are set as a two-layer network with ReLU activation in between. In some embodiments, all dimensions are 64, and thus the RGroupEncoder utilizes 16,640 parameters in total. In some alternative embodiments, the R-Group Encoder is constructed using any of the models disclosed in the above Definitions section.

[0204] Reaction Encoder. In some embodiments, the Reaction Encoder (ReactionEncoder) follows the same design as the RGroupEncoder, except that sum-pooling is utilized instead of mean-pooling to allow the network to focus on the multiple sets of R-Groups in the reaction. In some embodiments, all dimensions are 64, and thus the ReactionEncoder also utilizes 16,640 parameters in total. In some alternative embodiments, the Reaction Encoder is constructed using any of the models disclosed in the above Definitions section.

[0205] Synthon Key Generator. In some embodiments, the Synthon Key Generator (SynthonKeyGenerator) is an MLP that produces a synthon key from a synthon representation. In some embodiments, a linear layer is used. In some embodiments, both the input and output dimensions are set to 64, and thus, in such embodiments, the SynthonKeyGenerator utilizes 4,160 parameters in total. In some alternative embodiments, the Synthon Key Generator is constructed using any of the models disclosed in the above Definitions section.

[0206] Reaction Key Generator. In some embodiments, the Reaction Key Generator (ReactionKeyGenerator) is an MLP that produces a reaction key from a reaction representation. In some embodiments, a linear layer is used. In some embodiments, both the input and output dimensions are set to 64, and in some embodiments, the ReactionKeyGenerator utilizes 4,160 parameters in total. In some alternative embodiments, the Reaction Key Generator is constructed using any of the models disclosed in the above Definitions section.

[0207] Molecular encoder. In some embodiments, the Molecular Encoder produces molecular queries and utilizes the same message passing design as the Synthon Encoder. In some such embodiments, the node, edge, and graph features are all set to 64, and four layers of message passing are used. However, in some embodiments, unlike the Synthon Encoder, the Molecular Encoder has an additional variational linear layer that produces a conditional mean and a conditional log-variance vector from the graph features produced by the final message passing round. In some embodiments, the variational linear layer takes 64-dimensional graph features as input and produces a 128-dimensional output, which is split into mean and log-variance parts. In some embodiments, the Molecular Encoder utilizes a total of 152,832 + 8,320 = 161,152 parameters. In some alternative embodiments, any of the models disclosed in the above-defined section are used to construct a molecular encoder.

[0208] Molecular query processing network. In some embodiments, as a result of the VAE objective, the molecular query is regularized to approximate the previous p(z). In order to allow the decoder to better utilize these features, in some embodiments, the molecular query is processed by an MLP before being passed to the reaction and synthon query generators. For simplicity, in some embodiments, a simple two-layer MLP with intermediate ReLU activations is chosen; all dimensions are 64, so 8,320 parameters are used. In some embodiments, any of the models disclosed in the above-defined section are used instead of such MLPs.

[0209] Reaction query generator. In some embodiments, the Reaction Query Generator is an MLP that produces reaction queries from molecular queries. In some embodiments, a two-layer network with intermediate ReLU activations is used. In some embodiments, all dimensions are set to 64, so the Reaction Query Generator utilizes a total of 8,320 parameters. In some embodiments, any of the models disclosed in the above-defined section are used instead of such MLPs for the reaction query generator.

[0210] Synthon Query Generator. In some embodiments, the Synthon Query Generator (SynthonQueryGenerator) is an MLP that produces a synthetic query from a molecular query, a reaction representation, and an R-group representation. In general, in some embodiments, when the common dimension 64 is used throughout, these three feature types are concatenated, and in order to keep the implementation simple, in some embodiments, a summation is used instead of concatenation (which can be shown to be equivalent to concatenating with an additional constraint to the weight matrix of the subsequent linear layer). Similar to the Reaction Query Generator, in some embodiments, a two-layer MLP with intermediate ReLU activations, resulting in a total of 8,320 parameters for the Synthon Query Generator. In some alternative embodiments, any of the models disclosed in the above-defined section are used instead of such MLPs for the Synthon Query Generator.

[0211] Examples

[0212] Example 1 - Comparison of disclosed models with JT-VAE and RationaleRL.

[0213] Data.

[0214] To demonstrate the capabilities of the presently disclosed systems and methods on real-world combinatorial synthesis catalog types employed in today’s large-scale hit-finding programs, an example experiment was conducted utilizing the Enamine REadily AccessibLe (REAL) library, which consists of 340K synthetic substructures and over a thousand reactions. The reactions in REAL range from two to four components, and the number of synthetic substructures per R-group ranges from single-digit to tens of thousands. The REAL library collectively describes a chemical space of over 16 billion commercially available compounds [4], which can be obtained at low cost in about three to four weeks. Advantageously, the library’s use with the presently disclosed systems and methods can be used to reproduce the example experiment and facilitate further research on combinatorial synthesis libraries in the machine learning community.

[0215] Training.

[0216] During training, subsets of the library were sampled as follows. Out of the approximately 1300 reaction types in the REAL database, 20 reactions were first sampled uniformly at random, and then 100 products per reaction were sampled, including the relevant synthetic substructures in the library subsets. Thus, these library subsets each described approximately 300K-1.5M compounds, which is significantly less than the complete library containing 16 billion compounds. See Algorithm 1 above for details.

[0217] Testing. For test-time inference, decoding was performed on the full library of 160B compounds. This constitutes a test-time distribution shift relative to training, but it was observed that the disclosed system and method generalizes well to the full library without modification. For completeness, an analysis of the test-time distribution shift is provided in Figure 8

[0218] As described in Algorithm 1, a small subset of the full library was sampled at each training iteration to enable tractability. In particular, the library subsampler utilized the first sample uniformly across reactions and then sampled a constant number of products randomly within each reaction; the synthesis children associated with these sampled products constituted the synthesis children in the library subset. In training the CSLVAE model used in this experiment, 20 reactions and 100 products per reaction were sampled, resulting in a small batch of 2000 products. As described herein, each of these associated library subsets described a chemical space of approximately 300K-1.5M compounds. However, at test-time, decoding was performed on the full library of 16B compounds, which constitutes a rather dramatic test-time distribution shift. Figure 8 The magnitude of the test-time distribution shift on reconstruction quality (measured by average likelihood) is demonstrated. Starting from the five library subsets as described above, 2000 compounds were drawn for each subset; each of the five plots is represented by a different line in the plot. The library was then further increased by first including all synthesis children in 20 sampled reactions and computing the average reconstruction likelihood of the same 2000 products from the expanded library, and by adding all synthesis children of 100 randomly sampled additional reactions, and then adding all synthesis children of another 100 randomly sampled additional reactions, and finally including all synthesis children and all reactions. At each step, the library subset described a larger and larger chemical space. It was observed that the average likelihood of the library size decreased in a roughly linear-log manner due to this distribution shift.

[0219] Molecule reconstruction and generation.

[0220] An embodiment of the disclosed system and method (CSLVAE) was compared to two existing molecular graph generation models: JT-VAE

[23] and RationaleRL

[25] . All three models were trained from scratch on the Enamine REAL library.

[0221] ​In JT-VAE, molecular graphs are represented by a tree of connections on chemical fragments. The decoding process first generates the tree of connections in a depth-first manner, places fragments in each node, and then subsequently orients fragments to match attachment points. On the other hand, RationaleRL takes a starting rationale as input. The goal of the decoder is to complete the molecule in a self-recursive manner (one graph edit at a time). In this instance, a product is taken from the library and all but one synthon is removed, and the resulting graph is taken as the starting rationale. Thus, in this instance, the task of RationaleRL is to generate the missing synthon.

[0222] Table 3 summarizes the main findings of this exercise. First, it is worth noting that due to the inductive nature of the library encoder, the disclosed system and method implementation used has approximately 10 times fewer parameters than the two alternatives considered. All three methods achieve 100% chemical validity, but the disclosed system and method achieves this result without explicit validity checks. The average likelihood is computed by taking the average of the likelihood of reconstructing each compound over a large number of products sampled from the library. This is a measure of the ability of the model to reconstruct complete molecular graphs (e.g., how likely is it on average to reproduce the query molecule through the decoder), and can also be loosely interpreted as a measure of coverage / reachability (e.g., how much of the library can it faithfully cover). Finally, the example experiment highlights the challenge faced by existing graph generation models when applied to a super-large combinatorial synthesis library, namely that they struggle to reliably generate compounds within the library. For JT-VAE, less than 1 out of 34 compounds were found in REAL. On the other hand, RationaleRL generated a library-in complement in about half the cases (see Figure 7 ), but it has the advantage that it provides a starting rationale in the form of a compound from REAL with all but one synthon removed. In contrast, the disclosed system and method guarantees by design that the result comes from the library.

[0223] Table 3: Comparison of RationaleRL, JT-VAE, and CSLVAE on synthesis-based generative modeling

[0224]

[0225] Dataset preparation.

[0226] The Enamine REAL library is a combinatorial synthesis library of approximately 1300 reaction types, ranging from 2- to 4-component reactions, and approximately 340K synthons. The REAL library collectively describes over 16B chemical space of on-demand manufactured compounds. For the two baseline models currently compared, memory issues arose when using the authors’ provided code on the full REAL library (at the vocabulary generation step as well as when writing products to disk). Therefore, the two baselines were trained and evaluated on a subset of the full REAL library. The CSLVAE (model of the present disclosure) did not face memory limitations, it was trained on the full library and evaluated on it. Therefore, RationaleRL and JT-VAE can be compared on a per-project basis (each trained on the same subset of REAL), while the CSLVAE’s results reflect training on the larger and more diverse full REAL library. RationaleRL and JT-VAE were not developed with the search of combinatorial synthesis libraries in mind, and their use in this comparison serves as an attempt to compare the disclosed method (CSLVAE) to the state-of-the-art application of a generative model that is off-the-shelf and unmodified.

[0227] To construct the data on which RationaleRL and JT-VAE were trained, the 1300 reaction types were ordered according to the number of products contained in each reaction, and 50 medium-sized reactions were selected. These reactions collectively describe 125M chemical space of compounds. From each reaction, products were sampled so as to represent all synthons, totaling ~500K compounds for the training set.

[0228] RationaleRL details.

[0229] With the pre-training phase of RationaleRL, a graph-based variational autoencoder is trained that seeks to reconstruct molecular graphs from starting rationale (and does not require RL, as the name implies; this is part of the fine-tuning phase, not used here). Given a starting rationale and a complete molecule, RationaleRL’s decoder completes the molecule autoregressively, atom-by-atom, bond-by-bond. To form the starting rationale, a product of REAL is taken and all but one synthon is removed. Therefore, the task of RationaleRL is to complete the missing synthon given the complete molecule (as input to the encoder) and the starting rationale (as input to the decoder, as well as latent code). Figure 7It is shown that the probability of completion producing products in the library by RationaleRL decreases sharply as the number of different reactions in the training increases; after including 50 reactions, less than half of the completions produce products in the REAL library. These experiments are based on the authors’ provided code, available at https: / / github.com / wengong-jin / multiobj-rationale.

[0230] JT-VAE details.

[0231] JT-VAE is a graph-based variational autoencoder that generates molecules according to the tree-like structure of fragments. Unlike RationaleRL, JT-VAE samples chemical fragments in an autoregressive manner, rather than atoms or chemical bonds. Prior to training, the vocabulary generation step described in the JT-VAE paper was applied to the sample products from the REAL subset used in the baseline experiments, which collectively produced 325 fragments. These experiments are based on the authors’ provided code, available at https: / / github.com / wengong-jin / multiobj-rationale. https: / / github.com / wengong-jin / icml18-jtnn

[0232] Details of the disclosed model (CSLVAE).

[0233] During training, we used an annealing schedule for β

[49] (see Algorithm 1), starting at β = 0 and increasing by 1e-5 every 2000 iterations, with a maximum of β = 1. Training was performed for a total of 200K iterations, during which the CSLVAE had observed a total of 2000 200K = 400M compounds (although due to the batched sampling strategy, not 400M unique compounds were observed). Thus, by the time training stopped, the CSLVAE had seen no more than 2.5% of the entire REAL library.

[0234] Example 2 - Latent space visualization.

[0235] The latent space learned by the disclosed systems and methods was qualitatively examined. It is of interest to verify whether the proposed model has learned a latent space that varies relatively smoothly over the covered chemical space (e.g., small perturbations to a query induce only minor edits to the resulting molecular graph). Two checks were performed: latent space interpolation and local neighborhood visualization.

[0236] Figure 4A Examples of interpolations contained in the latent space. In particular, a molecular query for a starting compound (top left) and a target compound (bottom right) was interpolated in raster order. The molecules immediately adjacent to the starting and target compounds are the relevant reconstructions. The products were decoded from the full REAL library of 16 billion compounds. In Figure 4A ​For each molecule below, the bottom row is the Tanimoto similarity (5) of each molecule to the starting and target molecules, respectively. It is observed that interpolations traverse regions of chemical space that are progressively less (more) similar to the starting (comparing target) compound.

[0237] Figure 4B The latent space around randomly sampled products from the REAL library is visualized. Following previous work

[29] , a random 2D plane in the high-dimensional latent space is formed by sampling in two random directions around a molecular query (center compound) and decoding the resulting products using the argmax decision rule. It is observed that the latent space is smooth, as molecules are gradually transformed, only small edits are made (e.g., one synthetic at a time, modification of a smaller functional group) when motion in the latent space is small, and molecular scaffolds are generally locally conserved.

[0238] Example 3 - Analog retrieval via autoencoding.

[0239] The disclosed system and method are used to find analogs of a query compound in a large CSL. In Figure 5A and 5B , the disclosed model of the present disclosure presents two classes of molecules: molecules in the library ( Figure 5A ) and molecules not in the library ( Figure 5B ). Figure 5A Each query molecule (top left) of Figure 5B is encoded and randomly decoded fifteen times using the disclosed model (e.g., shown in Figure 1A , 1B and 3). Thus, given a molecular query, a conditioned random completion is generated from the decoder. In both cases, autoencoding retrieves highly similar compounds as measured by Tanimoto similarity. For the in-library example, the model is able to successfully retrieve the query compound (third row, second column of Figure 5A ). Furthermore, it is observed that in many cases, the compounds returned by autoencoding have the same reaction type as the query molecule, but differ in one or two synthons. For the out-of-library example, the disclosed system and method discovers scaffold-related compounds with high Tanimoto similarity, demonstrating the utility of this approach for fast analog search in large (non-enumerable) libraries.

[0240] Example 4 - Post-hoc density estimation

[0241] The use of post-hoc density estimation on latent codes corresponding to products uniformly sampled from the library is disclosed above as a way to force random samples from the CSL VAE to more closely track uniform random sampling from the library. Figure 9 Algorithm 2 in

[0242] Experiments were conducted to show that Algorithm 2 achieved the expected results. The experiments were conducted as follows. 10,000 molecules were uniformly randomly drawn from the library and treated as the training set for the posterior density estimator. Three density estimators were considered that increase expressivity: a multivariate normal distribution (MVNormal), a mixture of five normal distributions (MoG-5), and a mixture of ten normal distributions (MoG-10). Standard sampling methods for the isotropic multivariate normal prior were compared. Thus, four alternatives for sampling latent codes were used in this experiment, which were subsequently decoded into compounds from the library. Another 10,000 molecules were drawn from the library, also uniformly at random, as a reference set for comparison.

[0243] Table 4: Dispersion between query sampling strategies and the reference set of compounds uniformly randomly sampled from the library.

[0244]

[0245] Following

[41] , the above generated molecule sets were compared to the reference molecule set on the following computable molecular properties: synthetic accessibility (SA), quantitative estimate of drug-likeness (QED), molecular weight (MW), and the log of the octanol-water partition coefficient (logP). In particular, the Jensen-Shannon distance (square root of the Jensen-Shannon divergence) between the distributions of these properties for the reference set and each of the discussed sets was computed. Table 4 summarizes the results of this exercise. Three points are worth noting: (a) the reference compounds and the compounds sampled for training the posterior density estimator have low dispersion on the various properties, (b) sampling from the prior produces compounds with high dispersion relative to uniform sampling in the library, and (c) using more expressive density estimators for the latent codes results in increasingly low dispersion on the various properties from the reference set as they are able to better match the distribution of latent codes for the training set (interchangeable with the reference set).

[0246] Example 5 - Comparison to existing analog enumeration methods

[0247] In Example 5, the analogizing ability of CSLVAE was attempted to be compared to that of Arthor, the state-of-the-art commercial similarity search tool for synthetic libraries developed by NextMove Software. Arthor uses a custom ECFP4 bit vector representation of molecules to perform analogical enumeration, returning compounds with high Tanimoto similarity according to this fingerprint. For a given query compound, the top 100 analogs returned by Arthor from REAL were enumerated. Similarly, each query compound was encoded with the CSLVAE encoder and produced a corresponding 100 random decodings. For each analog, its RDKit ECFP4 tanimoto similarity was computed with the query compound and the top 1 analog was retained. The distribution of tanimoto similarities of the top 1 analogs returned in this way was compared between Arthor and CSLVAE. As a control, a simple random baseline strategy was used, randomly sampling 100 compounds from REAL and again selecting the top 1 analog based on RDKit ECFP4 tanimoto similarity. Since both CSLVAE and the random baseline constitute random strategies, this process was repeated 30 times for each query compound and the average top 1 tanimoto similarity was taken.

[0248] For the query compounds, 24 out of 51 novel drugs approved by the FDA in 2021 were used, screening out drugs that do not meet the conventional small molecule criteria (such as monoclonal antibodies); the compounds used in this experiment are shown in Table 1. Figure 10 Figure 11 The boxplot of the top 1 tanimoto similarity of Arthor, CSLVAE, and the random baseline is shown.

[0249] While CSLVAE discovered more distant ECFP4 analogs compared to Arthor (the gold standard for fingerprint similarity search), it was still able to identify analogs of unknown novel drugs in a conventional way. In this regard, a tanimoto similarity threshold in the range of 0.3-0.35 is commonly used to indicate whether a pair of molecules can be considered as analogs

[0250] ​In particular, it is worth noting that the resource intensity of CSLVAE is much lower than Arthor, which is specifically designed for fast and efficient fingerprint-based analog enumeration and requires proper infrastructure and setup. For these reasons, it is difficult to make a direct apples-to-apples comparison of computational requirements. However, the following relevant information was derived from this experiment. The CSLVAE experiment was run on a machine equipped with a NVIDIA Tesla K80 GPU and an Intel Xeon E5-2686 CPU. On average, using this setup (encoding and decoding), 100 analog samples using CSLVAE for a given query was completed in 11.41 seconds. Furthermore, all parameters and buffers of the trained CSLVAE model (including the representations and keys of the synthetic substructures, R-groups, and reactions) only require 170 MB of memory. In comparison, the Arthor experiment was run in a distributed manner on 100 pods, each equipped with 8 CPUs, and the first 100 analog enumerations took a total of 32.46 seconds, with a total CPU time of approximately 25,968 seconds. In addition, Arthor requires a considerable amount of memory and storage to be invested to perform analog enumeration; our internal setup uses 3 GB per fragment and issues a 64 GB RAM request for each Arthor worker.

[0251] We note that CSLVAE is able to represent large CSLs with significantly fewer resources and perform analog retrieval with significantly improved execution time (potentially three orders of magnitude faster) thanks to its decoding strategy, which leverages parallel synthetic substructure lookup, thereby requiring a number of keys comparable to the number of synthetic substructures in the library, rather than a number of keys comparable to the number of products in the library, and also allows for a similarity search in time that is logarithmic (rather than linear) in the number of products in the library.

[0252] Example 6 - Encoder transfer to molecular property prediction

[0253] The CSLVAE training objective can be seen as a kind of contrastive pretext task that seeks to align the representation of a given molecule with the representation corresponding to the extraction instructions in the CSL. It is therefore natural to wonder whether the encoder of a trained CSLVAE model can exhibit good transfer performance in prediction tasks that can be of interest. To investigate, the MLP trained on CSLVAE was compared to MLPs trained on molecular fingerprints (ECFP4 and ECFP6) for molecular property prediction tasks. The octanol-water partition coefficient (logP) and the quantitative estimate of drug similarity (QED) [6] were used as targets for prediction.

[0254] For this experiment, the dataset was constructed by uniformly randomly drawing 100K compounds from REAL, using an 80-10-10 split to divide the examples into training, validation, and test folds. For each compound, in addition to its ECFP4 and ECFP6 fingerprints, its CSLVAE query was extracted as its feature descriptor. Using the training fold, an MLP was fitted to each feature descriptor to predict the logP and QED scores of the molecules, respectively. The iteration that achieved the lowest validation RMSE was selected, and its test RMSE was recorded. This was repeated five times, and the average test RMSE and standard deviation were reported. To demonstrate the extent to which the CSLVAE learned molecular features that predict such molecular properties for out-of-domain compounds, this exercise was repeated on a dataset of 250K molecules from ZINC. Table 5 summarizes the results of this exercise.

[0255] Table 5: Encoder transfer based on logP and QED prediction. Cells report the average RMSE ± 1 standard deviation, computed over five runs.

[0256]

[0257] The results of this experiment confirm that the latent space learned by the CSLVAE can indeed be used to successfully predict quantities like logP and QED, especially in the in-domain case, where it outperforms predictors fitted to chemical fingerprints. However, in the out-of-domain case, the predictor fitted on ECFP6 fingerprints performs significantly better than the predictor fitted on CSLVAE queries, suggesting that the features learned by the CSLVAE can have lost some relevant prediction information about the input molecules that is significantly different from the CSL it was trained on.

[0258] Example 7 - Overview of CSLVAE architecture used in examples.

[0259] Table 6 summarizes the number of parameters used in the example CSLVAE architecture of the examples of the present disclosure.

[0260] Table 6: Overview of CSLVAE architecture used in examples

[0261]

[0262]

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[0325] CONCLUSION

[0326] For the purposes of explanation, the preceding description has been described with reference to particular implementations. The illustrative discussions above, however, are not intended to be exhaustive or to limit the described implementations to the precise forms disclosed. Many modifications and variations are possible in light of the above teachings. It is intended that the selected and described implementations be considered as part of a total disclosure, and be considered for what they can contribute to the practice of the application in various embodiments.

Claims

1. A computer system for querying a library of combinatorial synthesis of multiple compounds, wherein The combinatorial synthesis library represents multiple reaction types. Each of the multiple reaction types has a corresponding mapping to the corresponding multiple reactants, and Each of the multiple reactants has a corresponding mapping to the multiple synthons, and the computer system includes: One or more central processing units; One or more graphics processors, wherein each of the one or more graphics processors includes 100 or more cores; as well as A memory addressable by the one or more central processing units, the memory storing at least one program for execution at least in part by the one or more graphics processors, the at least one program comprising instructions for: (A) Inputting a query into a molecular encoder model, wherein the query is a single graph, wherein the molecular encoder model includes a message passing neural network, the message passing neural network including multiple message passing layers that collectively include a first plurality of parameters, thereby obtaining a query vector by applying the first plurality of parameters to the single graph; (B) Input the query vector into a reaction query generator model that includes a second plurality of parameters, thereby obtaining a first reaction type among the plurality of reaction types by applying the second plurality of parameters to the query vector, which is the output of the reaction query generator model; (C) By inputting the corresponding reactant into a synthesizer query generator model including a third plurality of parameters, and thereby obtaining a corresponding synthesizer as the output of the synthesizer query generator model by applying the third plurality of parameters to the corresponding reactant, a corresponding synthesizer corresponding to each of the first plurality of reactants of the first reaction type is determined from the corresponding plurality of synthesizers mapped to the corresponding reactant, thereby determining a set of synthesizers, each of the synthesizers in the set corresponding to a reactant in the first plurality of reactants; and (D) Identify the molecular structures in the combinatorial synthesis library, which includes the set of synthons arranged according to synthesis rules associated with the first reaction type.

2. The computer system according to claim 1, wherein the reaction query generator model is a two-layer perceptron with intermediate ReLU activation.

3. The computer system according to claim 1, wherein the synthetic subquery generator model is a two-layer perceptron with intermediate ReLU activation.

4. The computer system according to claim 1, wherein The first plurality of parameters includes 100,000 parameters. The second set of parameters includes 5,000 parameters, and The third set of multiple parameters includes 5,000 parameters.

5. The computer system according to claim 1, wherein... The single graph includes multiple nodes and multiple edges, and Each of the plurality of nodes is connected to another node of the plurality of nodes through at least one of the plurality of edges.

6. The computer system of claim 5, wherein each of the plurality of nodes is associated with: (i) The corresponding element type among multiple element types. (ii) The degree of a node among multiple node degrees. (iii) Hybridization in multiple hybridization (iv) Multiple bonded hydrogens, (v) The formal charges in a set of formal charges, and (vi) Aromatic binary indicator.

7. The computer system of claim 6, wherein each of the plurality of keys is associated with: (i) Key type, (ii) Conjugate binary indicators (iii) A binary indicator of whether the corresponding key is within the loop, and (iv) Stereochemical indications.

8. A method for querying a combinatorial synthesis library comprising multiple compounds, wherein The combinatorial synthesis library represents multiple reaction types. Each of the multiple reaction types has a corresponding mapping to the corresponding multiple reactants, and Each corresponding reactant in a plurality of reactants has a corresponding mapping to the corresponding plurality of synthons, and The method is executed on a computer system, the computer system comprising: One or more central processing units; One or more graphics processors, wherein each of the one or more graphics processors includes 100 or more cores; as well as A memory addressable by the one or more central processing units, the memory storing at least one program executable at least partially by the one or more graphics processors, the at least one program including instructions to perform the method, the method comprising: (A) Inputting a query into a molecular encoder model, wherein the query is a single graph, wherein the molecular encoder model includes a message passing neural network, the message passing neural network including multiple message passing layers that collectively include a first plurality of parameters, thereby obtaining a query vector by applying the first plurality of parameters to the single graph; (B) Input the query vector into a reaction query generator model that includes a second plurality of parameters, thereby obtaining a first reaction type among the plurality of reaction types by applying the second plurality of parameters to the query vector, which is the output of the reaction query generator model; (C) By inputting the corresponding reactant into a synthesizer query generator model including a third plurality of parameters, and thereby obtaining a corresponding synthesizer as the output of the synthesizer query generator model by applying the third plurality of parameters to the corresponding reactant, a corresponding synthesizer for each of the first plurality of reactants is determined from the corresponding plurality of synthesizers mapped to the corresponding reactant, thereby determining a set of synthesizers, each synthesizer in the set of synthesizers corresponding to a reactant in the first plurality of reactants; and (D) Identify the molecular structures in the combinatorial synthesis library, which includes the set of synthons arranged according to synthesis rules associated with the first reaction type.

9. A computer-readable storage medium storing one or more programs, said one or more programs comprising instructions, which, when executed by a computer system having one or more central processing units and one or more graphics processors, each of said one or more graphics processors comprising 100 or more cores, and memory causing the computer system to query a composition library, wherein... The combinatorial synthesis library represents multiple reaction types. Each of the multiple reaction types has a corresponding mapping to the corresponding multiple reactants, and Each corresponding reactant in a plurality of reactants has a corresponding mapping to the plurality of synthons. The query of the combined synthesis library is performed at least in part by the one or more graphics processors, through methods including: (A) Inputting a query into a molecular encoder model, wherein the query is a single graph, wherein the molecular encoder model includes a message passing neural network, the message passing neural network including multiple message passing layers that collectively include a first plurality of parameters, thereby obtaining a query vector by applying the first plurality of parameters to the single graph; (B) Input the query vector into a reaction query generator model that includes a second plurality of parameters, thereby obtaining a first reaction type among the plurality of reaction types by applying the second plurality of parameters to the query vector, which is the output of the reaction query generator model; (C) By inputting the corresponding reactant into a synthesizer query generator model including a third plurality of parameters, and thereby obtaining a corresponding synthesizer as the output of the synthesizer query generator model by applying the third plurality of parameters to the corresponding reactant, a corresponding synthesizer for each of the first plurality of reactants is determined from the corresponding plurality of synthesizers mapped to the corresponding reactant, thereby determining a set of synthesizers, each synthesizer in the set of synthesizers corresponding to a reactant in the first plurality of reactants; and (D) Identify the molecular structures in the combinatorial synthesis library, which includes the set of synthons arranged according to synthesis rules associated with the first reaction type.

10. A computer system for querying a library of combinatorial synthesis of multiple compounds, wherein The combinatorial synthesis library represents multiple reaction types. Each of the multiple reaction types has a corresponding mapping to the corresponding multiple reactants, and Each of the multiple reactants has a corresponding mapping to the multiple synthons, and the computer system includes: One or more processors; A memory addressable by the one or more processors, the memory storing at least one program executable by the one or more processors, the at least one program comprising instructions for: (A) Inputting a query into a molecular encoder model, wherein the query is an arbitrary graph, wherein the molecular encoder model includes a first plurality of parameters, thereby obtaining a query vector by applying the first plurality of parameters to the arbitrary graph; (B) Input the query vector into a reaction query generator model that includes a second plurality of parameters, thereby obtaining a first reaction type among the plurality of reaction types by applying the second plurality of parameters to the query vector, which is the output of the reaction query generator model; (C) By inputting the corresponding reactant into a synthesizer query generator model including a third plurality of parameters, and thereby obtaining a corresponding synthesizer as the output of the synthesizer query generator model by applying the third plurality of parameters to the corresponding reactant, a corresponding synthesizer corresponding to each of the first plurality of reactants of the first reaction type is determined from the corresponding plurality of synthesizers mapped to the corresponding reactant, thereby determining a set of synthesizers, each of the synthesizers in the set corresponding to a reactant in the first plurality of reactants; and (D) Identify the molecular structures in the combinatorial synthesis library, which includes the set of synthons arranged according to synthesis rules associated with the first reaction type.

11. The computer system of claim 10, wherein the reaction query generator model is a two-layer perceptron with intermediate ReLU activation.

12. The computer system of claim 10, wherein the synthetic subquery generator model is a two-layer perceptron with intermediate ReLU activation.

13. The computer system according to claim 10, wherein The first plurality of parameters includes 100,000 parameters. The second set of parameters includes 5,000 parameters, and The third set of multiple parameters includes 5,000 parameters.

14. The computer system of claim 10, wherein The arbitrary graph includes multiple nodes and multiple edges, and Each of the plurality of nodes is connected to another node of the plurality of nodes through at least one of the plurality of edges.

15. The computer system of claim 14, wherein each of the plurality of nodes is associated with: (i) The corresponding element type among multiple element types. (ii) The degree of a node among multiple node degrees. (iii) Hybridization in multiple hybridization (iv) Multiple bonded hydrogens, (v) The formal charges in a set of formal charges, and (vi) Aromatic binary indicator.

16. The computer system of claim 15, wherein each of the plurality of keys is associated with: (i) Key type, (ii) Conjugate binary indicators (iii) A binary indicator of whether the corresponding key is within the loop, and (iv) Stereochemical indications.

17. A method for querying a combinatorial synthesis library comprising multiple compounds, wherein The combinatorial synthesis library represents multiple reaction types. Each of the multiple reaction types has a corresponding mapping to the corresponding multiple reactants, and Each corresponding reactant in a plurality of reactants has a corresponding mapping to the corresponding plurality of synthons, and The method is executed on a computer system, the computer system comprising: One or more processors; A memory addressable by the one or more processors, the memory storing at least one program executable by the one or more processors, the at least one program including instructions for performing a method, the method comprising: (A) Inputting a query into a molecular encoder model, wherein the query is an arbitrary graph, the molecular encoder model includes a first plurality of parameters, thereby obtaining a query vector by applying the first plurality of parameters to the arbitrary graph; (B) Input the query vector into a reaction query generator model that includes a second plurality of parameters, thereby obtaining a first reaction type among the plurality of reaction types by applying the second plurality of parameters to the query vector, which is the output of the reaction query generator model; (C) By inputting the corresponding reactant into a synthesizer query generator model including a third plurality of parameters, and thereby obtaining a corresponding synthesizer as the output of the synthesizer query generator model by applying the third plurality of parameters to the corresponding reactant, a corresponding synthesizer for each of the first plurality of reactants is determined from the corresponding plurality of synthesizers mapped to the corresponding reactant, thereby determining a set of synthesizers, each synthesizer in the set of synthesizers corresponding to a reactant in the first plurality of reactants; and (D) Identify the molecular structures in the combinatorial synthesis library, which includes the set of synthons arranged according to synthesis rules associated with the first reaction type.

18. A computer-readable storage medium storing one or more programs, said one or more programs comprising instructions, which, when executed by said computer system having one or more processors and a memory that causes the computer system to query a composite library, wherein The combinatorial synthesis library represents multiple reaction types. Each of the multiple reaction types has a corresponding mapping to the corresponding multiple reactants, and Each corresponding reactant in a plurality of reactants has a corresponding mapping to the plurality of synthons. By including the following methods: (A) Inputting a query into a molecular encoder model, wherein the query is an arbitrary graph, the molecular encoder model includes a first plurality of parameters, thereby obtaining a query vector by applying the first plurality of parameters to the arbitrary graph; (B) Input the query vector into a reaction query generator model that includes a second plurality of parameters, thereby obtaining a first reaction type among the plurality of reaction types by applying the second plurality of parameters to the query vector, which is the output of the reaction query generator model; (C) By inputting the corresponding reactant into a synthesizer query generator model including a third plurality of parameters, and thereby obtaining a corresponding synthesizer as the output of the synthesizer query generator model by applying the third plurality of parameters to the corresponding reactant, a corresponding synthesizer for each of the first plurality of reactants is determined from the corresponding plurality of synthesizers mapped to the corresponding reactant, thereby determining a set of synthesizers, each synthesizer in the set of synthesizers corresponding to a reactant in the first plurality of reactants; and (D) Identify the molecular structures in the combinatorial synthesis library, which includes the set of synthons arranged according to synthesis rules associated with the first reaction type.

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