Deep Evolutionary Learning for Molecular Design

1 INTRODUCTION . A drug is a molecule that binds to a target ( e.g . protein ) to inhibit or activate specific pathways in pathogens or host cells that cause abnormal phenotype . Drug discovery and development is a costly and time-consuming process , which is compounded by personalized medicines development for cancer or other complex and rare diseases . Computational drug discovery has been shown to accelerate the whole discovery process using simulations and machine intelligence . However , challenge remains in this field by demands for a robust and unbiased feature representation theories for molecules and their corresponding receptors , and efficient search algorithms . The rise of AI and data science provides us with a unique opportunity to reevaluate the problem and develop fast intelligent search or design approaches ( Gromski et al. , 2019 ; Chen et al. , 2018 ) . These new technologies claim differences from the traditional ones in two aspects : ( 1 ) features can be automatically learned using embedding techniques on a large number of training samples , and ( 2 ) high-level relationships ( in supervised case ) and complex distributions ( in unsupervised case ) can be captured using appropriate deep architectures . Recently , new representation theories and architectures have been proposed in the domain of molecular generation . There exist two new major methods to present a molecule for a machine learning algorithm . The first method converts a molecule structure to a string , such as the simplified molecular-input line-entry system ( SMILES ) string ( Weininger , 1988 ) , and adopt natural language processing ( NLP ) methods for supervised or unsupervised learning . The second uses an undirected graph to present a molecular structure and applies graph convolutional neural networks ( Duvenaud et al. , 2015 ) . Three major families of AI algorithms have been developed for novel drug discovery : deep generative models ( DGMs ) , reinforcement learning , and the combination of both . As one family of major neural probabilistic models for data modelling , generative autoencoders ( e.g . variational autoencoder ( VAE ) ( Kingma & Welling , 2014 ) ) have been adopted to learn on either SMILES strings ( Romez-Bombarelli et al. , 2018 ) or molecular graphs ( Simonovsky & Komodakis , 2018 ) with corresponding physical and biochemical properties for molecular generation . By integrating the generative adversarial nets and autoencoders , adversarial autoencoders ( AAEs ) have also been well applied to molecular design ( Kadurin et al. , 2017 ) . The advantage of using generative autoencoders is that , molecules , as discrete objects in our world , are mapped to the continuous latent space , whose landscape can be organized by their properties , which helps generate new structures with preferred property values . However , critical problems remain due to imperfect representation methods . When SMILES strings are used in VAE , the model suffers from imbalance of tokens in embedding , generation of invalid structures , and the problem where two almost identical molecules have markedly different canonical SMILES strings . When using graph as molecular representation in VAE , a technical difficulty is to design an effective graph decoder . In addition to other heuristic methods , a SMILES decoder can be used to pair with a graph encoder . While DGMs offer convenience of searching in latent space , reinforcement learning algorithms can directly search in the molecules ’ structural space by adding or deleting bounds and atoms ( Zhou et al. , 2019 ) . In the Markov decision process ( MDP ) for drug design , the agent is a molecular generator , the molecular structure indicates the state , the actions are modifications to the current structure , and a simulator ( e.g . surrogate model ) is often used as the environment to provide reward . Furthermore , generative and predictive models can be integrated in MDP to form deep reinforcement learning ( DRL ) methods , where the generative model is trained as a policy approximation and the predictive model can be used as a value function approximation ( You et al. , 2018 ; Popova et al. , 2018 ) . Search in the discrete input space and inefficient learning are arguable concerns to be addressed when applying reinforcement-learning-based solutions for compound design . Interestingly , as an old peer of reinforcement learning for black-box optimizations , evolutionary computation ( EC ) methods ( Eiben & Smith , 2015 ) have been catching up with promising performances in modern optimization , design and modelling problems . Besnard et al . ( 2012 ) present a strategy for evolution of ligands along multiple properties in the structural space , where a library of knowledge-based chemical structural transformation is used as the mutation operator . Interactions between EC and neural networks have mainly focused on network evolution and neural surrogate models for fitness functions . For examples , EC has been used at a large scale for neuroevolution that leads to evolution of neural network architectures ( Stanley et al. , 2019 ) ; feedforward neural network is commonly used as fitness function in EC ( Mandal et al. , 2019 ) . Furthermore , it has been recently discovered that evolutionary strategy ( ES ) can perform competitively with reinforcement learning in game AI ( Salimans et al. , 2017 ) . ES ( Wierstra et al. , 2014 ) and estimation of distribution algorithms ( EDA ) ( Hauschild & Pelikan , 2011 ) build parameterized search distributions over promising points and either employ gradient information or sample from such a probabilistic model to find better points . Both probabilistic strategies from EC can potentially be used as alternatives to Bayesian optimization ( BO ) in ( continuous ) black-box optimizations . A single-objective BO has been recently applied to molecule optimization in the latent space of VAE ( Romez-Bombarelli et al. , 2018 ) . Since model learning is essentially parameter estimation from the statistical modelling perspective , the quality of data in deep learning is crucial for model performance . Data augmentation is becoming a new strategy in deep learning to improve the training of a model . For example , in computer vision , transformations ( such as rotation and flipping ) of images are used to increase the sample size when the original data set is insufficient ( Perez & Wang , 2017 ; Cubuk et al. , 2019 ; Shorten & Khoshgoftaar , 2019 ) . In NLP , a text dataset can be augmented using tricks such as replacing words or phrases with their synonyms ( Wei & Zou , 2019 ) , and resorting aids from other language models ( e.g . word embedding and neural machine translations ) ( Sennrich et al. , 2016 ; Wei & Zou , 2019 ) . Basically , these methods either increase the data by transforming existing information which can only alleviate the limit of certain techniques ( e.g . convolution ) , or indirectly borrow new information from other sources ( e.g . methods in NLP ) . In summary , even though modern machine learning , evolutionary computation , and data science methods have been applied to molecular design and achieved promising results , we are still challenged by three chief issues . ( 1 ) An effective representation method for compound structures , that is encoding-decoding friendly and invariant to multimorphic forms , is still missing . ( 2 ) New ideas are expected for effective representation and coding of discrete structures in EC . And , ( 3 ) quality of data can be further improved as current data augmentation tricks only increase the number of samples but does not specifically address data quality . In this paper , we propose a novel deep evolutionary learning ( DEL ) process that combines the merits of deep generative model and multi-objective evolutionary computation together for molecular design . Specifically , our work has three major contributions . ( 1 ) In our approach , latent representations of phenotypic samples in a population serve as genotypic codes for evolutionary operations.This approach differs from traditional evolutionary algorithms that search in the original space of a problem . Specifically , our framework ’ s DGM encoder projects molecular structures in a population from discrete space to continuous latent space where evolutionary operations are applied to help explore the latent representation space . Subsequently , the DGM decoder maps the genotypic representation to the phenotypic space for generating new molecules with desired property values . ( 2 ) In each evolutionary generation , the newly formed population containing novel competitive molecules can be used to further fine-tune the DGM . This approach is an innovative data augmentation strategy that enriches training data with novel high- quality samples . The whole DEL process implements a new learning paradigm that co-evolves data and model alternatingly through multiple evolutionary generations . ( 3 ) Our comprehensive experiments demonstrate that DEL is able to produce populations of novel samples with improved values of properties and outperforms state-of-the-art multi-objective BO algorithms ( MOBO ) . 2 METHOD . The proposed deep evolutionary learning ( DEL ) process combines deep learning and multi-objective EC through the latent representation space of molecules . One of the theoretical innovations of our approach is that it demonstrates that EC methods are extendable to corresponding deep versions . The main idea is illustrated in Figure 1a and formally presented in Algorithm 1 ( see Appendix A.1 ) . This algorithm consists of the following steps . ( a ) A VAE ( as molecule modeller ) and a multilayer perceptron neural network ( MLP , property predictor as regularizer ) are pretrained using all the original training data to start the first evolutionary generation , or , if not in the first generation , using samples from the previous population . ( b ) Training samples ( if first generation ) or population samples ( otherwise ) are projected to the latent space using the encoder of the VAE . ( c ) Based on non-dominated ranking and crowding distances of samples with respect to multiple properties , evolutionary operations ( selection , recombination/crossover and mutation ) are conducted on the latent representations of the samples . ( d ) Given these new latent codes after evolutionary operations , new molecule samples are generated by the decoder of the VAE . ( e ) Properties of these generated samples are obtained using a simulator ( e.g . RDKit ( Landrum , 2006 ) in our experiment ) . ( f ) New samples with good desired properties and good samples from the previous generation form the new population . ( g ) Steps ( b-f ) are iterated for multiple generations . ( h ) The final population is returned . The major advantages of our DEL algorithm over existing interactions between EC and neural networks can be explained as follows . ( a ) We directly evolve a collection of data rather than many neural network structures and parameters . Data evolution tends to be more efficient than direct evolution of model structures and parameters . ( b ) The single neural network model ( i.e . DGM in DEL ) can be indirectly improved through learning on the evolved data with modern gradient-based variational learning and inference algorithms . Thus , the improvement of populations along evolutionary generations can be viewed as an effective data augmentation strategy that includes novel and highquality samples for further training of the neural network . ( c ) The continuous latent representation space established by the encoder of DGM can be naturally used as encoding ( genotypic ) space for evolutionary computation . Thus , evolutionary operations are carried out in the latent space instead of the discrete structural input space , allowing more efficient and smooth exploration , because the latent space is often multimodal and can be organized by properties ( regularized by the property predictor ) and evolutionary operations in this space can help the search escape from local regions and explore new regions of interest . ( d ) The multi-objective operations - non-dominated sorting and crowding distance , can help identify competitive and diverse parent samples to breed offspring . In summary , DEL takes advantages of both multi-objective EC and probabilistic neural model learning . The DGM , multi-objective components ( non-dominated sorting and crowding distance ) , evolutionary operations , formation of new populations are discussed in details as below .

Summary: The paper proposes to tackle multi-objective optimization of molecular properties by combining a genetic algorithm with a fragment-based generative model of SMILES strings. Using a generative model allows to perform evolution in the latent space, as opposed to molecule space. Experiments show the model can produce a rich Pareto front of samples, outperforming bayesian optimization ran in the latent space of the same generative model.