Machine learning on trees has been mostly focused on trees as input to algorithms. Much less research has investigated trees as output, which has many applications, such as molecule optimization for drug discovery, or hint generation for intelligent tutoring systems. In this work, we propose a novel autoencoder approach, called recursive tree grammar autoencoder (RTG-AE), which encodes trees via a bottom-up parser and decodes trees via a tree grammar, both learned via recursive neural networks that minimize the variational autoencoder loss. The resulting encoder and decoder can then be utilized in subsequent tasks, such as optimization and time series prediction. RTG-AEs are the first model to combine variational autoencoders, grammatical knowledge, and recursive processing. Our key message is that this unique combination of all three elements outperforms models which combine any two of the three. In particular, we perform an ablation study to show that our proposed method improves the autoencoding error, training time, and optimization score on synthetic as well as real datasets compared to four baselines. We further prove that RTG-AEs parse and generate trees in linear time and are expressive enough to handle all regular tree grammars.
MIT-IBM Watson AI Lab（MIT-IBM沃森人工智能实验室）；IBM Research（IBM研究院）
Molecular optimization aims to discover novel molecules with desirable properties. Two fundamental challenges are: (i) it is not trivial to generate valid molecules in a controllable way due to hard chemical constraints such as the valency conditions, and (ii) it is often costly to evaluate a property of a novel molecule, and therefore, the number of property evaluations is limited. These challenges are to some extent alleviated by a combination of a variational autoencoder (VAE) and Bayesian optimization (BO). VAE converts a molecule into/from its latent continuous vector, and BO optimizes a …
Samsung AI Center（三星人工智能中心）；Rutgers University（罗格斯大学）
Inference networks of traditional Variational Autoencoders (VAEs) are typically amortized, resulting in relatively inaccurate posterior approximation compared to instance-wise variational optimization. Recent semi-amortized approaches were proposed to address this drawback; however, their iterative gradient update procedures can be computationally demanding. To address these issues, in this paper we introduce an accurate amortized inference algorithm. We propose a novel recursive mixture estimation algorithm for VAEs that iteratively augments the current mixture with new components so as to ma…
Recursive Variational Autoencoders for 3D Blood Vessel Generative Modeling
Consejo Nacional de Investigaciones Científicas y Técnicas（阿根廷国家科学与技术研究院）；Universidad Torcuato Di Tella（托科托迪塔拉大学）；Depto. Ing. Eléctrica y Computadoras, Universidad Nacional del Sur（国家南部大学电子工程与计算机系）
Robotics Institute（机器人研究所）；Carnegie Mellon University（卡内基梅隆大学）；Department of Mechanical Engineering（机械工程系）
Robots have been used in all sorts of automation, and yet the design of robots remains mainly a manual task. We seek to provide design tools to automate the design of robots themselves. An important challenge in robot design automation is the large and complex design search space which grows exponentially with the number of components, making optimization difficult and sample inefficient. In this work, we present Grammar-guided Latent Space Optimization (GLSO), a framework that transforms design automation into a low-dimensional continuous optimization problem by training a graph variational a…
We present a syntax-infused variational autoencoder (SIVAE), that integrates sentences with their syntactic trees to improve the grammar of generated sentences. Distinct from existing VAE-based text generative models, SIVAE contains two separate latent spaces, for sentences and syntactic trees. The evidence lower bound objective is redesigned correspondingly, by optimizing a joint distribution that accommodates two encoders and two decoders. SIVAE works with long short-term memory architectures to simultaneously generate sentences and syntactic trees. Two versions of SIVAE are proposed: one ca…
Tree data occurs in many forms, such as computer programs, chemical molecules, or natural language. Unfortunately, the non-vectorial and discrete nature of trees makes it challenging to construct functions with tree-formed output, complicating tasks such as optimization or time series prediction. Autoencoders address this challenge by mapping trees to a vectorial latent space, where tasks are easier to solve, and then mapping the solution back to a tree structure. However, existing autoencoding approaches for tree data fail to take the specific grammatical structure of tree domains into accoun…
Georgia Institute of Technology（佐治亚理工学院）；Stony Brook University（石溪大学）；Ant Financial（蚂蚁金服）
Deep generative models have been enjoying success in modeling continuous data. However it remains challenging to capture the representations for discrete structures with formal grammars and semantics, e.g., computer programs and molecular structures. How to generate both syntactically and semantically correct data still remains largely an open problem. Inspired by the theory of compiler where the syntax and semantics check is done via syntax-directed translation (SDT), we propose a novel syntax-directed variational autoencoder (SD-VAE) by introducing stochastic lazy attributes. This approach c…
University of Notre Dame（圣母大学）；Indiana University（印第安纳大学）
It is natural for probabilistic programs to use conditionals to express alternative substructures in models, and loops (recursion) to express repeated substructures in models. Thus, probabilistic programs with conditionals and recursion motivate ongoing interest in efficient and general inference. A factor graph grammar (FGG) generates a set of factor graphs that do not all need to be enumerated in order to perform inference. We provide a semantics-preserving translation from first-order probabilistic programs with conditionals and recursion to FGGs.
University of Copenhagen（哥本哈根大学）；Aalto University（阿尔托大学）；Technical University of Denmark（丹麦技术大学）
Variational Autoencoders are powerful models for unsupervised learning. However deep models with several layers of dependent stochastic variables are difficult to train which limits the improvements obtained using these highly expressive models. We propose a new inference model, the Ladder Variational Autoencoder, that recursively corrects the generative distribution by a data dependent approximate likelihood in a process resembling the recently proposed Ladder Network. We show that this model provides state of the art predictive log-likelihood and tighter log-likelihood lower bound compared t…
Invertible transformation of large graphs into fixed dimensional vectors (embeddings) remains a challenge. Its overcoming would reduce any operation on graphs to an operation in a vector space. However, most existing methods are limited to graphs with tens of vertices. In this paper we address the above challenge with recursive neural networks - the encoder and the decoder. The encoder network transforms embeddings of subgraphs into embeddings of larger subgraphs, and eventually into the embedding of the input graph. The decoder does the opposite. The dimension of the embeddings is constant re…
Digital and Cognitive Musicology Lab（数字与认知音乐学实验室）；École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
Probabilistic context-free grammars (PCFGs) and dynamic Bayesian networks (DBNs) are widely used sequence models with complementary strengths and limitations. While PCFGs allow for nested hierarchical dependencies (tree structures), their latent variables (non-terminal symbols) have to be discrete. In contrast, DBNs allow for continuous latent variables, but the dependencies are strictly sequential (chain structure). Therefore, neither can be applied if the latent variables are assumed to be continuous and also to have a nested hierarchical dependency structure. In this paper, we present Recur…
Tree-structured recursive neural networks (TreeRNNs) for sentence meaning have been successful for many applications, but it remains an open question whether the fixed-length representations that they learn can support tasks as demanding as logical deduction. We pursue this question by evaluating whether two such models---plain TreeRNNs and tree-structured neural tensor networks (TreeRNTNs)---can correctly learn to identify logical relationships such as entailment and contradiction using these representations. In our first set of experiments, we generate artificial data from a logical grammar …
Mila / University of Montreal（Mila / 蒙特利尔大学）；Dept. of Linguistics（语言学系）；Mila / McGill University（Mila / 麦吉尔大学）；Microsoft Research（微软研究院）；Canada CIFAR AI Chair（加拿大CIFAR人工智能主席）
We model the recursive production property of context-free grammars for natural and synthetic languages. To this end, we present a dynamic programming algorithm that marginalises over latent binary tree structures with $N$ leaves, allowing us to compute the likelihood of a sequence of $N$ tokens under a latent tree model, which we maximise to train a recursive neural function. We demonstrate performance on two synthetic tasks: SCAN (Lake and Baroni, 2017), where it outperforms previous models on the LENGTH split, and English question formation (McCoy et al., 2020), where it performs comparably…
In this paper we explore how machine learning techniques can be applied to the discovery of efficient mathematical identities. We introduce an attribute grammar framework for representing symbolic expressions. Given a set of grammar rules we build trees that combine different rules, looking for branches which yield compositions that are analytically equivalent to a target expression, but of lower computational complexity. However, as the size of the trees grows exponentially with the complexity of the target expression, brute force search is impractical for all but the simplest of expressions.…
University of Edinburgh（爱丁堡大学）；Facebook AI Research（Facebook人工智能研究院）
There has been considerable attention devoted to models that learn to jointly infer an expression's syntactic structure and its semantics. Yet, \citet{NangiaB18} has recently shown that the current best systems fail to learn the correct parsing strategy on mathematical expressions generated from a simple context-free grammar. In this work, we present a recursive model inspired by \newcite{ChoiYL18} that reaches near perfect accuracy on this task. Our model is composed of two separated modules for syntax and semantics. They are cooperatively trained with standard continuous and discrete optimiz…
