Optimization of discrete structures aims at generating a new structure with the better property given an existing one, which is a fundamental problem in machine learning. Different from the continuous optimization, the realistic applications of discrete optimization (e.g., text generation) are very challenging due to the complex and long-range constraints, including both syntax and semantics, in discrete structures. In this work, we present SAGS, a novel Simulated Annealing framework for Graph and Sequence optimization. The key idea is to integrate powerful neural networks into metaheuristics (e.g., simulated annealing, SA) to restrict the search space in discrete optimization. We start by defining a sophisticated objective function, involving the property of interest and pre-defined constraints (e.g., grammar validity). SAGS searches from the discrete space towards this objective by performing a sequence of local edits, where deep generative neural networks propose the editing content and thus can control the quality of editing. We evaluate SAGS on paraphrase generation and molecule generation for sequence optimization and graph optimization, respectively. Extensive results show that our approach achieves state-of-the-art performance compared with existing paraphrase generation methods in terms of both automatic and human evaluations. Further, SAGS also significantly outperforms all the previous methods in molecule generation.
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Most physical processes posses structural properties such as constant energies, volumes, and other invariants over time. When learning models of such dynamical systems, it is critical to respect these invariants to ensure accurate predictions and physically meaningful behavior. Strikingly, state-of-the-art methods in Gaussian process (GP) dynamics model learning are not addressing this issue. On the other hand, classical numerical integrators are specifically designed to preserve these crucial properties through time. We propose to combine the advantages of GPs as function approximators with structure preserving numerical integrators for dynamical systems, such as Runge-Kutta methods. These integrators assume access to the ground truth dynamics and require evaluations of intermediate and future time steps that are unknown in a learning-based scenario. This makes direct inference of the GP dynamics, with embedded numerical scheme, intractable. Our key technical contribution is the evaluation of the implicitly defined Runge-Kutta transition probability. In a nutshell, we introduce an implicit layer for GP regression, which is embedded into a variational inference-based model learning scheme.
Molecular Dynamics (MD) simulation is a powerful tool for understanding the dynamics and structure of matter. Since the resolution of MD is atomic-scale, achieving long time-scale simulations with femtosecond integration is very expensive. In each MD step, numerous redundant computations are performed which can be learnt and avoided. These redundant computations can be surrogated and modeled by a deep learning model like a Graph Neural Network (GNN). In this work, we developed a GNN Accelerated Molecular Dynamics (GAMD) model that achieves fast and accurate force predictions and generates trajectories consistent with the classical MD simulations. Our results show that GAMD can accurately predict the dynamics of two typical molecular systems, Lennard-Jones (LJ) particles and Water (LJ+Electrostatics). GAMD's learning and inference are agnostic to the scale, where it can scale to much larger systems at test time. We also performed a comprehensive benchmark test comparing our implementation of GAMD to production-level MD softwares, where we showed GAMD is competitive with them on the large-scale simulation.
The inductive biases of graph representation learning algorithms are often encoded in the background geometry of their embedding space. In this paper, we show that general directed graphs can be effectively represented by an embedding model that combines three components: a pseudo-Riemannian metric structure, a non-trivial global topology, and a unique likelihood function that explicitly incorporates a preferred direction in embedding space. We demonstrate the representational capabilities of this method by applying it to the task of link prediction on a series of synthetic and real directed graphs from natural language applications and biology. In particular, we show that low-dimensional cylindrical Minkowski and anti-de Sitter spacetimes can produce equal or better graph representations than curved Riemannian manifolds of higher dimensions.
Drug Discovery is a fundamental and ever-evolving field of research. The design of new candidate molecules requires large amounts of time and money, and computational methods are being increasingly employed to cut these costs. Machine learning methods are ideal for the design of large amounts of potential new candidate molecules, which are naturally represented as graphs. Graph generation is being revolutionized by deep learning methods, and molecular generation is one of its most promising applications. In this paper, we introduce a sequential molecular graph generator based on a set of graph neural network modules, which we call MG^2N^2. At each step, a node or a group of nodes is added to the graph, along with its connections. The modular architecture simplifies the training procedure, also allowing an independent retraining of a single module. Sequentiality and modularity make the generation process interpretable. The use of graph neural networks maximizes the information in input at each generative step, which consists of the subgraph produced during the previous steps. Experiments of unconditional generation on the QM9 and Zinc datasets show that our model is capable of generalizing molecular patterns seen during the training phase, without overfitting. The results indicate that our method is competitive, and outperforms challenging baselines for unconditional generation.
Despite the recent success of graph neural networks (GNN), common architectures often exhibit significant limitations, including sensitivity to oversmoothing, long-range dependencies, and spurious edges, e.g., as can occur as a result of graph heterophily or adversarial attacks. To at least partially address these issues within a simple transparent framework, we consider a new family of GNN layers designed to mimic and integrate the update rules of two classical iterative algorithms, namely, proximal gradient descent and iterative reweighted least squares (IRLS). The former defines an extensible base GNN architecture that is immune to oversmoothing while nonetheless capturing long-range dependencies by allowing arbitrary propagation steps. In contrast, the latter produces a novel attention mechanism that is explicitly anchored to an underlying end-toend energy function, contributing stability with respect to edge uncertainty. When combined we obtain an extremely simple yet robust model that we evaluate across disparate scenarios including standardized benchmarks, adversarially-perturbated graphs, graphs with heterophily, and graphs involving long-range dependencies. In doing so, we compare against SOTA GNN approaches that have been explicitly designed for the respective task, achieving competitive or superior node classification accuracy.
We present Neural A*, a novel data-driven search method for path planning problems. Despite the recent increasing attention to data-driven path planning, a machine learning approach to search-based planning is still challenging due to the discrete nature of search algorithms. In this work, we reformulate a canonical A* search algorithm to be differentiable and couple it with a convolutional encoder to form an end-to-end trainable neural network planner. Neural A* solves a path planning problem by encoding a problem instance to a guidance map and then performing the differentiable A* search with the guidance map. By learning to match the search results with ground-truth paths provided by experts, Neural A* can produce a path consistent with the ground truth accurately and efficiently. Our extensive experiments confirmed that Neural A* outperformed state-of-the-art data-driven planners in terms of the search optimality and efficiency trade-off, and furthermore, successfully predicted realistic human trajectories by directly performing search-based planning on natural image inputs.
Graph Neural Networks (GNNs) are based on repeated aggregations of information across nodes' neighbors in a graph. However, because common neighbors are shared between different nodes, this leads to repeated and inefficient computations. We propose Hierarchically Aggregated computation Graphs (HAGs), a new GNN graph representation that explicitly avoids redundancy by managing intermediate aggregation results hierarchically, eliminating repeated computations and unnecessary data transfers in GNN training and inference. We introduce an accurate cost function to quantitatively evaluate the runtime performance of different HAGs and use a novel HAG search algorithm to find optimized HAGs. Experiments show that the HAG representation significantly outperforms the standard GNN graph representation by increasing the end-to-end training throughput by up to 2.8x and reducing the aggregations and data transfers in GNN training by up to 6.3x and 5.6x, while maintaining the original model accuracy.
Attributed graph clustering is challenging as it requires joint modelling of graph structures and node attributes. Recent progress on graph convolutional networks has proved that graph convolution is effective in combining structural and content information, and several recent methods based on it have achieved promising clustering performance on some real attributed networks. However, there is limited understanding of how graph convolution affects clustering performance and how to properly use it to optimize performance for different graphs. Existing methods essentially use graph convolution of a fixed and low order that only takes into account neighbours within a few hops of each node, which underutilizes node relations and ignores the diversity of graphs. In this paper, we propose an adaptive graph convolution method for attributed graph clustering that exploits high-order graph convolution to capture global cluster structure and adaptively selects the appropriate order for different graphs. We establish the validity of our method by theoretical analysis and extensive experiments on benchmark datasets. Empirical results show that our method compares favourably with state-of-the-art methods.
Graph structured data are abundant in the real world. Among different graph types, directed acyclic graphs (DAGs) are of particular interest to machine learning researchers, as many machine learning models are realized as computations on DAGs, including neural networks and Bayesian networks. In this paper, we study deep generative models for DAGs, and propose a novel DAG variational autoencoder (D-VAE). To encode DAGs into the latent space, we leverage graph neural networks. We propose an asynchronous message passing scheme that allows encoding the computations on DAGs, rather than using existing simultaneous message passing schemes to encode local graph structures. We demonstrate the effectiveness of our proposed D-VAE through two tasks: neural architecture search and Bayesian network structure learning. Experiments show that our model not only generates novel and valid DAGs, but also produces a smooth latent space that facilitates searching for DAGs with better performance through Bayesian optimization.
How can we estimate the importance of nodes in a knowledge graph (KG)? A KG is a multi-relational graph that has proven valuable for many tasks including question answering and semantic search. In this paper, we present GENI, a method for tackling the problem of estimating node importance in KGs, which enables several downstream applications such as item recommendation and resource allocation. While a number of approaches have been developed to address this problem for general graphs, they do not fully utilize information available in KGs, or lack flexibility needed to model complex relationship between entities and their importance. To address these limitations, we explore supervised machine learning algorithms. In particular, building upon recent advancement of graph neural networks (GNNs), we develop GENI, a GNN-based method designed to deal with distinctive challenges involved with predicting node importance in KGs. Our method performs an aggregation of importance scores instead of aggregating node embeddings via predicate-aware attention mechanism and flexible centrality adjustment. In our evaluation of GENI and existing methods on predicting node importance in real-world KGs with different characteristics, GENI achieves 5-17% higher NDCG@100 than the state of the art.
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