Learning neural algorithms with graph structures

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Dai, Hanjun
Song, Le
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Graph structures, like syntax trees, social networks, and programs, are ubiquitous in many real world applications including knowledge graph inference, chemistry and social network analysis. Over the past several decades, many expert-designed algorithms on graphs have been proposed with nice theoretical properties. However most of them are not data-driven, and will not benefit from the growing scale of available data. Recent advances in deep learning have shown strong empirical performances for images, texts and signals, typically with little domain knowledge. However the combinatorial and discrete nature of the graph data makes it non-trivial to apply neural networks in this domain. Based on the pros and cons of these two, this thesis will discuss several aspects on how to build a tight connection between neural networks and the classical algorithms for graphs. Specifically: - Algorithm inspired deep graph learning: The existing algorithms provide an inspiration of deep architecture design, for both the discriminative learning and generative modeling of graphs. Regarding the discriminative representation learning, we show how the graphical model inference algorithms can inspire the design of graph neural networks for chemistry and bioinformatics applications, and how to scale it up with the idea borrowed from steady states algorithms like PageRank; for generative modeling, we build an HSMM inspired neural segmental generative modeling for signal sequences; and for a class of graphs, we leverage the idea of attribute grammar for syntax trees to help regulate the deep networks. - Deep learning enhanced graph algorithms: the algorithm framework has procedures that can be enhanced by learnable deep network components. We demonstrate by learning the heuristic function in greedy algorithms with reinforcement learning for combinatorial optimization problems over graphs, such as vertex cover and max cut, and optimal touring problem for real world applications like fuzzing. - Towards Inductive reasoning with graph structures: As the algorithm structure generally provides a good inductive bias for the problem, we take an initial step towards inductive reasoning for such structure, where we make attempts to reason about the loop invariant for program verification and the reaction templates for retrosynthesis structured prediction.
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