arXiv subjects
Publications and source records attributed to Ryoma Sato.
Graph neural networks (GNNs) are effective machine learning models for various graph learning problems. Despite their empirical successes, the theoretical limitations of GNNs have been revealed recently. Consequently, many GNN models have been proposed to overcome these limitations. In this survey, we provide a comprehensive overview of the expressive power of GNNs and provably powerful variants of GNNs.
Optimal transport is a machine learning problem with applications including distribution comparison, feature selection, and generative adversarial networks. In this paper, we propose feature-robust optimal transport (FROT) for high-dimensional data, which solves high-dimensional OT problems using feature selection to avoid the curse of dimensionality. Specifically, we find a transport plan with discriminative features. To this end, we formulate the FROT problem as a min--max optimization problem. We then propose a convex formulation of the FROT problem and solve it using a Frank--Wolfe-based optimization algorithm, whereby the subproblem can be efficiently solved using the Sinkhorn algorithm. Since FROT finds the transport plan from selected features, it is robust to noise features. To show the effectiveness of FROT, we propose using the FROT algorithm for the layer selection problem in deep neural networks for semantic correspondence. By conducting synthetic and benchmark experiments, we demonstrate that the proposed method can find a strong correspondence by determining important layers. We show that the FROT algorithm achieves state-of-the-art performance in real-world semantic correspondence datasets.
In this paper, from a theoretical perspective, we study how powerful graph neural networks (GNNs) can be for learning approximation algorithms for combinatorial problems. To this end, we first establish a new class of GNNs that can solve a strictly wider variety of problems than existing GNNs. Then, we bridge the gap between GNN theory and the theory of distributed local algorithms. We theoretically demonstrate that the most powerful GNN can learn approximation algorithms for the minimum dominating set problem and the minimum vertex cover problem with some approximation ratios with the aid of the theory of distributed local algorithms. We also show that most of the existing GNNs such as GIN, GAT, GCN, and GraphSAGE cannot perform better than with these ratios. This paper is the first to elucidate approximation ratios of GNNs for combinatorial problems. Furthermore, we prove that adding coloring or weak-coloring to each node feature improves these approximation ratios. This indicates that preprocessing and feature engineering theoretically strengthen model capabilities.
Hard instances, which require a long time for a specific algorithm to solve, help (1) analyze the algorithm for accelerating it and (2) build a good benchmark for evaluating the performance of algorithms. There exist several efforts for automatic generation of hard instances. For example, evolutionary algorithms have been utilized to generate hard instances. However, they generate only finite number of hard instances. The merit of such methods is limited because it is difficult to extract meaningful patterns from small number of instances. We seek for a probabilistic generator of hard instances. Once the generative distribution of hard instances is obtained, we can sample a variety of hard instances to build a benchmark, and we can extract meaningful patterns of hard instances from sampled instances. The existing methods for modeling the hard instance distribution rely on parameters or rules that are found by domain experts; however, they are specific to the problem. Hence, it is challenging to model the distribution for general cases. In this paper, we focus on graph problems. We propose HiSampler, the hard instance sampler, to model the hard instance distribution of graph algorithms. HiSampler makes it possible to obtain the distribution of hard instances without hand-engineered features. To the best of our knowledge, this is the first method to learn the distribution of hard instances using machine learning. Through experiments, we demonstrate that our proposed method can generate instances that are a few to several orders of magnitude harder than the random-based approach in many settings. In particular, our method outperforms rule-based algorithms in the 3-coloring problem.