Ryoma Sato

Makoto Yamada, Yuki Takezawa, Ryoma Sato et al.

Wasserstein distance, which measures the discrepancy between distributions, shows efficacy in various types of natural language processing (NLP) and computer vision (CV) applications. One of the challenges in estimating Wasserstein distance is that it is computationally expensive and does not scale well for many distribution comparison tasks. In this paper, we aim to approximate the 1-Wasserstein distance by the tree-Wasserstein distance (TWD), where TWD is a 1-Wasserstein distance with tree-based embedding and can be computed in linear time with respect to the number of nodes on a tree. More specifically, we propose a simple yet efficient L1-regularized approach to learning the weights of the edges in a tree. To this end, we first show that the 1-Wasserstein approximation problem can be formulated as a distance approximation problem using the shortest path distance on a tree. We then show that the shortest path distance can be represented by a linear model and can be formulated as a Lasso-based regression problem. Owing to the convex formulation, we can obtain a globally optimal solution efficiently. Moreover, we propose a tree-sliced variant of these methods. Through experiments, we demonstrated that the weighted TWD can accurately approximate the original 1-Wasserstein distance.

Ryoma Sato, Makoto Yamada, Hisashi Kashima

The research process includes many decisions, e.g., how to entitle and where to publish the paper. In this paper, we introduce a general framework for investigating the effects of such decisions. The main difficulty in investigating the effects is that we need to know counterfactual results, which are not available in reality. The key insight of our framework is inspired by the existing counterfactual analysis using twins, where the researchers regard twins as counterfactual units. The proposed framework regards a pair of papers that cite each other as twins. Such papers tend to be parallel works, on similar topics, and in similar communities. We investigate twin papers that adopted different decisions, observe the progress of the research impact brought by these studies, and estimate the effect of decisions by the difference in the impacts of these studies. We release our code and data, which we believe are highly beneficial owing to the scarcity of the dataset on counterfactual studies.

Yuki Takezawa, Han Bao, Kenta Niwa et al.

SGD with momentum is one of the key components for improving the performance of neural networks. For decentralized learning, a straightforward approach using momentum is Distributed SGD (DSGD) with momentum (DSGDm). However, DSGDm performs worse than DSGD when the data distributions are statistically heterogeneous. Recently, several studies have addressed this issue and proposed methods with momentum that are more robust to data heterogeneity than DSGDm, although their convergence rates remain dependent on data heterogeneity and deteriorate when the data distributions are heterogeneous. In this study, we propose Momentum Tracking, which is a method with momentum whose convergence rate is proven to be independent of data heterogeneity. More specifically, we analyze the convergence rate of Momentum Tracking in the setting where the objective function is non-convex and the stochastic gradient is used. Then, we identify that it is independent of data heterogeneity for any momentum coefficient $β\in [0, 1)$. Through experiments, we demonstrate that Momentum Tracking is more robust to data heterogeneity than the existing decentralized learning methods with momentum and can consistently outperform these existing methods when the data distributions are heterogeneous.

Ryoma Sato, Yuki Takezawa, Han Bao et al.

We propose Easymark, a family of embarrassingly simple yet effective watermarks. Text watermarking is becoming increasingly important with the advent of Large Language Models (LLM). LLMs can generate texts that cannot be distinguished from human-written texts. This is a serious problem for the credibility of the text. Easymark is a simple yet effective solution to this problem. Easymark can inject a watermark without changing the meaning of the text at all while a validator can detect if a text was generated from a system that adopted Easymark or not with high credibility. Easymark is extremely easy to implement so that it only requires a few lines of code. Easymark does not require access to LLMs, so it can be implemented on the user-side when the LLM providers do not offer watermarked LLMs. In spite of its simplicity, it achieves higher detection accuracy and BLEU scores than the state-of-the-art text watermarking methods. We also prove the impossibility theorem of perfect watermarking, which is valuable in its own right. This theorem shows that no matter how sophisticated a watermark is, a malicious user could remove it from the text, which motivate us to use a simple watermark such as Easymark. We carry out experiments with LLM-generated texts and confirm that Easymark can be detected reliably without any degradation of BLEU and perplexity, and outperform state-of-the-art watermarks in terms of both quality and reliability.

Yuki Takezawa, Ryoma Sato, Han Bao et al.

In recent years, large language models (LLMs) have achieved remarkable performances in various NLP tasks. They can generate texts that are indistinguishable from those written by humans. Such remarkable performance of LLMs increases their risk of being used for malicious purposes, such as generating fake news articles. Therefore, it is necessary to develop methods for distinguishing texts written by LLMs from those written by humans. Watermarking is one of the most powerful methods for achieving this. Although existing watermarking methods have successfully detected texts generated by LLMs, they significantly degrade the quality of the generated texts. In this study, we propose the Necessary and Sufficient Watermark (NS-Watermark) for inserting watermarks into generated texts without degrading the text quality. More specifically, we derive minimum constraints required to be imposed on the generated texts to distinguish whether LLMs or humans write the texts. Then, we formulate the NS-Watermark as a constrained optimization problem and propose an efficient algorithm to solve it. Through the experiments, we demonstrate that the NS-Watermark can generate more natural texts than existing watermarking methods and distinguish more accurately between texts written by LLMs and those written by humans. Especially in machine translation tasks, the NS-Watermark can outperform the existing watermarking method by up to 30 BLEU scores.

Ryoma Sato

Graph Neural Networks (GNNs) are popular models for graph learning problems. GNNs show strong empirical performance in many practical tasks. However, the theoretical properties have not been completely elucidated. In this paper, we investigate whether GNNs can exploit the graph structure from the perspective of the expressive power of GNNs. In our analysis, we consider graph generation processes that are controlled by hidden (or latent) node features, which contain all information about the graph structure. A typical example of this framework is kNN graphs constructed from the hidden features. In our main results, we show that GNNs can recover the hidden node features from the input graph alone, even when all node features, including the hidden features themselves and any indirect hints, are unavailable. GNNs can further use the recovered node features for downstream tasks. These results show that GNNs can fully exploit the graph structure by themselves, and in effect, GNNs can use both the hidden and explicit node features for downstream tasks. In the experiments, we confirm the validity of our results by showing that GNNs can accurately recover the hidden features using a GNN architecture built based on our theoretical analysis.

Ryoma Sato

Labeling data is one of the most costly processes in machine learning pipelines. Active learning is a standard approach to alleviating this problem. Pool-based active learning first builds a pool of unlabelled data and iteratively selects data to be labeled so that the total number of required labels is minimized, keeping the model performance high. Many effective criteria for choosing data from the pool have been proposed in the literature. However, how to build the pool is less explored. Specifically, most of the methods assume that a task-specific pool is given for free. In this paper, we advocate that such a task-specific pool is not always available and propose the use of a myriad of unlabelled data on the Web for the pool for which active learning is applied. As the pool is extremely large, it is likely that relevant data exist in the pool for many tasks, and we do not need to explicitly design and build the pool for each task. The challenge is that we cannot compute the acquisition scores of all data exhaustively due to the size of the pool. We propose an efficient method, Seafaring, to retrieve informative data in terms of active learning from the Web using a user-side information retrieval algorithm. In the experiments, we use the online Flickr environment as the pool for active learning. This pool contains more than ten billion images and is several orders of magnitude larger than the existing pools in the literature for active learning. We confirm that our method performs better than existing approaches of using a small unlabelled pool.

Ryoma Sato

Word embeddings are one of the most fundamental technologies used in natural language processing. Existing word embeddings are high-dimensional and consume considerable computational resources. In this study, we propose WordTour, unsupervised one-dimensional word embeddings. To achieve the challenging goal, we propose a decomposition of the desiderata of word embeddings into two parts, completeness and soundness, and focus on soundness in this paper. Owing to the single dimensionality, WordTour is extremely efficient and provides a minimal means to handle word embeddings. We experimentally confirmed the effectiveness of the proposed method via user study and document classification.

Ryoma Sato, Marco Cuturi, Makoto Yamada et al.

Comparing two probability measures supported on heterogeneous spaces is an increasingly important problem in machine learning. Such problems arise when comparing for instance two populations of biological cells, each described with its own set of features, or when looking at families of word embeddings trained across different corpora/languages. For such settings, the Gromov Wasserstein (GW) distance is often presented as the gold standard. GW is intuitive, as it quantifies whether one measure can be isomorphically mapped to the other. However, its exact computation is intractable, and most algorithms that claim to approximate it remain expensive. Building on \cite{memoli-2011}, who proposed to represent each point in each distribution as the 1D distribution of its distances to all other points, we introduce in this paper the Anchor Energy (AE) and Anchor Wasserstein (AW) distances, which are respectively the energy and Wasserstein distances instantiated on such representations. Our main contribution is to propose a sweep line algorithm to compute AE \emph{exactly} in log-quadratic time, where a naive implementation would be cubic. This is quasi-linear w.r.t. the description of the problem itself. Our second contribution is the proposal of robust variants of AE and AW that uses rank statistics rather than the original distances. We show that AE and AW perform well in various experimental settings at a fraction of the computational cost of popular GW approximations. Code is available at \url{https://github.com/joisino/anchor-energy}.

Ryoma Sato, Shinji Ito

We point out that EXP3 can be implemented in constant time per round, propose more practical algorithms, and analyze the trade-offs between the regret bounds and time complexities of these algorithms.

Yuki Takezawa, Han Bao, Ryoma Sato et al.

Gradient descent and its variants are de facto standard algorithms for training machine learning models. As gradient descent is sensitive to its hyperparameters, we need to tune the hyperparameters carefully using a grid search. However, the method is time-consuming, particularly when multiple hyperparameters exist. Therefore, recent studies have analyzed parameter-free methods that adjust the hyperparameters on the fly. However, the existing work is limited to investigations of parameter-free methods for the stepsize, and parameter-free methods for other hyperparameters have not been explored. For instance, although the gradient clipping threshold is a crucial hyperparameter in addition to the stepsize for preventing gradient explosion issues, none of the existing studies have investigated parameter-free methods for clipped gradient descent. Therefore, in this study, we investigate the parameter-free methods for clipped gradient descent. Specifically, we propose Inexact Polyak Stepsize, which converges to the optimal solution without any hyperparameters tuning, and its convergence rate is asymptotically independent of $L$ under $L$-smooth and $(L_0, L_1)$-smooth assumptions of the loss function, similar to that of clipped gradient descent with well-tuned hyperparameters. We numerically validated our convergence results using a synthetic function and demonstrated the effectiveness of our proposed methods using LSTM, Nano-GPT, and T5.

Ryoma Sato

We propose Zero-Error Horizon (ZEH) for trustworthy LLMs, which represents the maximum range that a model can solve without any errors. While ZEH itself is simple, we demonstrate that evaluating the ZEH of state-of-the-art LLMs yields abundant insights. For example, by evaluating the ZEH of GPT-5.2, we found that GPT-5.2 cannot even compute the parity of a short string like 11000, and GPT-5.2 cannot determine whether the parentheses in ((((()))))) are balanced. This is surprising given the excellent capabilities of GPT-5.2. The fact that LLMs make mistakes on such simple problems serves as an important lesson when applying LLMs to safety-critical domains. By applying ZEH to Qwen2.5 and conducting detailed analysis, we found that while ZEH correlates with accuracy, the detailed behaviors differ, and ZEH provides clues about the emergence of algorithmic capabilities. Finally, while computing ZEH incurs significant computational cost, we discuss how to mitigate this cost by achieving up to one order of magnitude speedup using tree structures and online softmax.

Ryoma Sato

We propose training-free graph neural networks (TFGNNs), which can be used without training and can also be improved with optional training, for transductive node classification. We first advocate labels as features (LaF), which is an admissible but not explored technique. We show that LaF provably enhances the expressive power of graph neural networks. We design TFGNNs based on this analysis. In the experiments, we confirm that TFGNNs outperform existing GNNs in the training-free setting and converge with much fewer training iterations than traditional GNNs.

Ryoma Sato

Users are dissatisfied with services. Since the service is not tailor-made for a user, it is natural for dissatisfaction to arise. The problem is, that even if users are dissatisfied, they often do not have the means to resolve their dissatisfaction. The user cannot alter the source code of the service, nor can they force the service provider to change. The user has no choice but to remain dissatisfied or quit the service. User-side realization offers proactive solutions to this problem by providing general algorithms to deal with common problems on the user's side. These algorithms run on the user's side and solve the problems without having the service provider change the service itself.

Ryoma Sato

We propose PRISM to enable users of machine translation systems to preserve the privacy of data on their own initiative. There is a growing demand to apply machine translation systems to data that require privacy protection. While several machine translation engines claim to prioritize privacy, the extent and specifics of such protection are largely ambiguous. First, there is often a lack of clarity on how and to what degree the data is protected. Even if service providers believe they have sufficient safeguards in place, sophisticated adversaries might still extract sensitive information. Second, vulnerabilities may exist outside of these protective measures, such as within communication channels, potentially leading to data leakage. As a result, users are hesitant to utilize machine translation engines for data demanding high levels of privacy protection, thereby missing out on their benefits. PRISM resolves this problem. Instead of relying on the translation service to keep data safe, PRISM provides the means to protect data on the user's side. This approach ensures that even machine translation engines with inadequate privacy measures can be used securely. For platforms already equipped with privacy safeguards, PRISM acts as an additional protection layer, reinforcing their security furthermore. PRISM adds these privacy features without significantly compromising translation accuracy. Our experiments demonstrate the effectiveness of PRISM using real-world translators, T5 and ChatGPT (GPT-3.5-turbo), and the datasets with two languages. PRISM effectively balances privacy protection with translation accuracy.

Ryoma Sato

Traditionally, recommendation algorithms have been designed for service developers. But recently, a new paradigm called user-side recommender systems has been proposed. User-side recommender systems are built and used by end users, in sharp contrast to traditional provider-side recommender systems. Even if the official recommender system offered by the provider is not fair, end users can create and enjoy their own user-side recommender systems by themselves. Although the concept of user-side recommender systems is attractive, the problem is they require tremendous communication costs between the user and the official system. Even the most efficient user-side recommender systems require about 5 times more costs than provider-side recommender systems. Such high costs hinder the adoption of user-side recommender systems. In this paper, we propose overhead-free user-side recommender systems, RecCycle, which realizes user-side recommender systems without any communication overhead. The main idea of RecCycle is to recycle past recommendation results offered by the provider's recommender systems. The ingredients of RecCycle can be retrieved ``for free,'' and it greatly reduces the cost of user-side recommendations. In the experiments, we confirm that RecCycle performs as well as state-of-the-art user-side recommendation algorithms while RecCycle reduces costs significantly.

Ryoma Sato

Most machine learning models are designed to maximize predictive accuracy. In this work, we explore a different goal: building classifiers that are interesting. An ``interesting classifier'' is one that uses unusual or unexpected features, even if its accuracy is lower than the best possible model. For example, predicting room congestion from CO2 levels achieves near-perfect accuracy but is unsurprising. In contrast, predicting room congestion from humidity is less accurate yet more nuanced and intriguing. We introduce EUREKA, a simple framework that selects features according to their perceived interestingness. Our method leverages large language models to rank features by their interestingness and then builds interpretable classifiers using only the selected interesting features. Across several benchmark datasets, EUREKA consistently identifies features that are non-obvious yet still predictive. For example, in the Occupancy Detection dataset, our method favors humidity over CO2 levels and light intensity, producing classifiers that achieve meaningful accuracy while offering insights. In the Twin Papers dataset, our method discovers the rule that papers with a colon in the title are more likely to be cited in the future. We argue that such models can support new ways of knowledge discovery and communication, especially in settings where moderate accuracy is sufficient but novelty and interpretability are valued.

Ryoma Sato, Shinji Ito

While classical formulations of multi-armed bandit problems assume that each arm's reward is independent and stationary, real-world applications often involve non-stationary environments and interdependencies between arms. In particular, selecting one arm may influence the future rewards of other arms, a scenario not adequately captured by existing models such as rotting bandits or restless bandits. To address this limitation, we propose the influential bandit problem, which models inter-arm interactions through an unknown, symmetric, positive semi-definite interaction matrix that governs the dynamics of arm losses. We formally define this problem and establish two regret lower bounds, including a superlinear $Ω(T^2 / \log^2 T)$ bound for the standard LCB algorithm (loss minimization version of UCB) and an algorithm-independent $Ω(T)$ bound, which highlight the inherent difficulty of the setting. We then introduce a new algorithm based on a lower confidence bound (LCB) estimator tailored to the structure of the loss dynamics. Under mild assumptions, our algorithm achieves a regret of $O(KT \log T)$, which is nearly optimal in terms of its dependence on the time horizon. The algorithm is simple to implement and computationally efficient. Empirical evaluations on both synthetic and real-world datasets demonstrate the presence of inter-arm influence and confirm the superior performance of our method compared to conventional bandit algorithms.

Ryoma Sato

We propose a new approach that enables end users to directly solve the cold start problem by themselves. The cold start problem is a common issue in recommender systems, and many methods have been proposed to address the problem on the service provider's side. However, when the service provider does not take action, users are left with poor recommendations and no means to improve their experience. We propose an algorithm, Pretender, that allows end users to proactively solve the cold start problem on their own. Pretender does not require any special support from the service provider and can be deployed independently by users. We formulate the problem as minimizing the distance between the source and target distributions and optimize item selection from the target service accordingly. Furthermore, we establish theoretical guarantees for Pretender based on a discrete quadrature problem. We conduct experiments on real-world datasets to demonstrate the effectiveness of Pretender.

Yuki Takezawa, Ryoma Sato, Han Bao et al.

Decentralized learning has recently been attracting increasing attention for its applications in parallel computation and privacy preservation. Many recent studies stated that the underlying network topology with a faster consensus rate (a.k.a. spectral gap) leads to a better convergence rate and accuracy for decentralized learning. However, a topology with a fast consensus rate, e.g., the exponential graph, generally has a large maximum degree, which incurs significant communication costs. Thus, seeking topologies with both a fast consensus rate and small maximum degree is important. In this study, we propose a novel topology combining both a fast consensus rate and small maximum degree called the Base-$(k + 1)$ Graph. Unlike the existing topologies, the Base-$(k + 1)$ Graph enables all nodes to reach the exact consensus after a finite number of iterations for any number of nodes and maximum degree k. Thanks to this favorable property, the Base-$(k + 1)$ Graph endows Decentralized SGD (DSGD) with both a faster convergence rate and more communication efficiency than the exponential graph. We conducted experiments with various topologies, demonstrating that the Base-$(k + 1)$ Graph enables various decentralized learning methods to achieve higher accuracy with better communication efficiency than the existing topologies.

Ryoma Sato

Suppose we have a black-box function (e.g., deep neural network) that takes an image as input and outputs a value that indicates preference. How can we retrieve optimal images with respect to this function from an external database on the Internet? Standard retrieval problems in the literature (e.g., item recommendations) assume that an algorithm has full access to the set of items. In other words, such algorithms are designed for service providers. In this paper, we consider the retrieval problem under different assumptions. Specifically, we consider how users with limited access to an image database can retrieve images using their own black-box functions. This formulation enables a flexible and finer-grained image search defined by each user. We assume the user can access the database through a search query with tight API limits. Therefore, a user needs to efficiently retrieve optimal images in terms of the number of queries. We propose an efficient retrieval algorithm Tiara for this problem. In the experiments, we confirm that our proposed method performs better than several baselines under various settings.

Yuki Takezawa, Ryoma Sato, Zornitsa Kozareva et al.

The Wasserstein barycenter has been widely studied in various fields, including natural language processing, and computer vision. However, it requires a high computational cost to solve the Wasserstein barycenter problem because the computation of the Wasserstein distance requires a quadratic time with respect to the number of supports. By contrast, the Wasserstein distance on a tree, called the tree-Wasserstein distance, can be computed in linear time and allows for the fast comparison of a large number of distributions. In this study, we propose a barycenter under the tree-Wasserstein distance, called the fixed support tree-Wasserstein barycenter (FS-TWB) and its extension, called the fixed support tree-sliced Wasserstein barycenter (FS-TSWB). More specifically, we first show that the FS-TWB and FS-TSWB problems are convex optimization problems and can be solved by using the projected subgradient descent. Moreover, we propose a more efficient algorithm to compute the subgradient and objective function value by using the properties of tree-Wasserstein barycenter problems. Through real-world experiments, we show that, by using the proposed algorithm, the FS-TWB and FS-TSWB can be solved two orders of magnitude faster than the original Wasserstein barycenter.

Ryoma Sato

Package-to-group recommender systems recommend a set of unified items to a group of people. Different from conventional settings, it is not easy to measure the utility of group recommendations because it involves more than one user. In particular, fairness is crucial in group recommendations. Even if some members in a group are substantially satisfied with a recommendation, it is undesirable if other members are ignored to increase the total utility. Many methods for evaluating and applying the fairness of group recommendations have been proposed in the literature. However, all these methods maximize the score and output only one package. This is in contrast to conventional recommender systems, which output several (e.g., top-$K$) candidates. This can be problematic because a group can be dissatisfied with the recommended package owing to some unobserved reasons, even if the score is high. To address this issue, we propose a method to enumerate fair packages efficiently. Our method furthermore supports filtering queries, such as top-$K$ and intersection, to select favorite packages when the list is long. We confirm that our algorithm scales to large datasets and can balance several aspects of the utility of the packages.

Ryoma Sato, Makoto Yamada, Hisashi Kashima

The word mover's distance (WMD) is a fundamental technique for measuring the similarity of two documents. As the crux of WMD, it can take advantage of the underlying geometry of the word space by employing an optimal transport formulation. The original study on WMD reported that WMD outperforms classical baselines such as bag-of-words (BOW) and TF-IDF by significant margins in various datasets. In this paper, we point out that the evaluation in the original study could be misleading. We re-evaluate the performances of WMD and the classical baselines and find that the classical baselines are competitive with WMD if we employ an appropriate preprocessing, i.e., L1 normalization. In addition, we introduce an analogy between WMD and L1-normalized BOW and find that not only the performance of WMD but also the distance values resemble those of BOW in high dimensional spaces.

Ryoma Sato

Fairness is a crucial property in recommender systems. Although some online services have adopted fairness aware systems recently, many other services have not adopted them yet. In this work, we propose methods to enable the users to build their own fair recommender systems. Our methods can generate fair recommendations even when the service does not (or cannot) provide fair recommender systems. The key challenge is that a user does not have access to the log data of other users or the latent representations of items. This restriction prohibits us from adopting existing methods designed for service providers. The main idea is that a user has access to unfair recommendations shown by the service provider. Our methods leverage the outputs of an unfair recommender system to construct a new fair recommender system. We empirically validate that our proposed method improves fairness substantially without harming much performance of the original unfair system.

Yuki Takezawa, Ryoma Sato, Makoto Yamada

To measure the similarity of documents, the Wasserstein distance is a powerful tool, but it requires a high computational cost. Recently, for fast computation of the Wasserstein distance, methods for approximating the Wasserstein distance using a tree metric have been proposed. These tree-based methods allow fast comparisons of a large number of documents; however, they are unsupervised and do not learn task-specific distances. In this work, we propose the Supervised Tree-Wasserstein (STW) distance, a fast, supervised metric learning method based on the tree metric. Specifically, we rewrite the Wasserstein distance on the tree metric by the parent-child relationships of a tree and formulate it as a continuous optimization problem using a contrastive loss. Experimentally, we show that the STW distance can be computed fast, and improves the accuracy of document classification tasks. Furthermore, the STW distance is formulated by matrix multiplications, runs on a GPU, and is suitable for batch processing. Therefore, we show that the STW distance is extremely efficient when comparing a large number of documents.

Ryoma Sato, Makoto Yamada, Hisashi Kashima

Choosing a publication venue for an academic paper is a crucial step in the research process. However, in many cases, decisions are based solely on the experience of researchers, which often leads to suboptimal results. Although there exist venue recommender systems for academic papers, they recommend venues where the paper is expected to be published. In this study, we aim to recommend publication venues from a different perspective. We estimate the number of citations a paper will receive if the paper is published in each venue and recommend the venue where the paper has the most potential impact. However, there are two challenges to this task. First, a paper is published in only one venue, and thus, we cannot observe the number of citations the paper would receive if the paper were published in another venue. Secondly, the contents of a paper and the publication venue are not statistically independent; that is, there exist selection biases in choosing publication venues. In this paper, we formulate the venue recommendation problem as a treatment effect estimation problem. We use a bias correction method to estimate the potential impact of choosing a publication venue effectively and to recommend venues based on the potential impact of papers in each venue. We highlight the effectiveness of our method using paper data from computer science conferences.

Ryoma Sato, Makoto Yamada, Hisashi Kashima

This study examines the time complexities of the unbalanced optimal transport problems from an algorithmic perspective for the first time. We reveal which problems in unbalanced optimal transport can/cannot be solved efficiently. Specifically, we prove that the Kantorovich Rubinstein distance and optimal partial transport in the Euclidean metric cannot be computed in strongly subquadratic time under the strong exponential time hypothesis. Then, we propose an algorithm that solves a more general unbalanced optimal transport problem exactly in quasi-linear time on a tree metric. The proposed algorithm processes a tree with one million nodes in less than one second. Our analysis forms a foundation for the theoretical study of unbalanced optimal transport algorithms and opens the door to the applications of unbalanced optimal transport to million-scale datasets.

Mathis Petrovich, Chao Liang, Ryoma Sato et al.

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.

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.

Ryoma Sato, Makoto Yamada, Hisashi Kashima

Graph neural networks (GNNs) are powerful machine learning models for various graph learning tasks. Recently, the limitations of the expressive power of various GNN models have been revealed. For example, GNNs cannot distinguish some non-isomorphic graphs and they cannot learn efficient graph algorithms. In this paper, we demonstrate that GNNs become powerful just by adding a random feature to each node. We prove that the random features enable GNNs to learn almost optimal polynomial-time approximation algorithms for the minimum dominating set problem and maximum matching problem in terms of approximation ratios. The main advantage of our method is that it can be combined with off-the-shelf GNN models with slight modifications. Through experiments, we show that the addition of random features enables GNNs to solve various problems that normal GNNs, including the graph convolutional networks (GCNs) and graph isomorphism networks (GINs), cannot solve.

Ryoma Sato, Makoto Yamada, Hisashi Kashima

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.

Ryoma Sato, Makoto Yamada, Hisashi Kashima

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.

Ryoma Sato, Makoto Yamada, Hisashi Kashima

The recent advancements in graph neural networks (GNNs) have led to state-of-the-art performances in various applications, including chemo-informatics, question-answering systems, and recommender systems. However, scaling up these methods to huge graphs, such as social networks and Web graphs, remains a challenge. In particular, the existing methods for accelerating GNNs either are not theoretically guaranteed in terms of the approximation error or incur at least a linear time computation cost. In this study, we reveal the query complexity of the uniform node sampling scheme for Message Passing Neural Networks, including GraphSAGE, graph attention networks (GATs), and graph convolutional networks (GCNs). Surprisingly, our analysis reveals that the complexity of the node sampling method is completely independent of the number of the nodes, edges, and neighbors of the input and depends only on the error tolerance and confidence probability while providing a theoretical guarantee for the approximation error. To the best of our knowledge, this is the first paper to provide a theoretical guarantee of approximation for GNNs within constant time. Through experiments with synthetic and real-world datasets, we investigated the speed and precision of the node sampling scheme and validated our theoretical results.