We propose a novel and efficient method for link prediction in bipartite networks, using \textit{formal concept analysis} (FCA) and the Transformer encoder. Link prediction in bipartite networks finds practical applications in various domains such as product recommendation in online sales, and prediction of chemical-disease interaction in medical science. Since for link prediction, the topological structure of a network contains valuable information, many approaches focus on extracting structural features and then utilizing them for link prediction. Bi-cliques, as a type of structural feature of bipartite graphs, can be utilized for link prediction. Although several link prediction methods utilizing bi-cliques have been proposed and perform well in rather small datasets, all of them face challenges with scalability when dealing with large datasets since they demand substantial computational resources. This limits the practical utility of these approaches in real-world applications. To overcome the limitation, we introduce a novel approach employing iceberg concept lattices and the Transformer encoder. Our method requires fewer computational resources, making it suitable for large-scale datasets while maintaining high prediction performance. We conduct experiments on five large real-world datasets that exceed the capacity of previous bi-clique-based approaches to demonstrate the efficacy of our method. Additionally, we perform supplementary experiments on five small datasets to compare with the previous bi-clique-based methods for bipartite link prediction and demonstrate that our method is more efficient than the previous ones.

In this paper we propose that a restricted version of logical inference can be implemented with self-attention networks. We are aiming at showing that LLMs (Large Language Models) constructed with transformer networks can make logical inferences. We would reveal the potential of LLMs by analyzing self-attention networks, which are main components of transformer networks. Our approach is not based on semantics of natural languages but operations of logical inference. %point of view. We show that hierarchical constructions of self-attention networks with feed forward networks (FFNs) can implement top-down derivations for a class of logical formulae. We also show bottom-up derivations are also implemented for the same class. We believe that our results show that LLMs implicitly have the power of logical inference.

In this paper, we propose a novel method for extracting information from HTML tables with similar contents but with a different structure. We aim to integrate multiple HTML tables into a single table for retrieval of information containing in various Web pages. The method is designed by extending tree-structured LSTM, the neural network for tree-structured data, in order to extract information that is both linguistic and structural information of HTML data. We evaluate the proposed method through experiments using real data published on the WWW.

We propose BERT4FCA, a novel method for link prediction in bipartite networks, using formal concept analysis (FCA) and BERT. Link prediction in bipartite networks is an important task that can solve various practical problems like friend recommendation in social networks and co-authorship prediction in author-paper networks. Recent research has found that in bipartite networks, maximal bi-cliques provide important information for link prediction, and they can be extracted by FCA. Some FCA-based bipartite link prediction methods have achieved good performance. However, we figured out that their performance could be further improved because these methods did not fully capture the rich information of the extracted maximal bi-cliques. To address this limitation, we propose an approach using BERT, which can learn more information from the maximal bi-cliques extracted by FCA and use them to make link prediction. We conduct experiments on three real-world bipartite networks and demonstrate that our method outperforms previous FCA-based methods, and some classic methods such as matrix-factorization and node2vec.

The differentiable implementation of logic yields a seamless combination of symbolic reasoning and deep neural networks. Recent research, which has developed a differentiable framework to learn logic programs from examples, can even acquire reasonable solutions from noisy datasets. However, this framework severely limits expressions for solutions, e.g., no function symbols are allowed, and the shapes of clauses are fixed. As a result, the framework cannot deal with structured examples. Therefore we propose a new framework to learn logic programs from noisy and structured examples, including the following contributions. First, we propose an adaptive clause search method by looking through structured space, which is defined by the generality of the clauses, to yield an efficient search space for differentiable solvers. Second, we propose for ground atoms an enumeration algorithm, which determines a necessary and sufficient set of ground atoms to perform differentiable inference functions. Finally, we propose a new method to compose logic programs softly, enabling the system to deal with complex programs consisting of several clauses. Our experiments show that our new framework can learn logic programs from noisy and structured examples, such as sequences or trees. Our framework can be scaled to deal with complex programs that consist of several clauses with function symbols.

Neural machine translation models are used to automatically generate a document from given source code since this can be regarded as a machine translation task. Source code summarization is one of the components for automatic document generation, which generates a summary in natural language from given source code. This suggests that techniques used in neural machine translation, such as Long Short-Term Memory (LSTM), can be used for source code summarization. However, there is a considerable difference between source code and natural language: Source code is essentially {\em structured}, having loops and conditional branching, etc. Therefore, there is some obstacle to apply known machine translation models to source code. Abstract syntax trees (ASTs) capture these structural properties and play an important role in recent machine learning studies on source code. Tree-LSTM is proposed as a generalization of LSTMs for tree-structured data. However, there is a critical issue when applying it to ASTs: It cannot handle a tree that contains nodes having an arbitrary number of children and their order simultaneously, which ASTs generally have such nodes. To address this issue, we propose an extension of Tree-LSTM, which we call \emph{Multi-way Tree-LSTM} and apply it for source code summarization. As a result of computational experiments, our proposal achieved better results when compared with several state-of-the-art techniques.

Stephen Muggleton gave the invited talk "Meta-Interpretive Inductive Logic Programming (ILP) is a research area Learning: achievements and challenges". Meta-Interpretive formed at the intersection of Machine Learning and logicbased Learning (MIL) is an ILP technique aimed at supporting knowledge representation. ILP has originally used learning of recursive definitions, by automatically introducing logic programming as a uniform representation language sub-definitions that allow decomposition into a hierarchy for examples, background knowledge and hypotheses for of reusable parts (Muggleton et al. 2014; 2015). ILP has also explored several connections (or abducing) first-order clauses whose heads unify with with statistical learning and other probabilistic approaches, a given goal. MIL additionally fetches higher-order metarules expanding research horizons significantly. A recent survey whose heads unify with the goal and saves the resulting of ILP can be seen in (Muggleton et al. 2012).

Discovering causal relations among observed variables in a given data set is a major objective in studies of statistics and artificial intelligence. Recently, some techniques to discover a unique causal model have been explored based on non-Gaussianity of the observed data distribution. However, most of these are limited to continuous data. In this paper, we present a novel causal model for binary data and propose an efficient new approach to deriving the unique causal model governing a given binary data set under skew distributions of external binary noises. Experimental evaluation shows excellent performance for both artificial and real world data sets.

Discovering causal relations among observed variables in a given data set is a main topic in studies of statistics and artificial intelligence. Recently, some techniques to discover an identifiable causal structure have been explored based on non-Gaussianity of the observed data distribution. However, most of these are limited to continuous data. In this paper, we present a novel causal model for binary data and propose a new approach to derive an identifiable causal structure governing the data based on skew Bernoulli distributions of external noise. Experimental evaluation shows excellent performance for both artificial and real world data sets.