How can we classify multi-way data such as network traffic logs with multi-way relations between source IPs, destination IPs, and ports? Multi-way data can be represented as a tensor, and there have been several studies on classification of tensors to date. One critical issue in the classification of multi-way relations is how to extract important features for classification when objects in different multi-way data, i.e., in different tensors, are not necessarily in correspondence. In such situations, we aim to extract features that do not depend on how we allocate indices to an object such as a specific source IP; we are interested in only the structures of the multi-way relations. However, this issue has not been considered in previous studies on classification of multi-way data. We propose a novel method which can learn and classify multi-way data using neural networks. Our method leverages a novel type of tensor decomposition that utilizes a target core tensor expressing the important features whose indices are independent of those of the multi-way data. The target core tensor guides the tensor decomposition into more effective results and is optimized in a supervised manner. Our experiments on three different domains show that our method is highly accurate, especially on higher order data. It also enables us to interpret the classification results along with the matrices calculated with the novel tensor decomposition.

We report on a project aiming at developing a system that solves a wide range of math problems written in natural language. In the system, formal analysis of natural language semantics is coupled with automated reasoning technologies including computer algebra, using logic as their common language. We have developed a prototype system that accepts as its input a linguistically annotated problem text. Using the prototype system as a reference point, we analyzed real university entrance examination problems from the viewpoint of end-to-end automated reasoning. Further, evaluation on entrance exam mock tests revealed that an optimistic estimate of the system’s performance already matches human averages on a few test sets.